Schedule

ICNPAA 2016 Schedule

S4. Control of nonlinear systems under deterministic and stochastic loads

The vibration control of nonlinear engineering systems under deterministic and stochastic loads is a challenging and fascinating field in research and applications.
The aim of the present symposium is . . . to bring together leading scientists and young researchers in applied mathematics, mechanics and engineering sciences to further develop and apply control methods to nonlinear engineering systems.
Topics include, but are are not limited to, passive, active and semi-active control systems, global control, integrity measures in dynamical systems, control of chaos, control algorithms, base isolation and nonlinear vibrations and instabilities of mechanical systems and structures under deterministic and stochastic loads.
Organizors: J.M. Balthazar and P.B. Gonçalves (Brazil), E. Souza de Cursi (France), M. Hajj (USA), S. Lenci (Italy)
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Title Author Status Abstract
Polynomial Chaos and Lie Groups: Application in a Gyroscopic System with Uncertainties Colon Approved Stochastic processes in Lie groups is a well-developed theory in the Mathematics community, particularly for the case of rotations (elements of the Lie group SO(3)). This theory finds many application . . .s in Mechanical Systems, particularly in the Theory of Mechanisms and Robotics, where the Kinematics and Dynamics can be formulated by using Lie group concepts. We apply this theory for the mathematical model of a gyroscopic system with some stochastic parameters, and use polynomial chaos for the simulation of the resulting stochastic differential system of equations in order to evaluate the uncertainty quantification of the output. We also apply a closed-loop control law in this gyroscopic system and evaluate its robustness by the polynomial chaos method of simulation.
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Automotive Computational Model under Stochastic Disturbances Colon Approved In this work, we present a mathematical (computational) model of a car’s longitudinal and vertical dynamics, with their relevant control systems, and assume that certain parameters and random variable . . .s and some inputs are stochastic processes. In order to evaluate the performance of the control systems, we apply the Polynomial Chaos method, using the nonintrusive approach, which is more eficiente than the plain Monte Carlo method. In particular, we evaluate the performance of an active suspension system designed to achieve good disturbance attenuation in the chassis, in order to maximize passengers comfort. Several different types of stochastic disturbances are tested and simulation results are presented.
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Computational Analysis of Unmanned Aerial Vehicle (UAV) ABU DARAG Approved A computational exercise has been performed to validate the aerodynamics properties of a novel UAV utilizing a cascade propeller engine. The UAV-SUST has been designed and fabricated at the Department . . . of Aeronautical Engineering at Sudan University of Science and Technologyin order to meet the specifications required for surveillance and reconnaissance mission. It is classified as a medium range and medium endurance UAV. A commercial CFD solver is used to simulate steady and unsteady aerodynamics characteristics on the entire wing and fuselage of the aircraft. In addition to Lift Coefficient (CL), Drag Coefficient (CD) and Pitching Moment Coefficient (CM), the pressure and velocity contours are illustrated. The aerodynamics parameters are represented a very good agreement with the design consideration at angle of attack ranging from 3 to 20 degrees. Moreover, the visualization of the velocity field and static pressure contours is indicated a satisfactory agreement with the proposed design. The turbulence is predicted by enhancing different turbulence models within the computational fluid dynamics code.
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State of the Art Review of Semi-Active Control for Magnetorheological Dampers Mughal Approved Earthquakes causes severe damage to badly designed structures or buildings to fail or collapse, and also have caused some damage to well-designed structures to malfunction due to the damage or failure . . . of the equipment housed in the structure or building. The use magnetorheological dampers to mitigate the effect of external excitation is increased to resolve this. This article is a state of the art review of nonlinear analytical models to understand the efficacy of semi-active control theory for magnetorheological dampers. A nonlinear semi active control law is desired to be designed which atleast guarantees analytical closed loop stability in order to mitigate the effect of perturbations and drive the desired output to equilibrium.
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Stationary Action and Hamilton-Jacobi Theory McEneaney Approved Stationary-action formulations of conservative dynamical systems are considered. Use of stationary-action formulations allow one to generate fundamental solutions for classes of two-point boundary-val . . .ue problems. For such a problem, one solves for stationary points of the payoff as a function of the input rather than for minima or maxima of the payoff. Nonetheless, a Hamilton-Jacobi partial differential equation (HJ PDE) is obtained for a class of problems subsuming the stationary-action formulation. Although convexity (or concavity) of the payoff is lost as one propagates forward, stationary points continue to exist, and the relationship to the correct solution of the HJ PDE is maintained. The HJ PDE corresponding to stationary action also appears as the semiclassical limit of the Maslov dequantization of the Schrodinger equation. A verification result for solutions of the pre-limit PDE where the system dynamics are driven by a complex-valued stochastic input process is obtained through application of stationary-action techniques. The verification result holds for arbitrary-duration problems, which extends existing results that are valid for limited durations.
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Non-Fragile Observer-Based Controller for Vibration Control of Uncertain Mechanical Systems Oveisi Approved This paper proposes a robust disturbance rejection, non-fragile observer-based controller, for a class of linear systems with structured uncertainty. The robust quadratic stability is guaranteed by th . . .e use of Lyapunov theorem. In order to address the fragility problem, two sets of time-dependent uncertainty sources are considered for the controller and the observer gain in the design procedure. The designed controller is presented in linear matrix equality/inequalities (LME/LMIs) platform. In order to evaluate the performance of the controller, it is implemented in real-time on a mechanical system with the aim of vibration suppression. The plant under study is a multi-input single output (MISO) clamped-free piezo-laminate smart beam. The nominal mathematical reduced-order model of the beam with piezo-actuators is used to design the proposed controller and then the controller is implemented experimentally on the full-order real system. The results show that the closed-loop system has a robust performance regarding disturbance rejection in the presence of the structured uncertainty and in the presence of the nonlinear/unmodelled dynamics.
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Quasi-Periodic Dynamics of a High Angle of Attack Aircraft G Approved High angle of attack maneuvers closer to stall is a commonly accessed flight regime especially in case of fighter aircrafts. Stall and post-stall dynamics are dominated by nonlinearities which make th . . .e analysis further difficult. Presence of external factors such as wind adds more complexity to the system. Rich nonlinearities point the possibility of existence of chaotic solutions. Past studies in this area confirm the development of such solutions via period doubling. These studies are more concentrated on very high angles of attack which may not be easily accessible practically. This paper examines the possibility of existence of chaotic solutions in the lower, more accessible areas in the post stall domain. The analysis is composed of the study of effect of external wind as an agent to drive the system towards the possibility of a chaotic solution. Investigations reveal presence of quasi-periodic solutions, which are characterized by two incommensurate frequencies. This solution appears when the control parameter, i.e., wind, is varied and time simulation is done. The solution corresponds to the value of angle of attack in the lower region of the angle of attack versus elevator bifurcation curve in the post-stall region. The bifurcation analysis is done for a level flight scenario with elevator deflection as the continuation parameter. A steady wind is considered for the analysis and explores the possibility of chaotic motion by increasing the wind in a step wise manner. It is found that wind adds extra energy to the system which in turn drives the system in to chaos. The analysis is done with the help of phase portrait, Poincare map and amplitude spectrum and a quasi-periodic route to chaos via torus doubling is also presented.
Keywords: Chaos, Quasi-periodicity, Non-linear Modeling, Stall, Wind
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Damage propagation on a non-ideal vibrating system, with fractional spring and damping Oliveira Approved C Oliveira1,2, J M Balthazar1, A Nabarrete1, M.F. Westin1 , A M Tusset3 and S A David4
1 ITA-Aeronautics Technological Institute, Mechanical-Aeronautics Division,
São José dos Campos, SP, Brazil,
2 UF . . .GD, Federal University of Grande Dourados, Dourados, MS, Brazil
3 UTFPR – Federal University of Technology – Paraná, Ponta Grossa, PR, Brazil.
4 USP, University of São Paulo, SP, Brazil
E-mail: clivaldooliveira@ufgd.edu.br
Nonlinear physical phenomena are observed in the vibration of different electromechanical systems. This is the main reason for this important topic in engineering investigations.
The oscillatory phenomena of real systems cannot be only explained or solved on the basis of linear theory and it is important to introduce rational characteristics, or nonlinearities, into the mathematical models of such systems, in particular, electromechanical systems.
It is important to remark that the manifestations of a non-ideal energy source are often referred as Sommerfeld effect, that is, the considered oscillatory systems exhibit unstable motions in resonance. Furthermore, the visualization through the frequency response graphs is different depending on the way the analysis is performed. The change by raising or diminishing the frequency values can cause changing’s in the vibration behavior, as well as the transition character through the resonance.
In this work, we characterize the nonlinear dynamics of a non-ideal Duffing system mainly considering the stiffness parameter, but a small damping is also included. The nonlinear analysis is performed using the fractional calculus and some nonlinear dynamics tools, such as perturbation methods, Poincare maps and Test 0-1, in order to identify the chaotic behavior, bifurcations and the crack propagation. Fractional springs and damping are appearing in different contexts of systems with memory and hysteresis for the better comprehension of the physical phenomena involved.
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Hierarchical Control of Aerial Manipulation Vehicle Kannan Approved Aerial Manipulation can be defined as the technology in which an Aerial Vehicle has the capability to manipulate and interact with its environment. Simple examples of aerial vehicle for active tasking . . . include grasping, manipulation, grasping and transporting etc. The given applications of Aerial Manipulation systems have their own challenges such as highly nonlinear dynamic coupling, instabilities due to load disturbance, nonlinear contact dynamics etc.
The Aerial Manipulation Vehicle (AMV) considered here is a Quadrotor with a multilink robotic arm fixed to the base. The quadrotor and the manipulator are dynamically coupled by forming into a multibody system. Theoretically the system can be modelled using Euler-Lagrange techniques where the state vector includes the position and attitude states of the quadrotor along with the joint angles of the robotic arm. The inputs to the AMV include the forces and the torques generated by the four rotors of the quadrotor and manipulator joint torques. The key objective of the control design here is to achieve a reference point in the Cartesian space. That is given a reference point tf=(x,y,z) for the end-effector, the AMV should reach tf starting from initial condition ti=(x0,y0,z0). The control objective is obtained in a hierarchical fashion. The outer most-loop is the reference generator system. This system is a closed-loop inverse kinematic algorithm which generates position, position rates, yaw and yaw rates as well as manipulator joint angle and rates. The quadrotor uses the reference values to perform the outer loop position control, with attitude control (roll, pitch) in inner loop. It must be noted that the position and attitude of the end-effector depends on the position and attitude of the quadrotor itself and the joint angles of the robotic arm. The control of the highly complex hierarchical control involves a combination of Proportional, Integral and Derivative Action. The closed loop stability analysis of the hierarchical control structure is performed using Input-to-State Stability method applied to a cascade system. The performance of the control structure is evaluated for different end-effector reference scenarios in the SimMechanics simulation environment of Matlab/SIMULINK.
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Nonlinear Model Predictive Control for Cooperative Control of Space Robots Kannan Approved Advancement of space needs has challenged human capabilities to perform advanced on-orbit tasks such as construction, maintenance, inspection, astronaut assistance, debris manipulation etc. In order . . .to perform these tasks spacecraft with manipulators can be employed.
In the current problem we consider the scenario where two space robots are collectively manipulating a passive object. The passive objects include space structures for assembly or space debris etc. Here the two manipulators have to move the passive object from one position to another position in orbit. At the same time the two space manipulators should avoid colliding with each other and the passive object while not applying excessive force on the passive object and the second robot.
The given space problem can be simplified as a multi-agent problem with 2 space manipulators and a passive body. Here the satellite dynamic is considered as a point mass
with 3 transnational degrees of freedom. Each space manipulator has a rigid single link arm with a wrist type of joint attached to the body of the satellite.In the given multi-agent problem the Nonlinear Dynamic of robot ‘i’ is defined by an Ordinary Differential Equation (ODE) as a function of (xi, ui, xji, uji). Here ‘xi’ is the position of the robot ‘i’ with input ‘ui’, ‘xji’ is the relative position with the neighbor robot ‘xj’ and uji=uj+cj+cji is the forces from the second robot. Here ‘uj’ is the active forces on the robot ‘xj’ with ‘cj’ as the constraint force on the robot ‘xj’ and while ‘cji’ is the relative constraint force between ‘xi’ and ‘xj’. We propose a Nonlinear Model Predictive Control (NMPC) solution to the given problem. To implement the NMPC, the control input at each instant is determined by minimizing the performance index with receding horizon. The performance index is a function of state (xi) and input (ui) error functions from the nominal values. Here additional state and input constraints can also be included. The robustness of closed loop NMPC is discussed in performing the current scenario and can be further extended to include multiple robots.
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Mathematical modeling of a Bridge Crane Bueno Approved The problem of transportation and movimentation of heavy loads have allways been found in ports, airports, industrial complexes and construction sites. Cranes are mechanical systems that move heavy lo . . .ads both vertically and horizontally. In the recent years the cranes are becoming bigger, higher and faster and, due to the cables flexibility, the car movements can cause slightly damped oscillations, making the cranes operation slow. In this work, a bridge crane is modelled, and the nonlinear mathematical model is validated experimentally, attempting to develop a better understanding of the complex cranes dynamics.
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Study of effects due to elimination and resources downgrade of sensors in control techniques applied to a two-wheeled inverted pendulum Bueno Approved This paper presents comparisons considering the main characteristics of modeling methodologies and control techniques for a system based on operation of a two wheels inverted pendulum (TWIP), namely, . . .the method of obtaining the model mathematical equations, the type of driver used, number of required sensors and control objectives.
Firstly, a robust control strategy is applied to control TWIP’s velocity and displacement considering the use of six sensors. After, a project of a state observer is performed in order to reduce the number of sensors required in the application. The Matlab / Simulink environment is adopted to develop computer simulations considering the use of one of the TWIP models and a robust control strategy to control the speed and vehicle speed.
Through the simulation results of the system operation aspects are analyzed considering the influence on the stability of the system caused by the resolution and sampling rate of the sensors, the presence of noise on the sensor readings, general failure of sensors, by providing a conjugated feature oscillating engine for the system and the change of height values and user mass.
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Total Abstracts: 12

S17. New Methods and Applications in Aeroelasticity and Structural Mechanics/Dynamics

Abstract: New methods and applications are explored and tackled in order to realize future aircraft. A representative example is the coupling of sophisticated computational fluid dynamics (CFD) and th . . .e nonlinear computational structural dynamics (CSD) which is inevitable in the design of very light flexible aircraft structure undergoing large deformation. The aim of this session is to provide a unique opportunity to researchers to share cutting-edge information of the recent research activities on these issues. Methods in aeroelasticity and mechanics/dynamics, coupling with flight dynamics and applications are within the scope including optimization or inverse analysis.
 
Organizers: Toshiya Nakamura, Masato Tamayama, Jiro Nakamichi , Next Generation Aeronautical Innovation Hub Center, Japan Aerospace Exploration Agency (JAXA)

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Title Author Status Abstract
Dynamic Load Estimation for a Beam using Central-Difference Scheme and FEM Nakamura Approved Operational load monitoring is very useful in estimating the internal load and hence the usage of the structure based on the actual data. Today there is a strong background of the development of sensi . . .ng technology such as optical fibers (FBG) and data processing, enabling the application of inverse analysis with large degree of freedom. In the present study a method is proposed to estimate the dynamic load on a beam from measured strain data. The FE method is used to model the beam with the central-difference scheme for time-integration. If both the deflection and the slope (a derivative of the deflection) are given at all nodes, the problem is trivial. But since we do not have enough data, the problem becomes mathematically ill-posed and then a technique of inverse analysis is employed. Furthermore, because it is very hard to measure the deflection and slope directly in actual cases, we introduce an operation to transform the strain data, which is usually measured, into the deflection and slope in the numerical scheme of the load identification. The numerical study is not comprehensive at this time but the validity of the present method will be demonstrated.
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Stabilizing effects on 2D channel flow due to longitudinal wall oscillation Atobe Approved Influence of wall oscillation on laminar-turbulent transition of the plane Poiseuille flow is investigated analytically. The Floquet analysis using a time-dependent Orr-Sommerfeld equation expects tha . . .t the flow is stabilized or destabilized depending on the parameters. The velocity profiles for the analysis are assumed as the superposition of the plane Poiseuille flow and the Stokes layer. Also the collocation method is used in the wall-normal direction for making the monodromy matrix. Depending on the parameters, namely frequency Ω and amplitude Uw of the wall-oscillation, there is the stable region in Ω-Uw plane even though the Reynolod number is of supercritical.
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Reduced Order Modeling of Aeroelasticity Analysis for a Wing under Static Deformation Effect Tamayama Approved The full order analysis of aeroelasticity system, which solves Euler or Navier Stokes equations in time domain, is usually expensive in a sense of time consumed. To improve this defect arisen in the f . . .ull order analysis, the Reduced Order Modeling (ROM) method has been developed. If there is a pressure difference between upper and lower surfaces of a wing, aerodynamic forces loaded on the wing cause the wing static deformation. The ROM method, therefore, should have the capability to simulate the wing vibrations under static deformation effect. Some previous researches proposed that this capability is given by applying biases to the unsteady aerodynamic forces which are identified from the aerodynamic response caused by forced wing motions about the rigid wing, i.e. the wing stayed without its static deformation. And, here, the biases are corresponding to the static aerodynamic forces. This implies that the wing motion applied to the wing in order to acquire the aerodynamic response should be large enough to cover the range of wing static deformation. To conduct the full order aerodynamic analysis under a large wing motion is unstable in the CFD code used in this study. Then, another procedure is proposed in this study. The forced unsteady CFD simulation by the full order analysis is conducted about the wing deformed statically. On the other hand, the static deformation varies according to the free stream dynamic pressure, and, therefore, it is strongly sought to identify the aerodynamic model around the flutter dynamic pressure. In this study, this flutter dynamic pressure is initially predicted by the aeroelasticity ROM model composed of the aerodynamic model identified from the full order CFD results simulated around the rigid wing without static deformation. Then, the aerodynamic model is identified from the full order CFD results around the wing model deformed statically at the initially predicted flutter dynamic pressure stated above. At the venue, the simulation results acquired with the method described above will be presented.
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Simulation of Transonic Limit Cycle Oscillations using Nonlinear Aerodynamic Modeling Arizono Approved Limit cycle oscillations (LCO) are usually defined as self-sustained oscillations with limited amplitudes. The type of LCO are categorized as follows: (1) airfoils with stiffness nonlinearities, (2) d . . .elta wings with geometrical plate nonlinearities, (3) very high aspect ratio wings with both structural and aerodynamic nonlinearities, (4) nonlinear structural damping and (5) aerodynamic flows with large shock motions and flow separation.
In the transonic region, the presence of shocks on the wing surface introduces strong aerodynamic nonlinearities. The prediction of LCO amplitudes is much more difficult than the related problem of predicting the linear flutter boundary. Stickan et al. presented the LCO simulations of Aerostabil wing. The amplitudes of LCO by the simulation could not meet with the results of experiments.
Recent Computational Fluid Dynamics (CFD) solver can estimate the drag and the complicated flow such as the high lift configuration. This paper presents the prediction of LCO amplitude of Aerostabil wind tunnel model using the state-of-the-art CFD solver which is developed at JAXA.
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Total Abstracts: 4

S1. Analysis of Fractional Differential, Integral and Difference equations with Applications

Abstract: It has been demonstrated that fractional Dynamic systems equations represent better and more economical models than their counterpart of integer derivative models. Also, due to their applica . . .tions in various branches of sciences and engineering, the theoretical and numerical study of fractional dynamic systems has gained increased importance. In addition, differential equations involving Riemann Liouville derivatives have a special role in applications in Physics, Biological Sciences and Engineering. Qualitative and quantitative properties of Riemann Liouville and Caputo types of differential and integral and integro-differential equations are very useful in applications. Fractional differential equations are also referred to as equations with memory. Thus the study of fractional differential equations takes care of the global effect rather than the local effect as in the integer derivatives.
Organizer: Aghalaya S. Vatsala, University of Louisiana at Lafayette, Louisiana 70504, USA
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Title Author Status Abstract
New trends on Fractional operators and Applications Atangana Approved In this talk, we present a new direction of fractional calculus with some new definitions of fractional derivatives. New results in connection of the new calculus are presented together with some appl . . .ications. In addition, we propose a new interpretation to the concept of fractional derivative.
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Global solvability of a class of fractional integro-differential equations with applications Oukouomi Noutchie Approved In this talk, we consider a class of fractional differential equations arising in natural science and engineering. Semi-linear abstract Cauchy theory will be used to investigate the existence and uniq . . .ueness of solutions. In particular, perturbation methods will be developed to predict the asymptotic behaviour of solutions.
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Existence of solution for a higher order fractional differential equation Assia Approved In this talk, we establish sufficient conditions for the existence and uniqueness of solution for a class of higher order Caputo fractional initial value problems. We transform the posed problem to a . . .Volterra integral equation, then under Krasnoselskii-Krein type conditions and by using successive approximations, we discuss the existence and uniqueness questions. A numerical example is given to illustrate the obtained results.
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Generalized Monotone Method and Numerical Approach for Coupled Reaction Diffusion Systems Muniswamy Approved Study of coupled reaction diffusion systems are very useful in engineering and science. In this paper, we provide a methodology to construct the solution for the coupled reaction diffusion systems, w . . .ith initial and boundary conditions, where the forcing function is the sum of an increasing and decreasing function. It is known that the generalized monotone method coupled with coupled lower and upper solutions yield monotone sequences which converges uniformly and monotonically to coupled minimal and maximal solutions. In addition, the interval of existence is guaranteed by the lower and upper solutions, which are relatively easy to compute. Using the lower and upper solutions as the initial approximation, we develop a method to compute the sequence of coupled lower and upper solutions on the interval or on the desired interval of existence. Further, if the uniqueness conditions are satisfied, the coupled minimal and maximal solutions converge to a unique solution of the reaction diffusion systems. We will provide some numerical results as an application of our numerical approach.
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Riemann Lioville Dynamic Systems Versus Sequential Caputo dynamic Systems with Applications Vatsala Approved It is well known that dynamic models represented by fractional derivatives are more efficient and cost effective compared with its counterpart of dynamic models using integer derivatives. The most com . . .mon fractional derivatives that are used currently are the Riemann-Liouville and the Caputo derivative. The basic idea of fractional dynamic system is to use ‘q’ the order of the derivative as a parameter to improve the model. The order ‘q’ plays an important role as a parameter in the initial and boundary conditions of Riemann-Liouville dynamic systems, but not in the Caputo dynamic systems. In this talk, we bring the salient features of this parameter ‘q’ in the initial and boundary conditions in the sequential Caputo dynamic systems. We develop several results of Sequential Caputo derivative with initial and boundary conditions. As an application of this approach, we demonstrate that sequential Caputo sub and super hyperbolic equations yields the classical reaction diffusion equation and the wave equations as special cases. Also, we present some numerical results.
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Haar based numerical solution of Fredholm-Volterra fractional integro-differential equation with nonlocal boundary conditions SETIA Approved Fractional integro-differential equations have many applications in different fields of science and engineering like aerospace, nuclear engineering, chemistry, astronomy, biology, economics, potential . . . theory and electrostatics. One may find the exact solution of such fractional integro-differential equation but in some special cases only. This point has taken attention of lot of researchers and different methods have been proposed time-to-time like transform methods, homotopy analysis, Adomain decomposition method, variational iteration method etc. In this paper, a numerical method is proposed to solve the Fredholm-Volterra fractional integro-differential equation with non local boundary conditions by using Haar wavelets. A collocation based Galerkin’s method is applied by using Haar wavelets as basis functions over the interval [0,1). It converts the Fredholm-Volterra fractional integro-differential equation into a system of k linear equations. We need to incorporate m nonlocal boundary conditions in the same way. So all together it will give a system of (k+m) linear equations in (k+m) variables which can be solved. A variety of test examples are considered to illustrate the proposed method. In first and last examples, the order of fractional differential operator is considered 1/2 and 1/3 respectively which are less than 1. In second example, the order of fractional differential operator is considered 5/4 which is more than 1. First and last examples require only one nonlocal boundary condition while the second example needs two nonlocal boundary conditions. The error bounds have also been explored in all the test examples. The actual error is also measured with respect to a norm and the results are validated through error bounds.
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Numerical method to solve cauchy type singular integral equation with error bounds SETIA Approved Cauchy type singular integral equations with index zero naturally occur in the field of aerodynamics. Literature is very much developed for these equations and Chebyshev’s polynomials are most frequen . . .tly used to solve these integral equations. In this paper, a residual based Galerkin’s method has been proposed by using Legendre polynomial as basis functions to solve Cauchy singular integral equation of index zero. It converts the Cauchy singular integral equation into system of equations which can be easily solved. The test examples are given for illustration of proposed numerical method. Error bounds are derived as well as implemented in all the test examples.
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Integral equation in functional spaces / Generalized Lebesgue space()() firouz Approved The aim of this work is the study: the problem of existence of solutions for integral equation in different
functional spaces.
Then it is imperative to pass by an assumptional property: the compactnes . . .s of the integral operator.
The compactness of integral operator posses en general a big character in the resolution of several mathematics
problems such that the existence of solution for integral equation, this character is based on the theory of:
REISZ-FREDHOLM.
In this case and in ower these Integral equation in functional spaces.
We interested for the problem wish the the compactness of integral equation in functional spaces with using
fundamental mathematics properties such that the restriction and the prolengement
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On a nonlinear fractional boundary value problem TOREBEK Approved In this work we prove the existence and uniqueness of solutions for a class of the nonlinear third order fractional differential equation with boundary condition. An example is given to illustrate the . . . main results.
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Total Abstracts: 9

Applications on fractional operators to real world problems

Abstract: The concept of derivative with fractional order has attracted attention of many researchers in many branches of sciences, technology and engineering as it was found suitable mathematical too . . .ls for modeling real world problems. Many researchers around the globe are devoting their attention in proposing a better derivative with fractional order that can be used in almost all real world problems. For each definition proposed, new theory and applications need to be developed. This special section is therefore devoted to the discussion underpinning the latex development on theory, methods and applications of fractional calculus. The special section will include talks on: Theory on recent definitions of fractional derivative, modeling real world problems with fractional derivative, theory on fractional differential equations, numerical methods for fractional differential equations, analytical methods for differential equations and iterative methods.
 
Organizer: Abdon Atangana, Institute for groundwater studies
University of the Free State, Bloemfontein, South Africa
 
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Abstracts are being reviewed. A list of approved abstracts will appear soon.

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S3. Control and Estimation: Theory and Applications

Abstract: Feedback and control systems are all pervasive in nature as well as in human endeavors. The theory of control systems is a mature field in the minds of many; however, it continues to evolve . . .as new technologies are seen as areas to which it can be applied. Since the middle of the last century, the field of estimation has become inextricably entwined with control system theory, thus combining the two fields in the literature has become quite common. The purpose of this session is to bring together researchers who are working to advance the theory of control and estimation and those who are advancing the field of control and estimation through the application of the theory to new and advanced technologies.
Organizers: Stephen C. Stubberud, Oakridge Technology, Del Mar, CA, USA , Allen R. Stubberud, University of California, Irvine, Irvine, CA USA

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Title Author Status Abstract
Submarine Harbor Navigation Using Image Data Stubberud Approved The process of ingress and egress of a United States Navy submarine is a human-intensive process that takes numerous individuals to monitor locations and for hazards. Sailors pass vocal information to . . . bridge where it is processed manually. There is interest in using video imaging of the periscope view to more automatically provide navigation within harbors.
In this paper, video-based navigation is examined as a target-tracking problem. While some image-processing methods claim to provide range information, the moving platform problem and weather concerns, such as fog, reduce the effectiveness of these range estimates. The video-navigation problem then becomes an angle-only tracking problem. Angle-only tracking is known to be fraught with difficulties, due to the fact that the unobservable space is not the null space. When using a Kalman filter estimator to perform the tracking, significant errors arise which could endanger the submarine.
This work analyzes the performance of the Kalman filter when angle-only measurements are used to provide the target tracks. This paper addresses estimation unobservability and the minimal set of requirements that are needed to address it in this complex but real-world problem. Four major issues are addressed: the knowledge of navigation beacons’ locations, the minimal number of these beacons needed to maintain the course, levels of obscuration of these navigation beacons, and update rates of the angles of the beacons as the periscope rotates to monitor the actions in the harbor around the submarine. The goal is to address the problem of navigation to and from the docks, while maintaining the traversing of the harbor channel based on maritime rules relying solely on the image-based data. The minimal number of beacons will be considered. For this effort, the image correlation from frame to frame is assumed to be perfectly achieved. Variation in the update rates and the dropping of data due to rotation and obscuration is considered.
The example problem will address a simulated simple-harbor scenario of San Diego harbor. A set of reasonable initial conditions are assumed based on whether the submarine is in ingress or egress operations. Obscuration due to military and commercial traffic will reduce the use of certain beacons.
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A Unified Kalman Filter Stubberud Approved When considering problems of linear sequential estimation, two versions of the Kalman filter, the continuous-time version and the discrete-time version, are often used. (A hybrid filter also exists.) . . . In many applications in which the Kalman filter is used, the system to which the filter is applied is a linear continuous-time system, but the Kalman filter is implemented on a digital computer, a discrete-time device. The two general approaches for developing a discrete-time filter for implementation on a digital computer are: (1) approximate the continuous-time system by a discrete-time system (called discretization of the continuous-time system) and develop a filter for the discrete-time approximation; and (2) develop a continuous-time filter for the system and then discretize the continuous-time filter. Generally, the two discrete-time filters will be different, that is, it can be said that discretization and filter generation are not, in general, commutative operations. As a result, any relationship between a discrete-time filter and the continuous-time filter for the same continuous-time system may be obfuscated. This is particularly true when an attempt is made to generate the continuous-time version of the Kalman filter through a simple limiting process (the sample period going to zero) applied to the discrete-time filter. The correct result is, generally, not obtained.
In a 1961 research report, Kalman showed that the continuous-time Kalman filter can be obtained from a discrete-time Kalman filter by taking limits as the sample period goes to zero, if the white noise processes in the continuous-time system are properly defined. Using this basic concept, a discrete-time filter can be developed for a continuous-time system as follows: (1) discretize the continuous-time system using Kalman’s technique; and (2) develop a discrete-time filter for that discrete-time system. Kalman’s results show that the discrete-time filter generated in this way converges to the appropriate continuous-time filter as the sample period goes to zero. This not only makes the relationship between the discrete-time filter and the continuous-time filter transparent, but also lets the sample period be considered as a design parameter.
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Integration of Bio-Inspired, Control-Based Visual and Olfactory Data for the Detection of an Elusive Target Duong Approved In this paper, a technique is presented for integrating bio-inspired visual and olfactory receptor systems to search for elusive targets in practical environments in which the targets cannot be detect . . .ed by either data sensor individually. The bio-inspired Visual System is based on a model of the extended visual pathway which consists of saccadic eye movements and the visual pathway. This model enables powerful target detections from noisy and partially incomplete visual data. The Olfactory receptor algorithm is based on a spatial invariant independent component analysis, that was developed from a receptor-electronic nose (enose) at Caltech. It has been adapted to enable the detection of an odorant target in an unknown environment. The integration of these two systems provides an important approach to detecting unknown targets for many applications. In particular it may provide a cornerstone for developing effective and low cost intelliegnt system-on-a-chip for miniaturized UAVs or flying robots for future DOD and NASA missions.
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Observer based fault diagnostics for networked control systems in presence of delay Abdollahi Biron Approved The concept of wireless communication, provides the ability of remote controlling for large scale systems in industries. Therefore, each large scale system can be divided into (1) physical part contai . . .ning the hardware, plants, sensors and actuators and (2) cyber part containing the software, controllers and communication network. Usually, for a large scale system, controller is a decentralized controller containing several local controllers communicating to each other through the shared network. Also, sensors and actuators of the physical part of a large scale system, can communicate with the controller via communication network to send and receive information from the controllers. Hence, the whole system can be considered as a networked control system (NCS). The communication among different parts of the network system happens with delay effected which is one of the communication network inherent characteristics. A long with the network delay, there are always possibility to physical failures in sensors and actuators of the physical part of the system.
In this paper, we consider a communication network with unknown bounded delay and a distributed state feedback controller for the networked control system. Each controller receives data from other controllers as well as plant sensors which are imposed to the network delay and fault in the measurements. We propose an observer based fault diagnostics approach for networked control system to detect faults in presence of delay in communication network. The stability of estimation error dynamics and convergence to zero is proved by Lyapunov–Krasovskii and LMI approach. The results of applying the proposed fault diagnostics scheme in a case study will be presented and discussed in the paper.
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MODEL PREDICTIVE CONTROL: A NEW APPROACH Nagy Approved New methods are proposed in the paper for solution of the model predictive control problem. Nonlinear state space design techniques are also treated. For nonlinear state prediction (state evolution co . . .mputation) a newly established predictor, given in the form of an operator, is introduced and tested. Settling the problem may be obtained through application of the principle “direct stochastic optimum tracking” with a simple algorithm. The principle states that a predicted optimum stochastic trajectory (or output sequence) can be obtained by step-by-step optimum extension of a part of the trajectory (output sequence). The optimization method which implements the principle is called “optimized stochastic trajectory / output sequence tracking”. The model predictive control problem with I/O equations or state equations can be solved with this method through a sequence of two-stage optimizations and iteration in an optimum manner, even for linearizable nonlinear plants. Although concrete values of future disturbances are not known, the future nonlinear process, too, is considered as stochastic. Precondition for the optimum nonlinear solution is optimum state prediction, which is based in the paper on definition of virtual intersample points and linearization at these points. Increasing the number of intersample points may give better approximation of the evolving nonlinear trajectory of states, improving the accuracy of prediction. State estimation on virtual intersample sections between virtual intersample points may be done with linear predictor. The predicted state difference between two real sampling instants can be given with a sum, which may be replaced with an integral for the case of infinite virtual intersample points. This integral defines the so-called M-operator, which may be considered as optimum state predictor for linearizable nonlinear plants. Simulations show that applying the described techniques, exact following with estimated outputs is possible on a whole finite horizon (not regarding slight computational errors) with the derived algorithms, even for linearizable nonlinear plants, if the control signals are not constrained. Simulations also demonstrate the advantages of the M-operator based solution in comparison with application of the extended Kalman filter predictor.
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Total Abstracts: 5

S5. Delay Differential Equations Models in Life Sciences, Engineering and Economics

Abstract. The Session is dedicated to recent models from biology, medicine, technology and socio-economics that use differential equations with time lag. A major topic in this context is the study of . . .equilibria and of the existence of periodic solutions, including Hopf bifurcations. Talks presenting oscillatory phenomena in hematology, aircraft control (including Pilot Induced Oscillations) or economics are particularlly encouraged for submission.
Organisers:
Andrei Halanay, University Politehnica of Bucharest
Mihaela Neamtu, West University of Timisoara
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Title Author Status Abstract
On qualitative properties in nonlinear Volterra integro-differential equations with delay TUNC Approved This paper considers a class of scalar and vector non-linear Volterra integro-differential equations of first order with constant delay. We show stability, uniformly stability, boundedness, convergenc . . .e and square integrability of solutions. The technique of proof involves defining appropriate Lyapunov functionals. Our results improve the results obtained in literature.
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The stability analysis of a hypothalamic pituitary adrenal axis model with inclusion of the glucocorticoid receptor and memory Neamtu Approved This paper analyzes a model of the hypothalamic-pituitary-adrenal (HPA) axis that includes the glucocorticoid receptor in the pituitary. Due to the spatial separation between hypothalamus, pituitary a . . .nd adrenal glands, we introduce distributed time delays. The existence of the positive equilibrium point is proved and a local stability analysis with several types of delay kernels is provided. Also, the fractional model is taken into account. The last part contains some numerical simulations to illustrate the effectiveness of our theoretical findings.
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Stability analysis for a delay differential equations model of a hydraulic turbine speed governor SAFTA Approved The paper aims to model the dynamic behavior of a speed governor for a hydraulic turbine using an associated mathematical model. The nonlinear mathematical model newly introduced consists of a system . . .of delay differential equations (DDE) and will be compared to some already in use mathematical models that use ordinary differential equations (ODE). A new kind of nonlinearity is introduced through the time delay. The delays can characterize different running conditions of the speed governor. For example, it can happen that the spool displacement of the hydraulic amplifier is blocked due to oil impurities in the oil supply system and so the hydraulic amplifier has a time delay. Stability analysis of the equilibria of the model for the hydraulic control system is performed. Numerical simulations are presented to illustrate the characteristics of the new model as compared to the classical one.
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Dynamics of complex-valued fractional-order neuronal networks Radulescu Approved The dynamics of complex-valued fractional-order neuronal networks are investigated, focusing on stability, instability, Hopf bifurcations and chaos. Sufficient conditions for the asymptotic stability . . .and instability of a steady state of the network are derived, based on the complex system parameters and the fractional order of the system, considering simplified neuronal connectivity structures (hub and ring). In some specific cases, it is possible to identify the critical values of the fractional order for which Hopf bifurcations may occur. Numerical simulations results are presented to illustrate the theoretical findings and to investigate the stability of the limit cycles which appear due to Hopf bifurcations. Potential routes towards the onset of chaotic behavior are also explored numerically, when the fractional order of the system increases. (joint work with Eva Kaslik)
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Parameter estimation and sensitivity analysis for a mathematical model with time delays of leukemia Candea Approved D. Candea, A. Halanay, R. Radulescu
We consider a system of nonlinear delay differential equations that describes the interaction between three competing cell populations: healthy, leukemic and anti-l . . .eukemia T cells involved in Chronic Myeloid Leukemia (CML) under treatment with Imatinib. The aim of this work is establish which model parameters are the most important in the success or failure of leukemia remission under treatment using a sensitivity analysis of the model parameters. We aim to estimate the realistic values of the most significant parameters of the model which affect the evolution of CML during Imatinib treatment using some experimental data. For these parameters, steady states are calculated and their stability is analyzed and biologically interpreted.
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Influence of Delay on Dynamical Behaviour of Nonideal Pendulum Systems Shvets Approved Influence of Delay on Dynamical Behaviour of Nonideal Pendulum Systems
A.Yu. Shvets
National Technical University of Ukraine “Kyiv Polytechnic Institute”,
Kyiv, Ukraine
(e-mail: alex.shvets@bigmir.ne . . .t)
In mathematical modelling of oscillatory processes a mathematical model of
a relatively simple dynamical system is often used to study the dynamics of
much more complex systems. A typical example of this approach is the extensive
use of pendulum models to study the dynamics of systems of an entirely
different nature. Pendulum mathematical models are widely used to describe
the dynamics of various technical constructions, machines and mechanisms, in
the study of cardiovascular system, financial markets, etc. Such widespread
use of pendulum models makes it relevant to study directly the dynamics of
pendulum systems.
The mathematical models of nonideal (in sense of Sommerfeld-Kononenko) spherical pendulum systems,
taking into account the various factors of delay impacts, are constructed.
Significant influence of delay on the existence and stability of equilibrium states of such systems are shown.
It has been established that the presence of the delay leads the appearance of steady regular attractors
of different types (limit cycles and invariant toruses). It is proved that the presence of the delay
can generate the appearance of deterministic chaos in such systems. Built and analysed some
chaotic attractors of considered pendulum systems.
keywords: nonideal pendulum systems; delay factors, regular and chaotic attractors
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New results on the stability, boundedness and periodic solutions of some third-order delay nonlinear differential equations with multiple deviating arguments Adesina Approved A.T. Ademola, B.S.Ogundare, M.O. Ogundiran and O.A.Adesina
Department of Mathematics, Obafemi Awolowo University, Ile-Ife, Nigeria
In this paper, sufficient conditions for solutions that are periodic, . . . uniformly asymptotically stable and uniformly ultimately bounded are established for some third-order nonlinear differential equations with multiple deviating arguments. By employing Lyapunov’s second method, a complete Lyapunov functional is constructed and used to establish novel results that made relevant results on the subject matter in the literature to be particular cases of our results. Finally, the correctness and effectiveness of the results are tested with illustrations.
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Nonlinear dynamics in a fractional-order Morris-Lecar neuronal model Brandibur Approved A two-dimensional fractional-order Morris-Lecar neuronal model is analyzed, focusing on stability and instability properties. Moreover, we discuss the occurrence of Hopf bifurcations with respect to t . . .he fractional order of the system, which is chosen as bifurcation parameter. Numerical simulations exemplify the theoretical results, revealing rich spiking behavior. We also compare the results to similar ones obtained for the classical integer-order Morris-Lecar neuronal models. (joint work with Eva Kaslik)
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Stability and oscillations in a CML model Badralexi Approved We capture the evolution in competition of healthy and leukemic cells in Chronic Myelogenous Leukemia (CML) taking into consideration the response of the immune system. Delay-differential equations in . . . a Mackey-Glass approach are used. One starts with the study of stability of the equilibrium points of the system. Conditions on parameters for the local stability are given. Oscillatory behaviors occur naturally in biological phenomena. Thus, we investigate the periodic behavior of solutions and we obtain conditions for periodic solutions to appear through a Hopf bifurcation.
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Total Abstracts: 9

S6. Integral Equations and Their Applications in Science and Technology

Abstract: The aim of the session is to discuss both the theory of integral equations and their applications in engineering, mechanics, mathematical physics and so on. In particular, talks presenting t . . .he use of integral equations in the areas of aerodynamics, fluid mechanics and wave diffraction are especially welcomed. Special emphasis is also paid to nonlinear integral equations, functional integral equations and systems of integral equations. The theory of fractional integral equations and their numerous applications is also included. Thus, various topics of the theory of integral equations which have a wide range of applications will be considered.
Organizers: Jozef Banas, Department of Mathematics, Rzeszów University of Technology, Rzeszów, (Poland)
Luis Castro,CIDMA – Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, Aveiro, (Portugal)
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Title Author Status Abstract
A Fast Computational Technique for Solving General Nonlinear Integral Equations Fattahzadeh Approved In this work we propose a fast scheme for solving general nonlinear Integral equation by using Chebyshev fast method of Fourier transform (FFT). This method is based on replacement of unknown function . . . by truncated series of well known Chebyshev polynomials. The quadrature formulas which we use to calculate integral terms have been estimated by FFT. This is a grate advantages of this method which has lowest operation count in contrast to other works which use multi production of operational matrices which raise computational complexity or involve intermediate numerical techniques. Also convergence of this method is given and the numerical experiments show the applicability and accuracy of this method.
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Hyers-Ulam-Rassias stability for a class of Hammerstein integral equations Simões Approved We obtain sufficient conditions for the Hyers-Ulam stability and Hyers-Ulam-Rassias stability of a class of Hammerstein integral equations within both cases of finite and infinite intervals. These sta . . .bilities are analysed upon the consideration of fixed point arguments and weighted metrics. Some concrete examples will be presented to illustrate the theoretical results.
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Invertibility of Wiener-Hopf plus Hankel integral equations Silva Approved We will study operators arising in Wiener-Hopf plus Hankel integral equations.
Invertibility and Fredholm criteria for those operators are obtained in the framework of variable exponent Lebesgue spac . . .es on the real line. The main technique is based on appropriate factorizations of the corresponding Fourier symbols.
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Fourier cosine and Fourier sine integral equations and their convolutions Guerra Approved We will present a study for a class of integral equations associated with the Fourier cosine and Fourier sine transforms. The solvability of those equations is analysed. In addition, a Parseval type f . . .ormula and a Plancherel type theorem are obtained. Heisenberg uncertainty principles are also obtained, and new convolutions are derived for the integral equations under study.
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Some new properties and applications of a fractional Fourier transform Rodrigues Approved In this talk, we deal with the fractional Fourier transform in the form introduced a little while ago by Yuri Luchko. This transform is closely connected with the FC operators and has been already emp . . .loyed for solving of both the fractional diffusion equation and the fractional Schr\”odinger equation. In this paper, we continue investigation of the fractional Fourier transform and in particular prove some new operational relations for a linear combination of the left- and right-hand sided fractional derivatives. As an application of the obtained results, we provide a schema for solving the fractional differential equations with both left- and right-hand sided fractional derivatives without and with delays and give some examples of realization of our method for several fractional differential equations.
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On the solvability of a class of convolution integral equations with symmetry Castro Approved Convolution integral equations with symmetry appear naturally in boundary value problems for elliptic partial differential equations in symmetric or symmetrizable domains. We will be concentrated on a . . . class of those equations which is associated with the Helmholtz equation in a quadrant, where a possible solution is symmetrically extended to a half-plane. Characterizations of the normal solvability, Fredholm property, one-sided invertibility will be obtained for the consequent integral operators within a framework of Bessel potential spaces. Moreover, explicit factorization methods for such operators will be presented. The talk is based on joint works with F.-O. Speck.
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Some asymptotic properties of Fourier-Laplace transform of the Green’s Tensor for coupled thermoelastodynamics in 2D and 3D case Alipova Approved The dynamics of thermoelastic medium under the action of concentrated transient heat sources and mass forces is considered. It is known that the effect of such sources is modeled by representation of . . .the body force F, or heat source Q through the singular generalized functions. Fourier transformation in space coor-dinates and Laplace transformation in time were done for components of Green’s Tensor. Some asymptotic properties and symmetrical properties of Green’s Tensor for coupled Thermoelastodynamics in 2-dimensional case are considered: by approaching to infinity and zero, and symmetry properties by indexes and by ar-guments. Several Lemmas are proved: logarithmic singularities of the type ln p at p approaching to zero. The proved inequalities for parameters of Bessel’s function are valid for real p>0 and inequalities of Bessel functions in dynamical functions are proved also. It is obviously the confir-mation of physical statement of isotropic thermoelstic medium in 2D and 3D case.
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Shock Waves As Generalized Solutons Of Thermoelastodynamics Equations. On The Uniqueness Of Boundary Value Problems Solutions Alipova Approved Generalized solutions of coupled thermoelastodynamics equations are considered. By use of generalized functions theory, the conditions on jumps of stresses, velocities, temperature gradients and energ . . .y density on their fronts are received. The statements of four non-stationary boundary value problems of coupled thermoelasticity are given, for which uniqueness of decisions are proved taking into account shock thermoelastic waves.
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Total Abstracts: 8

S7. Inverse Problems: Theory and Application to Science and Engineering

Abstract: Inverse problems arise naturally in many branches of science and engineering where the values of some model parameters must be obtained from the observed data.
This sort of question is of gr . . .eat interest in many application areas in science and engineering including acoustics, aerodynamics, electromagnets, hydrological engineering, image analysis, shape design, structural dynamic modification and reconstruction, tomography, etc.
In the recent years, theory and applications of inverse problems have undergone a tremendous growth: They can be formulated in many mathematical areas and analyzed by different theoretical and computational techniques.
This session focuses on theory and application of inverse problems and includes talks on Inverse problems for differential and integral equations, Inverse problems and homogenization techniques, Regularization techniques, Statistical inverse problems, Numerical analysis of inverse problems, Computational Inverse Problems, and related areas.
Organizers: Prof. Herb Kunze, University of Guelph (Canada), Prof. Davide La Torre, University of Milan (Italy) and Khalifa University (UAE).
 
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Title Author Status Abstract
An inverse problem for a system of steady-state reaction-diffusion equations acting on a perforated domain Kunze Approved A perforated domain (or porous medium) is a material characterized by a partitioning of the total volume into a solid portion often called the matrix and a pore space usually referred to as holes. Mat . . .hematically speaking, these holes can be either materials different from that of the matrix or real physical holes. The treatment of an inverse problem on a perforated domain is complicated heavily by the presence of the perforations or holes.
In this work, we consider a coupled system of reaction-diffusion equations at steady-state acting on a perforated domain. Given observation data of the system components, we seek to estimate the coefficients/parameters in the model.
We build on past work in which we established and demonstrated results for solving the related inverse problem for a single equation. The method relies on relating the problem on the domain with holes to the problem on the domain with no holes. As we will see, the extension to a system of equations adds extra complexity and complications to the problem.
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An inverse problem for a mathematical model of aquaponic agriculture. Bobak Approved Aquaponics is a closed-loop agricultural system which uses a symbiotic relationship between aquatic organisms and aquatic macrophytes. The two major populations of interest are fish and plants, howe . . .ver the system is dependent on ammonia concentrations and nitrate concentrations to function sustainably. Organic nitrogen in fish waste naturally converts to ammonia through biological degradation. Ammonia is highly toxic to fish, and is an inefficient nutrient source for plants. In order for ammonia to be used as fertilizer for the plants, it must go through a natural microbial process called the Nitrogen Cycle and be transformed to Nitrate. Nitrate is a nutrient rich food source for plants and essential to the nutrient uptake process. Academic research into the aquaponics is just beginning to get momentum. To our knowledge, there is a distinct lack of reliable mathematical models and simulations available to analyze the stability of an aquaponic system.
In this work, we present an aquaponic system model and discuss solution behaviour. A sensitivity analysis helps us to identify the most impactful parameters in the model. Researchers at John Hopkins Center for a Liveable Future have provided us with a large set of data from their aquaponic lab; the data contains information about fish population, major concentrations present in the tank water, as well as harvesting information regarding the plant populations. We approach the parameter estimation inverse problem in several ways. By using simulated data, with low-amplitude noise added, we first demonstrate that the “collage method” for ODEs inverse problems works well for our model. We then discuss how the real-world data can be used to address the inverse problem, both with this mathematical machinery and via appropriate statistical analyses.
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Signal processing with Circle Inversion Map Systems Boreland Approved Given a circle C with centre o and radius r, inversion with
respect to C transforms the point p to the point p’ such that
p and p’ lie on the same radial half-line from o and d(o,p)d(o,p’)=r*r,
where . . .d is Euclidean distance. Circle inversion was introduced in Apollonius
of Prega’s book, Plane Loci, and has drawn interest in geometry.
In The Fractal Geometry of Nature, Mandelbrot briefly discusses successive
inversion with respect to a family of M circles.
In this talk, we establish that a system of circle inversion maps has
a unique set attractor living in the union of all of the circles.
Fractals literature develops the well-known concept of local iterated
function systems with grey-level maps, with applications to image
processing. We follow this path to establish a framework that uses
local circle inversion maps as the functions. We demonstrate the
results with examples.
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Collage-based Approaches for Elliptic Partial Differential Equations Inverse Problems Yodzis Approved The collage method for inverse problems has become well-established in the literature in recent years. Initial work developed a collage theorem, based upon Banach’s fixed point theorem, for treating i . . .nverse problems for ordinary differential equations (ODEs). Amongst the subsequent work was a generalized collage theorem, based upon the Lax-Milgram representation theorem, useful for treating inverse problems for elliptic partial differential equations (PDEs). Each of these two different approaches can be applied to elliptic PDEs in one space dimension.
In this work, we explore and compare how the two different approaches perform for selected problems: the estimation of the diffusivity for a steady-state heat equation and the estimation of the flexural rigidity for an Euler-Bernoulli beam problem. We include complicating factors, such as observational noise, point sources, and only having boundary measurements.
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Addaptive model reduction approach in optimal control applied to solve Transfer Equations Oulghelou Approved Optimal control of dynamical systems is of much interest in a wide range of applications,
such us aeronautics, design and mechanical systems. However, the main fear often encoun-
tered is the huge tim . . .e amount needed to perform a numerical simulation of those kind of
problems.
To overcome this issue, one would refer to model reduction methods, namely the Proper
Orthogonal Decomposition method, which consists in seeking the solution as a space time
decomposition. The spacial basis is obtained by the snapshots method [Sirovich et al. Quar-
terly of Applied Mathematics, 1987], whereas the temporal basis is the solution of the ROM
resulting from the Galerkin pojection of the considered problem onto the spatial basis. This
method was already applied in fluid flow control context [Bergmann et al. Journal of Com-
putational Physics, Volume 227, 2008]. However, the construcion of snapshots respectivly
to control parameters variations turns out to be expensive. A variant of the last approach
is to use a fixed adequate basis which fits with a range of control parameters [Tallet et al.
Numerical Heat Transfer Part B, to appear]. This approach shows to be faster, however it
strongly depends on the predefined trust region sampling of the control parameters.
To avoid these restrictions, we propose to use the Progressive Generalized Decomposition
(PGD) [Ammar et al. Journal of Non-Newtonian Fluid Mechanics, 2006], which is a method
that reacts within the control process as an automatic self basis corrector respectivly to con-
trol parameters variations.
The methodology is tested firstly on a boundary control problem of a Newtonian fluid flow
in a lid driven cavity governed by Stokes equations, and secondly on the control of Burgers
equations. the solution is accuratly approximated and a gain on simulation time is observed.
For the sake to expend the frame of the application of this methodology, we intend in the next
step to apply it to the Navier Stokes Equations.
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Stability Problem for Singular Dirac Equation System on Finite Interval ERCAN Approved In this study, we show the stability spectral problem for the singular Dirac system respect to two spectra on a finite interval. The meaning of the stability problem of differential operators is to . . .estimate the difference of their spectral functions when finite numbers of eigenvalues of operator overlap. The method is based on work by Ryabushko [12]. The paper [12] studied to what extent only finitely many eigenvalues in one or both spectra determine the potential. We obtain a bound for difference of the spectral functions for Singular Dirac equation system.
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Surface Pressure Sensitivities for the Measurement of the Mach Number and Angle of Attack of Supersonic Flows Stoia-Djeska Approved In this paper we present a method for the calculation of the sensitivities in the case of supersonic flows over a bi-splopes wedge. The sensitivities are of the pressures determined at some locations . . .on the wedge surface and are determined with respect to the time-dependent Mach number and to the angle of attack. Both of these parameters are included in the upstream boundary conditions in the numerical simulations. These sensitivities are necessary for the solution of the inverse problems in which the angle of attack and the Mach number are determined from the surface pressures measurements. The goal is the development of an air data sensor for a test vehicle which is intended to be used for drop tests from very high altitudes (Fukiba, 2012). The feasibility of the concept of such measurements was first demonstrated by (Cooper and Webster, 1951).
In this work, we use the adjoint equations of the 2D Euler equations of gas dynamics. The emphasis is on the correct formulation and implementation of the adjoint boundary conditions, in the framework of the imposition of the unsteady boundary conditions which include the Mach number and the angle of attack. Finally, we use an algorithm for the efficient solution of the forward and adjoint problem simultaneously, by using a piggy-back iteration process inside an one-shot method to advance in time. The numerical results show that a wedge with two slopes gives high sensitivities for both Mach number and angle of attack indirect measurements.
Bibliography
1. K. Fukiba and all. Numerical Study of Flow Angles and Mach number Measurement Using the Surface Pressure of a Supersonic Aircraft with Nose Cone. Tran. Japan Soc. Aero. Space. Sci. Vol. 55, No. 2, pp. 81-88, (2012).
2. M. Cooper, R.A. Webster. The Use of an Uncalibrated Cone for Determination of Flow Angles and mach Numbers at Supersonic Speeds. NACA Technical Note 2190. (1951).
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IFSM Fractal Image Compression, Sparsity, and Total Variation Minimization: A Multiobjective Approach La Torre Approved We consider the inverse problem associated with IFSM: Given a target function f, find an IFSM, such that its invariant fixed point f
is sufficiently close to f in the Lp distance. Forte and Vrscay (1 . . .995) showed how to reduce this problem to a quadratic optimization model. In this pa-
per, we extend the collage-based method developed by Kunze, La Torre and Vrscay (2013), by including:
– the minimization of the level of sparsity through the 1-norm instead of the 0-norm,
– the minimization of the total variation of the fixed point.
In our formulation, the minimization of the above criteria is treated as multiobjective problem.
The results of some numerical computations are presented.
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Total Variation Minimization for Measure-valued Images La Torre Approved We present a notion of total variation for measure-valued images. We introduce the total variation denoising problem and show an application
to the case of fractal transforms on the space of measure-v . . .alued images.
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Total Abstracts: 9

Mathematical Modeling of Tires

Abstract: This session invites papers that deal with mathematical modeling and testing of tires. The force and moment generation mechanism of tires depends on the tire-road interaction and tire struct . . .ure and materials properties. Authors who have developed models and test equipment simulating the behavior of the tire noise, vibration, handling, and wear are encouraged to submit their paper for this session.
Organizer : Saied Taheri, Virginia Tech, Blacksburg, VA 24060, USA
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Abstracts are being reviewed. A list of approved abstracts will appear soon.

Submit your abstract!

S8. Mathematical Problems in Combustion and Fire Science

Abstract: The session solicits papers on wide range of mathematical problems emerging in studies of combustion, and fires as its special case. Combustion systems in general exhibit extremely complex b . . .ehavior, resulting from interactions of various physical and chemical phenomena over a wide range of spatial and temporal scales.
Presentations on both theoretical and numerical studies are most welcome.
Particular topics of interest include, but not limited to
reaction-diffusion systems
theoretical analysis of relevant ODE and PDEs
asymptotic analysis
instabilities, bifurcations and chaos in combustion systems
efficient and novel numerical methods (such as Lattice Boltzmann methods)
stochastic methods
mathematical models and approaches for specific applied problems
One of driving objectives for this session is to identify mathematical problems that are important for progress, but not yet receiving deserved attention from mathematical community.
The session aims to provide enjoyable open forum for interaction of theoreticians, applied mathematicians, as well as industry users. Contributions revealing new, stimulating and controversial ideas are highly encouraged.
Organizer; Prof. Vasily Novozhilov, Victoria University (Australia)
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Title Author Status Abstract
Fire Suppression as a Thermal Implosion Novozhilov Approved The paper considers an inversion of a thermal explosion concept which we call thermal implosion.
One of natural applications of the proposed concept is a phenomenon of fire suppression.
Equations des . . .cribing thermal implosion will be proposed, and their analysis presented for some of the most fundamental cases.
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APPLICATION OF FRACTIONAL CALCULUS TO MODELLING TRANSIENT COMBUSTION OF SOLID PROPELLANTS KULISH Approved It was Zel’dovich, who first considered the transient combustion problem of solid propellants. Some more detailed models of that process have been developed afterwards. However, until today, numerical . . . methods remain the prevailing tool for modelling unsteady combustion processes. In this work, we demonstrate that at least one of the problems of the unsteady combustion theory, which previously investigated numerically, can be treated analytically by means of fractional calculus. The solution for the unsteady speed of combustion thus derived is then compared with the solution obtained by numerical means in previous studies. The comparison shows a good agreement between those results, especially for small values of time.
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ON THE POSSIBILITY TO DEVELOP AN ADVANCED NON-EQUILIBRIUM MODEL OF DEPRESSURISATION IN TWO-PHASE FLUIDS KULISH Approved Carbon dioxide is widely used as the power gas in the gas guns community due to its ease of handling, storability at room temperature, and high vapour pressure depending only upon temperature, but not . . . a tank size, as long as some liquid carbon dioxide remains in the tank. This high vapour pressure can be used as the pressurant, making it what is referred to as a self-pressurising propellant. However, as a two-phase substance, carbon dioxide does have its drawbacks: (1) vaporisation of liquefied CO2 inside a tank when shooting rapidly or a lot causes the tank to get cool, resulting in pressure fluctuations that makes the gun’s performance and accuracy worse, (2) solid carbon dioxide that is also known as dry ice can appear on the output valve of the tank while shooting and it can cause damage or slow the gun’s performance down, if it works its way into some control components, including the barrel of the gun. Hence, it is crucial to obtain a scientific understanding of carbon dioxide behaviour and further the discharge characteristics of a wide range of pressure-tank configurations. For the purpose of satisfying this goal, a comprehensive discharge mathematical model for carbon dioxide tank dynamics is required. In this paper, the possibility to develop an advanced non-equilibrium model of depressurisation in two-phase fluids is discussed.
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Effects of Initial and Boundary Conditions on Thermal Explosion Development Novozhilov Approved The paper presents some recent results concerning thermal explosion (autoigniiton) development.
The two problems are considered
1) Effects of initial temperature non-uniformities in the mixture. This . . .effect is considered both in steady mixtures,
as well as in dynamic mixtures subjected to developing natural convection.
2) Effects of oscillating temperature conditions at the boundaries surrounding reacting mixture. This type of boundary
conditions has never been considered before in thermal explosion studies. Such a problem is of major interest in applications
of thermal explosion theory to initiation of certain types of fires, namely fires involving various solid and biosolid materials.
In both cases, final results are critical conditions (boundaries) for thermal explosion, which are found using numerical modeling.
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How simulating wildland fires: the multiphase approach ? MORVAN Approved This communication demonstrates how the behaviour of wildland fires can be simulated using a multiphase formulation. This approach consists in solving the coupled system formed by the vegetation and t . . .he surrounding atmosphere, in assimilating the vegetation as a sparse porous media and performing a homogenization-like procedure. After a presentation of the physical and mathematical model, some numerical simulations are presented, illustrating various configurations of fires (surface fire, backfire, counter fire …), in various ecosystems (grass, shrubs), and under various external conditions (slope, wind) (Morvan et al 2009, Dupuy et al 2005, Morvan 2014). An analysis of the main scales associated with the physical mechanisms (radiation and convective heat transfer, atmospheric turbulence, combustion …) contributing to the ignition and the propagation of a forest fire (Morvan 2011) has been also proposed, with the identification of two modes of propagation, namely wind driven fire and plume dominated fire.
References
D. MORVAN, S. MERADJI, G. ACCARY “Physical modelling of fire spread in grasslands” Fire Safety Journal, Vol.44, pp. 50-61, 2009.
J.L. DUPUY, D. MORVAN “Physical modelling of forest fire behaviour in a fuel break” Int. J. Wildland Fire Vol.14, pp.141-151, 2005.
D. MORVAN “Wind effects, unsteady behaviours and regimes of propagation of surface fires in open field”, 2014, Combustion Science and Technology, Vol.186(7), pp.869-888.
D. MORVAN “Physical phenomena and length scales governing the behaviour of wildfires: a case for physical modelling”, 2011, Fire Tech. Vol.47, pp.437-460.
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Modelling Emission Turbulence-Radiation Interaction by using a Hybrid Flamelet/Stochastic Eulerian Field Method CONSALVI Approved The time-averaged Radiative Transfer Equation (RTE) introduces two unclosed terms, known as ‘absorption Turbulence Radiation Interaction (TRI)’ and ‘emission TRI’. Emission TRI is related to the non-l . . .inear coupling between fluctuations of the absorption coefficient and fluctuations of the Planck function and can be described without introduction any approximation by using a transported PDF method. In this study, a hybrid flamelet/ Stochastic Eulerian Field Model is used to solve the transport equation of the one-point one-time PDF. In this formulation, the steady laminar flamelet model (SLF) is coupled to a joint Probability Density Function (PDF) of mixture fraction, enthalpy defect, scalar dissipation rate, and soot quantities and the PDF transport equation is solved by using a Stochastic Eulerian Field (SEF) method. Soot production is modeled by a semi-empirical model and the spectral dependence of the radiatively participating species, namely combustion products and soot, are computed by using a Narrow Band Correlated-k (NBCK) model. The model is applied to simulate an ethylene/methane turbulent jet flame burning in an oxygen-enriched environment. Model results are compared with the experiments and the effects of taken into account Emission TRI on flame structure, soot production and radiative loss are discussed.
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Total Abstracts: 6

S10. Nonlinear analysis, optimal design and guidance of space systems with low thrust

Abstract: The scope of the special session covers all areas of the mathematical problems of the nonlinear analysis, optimal design and guidance of space systems equipped with low thrust engines and it . . .s practical implementations in the aerospace engineering.
The development of new space exploration missions requires creation of space systems with improved mass-power characteristics and economic indicators. One of possible problem solutions is the use of prospective power systems based on new physical principles that provides high technical characteristics. Such systems include, for example, electric rocket propulsion system and spacecraft with solar sail. It is also noteworthy that existing classical methods of multi-objective optimization are not efficient enough for the synthesis of such space systems. We dedicate our attention to development of new mathematical methods in this field.
The main directions of this special section:
– the mechanics and the dynamics of the space flight with low thrust, including electric propulsion and a solar sailing;
– the application of the optimal control theory to the synthesis control of spacecraft;
– the analysis of the control peculiarities of large spacecrafts;
– the guidance of spacecraft with low thrust, including functioning in conditions of gravitational fields of complex configuration;
– the methods development of complex polyoptimization of the trajectories and design parameters of spacecraft.
Special session request authors to participate
 
Organizers: Prof. Olga Starinova, Samara State Aerospace University (Russia), Prof. Cui Naigang, Harbin Institute of Technology (China).
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Title Author Status Abstract
Methods of Optimal Control Choice of Non-Keplerian Orbits Starinova Approved The developed method of iterative optimization of interplanetary missions with the low thrust, using sequence of movement specified mathematical models and design shape spacecraft, is realised. The ne . . .w articular analytical decision describing planar movement of spacecraft with solar electric propulsion is described, allowing to construct initial approach in the iterative scheme of optimization. Developed a method of modelling and optimization of interplanetary missions ballistic schemes, based on a combination of Pontryagin’s maximum principle formalism conditions of transversality and methods of the mathematical programming, allowing to consider restrictions characteristic for concrete interplanetary missions. Recommendations for choice design-ballistic parameters of the interplanetary missions spacecraft, received taking into account features nuclear and solar power plant for missions on delivery of a payload to orbits of Mars, expeditions the Earth–Mars–Earth are received.
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Boundary problem solution of an optimal control transfer between circular orbits for an electric propulsion spacecraft in an irregular gravitational field of an asteroid Shornikov Approved The paper deals with a two-point boundary problem of optimal control transfer between circular orbits for a spacecraft with an electric propulsion engine. The spacecraft manoeuvres in vicinity of the . . .asteroid Gaspra 951 with an irregular gravitational field. We propose to consider the irregular gravitational field of the asteroid as a superposition of relative gravitate points rotating near a single barycenter of the system. Consequently, the idea is to reduce the gravitational field simulation to the n-body problem. We use the proposed method for boundary value problem formalization. The task of control spacecraft’s transfer between circular orbits from 200 km to 100 km is considered. Authors propose a combination of the Pontryagin’s maximum principle and the Newton’s step by step approximation as solutions methods for the boundary problem. Authors developed a software for the boundary problem solution where operator is able to intervene in the calculation process: changing international step and increment. The main advantage of the introduced method is a remarkable increase of the solution’s convergence.
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Pulse-width control of electro-reaction engines for a station-keeping of land-survey satellite on sun-synchronous orbit Somov Approved We present a method for a station-keeping of a small land-survey satellite on a sun-synchronous orbit. We have developed mathematical models of the spacecraft orbital motion taking into account princi . . .pal disturbances and original scheme of the correcting engine unit (CEU) based on eight electro-reaction engines with pulse-width control of their thrust. The CEU is applied simultaneously for both correction of the satellite orbital motion and an unloading of onboard electromechanical driver from accumulated angular momentum.
We have developed algorithms for a pulse-width control of the CEU and have presented the research results for created algorithms. Numerical results are represented for a station-keeping of land-survey satellite on sun-synchronous orbit with respect to inclination and longitude of ascending node.
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An approach for the control method’s determination for an interplanetary mission with solar sail Gorbunova Approved This article is devoted to an interplanetary flight of a spacecraft with a solar sail. Model of solar sail spacecraft called Helios is designed by students of Samara State Aerospace University. We def . . .ine heliocentric motion of the solar sail spacecraft via Keplerian elements. Authors propose to use locally-optimal control laws for the solar sail control model. The obtained laws can provide rapid change of Keplerian elements or stabilize its values. Authors used combination technique for locally-optimal control laws to obtained several trajectories for interplanetary missions. The distinctive feature of the proposed method that parameters of osculating elements are used as destination phase coordinates. Authors have received the main ballistic parameters and the trajectories of the flights to libration points of Venus and Mercury. The exact optimal control is close to obtained solution by application locally-optimal control laws, and the difference in duration of the flight is only 10 %.
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Optimization methods of near-Earth and interplanetary flights with low thrust Salmin Approved The problem of improving the efficiency of space transport operations and control modes of the orbits of spacecraft now is particularly relevant.
The problem of improving the efficiency of space tran . . .sport operations and control modes of the orbits of spacecraft now is particularly relevant. One possible solution of this problem is the use of propulsion systems on the basis of the low-thrust electro-jet engines. Authors provides methods for the design-ballistic optimization of space missions with low-thrust electro-jet engines.
The optimization problem is divided into two independent:
– dynamic – is finding the optimal control programs and obtaining dynamic characteristics S for forward and reverse flight. This term denotes a measure of the energy expenditure to the control trajectory and the angular motion of the spacecraft, provided in the form of dependence (explicitly or implicitly) by the boundary conditions and design parameters. As dynamic characteristics normally used characteristic speed or time of flight with turn on the engine of the thruster.
– parametric – finding the optimal design parameters of the spacecraft and ballistic mission parameters.
Authors give the results of for solving a series applications for different classes of spacecraft, carrying out maneuvers with low thruster engines:
– Optimization of interplanetary flight to Mars automatic spacecraft with solar electric propulsion,
– Optimization of interplanetary manned mission Earth-Mars-Earth,
– Optimization flights with low-thrust in the Earth-Moon system,
– Optimization of the design-ballistic characteristics of reusable transfer vehicle,
– Optimization combination regimens excretion payload GSO,
– Evaluating the effectiveness of the orbital space system inspection,
– Evaluating the effectiveness of the use of electric propulsion to maintain a low-orbit Earth satellites.
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Approximate approach for optimization space flights with a small thrust on the basis of sufficient optimality conditions Salmin Approved Flight mechanics with a low-thrust is a new chapter of mechanics of space flight, considered plurality of all problems trajectory optimization and movement control laws and the design parameters of sp . . .acecraft.
Thus tasks associated with taking into account the additional factors in mathematical models of the motion of spacecraft becomes increasingly important , as well as additional restrictions on the possibilities of the thrust vector control. The complication of the mathematical models of controlled motion leads to difficulties in solving optimization problems. Authors proposed methods of finding approximate optimal control and evaluating their optimality based on analytical solutions. These methods are based on the principle of extending the class of admissible states and controls and sufficient conditions for the absolute minimum. Developed procedures of the estimation enabling to determine how close to the optimal founded solution, and indicate ways to improve them. Authors describes procedures of estimate for approximately optimal control laws for space flight mechanics problems, in particular for optimization flight low-thrust between the circular non-coplanar orbits, optimization the control angle and trajectory movement of the spacecraft during interorbital flights, optimization flights with low-thrust between arbitrary elliptical orbits Earth satellites.
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Control geostationary spacecraft in orbital plane using a low thrust engine Chetverikov Approved The control algorithm the parameters of the geostationary spacecraft’s orbit using low-thrust engine. We consider the only flat parameters, determining the geostationary spacecraft’s position in the o . . .rbit plane, namely, orbital period, eccentricity and longitude point of standing. Formulated plane problem of terminal control geostationary spacecraft. It is assumed that the corrective maneuver is implemented by creating a small transversal acceleration using electric low-thruster. Developed a discrete model of the geostationary spacecraft motion in the orbit plane under the influence of small transversal acceleration. The solution of this problem using traditional dynamic programming method based on the use of Bellman equation, is difficult to obtain, because the discrete model of geostationary spacecraft motion is a nonlinear system of equations. Therefore, the proposed approximate scheme of solving the problem based on the three-step algorithm of terminal control the orbital period, eccentricity and longitude point of standing. The result is solution flat problem of the terminal control in the analytical form. Analytical expressions for the cost estimate characteristic velocity of corrective maneuver. When modeling the motion of a geostationary spacecraft under the influence of a small transversal acceleration, algorithm showed high accuracy of solving the terminal control problem.
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Total Abstracts: 7

S11. Nonlinear Engineering Problems with Singularities

Abstract: The scope of Session may include but not limited to following scientific directions: Mechanical systems with critical parameters. Mechanical systems with configuration manifold having self- . . .intersections. Auto-oscillations, instability and shock inspired by dry friction. Problems of body motion in resisting medium. Nonlinear bifurcation problems in wind engineering.

Organizers: Dr. Yury Selyutskiy, Dr. Oleg Cherkasov and me, Dr. Marat Dosaev. Lomonosov Moscow State University.

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Title Author Status Abstract
Helicopter Flight Control by Dynamic Compensator Yaici Approved In a precedent paper a design process is described to achieve eigenstructure assignment using block poles placement. Systems described in state space equations are transformed to systems in matrix fra . . .ctions description (MFD), in which the denominator and the numerator are matrix polynomials. As for systems in state space description (SSD) the behavior is defined by the eigenstructure of its state matrix, the behavior of systems in MFD is defined by the latent structure (latent values and latent vectors) of the denominator. To such matrix polynomials we define block roots (called block poles for the denominator and block zeros for the numerator). From a set of latent values and corresponding latent vectors a block root can be constructed. Thus a desired eigenstructure can transformed to a desired latent structure, which is used to construct desired block poles.
The method proposed here allows the assignment of the whole set (and even more) of latent values and vectors obtained. The input-output feedback configuration has been chosen to design the compensator which allows the placement of block poles of a desired denominator constructed from a desired latent structure.
In this paper, the proposed design method is applied for attitude stabilization of a Lynx helicopter in hover. Helicopters are inherently unstable, very non-linear and highly cross coupled, and thus must be augmented with feedback control to reduce the pilot workload to an acceptable level. So a presentation of some research works on flight control is given, then the details of the design process of the compensator, starting from a desired eigenstructure, are presented. To validate the results, the output responses are compared to state and output feedback control responses, and some of these shapes are shown. The proposed method results has better parameters: a better peak angle, the initial response delay is more confined, and presents a better damping and shaping of the response. It was shown that the input-output feedback configuration was able to retain the performance of a state-feedback solution while using only measurable information.
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Treatment of flow singularity for exiting liquid jet from a hydrophobic channel Khayat Approved The flow of a slipping fluid jet is examined theoretically as it emerges from a channel at moderate Reynolds number. Poiseuille flow conditions are assumed to prevail far upstream from the exit. The p . . .roblem is solved using the method of matched asymptotic expansions. A similarity solution is obtained in the inner layer near the free surface, with the outer layer extending to the jet centerline. A slipping jet is found to contract very near and far from the channel exit but does not have a definite behavior in between, compared to for an adhering jet. Eventually, the jet reaches uniform conditions far downstream. As in the case of entry flow, there is a rapid departure in flow behavior for a slipping jet as the slip length. This rapid change is notably observed in the drop of boundary-layer thickness, increase in exit and relaxation lengths as well as in jet width with slip length. Finally, the connection with microchannel and hydrophobic flows is highlighted.
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Nonlinear Mathematical Models for Paths Maintaining Constant Normal Accelerations Pakdemirli Approved Authors: Mehmet Pakdemirli and Volkan Yıldız
Ordinary differential equation models describing paths for which the normal acceleration components of the objects remain constant is derived. The normal . . .acceleration component is important since this component is mainly responsible for the overturn or the side slip of the vehicle. Depending on the type of the tangential acceleration component, different mathematical models are derived to describe the path of constant normal accelerations. The equations and the initial conditions are cast into dimensionless forms. In their dimensionless forms, the paths are expressed in terms of the dimensionless path parameters. For constant velocity case, the equations yield circular arc solutions. For variable tangential accelerations, closed form solutions are not available. Depending of the model of the acceleration, the path may be described in terms of one or more dimensionless path parameters. Numerical solutions of the equations are obtained using an adaptive step size Runge-Kutta algorithm. Approximate solutions of the problem are also given using the perturbation theory. The approximate solutions and the numerical solutions are contrasted with each other. Potential application areas can be the design of highway curves, highway exits, railroads, route selection for ships and aircrafts.
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Range Maximization and Brachistochrone Problem with Dry Friction, Viscous Drag and Accelerating Force Cherkasov Approved Cherkasov O.Yu., Zarodnyuk A.V.
The range maximization problem and corresponding the brachistochrone problem
with Coulomb, viscous friction and accelerating force are considered. A maximum principle
. . .procedure allows to reduce optimal control problem to the boundary-value problem for a system
of two non-linear differential equations. Solution of this system is corresponding to the motion
under singular control. For the case of Coulomb friction effective application of the Kelley necessary
conditions allows to show that reaction of the curve is positive along extremal trajectory, thus extremal
control could be determined uniquely. The question of the optimality of the extremal trajectory is clarified.
For the case of viscous drag it is shown that the reaction of the curve could have single switching from
negative to positive value. Qualitative analysis of the solutions, based on phase plane method is carried out,
and typical features of the optimal trajectories are determined. The research fulfilled allows to substantiate the
results, discovered before as a result of numerical simulation or formulated as a hypothesis. Some results,
obtained earlier, are refined. Qualitative research is illustrated and verified by means of numerical simulation.
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Comparison of energy costs for different control laws of a vibratory robot Kulikovskaya Approved In the study there are introduced several control methods that maximize average velocity of the vibratory robot subject to several constraints. The robot is presented by a rigid box with a pendulum in . . .side it. It can move forwards and backwards and there is a Coulomb friction between the box and the surface. In the paper it is not only shown the difference and advantages of proposed control laws but there is also done a comparison between works done by motor for different control cases.
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Evolution of rotational motions of a rigid body similar to pseudoregular precession in the Lagrange case Leshchenko Approved Perturbed rotational motions of a rigid body similar to pseudoregular precession in the Lagrange case when perturbation torque slowly varying with time. Conditions are presented for the possibility o . . .f averaging the equations of motion with respect to the nutation angle is conducted. The averaged system of equations of motion is obtained. A mechanical model of the perturbations, corresponding to the body’s motion in a medium with linear dissipation, is considered. Evolution of the projection of the angular momentum vector onto the vertical, the body’s total energy and the projection of the angular velocity vector onto the axis of dynamic symmetry are determined. The obtained solutions have an independent value for applications.
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Mechanical Systems with Singularities Vitaly Approved Mechanisms with critical parameters are considered. Finding so-called dead center positions is shown. Mechanical systems having self-intersections in configurational manifold are presented. Stability . . .and bifurcations of equilibriums of mechanical systems will be discussed. Bifurcations of solutions in the problem of equilibrium of a slipper brake will be considered without and with the presence of an external force.
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On auto-oscillations of a plate in flow Selyutskiy Approved Self-sustaining oscillations (auto-oscillations) of bodies of different shape in flow is a well known phenomenon. It is observed both for streamlined (like plates or wings) or bluff bodies (cylinders) . . .. In order to describe this effect and related features, an attached oscillator model is used. Characteristics of limit cycles arising in the resulting dynamical system are analyzed depending on parameters. Evolution of limit cycles with changing flow speed is studied. It is shown that calculations performed in the framework of the model qualitatively agree with available experimental data.
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Electromechanical imitator of antilock braking modes of wheels with pneumatic tire and its application for the runways friction coefficient measurement Putov Approved The towed complex of prelanding control of runways friction coefficient for the purpose of ensuring the safe landing of aircraft runways is discussed. Measuring is carried out by rolling with sliding . . .measuring wheel along the proposed path of the aircraft wheels and calculating the friction coefficient on the measured force of sliding.
The paper deals with the problem of creation of automatically controlled braking device for the electromechanical tester with a pneumatic tire. The device allows you to simulate the antilock braking modes of measuring wheels, close to the braking modes other chassis. Such a system construction provides a correlation of friction coefficient results with the real braking performance of landing aircraft.
The development of a mathematical model of the electromechanical braking device executed on the basis of the braking synchronous generator is discussed. Mathematical model describes the dynamic processes of the braking measuring wheel and taking into account the following features: the elasticity of the tire in the contact patch, the elasticity of the transmission connecting the generator shaft with a measuring wheel hub, nonlinear effects of dry friction (Stribeck effect) and electromagnetic processes.
The development of a mathematical model of adaptive searchless control system of automatic electromechanical braking device with reference model and robust algorithm parameter settings is described. This algorithm provides a reproduction (imitation) of antilock braking modes of aircraft wheels during landing while suppressing their own undesirable nonlinear dynamics.
Mathematical modeling and computer investigation of friction coefficient values distribution, mathematical modeling of measurement process along the runway surface, as well as the influence of the shape and parameters of braking on the results of measurement are also given in detail. The results of the comparative analysis of mathematical models of the standard approximating dependencies of friction coefficient on sliding is briefly discussed. A complex of mathematical models based on the model Burchard and additive random processes is developed. This complex describes the distribution of the friction coefficient values along the runway with a variety of descriptive characteristics (snow, wet asphalt with snow, very wet asphalt, wet asphalt) with corresponding average values of friction coefficient.
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Modeling of indentation into inhomogeneous soft tissues Lyubicheva Approved Lyubicheva A.N., Goryacheva I.G., Dosaev M.Z., Su F.-Ch.
A simulation of a contact interaction of the indenter and inhomogeneous soft biological tissues is carried out. The soft tissue is modeled by . . .the incompressible elastic body which contains structural inhomogeneities (spherical or longitudinal inclusions). The elastic moduli of inclusions are higher than the bulk soft tissue modulus. These inclusions may be considered, in particular, as the models of the pathological growths. The indenter has the form of a hollow hemisphere (shell). It is the model of the mechanoreceptor developed in [1] to study the mechanical properties of soft tissues. The hydrostatic pressure can be applied inside the shell.
The numerical simulation of the contact interaction of the indenter and the inhomogeneous elastic layer is performed based on the finite element analysis. The contact characteristics (contact pressure distributions, dependences of the contact radius on penetration, etc.) and the internal stresses are calculated for various radii of the spherical inclusion and its positions related to the center of the contact zone. To study the influence of the longitudinal inclusion on contact characteristics and the internal stress distribution, the contact problem for the two layered body is considered. The lower layer is modeling an inclusion.
Based on the numerical analysis, the dependences of the contact area size, and contact pressure on penetration of the indenter into the sample for several values of the inclusion size, depth, its location, the ratio of the elastic moduli of inclusion and the surrounding material, but also for various values of hydrostatic pressure inside the shell were obtained. The possibility of an inverse problem solution for determining the mechanical properties of the inclusion, and its size by measuring the contact characteristics is discussed.
The developed method can be used during the laparoscopic operations for identification of the different kinds of soft tissue inhomogeneities.
Acknowledgements: this work was supported by Russian Foundation for Basic Research under grant 16-58-52033 MNT_a, 14-01-00372 А
[1] Yeh, C.-H., Su, F.-C., Goryacheva, I., Martynenko, Y., Dosaev, M.Z., Ju, M.-S., 2014. Image-assisted method for estimating local stiffness of soft tissues and calibration of bias due to aqueous humor effect. Sensors and Actuators A: Physical 212, 42-51.
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Stability domains for vane with viscose filling Dosaev Approved The motion of a four-blade axisymmetric vane with fixed point is considered in the constant flow of medium. This is a mechanical system with variable dissipation. Stability of the permanent rotation o . . .f vane in medium flow is studied. We consider the stability conditions for of this motion. Stability domains are found.
One can observe the opposition between external aerodynamic load and internal friction.
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A Predication model for combustion modes of the scramjet-powered aerospace vehicle based on the nonlinear features of the isolator flow field YANG Approved The supersonic combustion ramjet (scramjet) engine remains the most promising airbreathing engine cycle for hypersonic flight, particularly the high-performance dual-mode scramjet in the range of flig . . .ht Mach number from 4 to 7, because it can operates under different combustion modes. Isolator is a very key component of the dual-mode scramjet engine.
In this paper, nonlinear characteristics of combustion mode transition is theoretically analyzed. The discontinuous sudden changes of static pressure and Mach number are obtained as the mode transition occurs, which emphasizing the importance of predication and control of combustion modes.
In this paper, a predication model of different combustion modes is developed based on these these nonlinear features in the isolator flow field. The ground experimental results prove the validity of this predication model. And it can provide a valuable reference for control system design of the scramjet-powered aerospace vehicle.
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Total Abstracts: 12

S12. Simple and Robust Adaptive Control

Abstract: Theoretical contributions of the 1970s, based on Lyapunov stability theory, led to firstnproofs of stability and had an important role in the development of model reference adaptive control . . .(MRAC) methodologies. However, the need to know the order of the controlled plant and also the complexity of the resulting controller make the applicability of these methods difficult in real large order systems. Even if only prior knowledge on an upper bound of this order is needed, this does not help reducing the complexity of the adaptive controller. For example, the order of large flexible systems is theoretically infinite and even if the number of modes in real-world is finite, the order of the resulting controller is larger than anything that can be practically implemented.
The previous decades have seen developments of new adaptive control techniques under such names as “simple adaptive control (SAC)” and similar. Although they use different approaches, all these techniques tend to use adaptive controllers, which try to avoid the need for very large order and complex computations and, therefore, are suitable for application in real world systems.
Last few years have seen quite a few works that, though different, have something in common: each one deals with large realistic plants, such as robot manipulators, planes, missiles, re-entry vehicles, large processes, etc. Application designers have first tried classical design and ended up with less than satisfactory results, whereas the adaptive control techniques performed much better, both with respect to speed of response and accuracy of tracking and even with respect to noise reduction. Some papers treated the fine theoretical issues related to adaptive control dealing with uncertainties, variable environments, nonlinear systems or systems with delays.
The proposed special session invites prospective authors to present both their particular contributions to the theoretical problems related to stability and performance and the detailed presentation of their particular realistically large applications.
Organizer; Prof Itzhak Barkana
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Title Author Status Abstract
PASSIFICATION BASED SIMPLE ADAPTIVE CONTROL OF QUADROTOR ATTITUDE: ALGORITHMS AND TESTBED RESULTS Andrievsky Approved In the paper, the results of the Passification Method with the Implicit Reference Model (IRM) application for designing the simple adaptive controller for quadrotor attitude are presented. The IRM de . . .sign technique makes it possible to relax the matching condition, known for habitual MRAC systems, and leads to simple adaptive controllers, ensuring fast tuning the controller gains, high robustness with respect to nonlinearities in the control loop, to the external disturbances and the unmodeled plant dynamics. The simulation results are presented and compared with obtained by the standard PD- and feedback linearization control technique.
For experimental evaluation of the adaptive systems performance, the compact laboratory testbed has been created and launched. It is clear that testing the new control algorithms is connected with possibility of serious accidents due to the algorithmic drawbacks, programming mistakes, sensor errors, etc, which may cause quadrotor damage or breaking, and to injury the people, as well. For flight testing, the spacy area, which is free from different obstacles is demanded. Also, flight testing procedure is very time consuming for the researchers. To overcome the mentioned problems at the initial stage of real-world adaptive controllers design the indoor testbed has been used. The testbed allows to safely test new control algorithms in the laboratory area with a small space and promptly make changes in cases of failure.
The main part of the testbed is the quadrotor, which is installed on the 2DOF gimbal suspension, allowing the quadrotor to freely rotate on pitch and roll. The outer frame is mounted on the pillars and can rotate about the horizontal axis. The inner gimbal frame can rotate with respect to the outer one. Quadrotor is fixed in the middle of the inner frame. The quadrotor center of mass is fixed, eliminating an opportunity of unforeseen changes and the dangerous trajectory.
Pillars are mounted on the square support. Whole construction is made from wood and metal angle braces.
The tested quadrotor is based on radiating frame DJI 450 and supplied with Ardupilot Mega 2.6 autopilot with the IMU, the GPS the satellite navigation system. The brushless motors with external rotor DJI 2213 (250 W each) are used as actuators. The device is supplied with the Electronic Speed Controllers (ESC) DJI 30A Opto with current output up to 30 A and with operating voltages up to 14.8 V, rotors left and right rotation with the size 10 x 4.5 or 8 x 4.5 inches. The real-time data exchange with the operator’s PC is fulfilled by means of WiFi XBee modems.
The testing results of simple adaptive control of quadrotor pitch and roll angles, their comparison with ones, obtained via the simulations, and the parameter identification results are presented.
The work was performed in the IPME RAS, supported by RSF (grant 14-29-00142).
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Implementation of SAC in Target Tracking Loop Rusnak Approved The existing SAC architecture requires the knowledge of a model whose output is followed by the controlled system. This control architecture is suitable for motion control applications where the requi . . .red trajectory of the controller plant is known. The SAC algorithm uses the input of the trajectory generator, its state and output to drive the tracking error to zero (in the deterministic case).
However when tracking a target, e.g. by a radar, neither the target’s “input”, nor its state is available. Thus the existing SAC architecture cannot be implemented per se.
This paper presents updated SAC architecture and algorithm for target tracking applications. This new architecture uses a target state estimator in the SAC tracking loop where an appropriate model of the target is implemented. It is assumed that the target trajectory is modeled as a linear system with unknown initial conditions only (no input). Thus the SAC algorithm is fed by the estimated state and target model output instead of the true state and output. As the target estimation error converges to zero exponentially so does the respective target tracking error.
The adaptive loop stability is proved by constructing a proper Lyapunov function. The main difference between this Lyapunov function and the one used in the stability proof of the SAC algorithm is the decaying exponents resulted from the converging target state estimation error. The performance as usual is determined by the adaptive feed-forward.
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The new Theorem of Stability and Gain Convergence in Simple Adaptive Control Barkana Approved Convergence of the adaptive control gains when the presence of sufficient excitation is not available
has remained an open question for more than 30 years. The rather common opinion that in these case . . .s the
adaptive control gains do not actually converge and may continue wandering without reaching any limit
at all, even when asymptotically perfect tracking is reached, is disturbing to practitioners and potential
users of adaptive control. Recent publications have provided solutions to various aspects of this open
question within the particular frame of so-called Simple Adaptive Control methodology. However, a
thorough review of the problem shows that the solution to the ultimate behavior of the adaptive gains
when sufficient excitation is not available may still be considered incomplete. The present paper revisits
the issue in order to finally show that a new Theorem of Stability, which greatly simplifies stability
analysis for nonautonomous nonlinear systems, in combination with Gronwall-Bellman Lemma provide
the solution of the gain convergence problem. It is shown that the control gains do reach a constant
value at the end of adaptation process, thus allowing the conclusion that simple and robust adaptive
control systems can successfully be implemented in real-world systems.
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Simple Adaptive Control for Quadcopters with Saturated Actuators Borisov Approved The stabilization problem for quadcopters with saturated actuators is considered. A simple adaptive output control approach is proposed. The control law “consecutive compensator” is augmented with the . . . auxiliary integral loop and anti-windup scheme. Efficiency of the obtained regulator was confirmed by simulation of the quadcopter control problem.
The authors of this work are Oleg Borisov, Alexey Bobtsov, Anton Pyrkin, Vladislav Gromov.
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Adaptive sliding mode control for nonlinear systems with unknown time-varying uncertainties Liao Approved This paper proposes a new adaptation methodology for the control of a class of nonlinear systems with unknown time-varying bounded uncertainties. The proposed method does not require any prior knowled . . .ge of the uncertainties, including their bounds.
The main idea is developed under the structure of adaptive sliding mode control [1]. First, we set the thickness of the boundary layer as one of the design parameters. Then, a new adaptation algorithm is introduced to make the sliding gain increase outside the boundary layer and decrease inside the boundary layer automatically [2]. Based on Lyapunov theory, we can show that the system will reach the boundary layer within a finite time. Once the system enters the boundary layer, the sliding gain will start to decrease. If the gain is not sufficient to hold the system within the boundary layer, the control law will push the system outward to increase the gain. On the other hand, if the gain is overestimated compared to the value of current uncertainty, the control law will hold the system inside the boundary and the gain will keep decreasing until it becomes too small to hold the system inside the boundary layer and exit again. As the result, the system will converge to a domain which is slightly bigger than the boundary layer and the sliding gain shows an adaptation process for the time-varying uncertainties.
The overall control law ensures global stability of closed-loop systems. Also, it allows for the determination of an adequate gain with respect to the current uncertainty. To sum up, this method provides a minimum possible value of time-varying sliding mode control and reduces the high-frequency chattering behavior without requiring any knowledge of the uncertainties.
Reference:
[1] Huang, Ying-Jeh, Tzu-Chun Kuo, and Shin-Hung Chang. “Adaptive sliding-mode control for nonlinearsystems with uncertain parameters.” Systems, Man, and Cybernetics, Part B: Cybernetics, IEEE Transactions on 38.2 (2008): 534-539.
[2] Utkin, Vadim I., and Alexander S. Poznyak. “Adaptive sliding mode control.” Advances in sliding mode control. Springer Berlin Heidelberg, 2013. 21-53.
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Adaptive control of an unmanned aerial vehicle Putov Approved The paper deals with development and investigation of searchless adaptive control systems for unmanned aerial vehicle (UAV) in conditions of nonlinearity and uncertainty of dynamic characteristics and . . . effect of atmospheric turbulence and wind disturbances.
The general nonlinear system of differential equations describing the dynamics of rigid UAV is considered. The separation of the system into subsystems describing the longitudinal and lateral movement of the UAV and subsystem taking into account the influence of atmospheric turbulence and wind disturbances are also discussed.
Dependence (on the Mach number) of aerodynamic characteristics of ultra-light UAV (models 70V) obtained by experiment in the wind tunnel are described. An experimental model of ultra-light UAV 70V has the following parameters: maximum launch weight – 65 kg, wing area – 1.1, cruising speed – 140-160 km/h.
UAV is equipped with inertialess sensors of position, speed, altitude, spatial orientation, angular velocities and accelerations, and also with executive electric actuators ( maximum speed of control surfaces rotation is 200 deg/s). UAV actuators are simulated by inertial link with a time constant equal to 0.015.
Calculation of aerodynamic coefficients based on the numerical solution of the Navier-Stokes equations by finite volume method and made in ANSYSCFX. The coefficients of control surfaces efficiency were determined by linear discrete vortices method. Tests with a real UAV 70 V were made in the Aerospace Academy, Hanoi, Socialist Republic of Vietnam.
Development and investigation of two searchless adaptive control systems of UAV dynamics with reference models and with robust algorithms with parametric settings that provide L-dissipative of solutions is given in detail. Development of the first adaptive system based on the method of speed gradient and required accurate records of all nonlinearities of UAV mathematical model and parametric adaptation algorithms. Development of the second adaptive system is based on the approximate replacement of non-linear state variables functions of the UAV mathematical model to simplified nonlinearities majorizing nonlinear characteristics.
Investigation research of proposed adaptive control systems of ultralight UAV are presented. These results justify the choice of gains of robust parameter adaptation algorithms that provide L-dissipative of solutions studied adaptive systems.
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A Dynamic Controller Guaranteeing Almost Strict Positive Realness of the Interconnected System Kim Approved This paper addresses the problem of designing a dynamic controller for a given MIMO LTI system (not necessarily being strictly positive real) such that their interconnection becomes almost strictly p . . .ositive real (ASPR), i.e., the interconnected system can be rendered strictly positive real by a static output feedback controller. A Riccati-type characterization is given to guarantee the ASPRness of such interconnection, and is shown to be equivalent to the minimum phaseness of the interconnected system having vector relative degree {1,…,1}. Based on this, a particular interconnection structure of a system and controller is considered, i.e., dynamic controller interconnected in parallel with the system. Then, a sufficient condition is given for the existence of such dynamic controller, termed as parallel feedforward compensator (PFC), which guarantees the minimum phaseness and vector relative degree {1,…,1} of the parallel interconnected system. Finally, an observer-based construction of such PFC is given with the additional ability of assigning the zeros of the interconnected system.
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On the Synthesis of Nonlinear Sliding Mode Controller for the Autopilot Design of Free Flight System K B Approved Today’s rapid growth in air transportation demand leads to the problem of congestion in air traffic routes. Free flight concept is widely discussed as the solution to this problem in recent years. Fre . . .e flight is a decentralized method of air traffic management, in which each aircraft has the freedom to self-optimize its own route. Conflict detection and its subsequent resolution are the major challenges in the realization of this concept. Today’s modern navigation and surveillance equipment like Global Positioning System (GPS), Automatic Dependent Surveillance- Broadcast ADS-B, etc. can ensure accurate conflict predictions. Once a conflict is detected, it should be avoided through suitable conflict avoidance maneuvers. An autopilot capable of initiating these conflict free maneuvers should be thus a necessary component of any aircraft in free flight to ensure conflict avoided flight. Autopilot design for this purpose based on Sliding Mode Control (SMC) strategy is presented in this paper since SMC can guarantee the property of robustness which results in a highly confident autopilot design. SMC design based on a nonlinear aircraft model is being encompassed so that the drawbacks associated with linear SMC design are overcome. Four different approaches of SMC control law for nonlinear systems viz., 1) Linear feedback control with switched gains, 2) Augmented equivalent plus relay control, 3) Constant plus proportional reaching law method, 4) Power rate reaching law method, are considered here for the implementation of free flight autopilot system. The performances of all these four methods are validated through simulation studies using MATLAB considering typical free flight conflict avoidance scenarios. The four control laws are compared based on their ability to reduce chattering, maximum tolerance to parametric uncertainties and improved settling time so as to select the best controller among the four considered methods, which can be used for the autopilot implementation.
Keywords: Air Traffic Control, Chattering, Conflict, Free Flight, Resolution, Robustness, Sliding Mode Control
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A Direct Implicit Reference Model Adaptive Control for SIMO Linear Time Invariant Systems with Super-Twisting-Like Terms Popov Approved Alexander Popov, Vladimir Salikhov
The Implicit Reference Model (IRM) is a well-known approach simple
adaptive control of linear and some nonlinear systems. IRM adaptive
control is used for linear t . . .ime invariant systems with relative degree of
the plant equal amount of output. The order of reference equation is
equal to relative degree of the plant and can be significantly less then
the plant order. Moreover, the true plant order not need be known for
system design. Note also that matching condition in the form used for the
model reference systems is not necessary for implicit model reference
systems.
In the paper, the results of new recursive, finite-time parameter
estimation algorithm presented in recent work of Jaime Moreno, which
resembles the classical parameter estimation algorithms, but with extra
strong (not locally Lipschitz or discontinuous) nonlinear terms added, so
that the convergence and robustness properties of the classical IRM
algorithm are enhanced. These nonlinear terms are borrowed from the
Super-Twisting Algorithm, a second-order sliding mode algorithm proposed
for the first time by Arie Levant. It has been shown that a modification
of the Adjustment Mechanism of the classical Direct IRM, by adding Super-
Twisting-Like nonlinearities, is able to improve the robustness and
convergence properties. A Lyapunov based approach was used to prove these
properties. Some simulations have shown that the proposed algorithm
provides the IRM with a much faster convergence of the tracking
Error.
As illustration of the application and performance of the proposed
algorithm examples of aircraft attitude control problem are presented.
The aircraft is modeled as a linear time invariant plant with uncertain
parameters. Simulation results confirm the theoretical statements and
demonstrate high adaptability of the proposed control system.
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Bifurcation Analysis and Control of Aircraft Dynamics in Constrained Trims – A Direct Approach Vora Approved Dynamical systems theory has been applied to provide intuitive understanding of nonlinear dynamics of multi-parametric non-linear systems such as an aircraft. A Bifurcation Analysis and Continuation T . . .heory Methodology (BACTM) has been instrumental in studying nonlinear behavior of aircraft associated with onset of instabilities and loss of control. Numerical continuation, an integral part of the BACTM, is used to compute the steady state solutions and their local stability as function of a changing parameter of the system. While a single parameter continuation and bifurcation analysis is in-vogue to study bifurcations of an aircraft model, constrained conditions in which aircraft usually operate and call for deployment of two or more controls simultaneously, for example cruise flight conditions, require a two step Extended Bifurcation Analysis (EBA) technique for computation of trim and stability. The first step of EBA requiring computation of constrained equilibrium solutions and the second step for computing stability of constrained equilibrium solutions and bifurcations from constrained solutions. The EBA technique based on a continuation algorithm such as AUTO2000 has its own limitations and shortcomings when applied to analysis of dynamical systems under constraints.
In this paper, we present a direct numerical continuation approach to study constrained dynamics of multi-parameter nonlinear systems. An algorithmic modification in the continuation code completely eliminates the need of the second step of the EBA and associated computational issues. Problems which could not be analyzed under the framework of EBA earlier could now be studied with relative ease. The direct methodology is based on the continuation toolbox, MatCont, available in MATLAB® computing environment. The proposed direct methodology is applied to different aircraft dynamics problems to highlight its usefulness and capabilities.
Constrained flight trims of F18-HARV were studied for validation of the algorithm. Flight control problem such as gain scheduling was performed to develop a stability augmentation system for the aircraft over the entire flight envelope. Subsequently associated areas of loss of control were also studied. Thus a wide range of problems can be studied and analyzed with the proposed direct continuation methodology, which is generic enough to be applicable to any multi-parameter dynamical system.
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Adaptive synchronization of robot-manipulators for tracking problem Popov Approved Alexander Popov, Vladimir Salikhov, Dmitriy Lisin, Tagir Nigmatulin
It is an important issue to coordinate multiple robotsin carrying out
assembly tasks in modern manufacturing and space applicat . . .ions. An approach
where each robot-manipulator is controlled independently of the other ones may
lead to significant errors in the mutual position of the robots in the formation.
In the papers by Dong Sun the method is proposed taking into account in
the control law not only the local positional error, but also the synchronization
errors calculated via the relative positions of the neighbouring robots. The
problem is solved under uncertainty conditions, where the several robot
parameters are assumed unknown. . The modification of a known algorithm
Slotine and Li used to solve this problem. This algorithm can be attributed to the
class of Implicit Reference Model (IRM) algorithms.
We use results of new recursive and finite-time parameter estimation
Algorithm, presented in recent work of Jaime Moreno. This alhoritm resembles
the classical parameter estimation algorithms but with extra strong (not locally
Lipschitz or discontinuous) nonlinear terms added, so that the convergence and
robustness properties of the classical Slotine and Li algorithm are enhanced.
These nonlinear terms are borrowed from the Super-Twisting Algorithm,
a second-order sliding mode algorithm proposed for the first time by Arie Levant.
It has been shown that a modification of the Adjustment Mechanism of the
classical Slotine and Li by adding Super-Twisting-Like nonlinearities is able
to improve the robustness and convergence properties.
A Lyapunov based approach was used to prove these properties. Number of
simulations have shown that the proposed algorithm provides the IRM with a
much faster convergence of the tracking Error.
Some examples of tracking several planar manipulators control problem are
presented as illustration of the application and performance of the proposed
synchronization algorithm. The robot manipulators is modeled as plants
with uncertain parameters. Simulation results confirm the theoretical
statements and demonstrate high adaptability of the proposed control system.
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Total Abstracts: 11

S15. Stochastic Processes and Fields in Engineering

Abstract: This special session is devoted to applications of random functions of one or more variables to physical and engineering problems. We plan to discuss the newest applications to continuum phy . . .sics, earthquake engineering, financial engineering, partial differential equations with random initial conditions, etc. Researchers having various mathematical, physical, and engineering background, will participate in the session.
 
Organizer: Professor Anatoliy Malyarenko, Mälardalen University, Sweden.
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Title Author Status Abstract
Spectral expansions of tensor-valued random fields (invited talk) Malyarenko Approved Many physical quantities, like the temperature, the velocity of a turbulent fluid, the strain and the elasticity tensors of a deformable body, can be modelled as a homogeneous and isotropic tensor-val . . .ued random field. Calculating the spectral expansion of such a field is an interesting task, and such expansions have alot of practical applications.
We give an overview of the current state of art in the area. In particular, we show how various parts of mathematics, including Group Representations, Special Functions, Invariant Theory, and Geometry of Convex Compacta, interplay in obtaining mathematically interesting expansions.
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Scaling to RVE in Viscoelastic Random Composites Ostoja-Starzewski Approved This paper investigates the scaling from a mesoscale level to Representative Volume Element (RVE) of spatially random linear viscoelastic materials, focusing on the quasi-static properties. Requiring . . . the material statistics to be spatially homogeneous and ergodic, the mesoscale bounds on RVE response are developed from the Hill-Mandel homogenization condition adapted to viscoelastic materials. The bounds are obtained from two stochastic initial-boundary value problems set up, respectively, under uniform kinematic and traction boundary conditions. The scalings (or scale dependencies) of mesoscale bounds, in time and frequency domains, are obtained through computational mechanics for composites with planar random checkerboard microstructures. In general, the frequency dependent scaling to RVE can be described through a complex-valued scaling function, which generalizes the concept originally developed for linear elastic random composites. This scaling function is shown to apply for all different phase combinations on random checkerboards and, essentially, is only a function of the microstructure and mesoscale.
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Randomly Stopped Stochastic Processes Silvestrov Approved Dmitrii Silvestrov
Stockholm University
E-mail: silvestrov@math.su.se
A survey of models, problems and methods of asymptotic analysis for randomly stopped stochastic processes is presented in context . . .of various applications in statistics, engineering, finance and insurance.
References
[1] Silvestrov, D.S. (2004). Limit Theorems for Randomly Stopped Stochastic Processes.
Probability and Its Applications, Springer, London, xiv+398 pp.
[2] Silvestrov, D.S. (2014). American-Type Options. Stochastic Approximation Methods.
Volume I. De Gruyter Studies in Mathematics, 56, De Gruyter, Berlin, x+509 pp.
[3] Silvestrov, D.S. (2015). American-Type Options. Stochastic Approximation Methods.
Volume 2. De Gruyter Studies in Mathematics, 57, De Gruyter, Berlin, xi+558 pp.
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Anatoliy Malyarenko and Martin Ostoja-Starzewski. Random fields related to the symmetry classes of second-order symmetric tensors Malyarenko Approved A second-order symmetric tensor can either be orthotropic, transverse isotropic, or isotropic. For each of the above symmetry classes, we consider a homogeneous random field taking values in the fixed . . . point set of the class that is isotropic with respect to the natural representation of a certain closed subgroup of the orthogonal group. Such fields may model stochastic heat conduction, electric permittivity, etc. We find the spectral expansions of the introduced random fields.
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Approximation methods of European option pricing in multiscale stochastic volatility model Ni Approved Approximation methods of European option pricing in multiscale stochastic volatility model
Ying Ni, Betuel Canhanga, Anatoliy Malyarenko, Sergei Silvestrov
In the classical Black-Scholes model for fin . . .ancial option pricing, the asset price follows a geometric Brownian motion with constant volatility. Empirical findings such as volatility smile/skew, fat-tailed asset return distributions have suggested that the constant volatility assumption might not be realistic. A general stochastic volatility model, e.g. Heston model, GARCH model and SABR volatility model, in which the variance/volatility itself follows typically a mean-reverting stochastic process, has shown to be more effective in terms of capturing the empirical facts. However in order to capture more features of the volatility smile, researchers have suggested a multiscale stochastic volatility model which contains two volatility factors. These two volatility factors follow mean-reverting processes but at different reverting rates, with one factor reverting fast and the other one reverting slowly. In the present paper we consider the European option pricing problem under one type of the multiscale stochastic volatility model. Whereas an analytical solution to such problem is still missing there are several approximation methods using different approaches. We examine the properties of two existing approximation methods, namely the method by Chiarella and Ziveyi [2] using characteristics of PDEs, Fourier and Laplace transforms and the method by Canhanga et al. [1] using asymptotic expansions. Monte Carlo simulation with variance reduction techniques is implemented as a reference method.
[1] Canhanga B., Malyarenko, A., Ni, Y. and Silvestrov S. “Perturbation methods
for pricing European options in a model with two stochastic volatilities”. 3rd
SMTDA Conference Proceedings. 11-14 June 2014,Lisbon Porturgal, C. H. Skiadas
(Ed) 489-500 (2014).
[2] Chiarella, C., and Ziveyi, J. “American option pricing under two stochastic volatility
processes”. J. Appl. Math. Comput. 224:283-310 (2013).
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Fractional Poisson Random Fields Leonenko Approved We present new properties for the Fractional Poisson process and the Fractional Poisson fields on the plane. A martingale characterization
for Fractional Poisson processes is given. We extend this res . . .ult to Fractional Poisson fields, obtaining some other characterizations.
The fractional differential equations are studied. The covariance structure is given. Finally, we give some simulations of the Fractional
Poisson fields on the plane.
Joint work with G.Aletti (University of Milan, Italy) and E. Merzbach (Bar Ilan University, Israel).
[1] Aletti, G., Leonenko, N.N. and Marzbach, E. (2016) Fractional Poisson fields and martingales, submitted, http://arxiv.org/pdf/1601.08136.pdf
[2] Leonenko, N.N. and Merzbach, E.(2015) Fractional Poisson fields, Methodology and Computing in Applied Probability, 17, 155-168
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Total Abstracts: 6

S14. Statistics and Modeling

Abstract: We focuses on good practices in both modelling and statistics for engineering, Reliability, testing and physical sciences. Both applied and theoretical aspects are considered. In particular . . ., several issues important for mathematical Problems in Engineering, Aerospace and Science from statistical point of view will be covered, e.g. Quantization Dimension of Distributions, testing for reliability among others.
Organizers: Milan Stehlik, Professor at Institute of Statistics, University of Valparaíso, V Región, Valparaíso, Chile and Assoc. Professor at Johannes Kepler University, Linz, Austria
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Title Author Status Abstract
Recognition of human activities from situation based model SALIMA Approved The notion of learning includes many methods to build a model of reality from data or improving a partial model less general or by creating a new model. There are two main learning trends: (i) Artific . . .ial intelligence methods which are qualified as symbolic, (ii) the statistical methods, qualified as digital. The cognitive model proposed in this paper combine the two approaches for a better perception and context analysis in ambient intelligent environments to achieve human activities recognition.
Contextual informations are characterized by their imperfection (eg. sensors failure, ambiguity, inaccuracy). The objective is to take into account this imperfection to infer situations. The informations observed are divided into three levels: (i) the data delivered from sensor sources as temperature, accelerometer. (ii) the abstract context obtained by abstraction of information in understandable forms by humans as hot/cold climate, (iii) the situation such as activity; this is to achieve a higher level abstraction of context by merging several contexts.
Our aim is to combines a logical inference based on the formalism design situations, and the data-oriented methods for recognizing explicit contexts based on the theory of functions of beliefs. This will overcome some limitations and counterintuitive behaviors, namely the difficulty of isolating an informal knowledge and express it in formal terms required by logical notation.
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Estimating The Quantization Dimension of Distributions Poetzelberger Approved We present estimators of the dimension of the support of a probability distribution. These estimators are derived from the concept of quantization dimension. For the general case consistency results . . .are discussed. Versions of the estimators may be applied for instance to estimate the dimension of the driving Brownian motion of Itô processes or the dimension of the attractor of a dynamical system. A second application of estimators of dimension is the analysis of high-dimensional data X where the stochastic properties of X are explained by a vector of factors W in the sense that for a sufficiently smooth (Lipschitz) mapping f, X=f(W) and s:=\mbox{dim}(W)<<\mbox{dim}(X)=:d. Read More

Control charts and differentiation of sampling schemes among Phase I and Phase II Economou Approved Statistical process monitoring (SPM) is extensively used in order to secure not only the quality of the output of industrial processes but also to determine the state of processes. One of the main cha . . .llenges in SPM is the differentiation of sampling schemes among Phase I and Phase II that appears in many practical problems. A characteristic example of such a situation arises when we monitor measurements taken for example from a car repair station (Phase II) using control limits that were calculated using samples taken during the vehicle testing procedure carried out by the car manufacturer (Phase I). In the present work a new approach is proposed in order to overcome this change when passing from Phase I to Phase II without loosing all the available information from Phase I.
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IMPORTANCE ASSESMENT OF AGING MULTI-STATE WATER COOLING SYSTEM BY LZ-TPANSFORM METHOD Frenkel Approved Modern high-tech equipment requires precise temperature control and effective cooling below the ambient temperature. Greater cooling efficiencies will allow equipment to be operated for longer period . . .s without overheating, providing a greater return on investment and increased in availability of the equipment. This paper presents application of the Lz-transform method to importance assessment of aging multi-state water cooling system used in one of Israeli hospitals. The water cooling system consists of 3 principal sub-systems: chillers, heat exchanger and pumps. The performance of the system and the sub-systems is measured by their produced cooling capacity. Heat exchanger is an aging component. Straightforward Markov method applied to solve this problem will require building of a system model with numerous numbers of states and solving a corresponding system of multiple differential equations. Lz-transform method, which is used for calculation of the system elements importance, drastically simplified the solution. Numerical example is presented to illustrate the described approach.
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Total Abstracts: 4

S13. Soliton Theory and Integrability in Mathematical Physics

Abstract: In recent years, nonlinear differential equations have been extensively used to mathematical models of interesting and important phenomena that have been observed in broad science and techno . . .logy area. In the last decades, many powerful methods to construct exact and analytical solutions of nonlinear differential equations have been established and developed, which lead to one of the most excited advances of nonlinear science and theoretical physics. These relatively new methods proved to be fully synchronized with the complexities of the physical problems. Investigating integrability and finding exact solutions for nonlinear evolution equations also plays an important role in the study of nonlinear physical phenomena.
This special session aims to combine contributions across a variety of exact and analytical solutions of nonlinear differential equations, understanding integrability of system and dynamical behaviors (properties) of solutions for nonlinear evolutions and invite authors to submit original research and/or domain reviews in various methods. This session will become an international forum for researchers to present the most recent research and ideas about soliton theory and integrability in mathematical physics. Original research that reflects the recent theoretical advances and experimental results as well as new topics are invited on all aspects of object tracking.
Potential topics include, but are not limited to:
• Soliton Theory
• Conservation laws
• Painleve Analysis
• Fractional Differential equations
• Nonlinear Evolution equations
• Further equations in physics and applied mathematics.
Organizer: Abdelouahab Kadem Setif University Algeria ,Ahmet Bekir, Eskisehir Osmangazi University, Turkey, Melike Kaplan, Eskisehir Osmangazi University,Turkey Omer Unsal, Eskisehir Osmangazi University,, Turkey
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Title Author Status Abstract
Conservation laws and exact solutions of Boussinesq-Burger equation KAPLAN Approved The conservation laws play an important role in the solution and reduction of partial differential equations. Also obtaining exact solutions of these equations is a significant topic.
In . . .this work, we have studied conservation laws that is one of the applications of symmetries. Conservation laws has important place for differential equations and their solutions, also in all physics applications. This study deals with conservation laws of Boussinessq-Burger equation. We have used Noether approach and conservation theorem approach for finding conservation laws for this equation. Also finally, we have found exact solutions of this equation by using the modified simple equation method.
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The Auto- Bäcklund transformations for the (2 + 1)-dimensional Boiti-Leon-Manna-Pempinelli equation KAPLAN Approved More and more physical structures of nonlinear partial differential equations have attracted a lot of interests due to their applications in many important scientific problems. Apart from their theore . . .tical importance, they have remarkable applications to many physical systems such as mechanics, hydrodynamics, nonlinear optics, plasma and field theories and so on.
In this paper, the Auto-Bäcklund transformation connected with the homogeneous balance method (HB) are used to construct new exact solutions for (2+ 1)-dimensional Boiti-Leon-Manna-Pempinelli equation. New soliton and periodic solutions of many types are obtained.
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Multiple Scales Analysis and Travelling Wave Solutions for KdV Type Nonlinear Evolution Equations Ayhan Approved Nonlinear evolution equations are the mathematical models of problems that arise in many field of science. These equations has become an important field of study in applied mathematics in recent years . . .. We apply exact solution methods and multiple scale method which is known as a perturbation method to nonlinear evolution equations. Using exact solution methods we get travelling wave solutions expressed by hyperbolic functions, trigonometric functions and rational functions. Also we derive Nonlinear Schrödinger (NLS) type equations from Korteweg-de Vries (KdV) type nonlinear evolution equations and we get approximate solutions for KdV type equations using multiple scale method. The proposed methods are direct and effective and can be used for many nonlinear evolution equations. It is shown that these methods provide a powerful mathematical tool to solve nonlinear evolution equations in mathematical physics.
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A Family of Exact Travelling Wave Solutions of (2+1)-dimensional KdV4 Equation Ayhan Approved Nonlinear evolution equations have a wide range of applications in science and engineering. In recent years many powerful methods to construct exact solutions of nonlinear evolution equations. In this . . . paper we present extended simplest equation method (SEM) and the modification of the truncated expansion (MTEM) method for (2+1)-dimensional KdV4 equation to establish new exact solutions. So periodic and hyperbolic function solutions are obtained for this equation. The efficiency of the these methods for finding travelling wave solutions of the high order nonlinear evolution equations is demonstrated.
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The (G’/G)-expansion method for the nonlinear time fractional differential equations Ünsal Approved Fractional differential equations have been used nowadays frequently in various applications for modelling heat transfer, seismic wave analysis, signal processing, control theory and many other fract . . .ional dynamical systems.
Recently, some effective methods for fractional calculus were appeared in open literature, such as the exp-function method, the (G’/G)-expansion method, the first integral method, the simplest equation method, the auxiliary equation method, the ansatz method and topological solitons and the fractional sub-equation method.
The fractional complex transform has been suggested to convert fractional order differential equations with modified Riemann-Liouville derivatives into integer order differential equations, and the reduced equations can be solved by symbolic computation. The (G’/G)-expansion method can be used to construct the exact solutions for fractional differential equations. We applied the (G’/G)-expansion method with fractional complex transform for the time fractional advection–diffusion–reaction (ADR) equation and the (3 + 1)-dimensional time fractional KdV–Zakharov–Kuznetsov (KdV–ZK) equation. As a result, new types of exact analytical solutions are obtained.
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Singular 1-solution of the nonlinear variable-coefficient diffusion–reaction and mKdV equations Ünsal Approved The study of nonlinear evolution equations (NLEEs) is very important in various areas of applied mathematics and theoretical physics. Searching for exact soliton solutions of these equations plays an . . .important role in the study on the dynamics of those phenomena.
Recently, many effective methods of obtaining explicit solutions of NLEEs have been presented such as the variational iteration method, the Adomian decomposition method, the homotopy perturbation method, the (G’/G)-expansion method, the first integral method, the ansatz method and the exp-function method.
The ansatz method can be used to construct the exact solutions for NLEEs. In this study, the singular soliton solutions are revealed, for the nonlinear variable-coefficient diffusion–reaction and mKdV equations, with the aid of the ansatz method.
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Soliton solutions and other solutions to a nonlinear fractional differential equations Abdelouahab Approved Ömer ÜNSAL, Ahmet BEKİR, Özkan Güner
Abstract:
In the last decades, fractional calculus found many applications in various fields of applied mathematics, theoretical physics and engineering such as co . . .ntrol theory viscoelasticity, diffusion, control, modelling heat transfer, signal and image processing, and many other physical processes.
Many effective methods have been established to obtain the solutions of fractional differential equations (FDEs), such as the variational iteration method, the finite difference method, the fractional complex transform, the exponential function method, the functional variable method, the fractional sub-equation method, the ansatz method and the first integral method.
The theory of solitons is one of the very important areas of research in optics, plasma physics, fluid dynamics and engineering. Ansatz method and the functional variable method were used by many authors but, applications of these methods are rather rare in the nonlinear fractional differential equations.
The ansatz method and the functional variable method can be used to construct the exact solutions for fractional differential equations. We applied these methods with fractional complex transform for the (3 + 1)-dimensional time fractional KdV–Zakharov–Kuznetsov (KdV–ZK) equation.
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A Novel Generalized Kudryashov Method for Exact Solutions of Nonlinear Evolution Equations Koparan Approved Nonlinear evolution equations (NLEEs) and systems form the most fundamental theme in mathematical physics. Exact solutions of these equations play a crucial role in the suitable understanding of mecha . . .nisms of the various physical phenomena modeled by these NLEEs. For this reason, searching exact solutions of these equations have taken interest in recent years. In this paper, we have obtained new exact solutions of the Kaup-Boussinesq and Wu-Zhang systems by using the generalized Kudryashov method.
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Total Abstracts: 8

S9. New Era in Mathematics

Abstract: The session aims to present the latest advances in the field of Santilli
iso-, geno- and hyper-mathematics and their applications in mathematics, physics, mechanics, chemistry, biology, eng . . .ineering and other applied sciences. The proposed session intends to gather experts working on various actually important aspects of Santilli iso-, geno-, hyper- mathematics and to explore new connections between different research areas. We expect a fruitful exchange of new ideas and collaboration regarding the research development of these disciplines among the participants.
Organizer: Svetlin Georgiev, Sorbonne University, Paris, France
E-mail; sgg2000bg@yahoo.com,svetlingeorgiev1@gmail.com
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Title Author Status Abstract
How Can One Look at if Gravitational Wave Generation Has Semi Classical Features, and What This Implies About Compression of Vacuum Wave States, and Coherence/de Coherence? Beckwith Approved We argue in this document that initial vacuum state values possibly responsible for GW(Gravitational wave) generation in relic conditions in the initial onset of inflation may have a temporary un squ . . .eezed , possibly even coherent initial value, which would permit in certain models classical coherent initial gravitational wave states. The coherent states would be amendable to nucleation by classical/ highly non linear processes which would be almost immediately eliminated by compression and squeezing. Even though that the general background of incoherency for relic GW is a given. Furthermore, several arguments pro and con as to if or not initial relic GW should be high frequency will be presented, with the reason given why earlier string models did NOT favor low relic GW from the big bang.
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The influence of Latin squares autotopisms on the rocket propellant problem and the radar detection experiment Falcon Approved Latin square design is used as a statistical model in Engineering whose analysis of variance makes clear differences among distinct nuisance sources of variability. This model depends on the Latin squ . . .are that is used in the experiment and that is selected at random among a predetermined set of squares of a given order. In this work, we study the role that plays the autotopism group of a Latin square in the corresponding analysis of variance. Particularly, we focus on the effect that right-multiplication autotopisms of Latin squares produces on the rocket propellant problem and the radar detection experiment introduced by Montgomery in his fundamental monograph.
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The Cube in Art and Mathematics Trell Approved The Cube in Art and Universe
Erik TRELL, Alexander ANIMALU. Samuel EDEAGU
Starting with the mathematical roots of Cubism, a survey of the cube as eigenunit and generator in artistic and physical assem . . .blies and projections from the infinitesimal to the cosmic scale is made which involves the Euclidean space, the Diophantine equations, Fermat’s Last Theorem, and the isometric vector matrix realization of the electron and crystallization of the primordial Universe and periodic system of the elements.
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Some aspects of iso-differential calculus Georgiev Approved In this talk we define iso-derivative and deduct some of its properties. They are given some applications.
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On the iso-hyper-representation theory Dramalidis Approved Abstract
The hyper-representation theory appeared in mid 80’s. Nowdays, it is clear that this theory is refered to the very large class of hyperstructures since the Hv-structures are used. The main pr . . .oblem is that only few theorems, from the classical representation theory, can be transferred to hyperstructures. However, the main theory proves that there is a strong relation with the fundamental structures corresponding to each Hv-structure. Moreover, one can have results if the e-hyperstructures are used, that is the hyperstructures which are appropriate to Santilli’s iso-theory. We present the general problem and we give some results and applications on the topic.
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Helix hopes in Lie-Santilli addmissibility Dramalidis Approved Abstract
On ordinary non-square matrices of type mn one can define a hypermultiplication by using the so called hope: helix multiplication. We face the problem of the general Lie-Santilli admissibili . . .ty by using appropriate classes of matrices which can be used in Santilli’s iso-theory.
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Small Hypernumbers Dramalidis Approved Abstract
With the term “Small Hypernumbers” we mean that we have elements of an Hv-field of very thin type, weak associative, weak commutative and with finite fundamental field.
Especially, we focus o . . .ur study on the e-hyperfields wich have fundamental fields of two or three elements. We present and start to study the hypermatrix representation theory on those hypernumbers.
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1. Small Hypernumbers, 2. On the iso-hyper-representation theory, 3. Helix hopes in Lie-Santilli addmissibility, 4. The LV-hyperstructures in Santilli’s iso-theory Vougiouklis Approved 1.
Small Hypernumbers
T. Vougiouklis
Democritus University of Thrace, School of Education
68100 Alexandroupolis, Greece, tvougiou@eled.duth.gr
Abstract
With the term “Small Hypernumbers” we mean that . . . we have elements of an Hv-field of very thin type, weak associative, weak commutative and with finite fundamental field.
Especially, we focus our study on the e-hyperfields wich have fundamental fields of two or three elements. We present and start to study the hypermatrix representation theory on those hypernumbers.
AMS Sub. Class.: 20N20, 16Y99 Key words: hyperstructure, Hv-structure, hope.
Basic References
[1] Corsini P., Leoreanu V., Application of Hyperstructure Theory, Klower Academic Publishers, 2003.
[2] Davvaz B., Leoreanu V., Hyperring Theory and Applications, Int. Acad. Press, 2007.
[3] Davvaz B., Santilli R.M., Vougiouklis T., Studies of multi-valued hyper-structures for the characterization of matter-antimatter systems and their extension, Algebras, Groups and Geometries 28(1), 2011, 105-116.
[4] R.M. Santilli, Hadronic Mathematics, Mechanics and Chemistry, Vol.I,II,III,IV,V, Int. Academic Press, USA, 2008.
[5] Vougiouklis T., The fundamental relation in hyperrings. The general hyperfield, 4thAHA, Xanthi 1990, World Scientific, 1991, 203-211.
[6] Vougiouklis T., Hyperstructures and their Representations, Monographs in Mathematics, Hadronic, 1994.
[7] Vougiouklis T., Some remarks on hyperstructures, Contemporary Mathematics, Amer. Math. Society, 184, 1995, 427-431.
[8] Vougiouklis T., Enlarging Hv-structures, Algebras and Combinatorics, ICAC’97, Hong Kong, Springer–Verlag, 1999, 455-463.
[9] Vougiouklis T., On Hv-rings and Hv-representations, Discrete Mathematics, Elsevier, 208/209, 1999, 615-620.
[10] Vougiouklis T., The Lie-hyperalgebras and their fundamental relations, Southeast Asian Bulletin of Mathematics, V.37(4), 2013, 601-614.
[11] Vougiouklis T., Hypermathematics, Hv-structures, hypernumbers, hypermatrices and Lie-Santilli admissibility, American J. Modern Physics,4(5), 2015, 34-46.
2.
On the iso-hyper-representation theory
A. Dramalidis (1), N. Lygeros (2), T. Vougiouklis (1)
1 Democritus University of Thrace, School of Education, 68100 Alexandroupolis, Greece, adramali@psed.duth.gr, tvougiou@eled.duth.gr
2 Lgpc, University of Lyon, France, w@lygeros.org
Abstract
The hyper-representation theory appeared in mid 80’s. Nowdays, it is clear that this theory is refered to the very large class of hyperstructures since the Hv-structures are used. The main problem is that only few theorems, from the classical representation theory, can be transferred to hyperstructures. However, the main theory proves that there is a strong relation with the fundamental structures corresponding to each Hv-structure. Moreover, one can have results if the e-hyperstructures are used, that is the hyperstructures which are appropriate to Santilli’s iso-theory. We present the general problem and we give some results and applications on the topic.
3.
Helix hopes in Lie-Santilli addmissibility
A. Dramalidis, T. Vougiouklis
Democritus University of Thrace, School of Education, 68100 Alexandroupolis, Greece adramali@psed.duth.gr, tvougiou@eled.duth.gr
Abstract
On ordinary non-square matrices of type mxn one can define a hypermultiplication by using the so called hope: helix multiplication. We face the problem of the general Lie-Santilli admissibility by using appropriate classes of matrices which can be used in Santilli’s iso-theory.
4.
The LV-hyperstructures in Santilli’s iso-theory
N. Lygeros (1), T. Vougiouklis (2)
1 Lgpc, University of Lyon, France, w@lygeros.org
2 Democritus University of Thrace, School of Education, 68100 Alexandroupolis, Greece, tvougiou@eled.duth.gr
Abstract
The Level Variable (LV) construction is a hyperstructure containing a hyperoperation defined on every graded finite poset. More precisely, on graded posets with s levels we can use Hv-groups, one of them is an e-Hv-group S, needed in Santilli’s iso-theory, where we define an LV-hyperoperation and we obtain an e-Hv-group. The important result is that the fundamental structure is isomorphic to the fundamental group of the initial e-Hv-group S. We extend these constructions to Hv-fields in order to have ‘hypernumbers’ appropriate in Santilli’s iso-theory. Finally, we face the problem of enumeration of such constructions defined on finite small sets.
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Trajectories of antimatter asteroids in our Solar system Beghella Bartoli Approved The innovative Isodual Theory of Antimatter proposed by R. M. Santilli is able to provide a classical representation of neutral or charged antimatter bodies in a way compatible with available classica . . .l experimental evidence on antimatter. Since Earth appears to have been hit in the past by antimatter asteroids (as it seems to be the case for the 1908 Tunguska explosion in Siberia), the author presents in this paper an analysis of possible trajectories of an antimatter asteroid in our Solar System and the possibilities of collision with our planet under the assumption of the repulsive gravitational interaction between Earth and the antimatter asteroid. Moreover, an estimate of the minimum approach speed required for an antimatter asteroid to impact with Earth is theoretically and numerically identified at different distances from our planet, along with other considerations about the trajectories.
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Apparent need of antimatter galaxies for the stability of the universe Beghella Bartoli Approved Fritz Zwicky’s hypothesis, according to which the cosmological redshift is due to galactic light losing energy to intergalactic media, without need of Universe expansion, seems to have been recently c . . .onfirmed by recent mathematical, theoretical and experimental studies via measurements on Earth.
But the return to a static universe would imply the inevitable prediction that the universe should collapse due to gravitational attractions among galaxies. In this paper, we present apparently for the first time a cosmological model in which the stability of the universe is achieved under the condition of admitting an equal number of matter and antimatter galaxies (as they are hypothesized in Isodual Theory of Antimatter) at such a large mutual distance for which gravitational interactions are neglectable.
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EXACT AND INVARIANT REPRESENTATION OF NUCLEAR SPINS VIA ISOMATHEMATICS AND ISOMECHANICS BHALEKAR Approved EXACT AND INVARIANT REPRESENTATION OF NUCLEAR SPINS VIA ISOMATHEMATICS AND ISOMECHANICS
A. A. Bhalekar(1,2) and R. M. Santilli(1)
(1)Thunder Energies Corporation, Tarpon Springs, Florida, U. S. A.
(2 . . .) Department of Chemistry, R. T. M. Nagpur University, Amravati Road Campus, Nagpur – 440033, India
Email address:
anabha@hotmail.com (A. A. Bhalekar), research@thunder-energies.com (R. M. Santilli)
In the preceding talk at this conference R. M. Santilli has outlined the rudiments of the covering isomathematics and related isomechanics with particular reference to the time invariant representation of nucleons as extended, non-spherical and deformable particles, and indicated the fundamental relevance of the Lie-Santilli isotheory for the nuclear structure in terms of isonucleons (isoelectrons, isoprotons and isoneutrons) and based on it he described the nuclear magnetic moments of all stable nuclides starting from deuteron as isodeuteron. As discussed in the preceding talk a neutron and a deuteron, indeed, are constituted of isoprotons and isoneutrons that are the mutual penetrated states of the wavepackets of protons and electrons. We have extended this description to higher atomic number stable nuclides (upto Z= 82). The approach adopted has been to develop nuclear configurations which are commensurate with the observed nuclear spins. Since in our proposal we use only the isoelectrons, isoneutrons and isoprotons as basic constituents we are indeed incorporating isomathematics and isomechanics. However, the details of the quantitative hadronic mechanics of each isonuclides has not been completely investigated so far. But these nuclear configurations we believe would substantially assist in our future attempts. We have developed two approaches. The first one builds nuclear configurations taking isodeuterons, isoneutrons and isoprotons as basic constituents whereas the second one uses only the isoprotons and isoelectrons as basic nuclear constituents. Notice that when we use isodeuterons as basic nuclear constituents there is no room to speak of isoelectrons separately because each isodeuteron consists of two isoprotons and one isoelectron. It turns out that isoelectrons, indeed, serve as effective nuclear glue. Some preliminary generalizations of both the models would be discussed.
Reference:
A. A. Bhalekar and R. M. Santilli, Exact and Invariant Representation of Nuclear Magnetic Moments and Spins According to Hadronic Mechanics, Amer. J. Modern Phys., (2016) (In press). http://santilli-foundation.org/docs/nuclear-MM-spins.docx
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Mathematics of Space vs. Spaces of Hadronic Mathematics Johansen Approved While there is no astrophysics without the notion of space, there still is much dispute in theoretical physics about the basic architecture of space. Does ‘mind’ exist outside or inside space? Is spac . . .e a container for matter, is matter bending space, or is space itself built by an ‘organic’ algorithm? Does space have a dual nature including a subspace of antimatter? Is ‘vacuum’ to be understood as some underpinning subspace with inherent kinetics? Does there exist parallel universes or multiverses inside space? Does space have a layered structure, with laws for traffic of energy and information between layers, yet to become discovered? Viewed from the more abstract angle, answers to such questions can become stimulated from relevant and consistent ontological philosophy. Viewed from the more concrete angle, answers can become stimulated from significant observations and experiments. In between these two angles dwells the connecting body of mathematical physics, encompassing paradigmatic key notions of theoretical physics and related reservoirs of mathematical concepts and techniques. The paper will approach such questions in relation to the theory of hadronic mechanics, initiated by Ruggero Maria Santilli, and related hadronic mathematics (and geometry) establishing novel fields of isonumbers, genonumbers and hyperstructural numbers, with their respective isoduals. Hadronic mathematics has developed by contributions from several mathematicians, in recent years including extensive contributions to isocalculus from Svetlin Georgiev. The discussion in the paper will also present some reflections on recently published claims of discoveries of various macroscopic structures of antimatter by means of a novel kind of telescope, including claimed observations of so-called ITE-1 (dark) and ITE-2 (light) kinds of antimatter objects/”entities” close to Earth.
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Isomathematics and IsoAlgebras Muktibodh Approved Mathematics of 20th century is solely applicable to the dynamical systems wherein point like particles are moving in a vacuum under Hamiltonian interactions; known as Exterior Dynamical Systems. Appr . . .opriate generalization of 20th century mathematics , today known as Santilli isomathematics is applicable to the dynamical systems wherein the particles are extended, non-spherical and deformable, moving within a physical medium under Hamiltonian and non-Hamiltonian interactions; known as Interior Dynamical systems. IsoAlgebras play an important role in the development of Lie-Santill isotheory. In this paper we deal with the development of the central problem of construction of regular and irregular isorepresentations of Li-Santilli isotheory and its applications.
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Total Abstracts: 13

S16. Modelling, Simulation and Optimization in Engineering

Abstract:
In recent years, the use of Modelling, Simulation and Optimization techniques in engineering has accelerated with the advances in computational methods and resources. Modelling, Simulation . . .and Optimization has become an important part of the research repertoire, supplementing and in some cases replacing lengthy experimentation procedures.
Engineering parameters are difficult to predict and analyze before prototyping but modern modelling, simulation and optimization packages can replicate the actual phenomena in less time and cost. Modelling and simulation focuses on optimizing and predicting the performance and reducing the costs of complex systems that may involve multiple interacting disciplines, such as those found in automobiles, aircrafts, spacecrafts, industrial and manufacturing equipment, engineering operations and various consumer products.
The purpose of this session is to bring together users, developers, and researchers to present the latest theoretical and computational developments, applications, ideas, and problems related to Modelling, Simulation and Optimization. Papers may present innovative models, methods or the problem of solving engineering problems.
The multidisciplinary nature of this session invites papers on Modelling, Simulation and Optimization models, methods and approaches with applications in the various disciplines of engineering including but not limited to Mechanical Engineering, Manufacturing Engineering, Industrial Engineering, Engineering Operations, Aerospace Engineering, Electronics Engineering, Electrical Engineering, Bio-Medical Engineering, Computer Science and Engineering, Optimization Applications, and Renewable energy.
Organizers: Dr. Amer Farhan Rafique Faculty of Engineering, King Abdulaziz University,
Jeddah, Kingdom of Saudi Arabia , E-mail: afrafique@kau.edu.sa
Dr. Qasim Zeeshan , Faculty of Engineering Eastern Mediterranean University, Mersin, Turkey
E-mail: qasim.zeeshan@emu.edu.tr
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Title Author Status Abstract
A Survey of Multidisciplinary Design and Optimization in UAVs Rafique Approved As UAV Industry is a growing industry, designs developed by the traditional methods does not provide valid solutions or efficient designs. It was this time, MDO was suggested overtaking the existing s . . .ingle disciplinary optimization. This paper is focusing on Multidisciplinary design and optimization methods in UAVs covering the hierarchy of methods. It also goes through main methods developed from its origin. Some of algorithms are also explained into an understanding level. Pros & Cons of each methods and algorithms are discussed and characterized according to their convergence, consistency of solution, computation speed etc. Next step was to analyze documents on UAVs and their achievements and what has been done and up to what level.
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Total Abstracts: 1

S2. Clifford algebras, Clifford analysis and their applications

Abstract: We plan to have a special session on Clifford algebras, Clifford analysis and their applications. It aims to present the latest advances in the field of Clifford (geometric) algebras and t . . .heir applications in mathematics, physics, engineering and other applied sciences. The proposed session intends to gather experts working on various actually important aspects of Clifford algebras and to explore new connections between different research areas. We expect a fruitful exchange of new ideas and collaboration regarding the research development of this discipline among the participants
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Title Author Status Abstract
New Aspects on Moisil-Teodorescu System Georgiev Approved In this talk is considered the Moisil-Teodorescu system. It is investigated for existence of classical solutions. It is proposed new integral representation of the classical solutions. As an appli . . .cation, they are given continuous dependence and differentiability of the solutions with respect to the initial data and parameters.
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Uncertainty Principles For The Clifford-Fourier transform Jday Approved Many works are devoted to generalize the classical Fourier transform. In 2005, Sommen and Brackx introduce a generalization of the classical Fourier transform in the setting of Clifford analysis c . . .alled the Clifford-Fourier transform. Considering the integral expression of this Fourier transform, De Bie and Xu establish several properties for the Clifford-Fourier transform.\\
In this talk, we study uncertainty principles for the Clifford Fourier transform. Obviously, we give a generalization of Heisenberg’s inequality in Clifford analysis. Moreover, we provide analogues of Hardy’s theorem and Miyachi’s theorem for the Clifford-Fourier transform.
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Computational aspects of quaternionic polynomials Falcão Approved The processes of evaluating and factoring real or complex polynomials are very important problems and had received a lot of attention over the years. In the ring of quaternionic polynomials new proble . . .ms arise: the evaluation map at a quaternion is not a ring homomorphism and the structure of the zero-set of quaternionic polynomials is quite different from the complex case.
In this talk we are going to consider several algorithmic and numerical issues associated with quaternionic polynomials, namely their evaluation, factor and unfactor processes. The complexity and error bounds of quaternion arithmetic are also addressed in order to carry out rounding error analysis of several algorithms.
This is a joint work with F. Miranda, R. Severino and J. Soares.
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Recurrence relations for hypercomplex orthogonal polynomials Cacao Approved The theory of orthogonal polynomials of one real or complex variable and its generalization to higher dimensions is well established. Hypercomplex function theory (or Clifford analysis) provides an al . . .ternative approach to deal with arbitrary dimensions. In this context, we construct orthogonal polynomial systems of a hypercomplex variable and study some of their properties, including three-term recurrence relations.
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Quaternionic polynomials with multiple zeros: a numerical point of view Miranda Approved There are a lot of rootfinding algorithms especially designed for real or complex polynomials. Most of these methods however face difficulties in dealing with multiple roots or clusters of roots.
The . . .problem of finding a good definition of multiplicity for zeros of quaternionic polynomials is a rather complicated task. In this talk we analyze different concepts of multiple roots available in the literature taking into account the behavior of some quaternionic rootfinding methods in the presence of such roots.
This is a joint work with M.I. Falcão, R. Severino and M.J. Soares.
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Zeros and singularities of slice regular functions over alternative *-algebras Stoppato Approved The theory of slice regular functions over real alternative ∗-algebras has been introduced in [Ghiloni, Perotti, 2011] as a higher-dimensional generalization of the theories of: holomorphic complex fu . . .nctions; slice regular quaternionic functions [Gentili, Struppa, 2006]; slice monogenic functions [Colombo, Sabadini, Struppa, 2009]. Along with this generalization step, the larger class of slice functions has been defined.
Some recent developments in the theory concern the algebraic structure and the zero sets of slice functions, as well as the classification of the singularities of slice regular functions. Peculiar phenomena arise, which were not present in the complex or quaternionic case. The talk will provide examples of these phenomena and, time permitting, put them into context with the statement of general results.
This is joint work with Riccardo Ghiloni and Alessandro Perotti.
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Constructing multivariate polynomials in function theories over non-commutative algebras Malonek Approved The theory of polynomials in one or several variables is, in general, divided into three main parts, namely algebra, analysis, and geometry of polynomials. However, the division lines between these ar . . .eas are quite blurred. The algebraic aspect of the theory has close connections with special functions and combinatorics. In turn, the analytical aspect of the theory deals with questions that are typical in analysis concerning sometimes very subtle quantitative as well as qualitative properties. Needless to mention that besides of seeming a very old subject, polynomials did not loose their place in what are called modern mathematical theories. Among them those which are heavily relying on the use of non-commutative algebras also emerged in the last five or six decades for solving problems in the most diversified areas of application.
Analytical methods in generalizing complex function theory to higher dimensions by means of the use of non-commutative algebras, for example Clifford algebras, immediately implies the revision of the concept of a polynomial expressed as function of the chosen variables. In particular, dealing with polynomials as, in some sense, generalized holomorphic functions requires a large variety of different representations of polynomials suitably adapted to the solution of different concrete problems. This is caused by the fact that, in general, neither multiplication nor composition are operations closed in the set of generalized holomorphic functions. Naturally the question arises whether besides the peculiarities of the non-commutative algebras there exist sufficiently general approaches for constructing Clifford algebra valued polynomials defined in higher dimensional Euclidean spaces. After a short historical overview on how polynomials are used in hypercomplex function theory, our survey tries to give partial answers to some general questions, stressing at the same time a new matrix approach to the representation of generalized holomorphic polynomials.
This talk is based on joint work with I. Ca\c{c}\~{a}o, I. Falc\~{a}o, and G. Tomaz.
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Towards a quaternionic function theory linked with the Zernike spherical polynomials Morais Approved It is truly uncommon that a paper that has been set aside for almost eighty years finds its way back to scientific spotlight. Yet this is exactly what the 1934 paper by F. Zernike’s Nobel prize has ac . . .complished in the last decade. As a matter of fact, in the last years considerable attention has been paid to the role played by the Zernike Polynomials (ZPs) in many different fields of geometrical optics, optical engineering, and astronomy. The ZPs are the product of a normalization constant by radial polynomials and a pair of trigonometric functions (sine and cosine). These polynomials form a complete orthogonal set over the unit circle and are commonly used to describe balanced aberrations.
In this talk, we give a brief description of the theory and properties of the 3D Quaternionic Zernike Spherical Polynomials (QZSPs). A generalization and refinement of the QZSPs to functions vanishing outside the unit ball leads to the computation of the Weighted Quaternionic Zernike Spherical Functions (WQZSFs). In particular, the underlying functions are of three real variables and take on values in the quaternions (identified with $\mathbb{R}^4$). Also, in this talk, we prove that the WQZSFs are orthonormal over the unit ball with respect to a suitable weight function and allow, inside an embedding sphere, to be decomposed into 3D spherical monogenics. The representation of these functions are given explicitly and a summary of their fundamental properties is also discussed.
The talk is based on joint work with I. Ca{\c c}{\~a}o (University of Aveiro, Portugal).
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Poster on: Double Conformal Space Time Algebra Hitzer Approved First author: Robert Benjamin Easter.
We introduce the double conformal version of space-time algebra based multivector modeling of quartic and general quadric surfaces, Darboux cyclides, Dupin cycli . . .des, tori and pairs of standard conformal space-time algebra objects in Minkowski space. We can use extended Lorentz boost transformations and projections to three-dimensional Euclidean space to directionally dilate objects.
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Total Abstracts: 9

S18. Recent Integral Transforms Advances (RITA)

The papers in this session are expected to cover new and recent developmental advances in the theory of Integral transforms and consequent application aspects in mathematics areas as well as in variou . . .s fields of Engineering and Science. Full papers in this session can be considered on a case by case basis, and appropriate journals may be suggested by organizers as feasible.
Organizers:
Fethi Bin Muhammad Belgacem, Seenith Sivasundaram, Xiao-Jun Yang.
E-mail: fbmbelgacem@gmail.com
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Title Author Status Abstract
New approach for accelerating the non linear Schwarz iterations Nagid Approved A new approach using the vector epsilon algorithm is considered to accelerate the convergence of vector sequences derived from the discretization of non linear PDEs in the context of domain decomposit . . .ion. This
approach can be used to accelerate the convergence of Schwarz iterations
of a large class of linear and non linear reaction advection diusion problems. The proposed algorithm is very useful when the large systems of
linear or non linear equations have to be solved at each time step, with
one or more unknowns per grid block, depending on the formulation of the
discrete problem. Several test-cases of analytical problems are performed
in order to illustrate the interest of such algorithm. A large number of numerical test cases show the eciency of the proposed approach in terms of
CPU time. On the other hand, we noticed that the eectiveness depends
on the nature of the non linear PDE.
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Applications of the Sumudu Transform to Bernoulli Numbers and Polynomials Ahmed Approved In the present paper, we apply the Sumudu transform to the Bernoulli generic function (BGF), then the properties of this transformation are examined, in the goal of
re-extract some properties of Berno . . .ulli numbers and Polynomials. we show an excellent correlation between the Sumudu of BGF and Trigamma function.
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Applications of the Sumudu Transform to Euler Numbers and Polynomials Ahmed Approved The aim of this paper is to derive some properties of Euler numbers and Polynomials using the Sumudu transformation, we apply this transformation to the Euler
generic function (EGF), then we used the . . .relationship between the incomplete beta function and the Sumudu of EGF to re-extract some formulas.
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Total Abstracts: 3

S19. Wavelets Analysis, Fractional Advances and Applications (WAFAA)

Abstract:
The papers in this session are expected to cover recent and state of the art computational techniques and schemes pertaining to applications with waves, wavelets, fractals and fractional cal . . .culus. Full papers in this session can be considered on a case by case basis, and appropriate journals may be suggested by organizers as feasible.
Organizers:
Fethi Bin Muhammad Belgacem, Zakia Hammouch, Carlo Cattani.
E-mail: fbmbelgacem@gmail.com
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Title Author Status Abstract
Numerical Solution of Linear Quadratic Optimal Control Problems using CAS Wavelet Operational Matrix of Derivative Ahmed Approved In the present paper, a new CAS wavelet operational matrix of derivative is presented. After presenting relevant properties of the CAS wavelet, we apply its connected
operational matrix to differentia . . .tion. Then the optimal control problem is reduced to a system of algebraic equations. Numerical examples are presented to verify the efficiency and accuracy of the proposed algorithm. The results reveal that the method is accurate and easy to implement.
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Total Abstracts: 1

Aspects Integres dans les Mathematiques de Abbas Bahri- a Loving Eulogy II. (AIMABLE II)

In this this session presenters are welcome to present any aspects or connections to the Mathematics of the late Abbas Bahri, whether be of technical, professional, respect or simply of feeling and eu . . .logical nature. Ideas and proposals on how to further commemorate the life and legacy of Abbas Bahri woulkd be most welcome. Full papers in this session can be considered on a case by case basis, and appropriate journals may be suggested by organizers as feasible.
Organizers:
Fethi Bin Muhammad Belgacem, and Yomna Rebai,
E-mail: fbmbelgacem@gmail.com
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Abstracts are being reviewed. A list of approved abstracts will appear soon.

Submit your abstract!

M4: Modern approximation methodologies for functions and arrays in science and engineering computions

This mini symposium welcomes the contributions for the following topics mainly. However, some other areas which are closely related to the title issue and not listed below can also be considered to ha . . .ve foci for paper submissions.
* Univariate and/or multivariate function decompositions or approximations
* Decompositions of ordinary linear algebraic vectors and/or matrices
* Decompositions of multilinear algebraic structures like folvecs, folmats, multiway arrays
* Approximating the ODE and/or ODE Set solutions
* Approximating the PDE and/or PDE Set solutions
* Approximating the linear univariate and/or multivariate integral operators
* High Dimensional Model Representation Varieties
* Enhanced Multivariance Products Representation Varieties
Organizer: Metin Demiralp, İstanbul Technical University, Informatics Institute, Maslak, 34469, İstanbul, Türkiye (Turkey)
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Title Author Status Abstract
A Numerical Comparision between Bivariate Enhanced Multivariance Products Representation and Smoothing Bicubic Spline Method Tuna Approved \documentclass[12pt]{article}
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\large{\underline{\bf{A Numerical Comparision between Biva%
riate Enhanced Multivariance}}} \\%
\large{\underline{\bf{Products Representation and Bicubic %
Spline Method}}*} %%
\end{center}
\begin{center}
{\bf{S\”uha Tuna}} \\
{\textit{\.Istanbul Technical University, Informatics Institute, %
34469, Turkey (T\”URK\.IYE)}} %
\end{center}
\vskip1cm
%%%
\quad Enhanced Multivariance Products Representation (EMPR) %
is a powerful approximation method for multivariate data set%
s. It decomposes a given $N$-dimensional multivariate data %
set, say an $N$-way array, in terms of the less-way arrays. %
If given $N$-way array is denoted as $\fff$, the releva%
nt EMPR decomposition of the data under consideration can b%
e expressed as %
\begin{eqnarray}
\label{DEMPR}
\fff=f^{(0)}\prod_{r=1}^N\spt{r}+\sum_{j=1}^Nf_{i_j}^{(j)}%
\prod_{r=1\atop r\neq j}^N\spt{r}%
+\sum_{j,k=1\atop j Read More

High Dimensional Model Representation (HDMR) with Clustering for Image Retrieval Tunga Approved \documentclass{article}
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\title{High Dimensional Model Representation (HDMR) with Clustering for Image Retrieval}
\author{Ay\c seg\”ul Karc\i l\i\ }
\author{Burcu Tunga}
\affil{Mathematics Engineering Department, Faculty of Arts and Sciences \.Istanbul Technical University, 34469, Turkey (T\”URK\.IYE)}
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High Dimensional Model Representation (HDMR) is a decomposition method for multivariate functions which represents the function through low-variate terms such as constant, univariate, bivariate and higher variate ones. So that the original function can be reestablished using these terms. This algorithm is also valid for the multivariate data sets that is, the given data set is decomposed into low-variate data sets through HDMR. A digital image can be considered as a multivariate data set. In that case, HDMR decomposes the image. The previous researches show that when HDMR components are added, the exact representation is obtained.
In this study, we deal with image retrieval and use Columbia Object Image Library (COIL100). This database has $7200$ color images of $100$ different objects that is,
there are $72$ poses per object taken at pose intervals of $5$ degrees. We select a pose of an object from the database at first. Then, we discard that pose from the database and call it test image. We developed an HDMR based algorithm to find whether that object exists in that database. The algorithm first clusters the training images using constant HDMR component and finds which cluster the test image belongs to. Then, the algorithm computes the univariate HDMR components of the test image and the images of the cluster which the test image may be involved. Finally, Euler distance metric is used to find the similarity level between the test image and the training images of that cluster. The result is whether the test image is in that database or not. To measure the performance of the method, we run a matlab code many times. It is observed that a high percentage of success is obtained in retrieving the correct image.
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A TMEMPR Based Approach for Transforming Arrowheaded Matrices to Tridiagonal Forms OKAN Approved \documentclass[12pt]{article}
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\begin{center}
\large{\bf{A TMEMPR Based Approach for Transforming Arrowheaded Matrices
to Tridiagonal Forms}} \\%
\end{center}
\begin{center}
{\bf{Ayla Okan and Metin Demiralp}} \\
{\textit{\.Istanbul Technical University, Informatics Institute, %
34469, Turkey (T\”URK\.IYE)}} %
\end{center}
\vskip1cm
%%%
\quad In this work, we focused on designing a transformation from arrowheaded %
matrices to tridiagonal forms by using a novel method Tridiagonal Enhanced %
Multivariance Products Representation (TMEMPR). We have quite recently developed Arrowheading %
Enhanced Multivariance Products Representation decomposition method which produces arrowheaded %
matrices. However tridiagonal matrix forms are preferred in most scientific fields. %
Arrowheading Enhanced %
Multivariance Products Representation for a Kernel (AEMPRK) decomposition method %
which was developed and improved by M. Demiralp and his research group, is designed on bivariate functions such that %
written by the finite sum over certain binary products composed of univariate %
function. This representation enables us to decompose the given bivariate outer %
product sum function into three factor matrix product, $f(x,y)=\mathbf{U}(x)^T%
\mathbf{K}\mathbf{V}(y)$, where $\mathbf{K}$ is an arrowhead matrix %
which has only non-zero elements on its main diagonal, first row and column. %
$\mathbf{U}(x)$ and $\mathbf{V}(y)$ are the left and the right support %
vectors whose entries are generated from unit support functions. In addition, other %
new proposed decomposition method Tridiagonal Matrix Enhanced %
Multivariance Products Representation, TMEMPR is structured for infinite matrices %
involving denumerable infinitely many rows and columns. In TMEMPR, there is a comparably %
concise form with AEMPRK like three factor matrix product. However, when analyzed, the %
main differences are distinctly visible. For instance, the kernel matrix in TMEMPR form, %
is a tridiagonal matrix while in AEMPRK form is arrowheaded. Also, the left and right support %
matrices whose entities are generated from related initial support vectors are orthonormal %
while in AEMPRK decomposition, support functions do not need to be orthogonal to the %
other support functions instead of relevant initial supports. In this study, we aimed to design %
a very specific transformation approach such that transforms arrowhead matrices obtained via AEMPRK to tridiagonal matrix representation. The goal of this work is also to analysis the efficieny of this %
transformation approach by a few implementations.
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Certain Implementative Applications of Separate Node Ascending Derivatives Expansion (SNADE) Bodur Approved \documentclass[12pt]{article}
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\begin{center}
\large{\bf{Certain Implementative Applications of %
Separate Node Ascending Derivatives Expansion (SNADE)%
}}
\end{center}
\begin{center}
{\bf{Derya Bodur and Metin Demiralp}} \\
{\textit{\.Istanbul Technical University, Informatics Institute, %
34469, Turkey (T\”URK\.IYE)}} %
\end{center}
\vskip1cm
%%%
\quad In this work we focused on a very recently developed method %
called as “Separate Node Ascending Derivatives Expansion” (SNADE). %
SNADE can be considered as an infinite %
interpolation like Taylor Series Expansion. A Taylor Series is %
an infinite sum representation whose terms are %
calculated from the values of the function’s derivatives at a %
single point. This newly proposed method involves denumerable infinitely %
many nodes in contrast to Taylor Series Expansion. SNADE is based %
on derivative integration formula for a univariate function. Integral %
of derivative identity is not only required to be used for the target %
function but repetitiously for its all derivatives. It may not be %
required to be used in the same interval. %
In addition to all these, each derivative value becomes %
evaluated at a different independent variable value. %
This work is designed to emphasize the method’s interpolatory nature. %
For this purpose certain implementation results will be given and %
will be compared with well-known interpolation methods like Taylor %
Series Expansion.
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Transformational Tridiagonal Folmat Enhanced Multivariance Products Representation (TTFEMPR) Possibilities in Multivariate Array Decomposition Gündoğar Approved \documentclass[12pt]{article}
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\large{\bf{Transformational Tridiagonal Folmat Enhanced Multivariance Products Representation (TTFEMPR) Possibilities in Multivariate Array Decomposition}} %
\end{center}
\vskip1cm
\begin{center}
{\bf{Zeynep G\”undo\u gar and Metin Demiralp}} \\
{\textit{\.Istanbul Technical University, Informatics Institute, %
34469, Turkey (T\”URK\.IYE)}} %
\end{center}
%%%
\quad
Transformational Enhanced Multivariance Products Respresentation (TEMPR), %
inspired from Enhanced Multivariance Products Respresentation(EMPR) in order %
to improve efficiency of EMPR, is a decomposition method for multiway arrays. %
Philosophy behind the method is to apply EMPR method on a target multiway array’s %
image under specifically choosen transformation. EMPR is one of the divide-and-conquer methods to %
approximate target multiway array by the increasing multivariance starting from %
constancy. %
For $\mathcal{X}, \mathcal{Y}\in \mathcal{R}^{I_1\times I_2 \times\cdots\times I_N} $ %
transformation is defined as follows:%
\begin{equation}
\mathcal{T}\left( \mathcal{X}\right)=\mathcal{Y}
\end{equation}
How to choose the transformation changes depending on the structure of the problem %
and the multiway array such as logarithmic transformation, affine transformation, %
Möbius transformation etc… %
General component of a multiway array such as %
$\mathcal{X}\in \mathcal{R}^{I_1\times I_2 \times\cdots\times I_N} $ %
is symbolized as $X_{i_1,i_2,…,i_n}$. Each subscript of $X_{i_1,i_2,…,i_n}$ defines %
a way (i.e direction) and these ways are orthogonal to each other. Within this framework %
the ordinary linear algebraic entities, vectors and matrices can be considered respec%
tively one way and two way arrays. Due to the difficulty of decomposing multiway arrays %
which have more than two ways on each direction separately, adapting the properties %
of ordinary matrix algebra to the multiway arrays is important. In order to overcome %
this difficulty Demiralp and his group brought a new algebraic concept %
$X_{i_1,i_2,…,i_m;j_1,j_2,…,j_n}$ defined as “folded matrix” (Folmat). Folmat is a %
folded form of an ordinary algebraic matrix. Subscipts at the left side of semicolon are corresponding somehow row orderings while right ones are correlated to column %
orderings. %
Tridiagonal Matrix Enhanced Multivariance Product Representation (TMEMPR) method %
developed during studies on image reconstruction by Demiralp and his group is a recursive %
decomposion method. The compact formulation of this decomposition method can be given by
\begin{equation}
\mathbf{A}=\mathbf{U}\mathbf{\Sigma}\mathbf{V}
\end{equation}
where, $\mathbf{\Sigma}$ is tridiagonal matrix so that method takes its name from the %
structure of this matrix.The philosopy behind this method is to increase the dominance %
of constant and one-way terms by recursively applying EMPR to two-way term of the %
representation. As a result the idea of adapting the properties of Matrix algebra %
to the multiway arrays, a new method called Tridiagonal Folmat EMPR has come true in %
applying of TMEMPR on multiway arrays, however, folmats. %
In this work we will focus on Transformational TFEMPR, relatively new method in %
certain cases.
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Face Recognition using Tridiagonal Matrix Enhanced Multivariance Products Representation (TMEMPR) Korkmaz Özay Approved This study aims to retrieve face images from a database according to
a target face image. For this purpose, Tridiagonal Matrix Enhanced
Multivariance Products Representation (TMEMPR) is taken into con . . .sideration.
TMEMPR is a recursive algorithm based on Enhanced Multivariance
Products Representation (EMPR). TMEMPR decomposes a matrix into three
components which are a matrix of left support terms, a tridiagonal matrix
of weight parameters for each recursion, and a matrix of right support
terms, respectively. In this sense, there is an analogy between
Singular Value Decomposition (SVD) and TMEMPR. However TMEMPR is a
more flexible algorithm since its initial support terms (or vectors) can
be chosen as desired. Low computational complexity is another advantage
of TMEMPR because the algorithm has been constructed with recursions
of certain arithmetic operations without requiring any iteration. The
algorithm has been trained and tested with ORL face image database with
400 different grayscale images of 40 different people. TMEMPR’s
performance has been compared with SVD’s performance as a result.
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An Implementative Application of Probabilistic Evolution Theory : A Case Study for Two Particles Celestical Mechanical System TATAROGLU Approved \begin{center}
{\bf{Elif Tataro\u glu and Metin Demiralp}} \\
{\textit{\.Istanbul Technical University, Informatics Institute, %
34469, Turkey (T\”URK\.IYE)}} %
\end{center}
\vskip1cm
\noindent In thi . . .s work, we apply Probabilistic Evolution Theory %
to a two particles celestial mechanical system. By using recently %
developed Probabilistic Evolution Theory, for a given single ODE %
or a set of ODEs and their initial condition(s), to create a denu%
merably infinite set of ODEs with relevant initial conditions; we %
get linearity, homogeneity, and constant coefficient structure %
which facilitate the analysis quite a lot. The resulting infinite %
ODEs can be truncated at finite number of unknowns and ODEs toget%
her with the consistent number of initial conditions. %
One of the most important facts in the probabilistic evolution theo%
ry is the reducibility of the right hand side functions (descripti%
ve functions of the system under consideration) of the original ODE%
(s) to rather simple structures which facilitate the obtention of %
the solution pretty much. The space extension concept, based on the %
definition of extra unknown functions from the present ones in the %
given explicit ODEs, can be used in different varieties to this %
end. The best thing is to get the linearity in the resulting ODEs’ %
descriptive functions. However this can occur in only rather quite %
simple systems where the other methods can be used without necessi%
tating the probabilistic evolution theory. The second best simplici%
ty achievement in the descriptive functions is the conicality such %
that the resulting ODEs’ right hand sides become second degree multi%
nomials after the use of space extension. Many ODE(s) in practise %
have the structures enabling us to get conicality. %
Amongst other space extensions the constancy addition plays an impor%
tant and different role. It is defined as follows when the unknowns %
are denoted by the functions $\xi_1(t)$,…,$\xi_n(t)$ %
%——————————————————————–%
\begin{eqnarray}
x(t) \equiv \left[\begin{array}{c}%
\xi_{1}(t)\quad \cdots \quad \xi_{n}(t) \quad \xi_{n+1}(t)%
\end{array} \right]^T \equiv \left[\begin{array}{c}%
\boldsymbol{\xi(t)}^T\quad \xi_{n+1}(t) \end{array} \right]^T
\end{eqnarray}
%——————————————————————–%
where $\xi_{n+1}(t)$ is the additional space extension agent whose %
value remains constant through the evolution by definition while %
the vector $\boldsymbol{\xi(t)}$ is composed of $\xi_1(t)$,…,%
$\xi_n(t)$. This specific space extension is called \lq\lq Constan%
cy Added Space Extension (CASE)\rq\rq\ and permits us to further %
simplify the probabilistic evolution theoretical solution which is %
in Kronecker power series structure to an expression composed of %
Telescope matrices. %
By using this structure and the analytic probabilistic evolution %
theoretical structure, we can totally separate the expression %
to an infinite sum of binary products composed of analytic tempor%
al functions and initial value vector’s images under the %
certain matrix structures. The structure of the two particle celes%
tial mechanical systems allow us to have all these facilitations. %
Talk will include all these things as the presentation time permit%
s. %
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A Wavefunction Free Exponential Function Expectation Value Determination Based ODE Construction and Solution to Get Spectral Entities For the Systems Having Coulombic Attractions Kalay Approved \documentclass[12pt]{article}
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\begin{center}
\large{
\underline{\bf{A Wavefunction Free Exponential Function %
Expectation Value}}%
\vspace{1mm}
\underline{\bf{Determination Based ODE Construction and %
Solution to Get}} %
\vspace{4mm}
\underline{\bf{Spectral Entities For the Systems Having %
Coulombic Attractions}}} %
\vspace{1mm}
\end{center}
\begin{center}
{\bf{Berfin Kalay}} \\
{\textit{\.Istanbul Technical University, Informatics Institute, %
34469, Turkey (T\”URK\.IYE)}} %
\end{center}
\vspace{0.5cm}
%%%
In last few years we have focused on the construction of recursions %
amongst the expectation values of a basis set elements to get the %
energies and corresponding wavefunctions of the autonomous quantum %
systems whose Hamiltonians can be written as follows %
%———————————————————————%
\begin{eqnarray}
\widehat{H}\equiv\frac{1}{2}\widehat{p}^{\,2}+V\left(\widehat{q}%
\,\right)%
\end{eqnarray}
%———————————————————————%
where $\widehat{p}$ and $\widehat{q}$ stand for the momentum and %
position operators respectively. The reduced Planck constant and %
the mass parameter of the system have been taken as just $1$ for %
dealing with equations which are free of the physical units such %
as distance, mass and some others. The function $V$ depending on %
position only stands for the potential function of the system. For %
such systems and an appropriately chosen scalar function $f\left%
(\widehat{q}\right)$ depending on position only, the following expec%
tation value equation can be written %
%———————————————————————%
\begin{eqnarray}
-2\left\langle{V^{\prime}\left(\widehat{q}\,\right)%
f^{\prime}\left(\widehat{q}\,\right)}\right\rangle%
-\left\langle{V\left(\widehat{q}\,\right)f^{\prime%
\prime}\left(\widehat{q}\,\right)}\right\rangle%
+\frac{1}{4}\left\langle{f^{(4)}\left(\widehat{q}%
\,\right)}\right\rangle%
+2E\left\langle{f^{\prime\prime}\left(\widehat{q}%
\,\right)}\right\rangle=0%
\end{eqnarray}
%———————————————————————%
where the choice of $f$ is at our disposal and $E$ denotes one %
of the energies of the system under consideration while all expec%
tation values are evaluated under the wavefunction which is the %
eigenfunction corresponding to the energy $E$. %
By setting $f$ equal to a natural number power of position opera%
tor we could have been able to get a recursion amongst the expecta%
tion values of position operator’s natural number powers. We have %
also shown that this recursion has analytic solutions giving all %
energy values and corresponding eigenfunctions of a hydrogen like %
system.
In this work we extend this analysis to more comprehensive potenti%
al functions such that the coulombic attraction term is additively %
accompanied by certain powers of the position operator. We also %
change the functional structure of $f$ from the position operator’s %
natural number powers to an exponential function whose argument is %
a multiple of the position operator. Method works well again in the %
case of hydrogen-like systems. %
This work is based on private communications with Professor Demiralp.
\end{document}
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Recovery of Missing Data via Wavelets Followed by High-Dimensional Modeling Gürvit Approved In a scientific research missing observations can pose serious problems, affect the bias and can lead to misleading conclusions. Moreover missing data can make the construction of a mathematical model i . . .mpossible. The major objective is first to complete a matrix with missing data and then to construct a mathematical model based on the new prediction. In this article univariable case in data recovery is taken into consideration and without losing from the generality it is intended to be extended to multivariable case followed by a high dimensional modeling. Supposing that a portion of a data vector is missing in such a way that we have a minimal prior knowledge about the data structure, missing part must be recovered from the existing part of the data set. The only prerequisite information needed is the knowledge that would allow us to guess a matrix called a frame. As an example in image processing an inverse discrete cosine transform matrix would be a suitable frame. The main purpose here is to guess such a sparse frame that can represent complete data vector f. By a sparse representation we mean the majority of components being close to zero. In the present article the data imputation using the expected sparse representation is intended to be done in a wavelet or lifting scheme basis. Numerical implementation and the tabulation of the results will be given and the generalization to multivariate case will be discussed.
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Multivariate Numerical Integration via Fluctuationlessness Theorem: Case Study Baykara Approved In this work we come up with the statement of the Fluctuationlessness theorem recently conjectured and proven by M. Demiralp and its application to numerical integration of univariate functions by res . . .tructuring the Taylor expansion with explicit remainder term. The Fluctuationlessness theorem states that the matrix representation of an algebraic operator which multiplies its argument by a scalar univariate function, is identical to the image of the independent variable’s matrix representation over the same subspace via the same basis set, under that univariate function, when the fluctuation terms are ignored. Following this step an orthonormal basis set is formed and the necessary formulas for calculating the coefficients of the three term recursion formula are constructed. Then for multivariate numerical integration, instead of dealing with a single formula for multiple remainder terms, a new approach that is already mentioned for bivariate functions is taken into consideration. At every step of a multivariate integration one variable is considered and the others are held constant. In such a way, this gives us the possibility to get rid of the complexity of calculations. The trivariate case is taken into account and its generalization is step by step explained. At the final stage the implementation is done for some trivariate functions and the results are tabulated together with the implementation times. As a conclusion it can be said that the trivariate case as in the case of bivariate case gives us good results in precision as well as in duration. All the numerical calculations are done in Mathematica.
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A Novel Compression Algorithm for Hyperspectral Images Using Enhanced Multivariance Products Representation Tuna Approved A Novel Compression Algorithm for Hyperspectral Images Using
Enhanced Multivariance Products Representation
Aleksei Sukhanov, Süha Tuna, Behçet Uğur Töreyin
İstanbul Technical University, Informatics . . .Institute, 34469,
Turkey (TÜRKİYE)
Hyperspectral images, typically comprising hundreds of narrow
electro-magnetic frequency bands, is a collection of
spatio-spectral three-dimensional data. Reflected or emitted
electro-magnetic energy is stored as two dimensional matrices
for each frequency band forming a three way array corresponding
to the whole spectrum of interest. Due to the richness in the
spectral content, hyperspectral imaging has many uses across
various fields of interest including remote sensing and
material identification. The downside of hyperspectral images
is the large amount of data that needs to be taken into
consideration. Therefore, dimension reduction and compression
techniques have to be devised for effective use of hyperspectral
imagery. In this paper, Enhanced Multivariance Products
Representation (EMPR) which is a novel multi-way array
decomposition scheme based compression method is proposed
to express the hyperspectral multi-way array in terms of the
sum of outer products amongst the entities having less-way
arrays. Results pertaining to images from the publicly
available Airborne Visible/Infrared Imaging Spectrometer
(AVIRIS) dataset will be presented.
Ack.: The second author is grateful to Professor Demiralp for
his invaluable comments. This work is supported in part by the
Scientific and Technical Research Council of Turkey under National
Young Researchers Career Development Program
(3501 TUBITAK CAREER) grant with agreement number 114E200.
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More Practicalization of Probabilistic Evolution Theory: Case Studies for the Squarification of Telescope Matrices Kırkın Approved \begin{center}
{\bf{Melike Ebru K\i rk\i n and Metin Demiralp}} \\
{\textit{\.Istanbul Technical University, Informatics Institute, %
34469, Turkey (T\”URK\.IYE)}} %
\end{center}
\vspace{0.5cm}
%%%
Th . . .e probabilistic evolution theory (PET) has been developed in last %
few years to get a Kronecker power series solution to explicit ODEs %
or ODE sets where the right hand side functions, namely descriptive %
functions, are assumed to be autonomous, in other words, do not de%
pend on the independent (time) variable even though a space extensi%
on can bring the autonomy. PET assumes that the descriptive function%
s can be expanded into a Kronecker power series which is an infini%
te linear combination of the Kronecker powers of the system vector %
whose elements are the temporally varying unknown functions of the %
independent time variable. In many practically encountered circum%
stances it is possible to construct certain functions of the sys%
tem vector such that the descriptive functions of the ODEs or ODE %
sets construct on these functions become just having finite Krone%
cker powers of the system vector. To this end an important and %
very useful procedure we call \lq\lq space extension\rq\rq\ can %
be used and only multinomial Kronecker power series having only a %
finite number of first Kronecker powers of the system vector app%
ear as the descriptive functions. Even though the multinomiality %
in the support functions is a desired form, it is not the ultima%
te structure we prefer to have. The conicality (multinomialities
with second degree) are superior to any other multimomialities. %
However, even this form may create problems if have constant deg%
ree terms, by causing not triangularity but tridiagonality. To avo%
id tridiagonality a very specific space extension concept \lq\lq %
Constancy Adding Space Extension\rq\rq\ which simply adds a cons%
tant function into unknowns can be used. This also equippes us to %
reshape the first degree terms of the descriptive functions as %
we desire. When all these are done we can add the Kronecker pow%
ers of the system vector to the unknowns and construct a first %
order denumerable homogeneous infinite ODE set with constant co%
efficients can be obtained. This equation can be formally solved %
and an infinite sum solution can be obtained such that each term %
in the summand is a binary product of two factors, one scalar %
factor which temporally varies only and one vector factor which %
is in fact the image of an appropriate Kronecker power of the %
given initial value vector under a rectangular matrix we call %
\lq\lq Telescope Matrix\rq\rq. The telescope matrices have very %
sparse natures because of the Kronecker powers in their struc%
tures. This sparsity can be squeezed by using a very recently %
developed procedure in Demiralp group where it is called the %
\lq\lq Squarification of the telescope matrices\rq\rq. This %
reduces the images of the Kronecker powers of the initial vec%
tor under the telescope matrices to the images of the solely %
initial vector under certain square matrices created by this %
procedure from the telescope matrices such that the resulting %
square matrices depend on the initial vector nonlinearly. This %
presentation will explain this procedure conceptually and give %
certain scripting details, applying it in certain case studies. %
\end{document}
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A Space Pruning Approach to the Determination of Spectral Entities for a Quantum System Described by a Singular Potential Kalay Approved The space pruning approach is not a newly proposed idea and it finds its roots in late 1980s
when it was first proposed by M. Demiralp for the determination of spectral entities for
certain Coulombic . . .or secreened Coulombic Potentials. The singular potentials make the system
Hamiltonians singular at the singularity of the potential function. Hence the images of their
operands can not remain in the domain of those Hamiltonians. There appear overflow(s)
from their domains such that the overflows can be expressed in terms of certain linearly
independent functions which are not laying in the domain. This urges us to take an infinite
linear combination of elements from a complete basis set. The action of the Hamiltonian on
such a linear combination produces two additive expressions: (i) a new linear combination
of the abovementioned basis set elements, (ii) an overflow expression which can be stated
by another linear combination of singular functions (or the functions which do not obey
the conditions satisfied by the abovementioned basis set elements). The linear combination
coefficients in (ii) are linearly dependent on the linear combination coefficients in (i) and they
can be enforced to vanish by setting certain linear equations.
The quantum Hamiltonian of system with singular potential and 1 degree of freedom can
be given as follows
bH
1
2
bp2 + V (bq ) (1)
where bp and bq denote the momentum and position operators respectively. To facilitate the
analysis of this system, the reduced Planck constant and the mass parameter of the system
can be taken as just one for tackling with equations which are physical-unit-free (like free
of mass, distance and some other physical entities). V stands for the potential function and
is assumed to depend on position only. In our study we focus on the potentials decaying to
zero as the position tends to go to infinity. This brings the exponential decaying behavior to
the eigenfunctions of the above Hamiltonian as long as the system energy remains negative.
Hence, the infinity for the position is a singularity. Beyond that, we focus on to the cases
where the potential may have singularity at certain finite values of position. These facts urges
us to use an exponential decaying nature depending on the unknown energy of the system.
This behavior does not change in the images of the abovementioned linear combinations of
basis ste elements. On the other hand, the finite position singularities become worse as the
Hamiltonian acts on that linear combination. Nevertheless the linear combination coefficients
can be chosen in such a way that these worsenings can be removed. The result is a denumerable
infinite number row an column including algebraic equation whose matrix coefficient contains
the energy unknown parameters also. As a conclusion this set of linear algebraic equations
take us to the determination of linear combination coefficients and the energy parameter and
therefore the spectral entities of the system under consideration.
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Squarification of Telescope Matrices in the Probabilistic Evolution Theoretical Approach to the Two Particle Classical Mechanics as an Illustrative Implementation Gozukirmizi Approved There has been an increasing tendency in the Group for Science and Methods of Computing
(Demiralp’s group) to develop an analytical method for the construction of solutions to the
explicit ordinary di . . .fferential equation(s). To this end, the set of explicit ODEs have been
expressed in vector notation and then the right hand side is expanded into a Kronecker power
series which is a one-index infinite summation of additive terms each of which is a vector with
the same number of the unknown functions of the ODE(s) under consideration and stands
as a binary product of a matrix coefficient and a vector which is the Kronecker power of the
unknown functions vector such that the elements of these two factors increase in number as
the Kronecker power ascends.
The Kronecker power series are not unique in matrix coefficients because of the very specific
nature of the Kronecker power of the system vector (which is composed of the unknowns of
the considered ODE(s)). However this uncertainty in these matrix coefficients can be removed
by norm minimization of the relevant entities.
The most desired situation is the case where the right hand side vector’s Kronecker power
series terminates at the first degree powers, even though this can be achieved in the very
limited cases. However, it is possible to increase the number of unknowns by adding new
unknowns in terms of standing unknowns (this procedure is called space extension) such that
the resulting ODE(s) have conical right hand sides (second degree multinomials).
Even though the conicality seems to be the most desired circumstance the reality is not
so and it is possible to extend the space spanned by the unknowns of the ODE(s) under
consideration by adding a constant as a new unknown temporal function at our favor to
get more facilitation in conicality such that the resulting conical function has no constant
term and its first degree component becomes proportional to the relevant unit matrix. This
form of ODE(s) permit us to construct a Kronecker power series for the solution of this
ultimate form of ODE(s) at analytical level such that the Kronecker powers’ coefficients are
so-called Telescope matrices multiplied by a quite simple analytical temporal functions. The
very sparse nature of the Telescope matrices can be compacted to square matrices depending
on the initial value vector. This paper presents this procedure for the two particle problem
of classical mechanics supported by confirmative implementations together with comparison
with the well known solutions of the problem under consideration.
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Classical Symmetric Fourth Degree Potential Systems In Probabilistic Evolution Theoretical Perspective: Most Facilitative Conicalization and Squarification of Telescope Matrices Gozukirmizi Approved The companion paper of the second author includes a sufficiently comprehensive introduction
to the quite recently developed Probabilistic Evolution Theory. Therein, the basic issues in this
theory are . . . mentioned and the squarification concept is also presented. The latter issue have
gained a lot of importance when a recursive algorithm for the squarified telescope matrices
has recently been developed. The validity of the recursion seems to be proven by using math-
ematical induction. Even though we have been able to show the validity of the induction’s
initialization stage we have not been able to construct the general recursion’s validity yet.
However, all the implementations we have realized recently show that the recursion amongst
the squarified telescope matrices holds.
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Overflow Removal from the Images of an Infinite Linear Combination Over a Basis Function Set Under the Quantum System Hamiltonian to Evaluate the System’s Spectral Entities Abdulbaki Baykara Approved We focus on a single particle quantum system having one degree of freedom such that the
particle’s position can vary only in a finite interval of the real axis. This means that the wave
function of th . . .is system must vanish outside this interval. The system’s Hamiltonian (Hamilton
operator) is composed of two components: (i) kinetic energy correspondant which contains only
momentum operator; (ii) the potential term which depends on the position operator without
having any singularity for the positions in abovementioned interval. The spectral entities
are the eigenvalues and the eigenvectors of the system’s Hamilton operator. The relevant
eigenvalue problem is described by a second order ordinary differential equation accompanied
by the vanishing wave function conditions at the endpoints of the interval mentioned above.
As long as the potential function is assumed to be analytic on the interval of the position
variable as we do here, the Hamilton operator of the system is not singular at any interior
and end points of the interval. This implies that, the image of any function in the domain
of the Hamilton operator will never have a singularity on the considered interval. So, we can
take a complete basis function set spanning the domain of the Hamilton operator and then
construct an infinite linear combination of this set’s elements with unknown coefficients. The
image of this linear combination under the action of the Hamilton operator will also have
no singularity. The considered linear combination coefficients can be chosen in such a way
that the linear combination vanishes at the endpoints of the relevant interval by defining two
linear algebraic equations. The vanishing nature of the linear combination does not guarantee
the vanishing property of the image of the linear combination under the Hamılton operator
at the interval endpoints, unless two linearly independent linear algebraic equations imposed
amongst the linear combination coefficients. If these impositions are realized then the resulting
linear combination coefficients become having properties that both the linear combination
and its image under the action of the Hamilton operator vanish. By further linear equation
constructions via appropriate impositions, it is possible to make the images of the linear
combination under the action of zeroth and first powers of the Hamilton operator but its
any finite positive integer power. The imposition of each new set of algebraic equations on
the coefficients of the linear combination changes basis set in such a way that the linear
combination becomes a new infinite linear combination of the members of a new basis set. The
space, somehow chopped, or better stating, pruned. The new basis set can be used variationally
to determine the spectral entities and is expected to produce better quality approximations
to the spectral entities. Talk will present discussions on these types of issues.
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Total Abstracts: 16

M2: Engineering Mathematics: wavelets, fractals, networks and matrices in computational electromagnetics, antennas, fluid dynamics and biomathematics.

Abstract: This special section is devoted to Engineering Mathematics. Special focus is on the theory and applications of wavelets, fractals and networks. The fundamental role of applied matrix analy . . .sis, operator methods, iterated function systems, attractors and analysis of fractals will be emphasised. Session specially will highlight also the relevant Engineering Mathematics applications in computational electromagnetics, antennas, fluid dynamics, mechanics, materials, communication, information and aerospace technologies, life science and bioinformatics. This section thus will bring together researchers with various mathematical and engineering backgrounds sharing common interests in development of the theory and applications of wavelets, fractals, networks and matrix methods in science and engineering. The participants will present lectures on the newest developments and reviews of the “status of the art”. Complementing informal special meetings and discussions will be organized, where in particular various kinds of applications will be jointly explored and joint publications will be prepared.
Organizers: Prof. Sergei Silvestrov, Mälardalen University, Sweden, Dr. Milica Rancic, Mälardalen University, Sweden, Emanuel Guargilia, University of Salerno, Italy and Mälardalen University, Sweden
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Title Author Status Abstract
Double diffusive convection in a Porous Medium Layer Saturated with an Oldroyd Nanofluid Umavathi Approved J.C. Umavathi and Maurizio Sasso
Department of Engineering, University of Sannio, Piazza Roma 21, 82100 Benevento, Italy.
The onset of double diffusive convection in a horizontal layer of a porous me . . .dium saturated with an Oldroyd nanofluid is studied using linear and non-linear stability analysis. The modified Darcy- Oldroyd model is used for the momentum equation. The model used for the Oldroyd nanofluid incorporates the effects of Brownian motion and thermophoresis. The thermal energy equations include the diffusion and cross diffusion terms. The linear theory depends on normal mode technique and the onset criterion for stationary and oscillatory convection is derived analytically. The effects of various governing parameters viz., concentration Rayleigh number, nanofluid Lewis number, modified diffusivity ratio, Soret and Dufour parameters, Solutal Rayleigh number, Vadasz number, Lewis number, relaxation, and retardation parameters, viscosity ratio and conductivity ratio on the stationary and oscillatory convections are presented graphically. The non-linear theory based on the representation of Fourier series method is used to find the heat and mass transport. The effect of various parameters on transient heat and mass transfer is also brought out and nonlinear analysis depends on a minimal representation of double Fourier series. We also study the effect of time on transient Nusselt numbers which is found to be oscillatory when time is small. However, when time becomes very large all the three transient Nusselt values approaches to their steady state values.
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Numerical methods and asymptotic expansions for multi-paramenter stochastic differential equations modeling Canhanga Approved State of art, after Black-Scholes proposed in 1973 a model for pricing European Options under constant volatilities, Christoffersen in 2009 empirically showed “why multi factor stochastic volatility m . . .odels work so well”. Four years late Chiarella and Ziveyi solved the Christoffersen model considering an underlying asset whose price is governed by stochastic volatilities. Using the Duhamel’s principle they derived an integral form solution of the boundary value problem associated to the option price, applying method of characteristics, Fourier transforms and Laplace transforms they computed an approximate formula for pricing American options.
In this paper, considering Christoffersen model, we assume that the stochastic volatilities factors in the model are of mean reversion type changing with different speeds. We do the asymptotic expansion and present experimental and numerical studies for the second order asymptotic expansion and we compare the obtained results with results presented by Chiarella and Ziveyi.
Keywords: Option pricing model, asymptotic expansion, numerical studies .
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Asymptotic Expansions for Stationary Distributions of Perturbed Semi-Markov Processes Silvestrov Approved Dmitrii Silvestrov
Stockholm University
E-mail: silvestrov@math.sus.se
Sergei Silvestrov
Mälardalen University
E-mail: sergei.silvestrov@mdh.se
New algorithms for computing asymptotic expansions for s . . .tationary and quasi-stationary distributions of nonlinearly perturbed semi-Markov processes are presented. The algorithms are based on special techniques of sequential phase space reduction and some kind of “operational calculus” for Laurent asymptotic expansions applied to moments of hitting times for perturbed semi-Markov processes. These algorithms have an universal character. They can be applied to nonlinearly perturbed semi-Markov processes with an arbitrary asymptotic communicative structure of the phase space. The algorithms are computationally effective, due to a recurrent character of the corresponding computational procedures.
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Lie group analysis for MHD boundary layer flow and heat transfer over stretching sheet with viscous dissipation and uniform heat source Metri Approved Prashant G Metri*, Emanuel Guariglia* and Sergei Silvestrov*
*Division of Applied Mathematics, UKK, Mälardalen University , Västerås, Sweden
An analysis for the MHD boundary layer flow and heat transf . . .er towards stretching sheet is carried out via symmetry analysis. A steady two dimensional flow of an electrically conducting incompressible fluid flow over a stretching sheet. The flow is permeated by a uniform transverse magnetic field. The governing partial differential equations are reduced to a system of ordinary differential equations by the scaling symmetries. The symmetry groups admitted by the corresponding boundary value problem are obtained by using special Lie group transformations. The scaling of group transformations is applied to the governing equations. The system remains invariant due to some relation among the parameters of the transformations. After finding two absolute invariants a third order ordinary differential equation corresponding to momentum equation and second order differential equation corresponding to energy equation are derived. The equations along with boundary conditions solved numerically. Numerical solutions of these equations are obtained by using Runge-Kutta-Fehlberg scheme. Further more attention is paid to the effects of some physical parameters magnetic field (Mn), Prandtl number (Pr), Eckert number (Ec) and uniform heat source, on velocity and thermal boundary layer. The results thus obtained are presented graphically and discussed.
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INFLUENCE OF THE MAGNETIZATION VECTOR MISALIGNMENT ON RING PERMANENT MAGNET POSITIONED ABOVE SOFT MAGNETIC CILINDER Vuckovic Approved Ana VUČKOVIĆ*, Nebojša RAIČEVIĆ*, Mirjana PERIĆ*, Željko HEDERIĆ**
*University of Niš, Faculty of Electronic Engineering, Niš, Serbia
** J.J. Strossmayer University of Osijek, Faculty of Electrical E . . .ngineering, Osijek, Croatia
e-mail:ana.vuckovic@elfak.ni.ac.rs, nebojsa.raicevic@elfak.ni.ac.rs, mirjana.peric@elfak.ni.ac.rs, zeljko.hederic@etfos.hr
Permanent magnetism is one of the oldest continuously studied branches of the science but the utilization of permanent magnets themselves was limited it the past. Reason for this could be low force they could generate at the time. The application of permanent magnets has gained momentum since early ‘80s, thanks to the discovery of rare-earth materials with high energy production. In the past, scientists introduced wide variety of techniques for modelling permanent magnet configurations. Different numerical and analytical methods were proposed for determining the magnetic flux density generated by permanent magnets of various shapes and magnetic force between them. Generally, the Ampere’s current model and the Colombian approach are used. In order to overcome the drawbacks of numerical and analytical methods for permanent magnet modelling the semi-analytical approach is proposed in the paper.
Each modeling technique is based on certain assumptions that, at the end, introduce errors in results obtained. The manufacturing process of any permanent magnet based device is influenced by different inaccuracies. The most common performance degradation causes are: misalignment of the magnetization angle, variations in remanent flux density and relative permeability.
Permanent magnets can be magnetized using large magnetizing coils. If the magnetic axis of permanent magnet domains is not precisely aligned with the geometrical axis of the permanent magnet, the resulting magnetization will exhibit a small inclination with respect to the geometry. The reason lies in the fact that the magnetizing coil magnetic field is not totally uniform. In order to model magnetization vector misalignment and to estimate the influence that it has on the magnetic force, hybrid boundary element method (HBEM) is used and described in the paper. This method, developed at the Faculty of Electronic Engineering of Niš, along with semi-analytical approach based on fictitious magnetization charges and discretization technique is used for modelling the ring permanent magnet placed above the soft magnetic cylinder.
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Influence of metallization thickness on microstrip lines characteristic parameters distribution Peric Approved The effect of microstrip lines metallization thickness is very important for successful monolithic microwave integrated circuits (MMICs) optimization and design. In many cases, due to limitations of m . . .ethods, authors analyze structures with an infinitely thin metallization thickness that does not correspond to the real situation in practice. However, various methods take into account the finite dimension of metal conductors. Some of those methods are: the conformal mapping, the finite element method, the boundary element method, the finite difference method, the variational method, the method of lines, etc.
The calculation of characteristic parameters of shielded and covered multilayered microstrip lines, with finite metallization thickness which penetrates into dielectric substrates, will be presented in this paper. Also, the cases when the metallization thickness does not penetrate into substrates will be considered. The hybrid boundary element method (HBEM), developed at the Faculty of Electronic Engineering in Nis, is applied for those calculations. This semi-numerical method is based on combination of the boundary element method, the equivalent electrodes method and the point-matching method for the potential of the perfect electric conductor electrodes and for the normal component of the electric field at the boundary surface between any two dielectric layers.
The method is very simple and accurate comparing to the other methods. It is applied until now, by authors of this paper, for microwave transmission lines analysis. The characteristic parameters of open and shielded microstrip lines as well as covered and coupled structures are calculated using this method. Also, the method was successfully applied for electromagnetic field determination in the vicinity of cable terminations and magnetic force calculations of permanent magnets.
This paper has an aim to show that HBEM can handle with microstrip lines configurations where the metal conductors penetrate into dielectric layers. The quasi-static TEM approach is applied. Several microstrip lines geometries will be considered. The characteristic parameters results will be presented in tables and graphically. The authors expect a very good results agreement with those obtained by other researchers. Also, it will be shown that the method application does not have any limitation considering the number of dielectric layers.
Authors: Mirjana Peric, Slavoljub Aleksic and Ana Vuckovic
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Thermocapillary flow of a non-Newtonian nanoliquid film over an unsteady stretching sheet Narayana Approved Mahesha Narayana*, Prashant G Metri** ***, Sergei Silvestrov**
*Department of Mathematics, M. S. Ramaiah University of Applied Sciences, Bangalore, Karnataka, India
**Division of Applied Mathematics, . . .UKK, Mälardalen University , Västerås, Sweden
***Department of Mathematics, Gulbarga University Gulbarga, Karnataka, India
The influence of surface tension on the laminar flow of a thin film of a non-Newtonian nanoliquid over an unsteady stretching sheet is considered. Surface tension is assumed vary linearly with temperature. An effective medium theory (EMT) based model is used for the thermal conductivity of the nanoliquid. Metal and metal oxide nanoparticles are considered in carboxymethyl cellulose (CMC) – water base liquid. The unsteady boundary layer equations are transformed to a system of non-linear ordinary differential equations with the application of similarity transformations. Resultant two-point boundary value problem is solved numerically using a shooting method together with Runge-Kutta-Fehlberg and Newton-Raphson schemes. The effect of surface tension on the dynamics of the considered problem is presented graphically and analyzed in detail. The clear liquid results which form special case of the present study are in excellent agreement with the results reported in the literature.
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Hypergeometric Steady Solution of Hydromagnetic Nano Liquid Film Flow over an Unsteady Stretching Sheet Metri Approved Prashant G Metri*, Mahesha Narayana** and Sergei Silvestrov*
*Division of Applied Mathematics, UKK, Mälardalen University , Västerås, Sweden
**Department of Mathematics, M. S. Ramaiah University of Ap . . .plied Sciences, Bangalore, Karnataka, India
In this paper, we examine the MHD boundary layer flow and heat transfer characteristics of a laminar nanoliquid film over an unsteady stretching sheet is presented. The highly nonlinear partial differential equations governing flow and heat transport are simplified using similarity transformation. The analytical solutions of the resulting ODEs are obtained for some special case of nano liquid film using hypergeometric functions, and from which the analytical solutions of the original problem are presented. The influence of pertinent parameters such as the magnetic parameter, the solid volume fraction of nanoparticles and the type of nanofluid on the flow, heat transfer, Nusselt number and skin friction coefficient is discussed.
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Multi-Peaked Analytically Extended Function Representing Electrostatic Discharge (ESD) Currents Rancic Approved Karl Lundengård*, Milica Rančić*, Vesna Javor**, Sergei Silvestrov*
* Division of Applied Mathematics, UKK, Mälardalen University (MDH), Västerås, Sweden
** Department of Power Engineering, University . . . of Niš, Niš, Serbia
A number of current functions have been proposed in the literature to model the electrostatic discharge (ESD) currents. They are mostly based on exponential functions. Double exponential function or its four-term version, Pulse function or its multiples, two-terms Gaussian function or other functions may be used for this purpose, as well as the analytically extended function (AEF) presented in this paper. AEF gives good approximation of the IEC Standard 61000-4-2 function and experimentally measured ESD currents. Well-defined representation of real ESD currents is needed in order to establish realistic requirements for ESD generators used in testing the equipment and devices, as well as to provide and improve the repeatability of tests. It should be able to approximate the current for various test levels, test set-ups and procedures, and also for various ESD conditions such as approach speeds, types of electrodes, relative arc length, humidity, etc. A mathematical function is necessary for computer simulation of such phenomena, for verification of test generators and for improving standard waveshape definition.
In this paper we analyze the applicability of the multi-peaked AEF function to representation of different ESD currents. The AEF function has been previously proposed by the authors and successfully applied to lightning discharge modelling. To estimate its non-linear parameters, the Marquardt least-squares method (MLSM) is used.
Preliminary numerical experiments show that the AEF function could be successfully applied to modelling of ESD currents, adjusting its parameters by the developed MLSM procedure. This shall be illustrated through a number of numerical results, most important of them being the one corresponding to modelling of the IEC Standard 61000-4-2 waveshape.
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Data Classifications with Support Vector Machines and Generalized Support Vector Machine Qi Approved In the paper, we study the theory of support vector machine and the using for linear and nonlinear classi…cation of data. And we also used the notion of generalized support vector machine for data cla . . .ssi…cations. We show that the problem of generalized support vector machine is equivalent to the problem of generalized variational inequality and establish various results for the existence of solutions. Moreover, we provide several examples to support our results.
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Fractional derivative of the Zeta Functions and Functional Equations Guariglia Approved Emanuel Guariglia*, Sergei Silvestrov**
* Department of Physics “E. R. Caianiello”, University of Salerno, Fisciano, Italy
** Division of Applied Mathematics, UKK, Mälardalen University , Västerås, Sw . . .eden
Special functions are described by their functional equation. The case of the Riemann zeta function is one of the most popular. Its functional equation can be achieved by applying the periodic Poisson summation formula. This same procedure may be applied to derive the Hurwitz’s formula for the Hurwitz zeta function. In the attempt to discover the functional equations about their fractional derivatives, new properties of these latter have been discovered.
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INFLUENCE OF NOZZLE SHAPE, REYNOLDS NUMBER AND NOZZLE-TO-PLATE DISTANCE ON FLOW CHARACTERISTICS, WALL SHEAR RATE AND MASS TRANSFER GENERATED BY SUBMERGED ROUND IMPINGING JETS Montagné Approved Brice MONTAGNÉ (1) , Kodjovi SODJAVI (1), Amina MESLEM (2), Vaclav SOBOLIK (1)
(1) Laboratoire des Sciences de l’Ingénieur pour l’Environnement (LaSIE), Pôle Sciences et Technologie – Avenue Michel Cr . . .épeau 17042 La Rochelle Cedex 1, France
(2) LGCGM EA3913, Université Rennes, 1, 3 rue du Clos Courtel, BP 90422, 35704 Rennes Cedex 7, France
Heat, mass and momentum transfer induced on a wall by an impinging jet are linked to the jet control parameters. This study presents measurements of velocities, wall shear rates (γ) and mass transfer coefficient (Sh) for submerged impinging jets issued from three round nozzles having a same exit diameter D. Convergent nozzle (CONV), round orifice perforated on a flat plate (RO/P) and on a hemispherical surface (RO/H) were compared. Various types of jet control parameters have been used to provide a wide range of data. Apart from the nozzle shape, the jet Reynolds number (Re) and the nozzle-to-plate distance (H) were varied from 500 to 6500 and 2D to 8D, respectively.
Particle Image Velocimetry technique (PIV) was used to capture the jet flow field whereas the electrodiffusion technique (ED) was used to obtain γ distribution. The ED technique was extended for the measurement of local and global Sh on the wall. It uses an array of platinum electrodes 0.5 mm in diameter, flush mounted into a target wall and a redox reaction that took place in the aqueous solution.
For nozzle to wall spacing that falls within the jet potential core (H≤6D), the maximum value of γ and the local Sh is relatively constant and are located near the nozzle edge. Beyond the potential core, the maximum value of Sh is moved to the stagnation point and it decreases with increasing H.
The maximum values of γ and Sh are increasing functions of Re. Moreover, for H≤3D and beyond a critical Re number, a second maximum appears in the distribution of Sh.
The use of an orifice nozzle improves γ, local Sh, and global Sh. The global Sh measured on a target of 12.5 D in diameter, indicates a gain of 13% and 18% with RO/H and RO/P compared to the CONV nozzle.
The velocity field shows that the free jet region is more contracted for the orifice nozzles compared to the convergent nozzle. The vena contracta effect in orifice jets, more intense with RO/P than with RO/H, explains the observed improvement in terms of wall shear-rate and mass transfer.
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Calculating PageRank in a changing network Silvestrov Approved PageRank is a method which is used to rank the nodes of a network such as the network consisting of the webpages on the Internet and the links between them, other information and communication network . . .s or networks in data mining and network analysis of big data. Many real world networks change over time resulting in the need to re-calculate PageRank after a while. In this talk we will show how the old rank can be used to find the ranking in the new network for some simple changes in a network or strongly connected component part of the network. In particular three types of changes will be considered: 1) changes to the personalization vector used in PageRank, 2) adding or removing a single edge and 3) re-scaling the weight of all edges going out of a single vertex. In order to achieve this a non-normalised variation of PageRank will be used based on a sum of random walks on the network.
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Passive control of supplied air jets for thermal comfort improvement in ventilated spaces Pierre Approved Mixing ventilation is commonly used to control thermal comfort in a room by means of air jets generated from diffusers. Diffusers should distribute the fresh air and energy for heating or cooling, in . . .the entire occupied zone. Hence, the design of the diffuser must aim the ability to well mix the jet with the ambient air. The airflow pattern in the occupied zone is highly dependent on the geometry of the diffuser, even if all other factors are the same, such as room configuration, room heat loads levels and locations, position of the diffuser in the room, and supply air conditions. Enhancement of jet entrainment by means of lobes inserted into a diffuser, has been recently proposed as a promising and low-cost solution for improving the performance of HVAC systems. The present study aims the quantification of this effect on room air motion and subsequent thermal comfort. A commercial multi-cone circular ceiling diffuser is used to control indoor thermal conditions. The internal geometry of that diffuser can be arranged to produce either a vertical pattern distribution in heating conditions, or a horizontal pattern distribution in cooling conditions so as the jet attaches to the ceiling and spreads radially along its surface. Experimental investigations are made on jet characteristics and thermal comfort generated in a full scale model room by the multi-cone diffuser and its performance is compared with the innovative diffuser having similar geometry, and including inserted lobes. The impact of the inserted lobes is evaluated under same heating and cooling conditions.
A simplified manikin simulates the presence of a human body in the test room. Airflow pattern from the diffuser and its interaction with the heated manikin were analyzed with whole-field PIV technique. Thermal comfort was explored and analyzed based on traditional point measuring probes and the standard ISO 7730. Others specifications were checked such as noise and static pressure. It is revealed that the thermal comfort was significantly improved using the lobed diffuser compared to the conventional one in both cooling and heating conditions, without significant increases in pressure and noise level.
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Multi-Peaked Analytically Extended Function Representing Electrostatic Discharge (ESD) Currents Lundengård Approved A number of current functions have been proposed in the literature to model the electrostatic discharge (ESD) currents. They are mostly based on exponential functions. Double exponential function or i . . .ts four-term version, Pulse function or its multiples, two-terms Gaussian function or other functions may be used for this purpose, as well as the analytically extended function (AEF) presented in this paper. AEF gives good approximation of the IEC Standard 61000-4-2 function and experimentally measured ESD currents. Well-defined representation of real ESD currents is needed in order to establish realistic requirements for ESD generators used in testing the equipment and devices, as well as to provide and improve the repeatability of tests. It should be able to approximate the current for various test levels, test set-ups and procedures, and also for various ESD conditions such as approach speeds, types of electrodes, relative arc length, humidity, etc. A mathematical function is necessary for computer simulation of such phenomena, for verification of test generators and for improving standard waveshape definition.
In this paper we analyse the applicability of the multi-peaked AEF function to representation of different ESD currents. The AEF function has been previously proposed by the authors and successfully applied to lightning discharge modelling. To estimate its non-linear parameters, the Marquardt least-squares method (MLSM) is used.
Preliminary numerical experiments show that the AEF function could be successfully applied to modelling of ESD currents, adjusting its parameters by the developed MLSM procedure. This shall be illustrated through a number of numerical results, most important of them being the one corresponding to modelling of the IEC Standard 61000-4-2 waveshape.
Read More

Power series expansion of functions involving generalized Vandermonde matrices Österberg Approved Explicit expressions for power series expansions of functions involving generalized Vandermonde matrices are presented.
Many generalizations of Vandermonde matrices exist. Some considered generalizati . . .ons are those that arise from the relaxation of exponents in the ordinary Vandermonde matrices to be any non-negative integers, the element-wise application of the exponential function to the outer product of two argument vectors and the Birkhoff interpolation problem.
Of special interest are the power series expansion of quotients between generalized Vandermonde determinants, under suitable parameterizations.
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Identification and functional characterization of a glioma specific retroviral integration landscape Weishaupt Approved A variety of different methods, including the Sleeping Beauty and PiggyBac transposon systems as well as retroviruses, are currently used for the tagging of cancer genes in forward genetic screens. Co . . .mparisons of the insertional landscapes between some of these techniques have previously suggested that there might exist a certain degree of bias in how they integrate into the genome. Specifically, rather than integrating randomly, some retroviruses are now considered to integrate preferentially in regions involved in active transcription. As a consequence, using this system for the tagging of cancer genes one would expect different functional outcomes depending on the model cell and target cancer type. In this project we aim to characterize these functional differences in more detail on a set of glioma integration sites, which we previously derived using a PDGFB-MMLV retrovirus system. We propose here to compare the functional properties of this glioma integration landscape against a variety of other virus and tumor models available through the Retrovirus and Transposon tagged Cancer Gene Database (RTCGD). Specifically, we propose first to identify clusters of integration site, referred to as common insertion sites (CIS), which are either unique for distinct normal brain cells or glioma or shared with other tumors. Next we will determine dependencies between CIS in terms of co-occurrence or mutual exclusivity. Subsequently, for each of these sets of signature CIS, we will finally determine functional annotations and overrepresentation of certain biological pathways or genes sets.
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Test Application for Support Vector Machines: The Estimation of Adults’ Cognitive Skills through Certain Kernel Types based on WAIS-R Karaca Approved Test Application for Support Vector Machines: The Estimation of Adults’ Cognitive Skills through Certain Kernel Types based on WAIS-R
Abstract
Wechsler Adult Intelligence Scale—Revised (WAIS-R) is a . . .test designed for applications measuring adults’ cognitive skills. The test is comprised of data of 414 individuals (13 healthy and 401 unhealthy). Collected over 10 years, the data is applied on kernel types of support vector machine algorithm. Data classification performance is evaluated based on computation time and accuracy rate.
Keywords: Support Vector Machines, Classification, WAIS-R
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Iterated function systems, wavelets, fixed points, fractal attractors and commutative and non-commutative families of operators Silvestrov Approved In this talk I will present some results and constructions connecting iterated function systems, wavelets, fixed points, fractal attractors and commutative and non-commutative families of operators
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Total Abstracts: 19

M3: Mathematical modeling, numerical algorithms and aerospace techniques

Abstract: The session is dedicated to contributions on fluid mechanics, optimization and control from aerospace with application to various problems such as renewable energy problems.
Our session incl . . .udes but is not limited to the following topics:
Numerical algorithms and computing methods in aerodynamics;
CFD analysis on the rotor or on the rotor blades;
Aerodynamic design optimization (rotor, blades, airfoils);
Active or passive flow control methods;
Structural-response / Aeroelastic analysis;
Hybrid photovoltaic/wind energy systems;
Noise of wind turbines (prediction and reduction methods);
Computation of classes of models based on the experimental data;
Wind engineering.
Organizers: Alexandru DUMITRACHE , “Gheorghe Mihoc-Caius Iacob” Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy, Bucharest, ROMANIA Florin FRUNZULICA, Faculty of Aerospace Engineering, POLITEHNICA University of Bucharest, ROMANIA.
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Title Author Status Abstract
Bifurcation of transonic flows admitting a shock wave/ sonic surface interaction Kuzmin Approved In the 1990s and 2000s, numerical simulations revealed an instability of the 2D transonic flow over airfoils comprising a flat or nearly flat arc [1]. The instability is caused by an interaction of do . . .uble supersonic regions that arise and expand on the arc when the free-stream Mach number increases. The expansion is followed by an abrupt coalescence of the supersonic regions, crucial changes of the flow field, and non-unique steady states. In the 3D flow over wings, the supersonic regions may coalesce either gradually or abruptly, depending on the wing twist and sweep angle [2].
The non-uniqueness of transonic flow also arises in channels where a sonic surface forms over an expansion corner of the lower wall, while the shock wave appears due to a bend of the upper wall [3]. In practice such a problem may occur, e.g., when an intake encounters variations of the incoming flow because of a maneuvering flight of supersonic aircraft.
This work addresses 3D flow bifurcation in both divergent and convergent-divergent channels of rectangular cross section. A computational domain expands upstream of the channels in order to capture a detached shock wave. Numerical solutions of the unsteady Reynolds-averaged Navier-Stokes equations are obtained with a finite-volume solver of the second order accuracy using several turbulence models. We study bifurcations arisen due to the interaction of the expansion flow at the channel throat with the shock wave formed in front of the cowl. Computations show that the bifurcation band widens as the cowl slope angle or the distance between the cowl tip and throat increases. Inversely, when the distance decreases, the hysteresis shrinks and the flow becomes very sensitive to unsteady perturbations at adverse values of the free-stream Mach number.
In addition we examine the instability of transonic flow over a cylinder located above an expansion corner for several values of the expansion angle.
References
[1] A. Kuzmin. Non-unique transonic flows over airfoils. Computers and Fluids, Vol. 63, p. 1-8, 2012.
[2] A.N. Ryabinin, Transonic flow past symmetrical unswept and swept wings with elliptic nose. ARPN Journal of Engineering and Applied Sciences, Vol. 10, no. 20, p. 9359-9363, 2015.
[3] A. Kuzmin. Shock wave bifurcation in channels with a bend. Archive of Applied Mechanics, doi: 10.1007/s00419-015-1062-z, p. 1-9, 2015.
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Using Potential Flow Theory and Conformal Mapping Technique to Measure Pressure Differential on Airfoil Mughal Approved Flow around an airfoil to calculate pressure co-efficient variations at different relative velocities have always been an important/basic part of Aerodynamic Study. Potential flow theory is used to st . . .udy flow behavior on rankine half body, non rotating cylinder and rotating cylinder as it is more trackable. Falkan Skan Similarity Solution is taken to simulate the flow behavior on wedge. However, to use potential flow theory on usable airfoils the author have used conformal mapping to show a relation between realistic airfoil shapes and the knowledge gained from flow about cylinders. This method can further be used in the designing of an airfoil section. The author has used Joukowski Tranform to generate the flow around airfoils of various geometries and then utilized Kutta condition to force the stagnation point at the trailing edge. Co-efficient of pressure over the entire airfoil surface were calculated and corrected using Karman-Tsien compressibility correction equations. On the basis of this, the location of the ports to install the flush measurement system is suggested.
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Stability of shallow flows: a weakly nonlinear approach Kolyshkin Approved We analyze stability of shallow flows with free surface using weakly nonlinear theory.
Resistance forces in the system of equations are modeled using the Chezy formula. Previous studies
in a weakly n . . .onlinear regime are restricted to the use of the rigid-lid assumption. This assumption
implies that there are no perturbations on the free surface (which acts as a rigid lid). From
a stability point of view this assumption is justified for small Froude numbers.
Linear and weakly nonlinear analysis is used in the present paper to study stability of shallow flows.
The system of shallow water equations (without rigid lid assumption) is linearized in the neighborhood
of the base flow. The corresponding linear stability problem is solved numerically. Calculations show
stabilizing effect of the Froude number of the characteristics of the flow. Using the method of mutiple
scales we derive the amplitude evolution equation for the most unstable mode. It is shown that the
amplitude equation is the complex Shrodinger equation. The coefficients of the equation are evaluated in
closed form in terms of integrals. It is shown that in order to compute the coefficients of the Schrodinger
equation the following calculations should be made: (a) compute the eigenvalues and eigenfunctions of the
linear stability problem, (b) find the eigenfunctions of the corresponding adjoint problem, (c) solve three
linear boundary-value problems (one of the problems is resonantly forced), (d) compute the integrals
containing solutions found in parts (a)-(c). A pseudospectral collocation method based on Chebyshev
polynomials is used to perform numerical computations. A singular value decomposition method is used to
solve resonantly forced linear boundary value problem. Results of numerical computations are presented.
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Modelling of delamination growth in laminated plates using cohesive zone model techniques Chernyakin Approved The damage growth of delamination in composite structure was investigated numerically. An effective approach based on a cohesive zone model is proposed to simulate the delamination propagation in the . . .laminated composite materials subjected to the quasistatic loading. This technique is based on interaction of two coinciding surfaces which will represent reference surfaces of two connected shells. The cohesive zone model is used to define the cohesion area for potential delamination propagation. This approach was implemented in the ANSYS® software package and was validated on testing models that are commonly used for experimental research of fracture processes.
The buckling and post-buckling behavior of delamination in thin-walled plates subjected to 4-point bending is also presented in the paper. In order to determine the buckling load of delamination and to investigate the process of delamination propagation under compression loading the numerical study is carried out. The proposed approach gave close correlation with results obtained by other authors and allowed to make analysis of the damage growth and failure mechanisms contributing to collapse of composite structure. The successful prediction of delamination propagation under the combination of post-buckling deformations and several composite damage mechanisms has application for the next generation of composite aircraft constructions.
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Finite element analysis of panels with surface cracks Chernyakin Approved Dangerous conditions to the aerospace structures can often be caused by different defects which occur in the panels. Non-through surface cracks attract particular interest. Generally these cracks have . . . compound front form. In global practice defects are approximated with the semielliptical cracks to simplify calculation methods. In this case the defect is considered two-parameter and it is only defined by maximum depth and length.
The fracture mechanics analysis in the finite elements software ANSYS® is presented for cylindrical panels with semielliptical non-through surface cracks. Stress intensity factor values distribution for the crack front points is under analysis. These values were obtained by using invariant J-integral. J-integral values calculation was performed using the equivalent domain integral method. Accuracy of the fracture mechanics problem solution can be significantly increased by using regular mesh with multiple finite elements along the crack front. Fracture mechanics parameters investigation identified presence of edge effect common to the area where the crack front goes to the panel surface. Edge effect refers to the local maximum values which are much higher than the crack front end points values.
A universal formula for determining the stress intensity factor value at representative points of the front line is proposed.
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Fatigue life prediction for expansion bellows Chernyakin Approved In this paper the expansion bellows which was designed to make compensation for the mutual axial displacement of the fuel line flanges is considered.
The aim of this study to evaluate the performance . . .of the bellows under durability test conditions and estimate of durability according to the low-cycle strength criteria.
Considered bellows is a two-layer corrugated shell which works in very difficult conditions. At the same time there are all possible kinds of nonlinearities such as large displacements, advanced plastic deformations, contact interactions of the individual corrugations.
By using the finite element method the modeling of the stress-strain behavior of the bellows is carried out, taking into account physical and geometrical nonlinearities, contact interaction. It leads to an estimation of the accumulated plastic strains and enables the calculation of the fatigue life of bellows. It is performed by the low-cycle strength criteria using different assessment methods of the Basquin-Coffin-Manson`s equation parameters. The results of durability evaluation were compared with experimental data.
Obtained estimations of the bellows durability are in good agreement with the experimental data.
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Numerical Analysis of NREL VI Wind Turbine Rotor Performance Cernat Approved In the present study, a number of RANS simulations were performed on the well-known NREL VI wind turbine rotor. The simulations are based on finite volume method performed to characterize in detail th . . .e three-dimensional behavior of the flow in order to identify the re-circulation zones, which the classical methods of design, like blade element momentum theory cannot predict. This information is very useful in the rotor’s geometry optimization and the active flow control applied to increase the wind turbine performance.
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Numerical Study of Aerodynamic Effects on Road Vehicles Lifting Surfaces Cernat Approved Road vehicles aerodynamic performance analysis depends on the study of engine intake and cooling flow, internal ventilation, tire cooling, and overall external flow as the motion of air around a movin . . .g vehicle affects all of its components in one form or another. Due to the complex geometry of these, the aerodynamic interaction between the various body components is significant, resulting in vortex flow and lifting surface shapes. The present study, however focuses on the effects of external aerodynamics only, and in particular on the flow over the lifting surfaces.
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THE EFFECT OF WIND DIRECTION AND BUILDING SURROUNDINGS ON A MARINA BAY IN THE BLACK SEA Katona Approved The wind effect has usually a major importance in the marina bay. These environmental sites are an interplay between tourist and commercial activities, requiring a high-detailed and definition studies . . . of the dynamic fluid in the harbor. Computational Fluid Dynamics (CFD) has been used elaborately in urban surroundings research. However, most CFD studies were performed for harbors for only a confined number of wind directions and/or without considering the building surroundings effects. This paper presents the results of different simulations based on various wind flows and the CFD simulations of coupled urban wind flow and general wind directions upon a coastal semi-closed area. Thus the importance of wind effects on the evaluation of the marina bay will be pointed out to achieve a safe and secure mooring at the berth and eventually a good potential of renewable energy for an impending green harbor.
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Non Lyapunov stability of a constant spatially developing 2-D gas flow Tanasie Approved Different types of stabilities (global, local) and instabilities (global absolute, local convective) of the constant spatially developing 2-D gas flow are analyzed in the phase space of continuousl . . .y differentiable functions, endowed with the usual algebraic operations and the topology generated by the uniform convergence on the real axis. For this purpose the Euler equations linearized at the constant flow are used. The Lyapunov stability analysis was presented in [1] and this paper is a continuation of [1].
REFERENCE:
[1] A. M. Balint, St. Balint, R. Szabo – Lyapunov stability of a spatially developing constant 2D gas flow, submitted to ICNPAA. 2016
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Lyapunov stability of a spatially developing constant 2D gas flow Szabo Approved The Lyapunov stability of a spatially developing constant 2D gas flow is analyzed in a particular infinite dimensional phase space. The elements of the phase space are continuously differentiable func . . .tions, the algebraic operations are usual and the topology is that generated by the uniform convergence. The Lyapunov stability with respect to instantaneous, as well with respect to source produced permanent time harmonic perturbations are investigated. Some of the obtained results are completely different from those reported in the literature.
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Non Lyapunov stability of the constant spatially developing 1-D gas flow in presence of solutions having strictly positive exponential growth rate Balint Approved Different types of stabilities (global, local) and instabilities (global absolute, local convective) of the constant spatially developing 1-D gas flow is analyzed in the phase space of continuously . . .differentiable functions, endowed with the usual algebraic operations and the topology generated by the uniform convergence on the real axis. For this purpose the Euler equations linearized at the constant flow are used. The Lyapunov stability analysis was presented in [1] and this paper is a continuation of [1].
REFERENCE
[1] St. Balint and A. M. Balint , The Concepts of Well-Posedness and Stability in Different Function Spaces for the 1D Linearized Euler Equations, Abstract and Applied Analysis, Volume 2014, Article ID 872548, 10 pages. http://dx.doi.org/10.1155/2014/872548
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Rationality of Large Mass Method for Frequency Response Analysis Mehmood Approved Most of previous work on Large Mass (LM) Method by Kim Y.-W. and Jhung, M. J.for dynamic problems is related to the study of transient responses. This paper discusses the numerical effectiveness of La . . .rge Mass Method for frequency response problems in truss structures. The results achieved are of great importance for design of launch vehicle structures which must be capable of withstanding a wide range of frequencies for smooth operation of sensors. The paper also presents a very simple technique for developing an LM analysis model through programming language e.g. MATLAB.
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Numerical study of a finite volume scheme for incompressible Navier-Stokes equations based on SIMPLE-family algorithms. Alahyane Approved In this work, we present a numerical study of a finite volume scheme based on SIMPLE algorithm for incompressible Navier-Stokes problem. However, this algorithm still not applicable to a large categor . . .y of problems this could be understood from its stability and convergence, which depends strongly on the parameter of relaxation, in some cases this algorithm could have an unexpected behavior. Therefore, in our work we focus on this particular point to overcome this respected choice of relaxation parameter. This will be followed by numerical applications in image processing variety of fluid flow problems described by incompressible Navier-Stokes equations.
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Twin Flapping wings as an alternative method of harvesting energy from wind Alexandru Approved F. Frunzulica*,**, Al. Dumitrache**, M. Stoia-Djeska*
*POLITEHNICA University of Bucharest, Faculty of Aerospace Engineering, Polizu 1-6, RO-011061, Bucharest, Romania
Institute of Mathematical Statis . . .tics and Applied Mathematics, 13 Septembrie 13, sect.5, RO-050711, Bucharest, Romania
In the last decades, the wind energy became more attractive to Romania, and thus many resources are allocated to develop the energetic systems based on wind energy. In this work we have investigated the possibility to harvest the wind energy with an controlled pitch-plunge aeroelastic system composed by two wings in side-by-side configuration. Compared to the conventional systems using wind turbines which are based on transforming the wind energy into mechanical energy of a rotational horizontal or vertical axle rotor, the new proposed systems under consideration convert the wind energy into mechanical energy too, but of a coupled translation-rotation (plunge-pitch) motion, the wings oscillates in opposite directions. The pitch-plunge motion may be passively or actively controlled by the driving elastic system and by flap and/or slat controls for each wing. In the present study, aerodynamic analysis of twin-wing, in side-by-side position, is numerically investigated using an imposed motions for wings. Two-dimensional unsteady flow over system is performed with Ansys Fluent program, using Reynolds-Averaged Navier-Stokes model, completed by k – \omega Shear Stress Transport Turbulence model. Main parameters like individually coefficient of torque, and power coefficient of moving wings system are investigated. The results from our dual-wing found that a twin-wing device can produce more power compared to a single wing due to the strong unsteady flow interaction between the wings.
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ANALYSIS OF CONTROL SYSTEM RESPONSES FOR AIRCRAFT STABILITY AND EFFICIENT NUMERICAL TECHNIQUES FOR REAL-TIME SIMULATIONS ANDREI Approved The objectives of this paper are the study and the implementation of both aerodynamic and propulsion models, as linear interpolations using look-up tables in a database. The aerodynamic and propulsion . . . dependencies on state and control variable have been described by analytic polynomial models. Some simplifying hypotheses were made in the development of the nonlinear aircraft simulations. The choice of a certain technique to use depends on the desired accuracy of the solution and the computational effort to be expended. Each nonlinear simulation includes the full nonlinear dynamics of the bare airframe, with a scaled direct connection from pilot inputs to control surface deflections to provide adequate pilot control. The engine power dynamic response was modeled with an additional state equation as first order lag in the actual power level response to commanded power level was computed as a function of throttle position. The number of control inputs and engine power states varied depending on the number of control surfaces and aircraft engines. The set of coupled, nonlinear, first-order ordinary differential equations that comprise the simulation model can be represented by the vector differential equation. A linear time-invariant (LTI) system representing aircraft dynamics for small perturbations about a reference trim condition is given by the state and output equations present. The gradients are obtained numerically by perturbing each state and control input independently and recording the changes in the trimmed state and output equations. This is done using the numerical technique of central finite differences, including the perturbations of the state and control variables. For a reference trim condition of straight and level flight, linearization results in two decoupled sets of linear, constant-coefficient differential equations for longitudinal and lateral / directional motion. The linearization is valid for small perturbations about the reference trim condition. Experimental aerodynamic and thrust data are used to model the applied aerodynamic and propulsion forces and moments for arbitrary states and controls. There is no closed form solution to such problems, so the equations must be solved using numerical integration. Techniques for solving this initial value problem for ordinary differential equations are employed to obtain approximate solutions at discrete points along the aircraft state trajectory.
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PERFORMANCE ANALYSIS AND DYNAMIC MODELING OF A SINGLE-SPOOL TURBOJET ENGINE ANDREI Approved The research performed in this paper is focused on two main directions. The first objective is represented by the modeling a single-spool turbojet engine such that to calculate its performances for a . . .specified range of flight altitude and Mach number, as well as various engine operational regimes. From the numerical simulations which are based on thermo-dynamical analysis of the engine, have been determined parameter correlations, e.g. thrust -fuel flow, which enables the deduction of a control law for the fuel flow. From the thermo-dynamical analysis are obtained the values for significant engine parameters which are required by the engine’s dynamic study. The second objective refers to the study of the dynamic behavior of the turbojet engine, with appropriate dynamic modeling. The universal maps of both compressor and turbine are required for the dynamic analysis, and the thrust (as the engine’s main performance) is controlled in case of a single spool turbojet by a single parameter, i.e. the fuel flow; the determination of the necessary amount of fuel is done iteratively, with slight corrections, as perturbations of input fuel flow from the calculation of flow balance at turbine inlet and turbine exit.
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The Buckling Analysis of Elements of Stiffened Aircraft Structure Borisova Approved Investigation of stability of stiffened cylindrical thin shells involves great mathematical difficulties, connected with sufficiently high order of equations. These difficulties in most cases eliminat . . .e the possibility of analytical approach of such structures. In this cases numerical methods are used. Thin-walled profiles are commonly used as the reinforcing ribs. In many cases these structures under the acting external loads are compressed. Therefore, the problem of determination of the critical stress of compressed cylindrical shells stiffened by longitudinal ribs has great practical interest. In this paper we consider plate, as a limiting case of curved panels. A new approach, based on Ritz method, for buckling analysis of stiffened plates under axial compression with the discrete and eccentric location of the longitudinal elastic ribs, is developed. Suggested approximations of displacements allow to take into account the features of system wave formation. It takes into account the effect of warping of the cross section of the rod. Contact interaction of the plate and the rod is taken into account approximately by using the concept of reduced plate width. This method provides sufficient accuracy in determining critical loads. The results are compared with data, received by finite element method.
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Considering factorial series as time integration method Razafindralandy Approved Recently, a time integration method of ODE’s and PDE’s, based on a Taylor series decomposition of the solution, has been proposed. In this method, the series decomposition is followed by a Borel summa . . .tion procedure. This procedure, which consists in finding an (sectorial-wise) analytic solution from the Taylor series, is indeed necessary if the radius of convergence is zero. And if the Taylor series is convergent, the Borel summation acts like an extrapolation method outside the convergence disc, and speeds up the numerical resolution.
The most natural algorithm to realize the Borel summation is the Borel-Padé algorithm. It consists in computing the Borel transform of the series, replacing it by an analytic solution via a Padé approximant, and going back to the physical space thanks to a Laplace transformation. This algorithm has proven to be efficient in solving mechanics problems (explicit scheme, natural handling of some non-linearities, faster than some other explicit methods, good conservation properties for Hamilton systems, resolution of the Navier-Stokes equations, …).
The force, but also the weakness of the proposed algorithm is the use of Padé approximants. Indeed, on one hand, the latter are known to be an efficient tool in prolonging a convergent series outside its validity disk. They may also be usefull in finding poles and then in choosing the direction of the Laplace transform. On the other hand, the standard algorithm of Padé approximation requires the resolution of a linear problem which may be ill-conditioned and, sometimes, not inversible. Solutions to circumvent these problems exist but at extra costs.
The aim of this communication is to present an alternative to the Borel-Padé algorithm in the computation of the Borel sum of the series. It consists in representing directly the Borel sum as an inverse or generalised factorial series. We then explore the advantages and limits of this algorithm in the perspective of a time integration method.
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Nonlinear analysis and control of an aircraft in the neighbourhood of deep stall KOLB Approved When an aircraft is locked in a stable equilibrium at high angle-of-attack, we have to do with the so-called deep stall which is a very dangerous situation. Airplanes with T-tail are mainly concerned . . .with this phenomenon since the wake of the main wing flows over the horizontal tail and renders it ineffective but other aircrafts such as fighters can also be affected.
First the phase portrait and bifurcation diagram are determined and characterized (with three equilibria in a deep stall prone configuration). It allows to diagnose the configurations of aircrafts susceptible to deep stall and also to point out the different types of time evolutions.
Several techniques are used in order to determine the basin of attraction of the stable equilibrium at high angle-of-attack. They are based on the calculation of the stable manifold of the saddle-node equilibrium at medium angle-of-attack and on the Lyapounov method.
Then several ways are explored in order to try to recover from deep stall. They exploits static features (such as curves of pitching moment versus angle-of-attack for full pitch down and full pitch up elevators) or dynamic aspects (excitation of the eigenmodes and improvement of the aerodynamic efficiency of the tail).
Finally some properties of a deep stall prone aircraft are pointed out and some control tools are also implemented. We also try to apply this mathematical results in a concrete situation by taking into account the captors specificities or by estimating the relevant variables thanks to other available information.
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Nasedkin A.V., Nasedkina A.A., Kornievsky A.S. Modeling of nanostructured porous thermoelastic composites with surface effects Nasedkin Approved The paper considers an integrated approach to the determination of the material properties of nanoscale thermoelastic bulk (mixture) stochastically distributed composites of an arbitrary anisotropy cl . . .ass with account for their internal microstructure. ANSYS finite element package was used to simulate representative volumes and to calculate the effective moduli. This approach is based on the theory of effective moduli of composite mechanics, modeling of representative volumes and the finite element method. Here, the contact boundaries between material and pores were covered by the surface membrane elastic elements in order to take the surface effects into account.
For automated coating of internal boundaries of pores in the cubic representative volume the following algorithm was used. At the beginning, as a result of the formation of the porous structure, the finite element mesh from octanodal cubic elements was created, some of which had the material properties of thermoelastic material, and the other part of the elements had the material properties of the pores (with negligible elastic stiffness moduli). Further, only the finite elements with thermoelastic material properties were selected. The resulting elements on the outer boundaries were covered by four nodal target contact elements. Then, the contact elements, which were located on the external surfaces of the full representative volume, were removed, and the remaining contact elements were replaced by the four nodal membrane elastic elements. As a result, all the facets of the contact of thermoelastic structural elements with pores were coated by membrane finite elements.
The next step consisted in solving the static problems for obtained representative volume with the main boundary conditions which were conventional for effective moduli method. Further, in the ANSYS postprocessor the averaged stresses were calculated, both on the volume finite elements and on the surface finite elements. Finally, the effective moduli of porous composite with surface effects were calculated from the corresponding formulas of the effective moduli method by using the estimated average characteristics.
In the results of computational experiments, the following features were observed. If we compare two similar bodies, one of which has usual dimensions and the other is a nanoscale body, then for the nanosized body due to the surface stresses the effective stiffness will be greater than for the body with usual sizes. Furthermore, for the porous body of the usual size the effective elastic stiffness decreases with increasing porosity. Meanwhile, the effective stiffness of nanocomposite porous body with the same porosity may either decrease or increase depending on the values of surface moduli, dimensions and number of pores. This effect is explained by the fact that the sizes of the surface pore with surface stresses depend not only on the overall porosity, but also on the configuration, size and number of pores.
This work was supported by the Russian Science Foundation (grant number 15-19-10008).
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Aerodynamics investigations of a disc-wing UAV Florin Approved Alexandru DUMITRACHE**, Florin FRUNZULICA*,**, Sorin GRIGORESCU*,
Bogdan SUATEAN (PhD)*
*POLITEHNICA University of Bucharest, Romania
**Institute of Mathematical Statistics and Applied Mathematics, . . .Bucharest, Romania
An axi-symmetric disc-wing with hollowed out underside cavity and an elliptic cross-section is considered in a flow speed range up to 20 m/s. This type of wing can be used in the construction of a unmanned air vehicle (UAV) to achieve a high maneuverability. The purpose of this study is to understand the physics of flow around this type of wing in flight in order to determine appropriate methods of control. Passive flow control methods by which aerodynamic control moments can be generated are considered instead of those which use moving surfaces.
Flow control means such as vortex generators or synthetic jet allow to produce the control moments by a similar active flow control methods.
Also the Coanda effect is investigated with the result of the delay of boundary layer separation.
Numerical results are compared to the experimental ones and the conclusions identify the best methods for implementing flow control methods and the optimal shape of the disc-wing.
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Total Abstracts: 22

M5: Nonlinear Problems of Guidance, Navigation and Control

Abstract: The session topic is focused on modeling, nonlinear mathematical and computational research of the guidance, navigation and control systems for both information satellites, space astronomica . . .l observatories, space free-flying robots and all kinds of aeronautical vehicles. New methods and results will be presented from Russia (Moscow, Saint Petersburg, Samara, Kazan, Irkutsk), France (Paris, Toulouse), Germany, Italy, Spain and Turkey. Speakers from other countries are welcome for participation in the session, which also will contain papers submitted by members of the IFAC http://www.ifac-control.org/ Technical committee on Aerospace.
Organizers: Prof. Yevgeny Somov, Russia , Prof. Houria Siguerdidjane, France
 
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Title Author Status Abstract
Attitude guidance and control of the GLONASS navigation satellites at passage of singular orbit sites Somov Approved We have considered a logic of the GLONASS spacecraft (SC) attitude guidance laws during their passage of the singular orbit sites, namely large and small angles between the Sun and Earth directions ap . . .plied for definition of the solar-terrestrial reference frame (STRF). Moreover, we have studied problems on minimization of influence the solar pressure forces upon the SC mass centre and on calculation of the position errors by an onboard antenna phase centre with respect to the STRF. We developed algorithms for the SC anticipatory turn which are put both in the satellite onboard computer and in the consumer equipment. The algorithms allow to calculate both the SC guidance law on the SC yaw channel and corrections on position of its antenna phase centre applied in the consumer devices.
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Guidance and adaptive-robust attitude & orbit control of a small information satellite Somov Approved We have considered a small information satellite (for communication, radio-electronic and optoelectronic land-survey, etc.) which may be placed into an orbit with altitude from 600 to 1000 km. Diffe . . .rent disturbance factors necessitate correction of such satellite orbit motion intended for long-term (up to 15 years) operation. When a spacecraft (SC) is moving on orbit, its solar array panels are directed to the Sun, therefore, both the satellite inertia tensor and the satellite mass change because of fuel expenditure for the orbit station-keeping. The SC attitude and orbit control system (AOCS) contains a strap-down inertial navigation system with astronomic correction and a cluster of four reaction wheels, which is unloaded from an accumulated angular momentum due to the magnetic driver and also a correcting engine unit with the electro-reaction engines. We present the solution for the following problems:
1) analysis of the corrections required for the SC station-keeping on specified sun-synchronous orbits, relation of the SC orbital and angular motions with indicated AOCS;
2) development of algorithms for in-flight identification of the SC inertia tensor, synthesis of algorithms for the SC adaptive-robust control;
3) dynamical analysis of the AOCS with the elaborated control algorithms for a small land-survey satellite on a predetermined sun-synchronous orbit.
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Estimation of Land Remote Sensing Satellites Productivity Based on the Simulation Technique Kucherov Approved While designing land remote sensing satellites (LRSS), it is essential to satisfy the requirements to their efficiency indices. One of the most important efficiency indices is the satellite productivi . . .ty. Here, productivity is treated as a number of separate survey objects taken in a definite time.
There exist a couple of approaches to the determination of the LRSS productivity:
– using the survey objects data base containing coordinates of specific objects;
– based on queuing theory;
– using scheduling of the objects survey sequence with regard to maximum quantity of taken objects;
– based on the simulation technique.
This paper deals with the last method.
The algorithm includes the next items.
1. Computing time t is set equal to zero. The number of the taken survey objects N is set equal to zero.
2. Computing time is incremented by the step of simulation d.
The number of survey objects within the field of view is simulated using Monte-Carlo technique based on the hypothesis of Poisson distribution law.
3. The survey objects coordinates are simulated based on the hypothesis of their uniform distribution within the spacecraft field of view.
4.The time necessary for the survey objects being taken is calculated with regard to the spacecraft retargeting.
5. N is incremented by the number of objects taken within the interim d.
6. Jump to item 2 is fulfilled, unless the calculation is stopped by the user.
Thus the LRSS productivity may be estimated.
The above algorithm was implemented in the software. Illustrating examples are cited.
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Attitude guidance and simulation with animation of a land-survey satellite motion Somova Approved Nonlinear guidance problem has been solved for a land-survey satellte with analytical representation of the optimal angular guidance laws at scanning observation with given accuracy. A solving o . . .f the problem is based on polynomial interpolation for a vector function of the modified Rodrigues parameters. We also consider problem for optimization of spatial rotational maneuver by a land-survey satellite at its passage from any scanning route to other route with general kinematic boundary conditions – on an orientation quaternion, on vectors of angular rate and acceleration. For the nonlinear optimization problem we present an approximate analytic solution in the form of the smooth conjugated vector splines with different degrees. In result for a land-survey satellite we have obtained the vector polynomial guidance laws for all its operational modes. These guidance laws are applied for animation of the land-survey satellite spatial motion. In-flight support has provided for the attitude determination and control system (ADCS) of a land-survey satellite. The support is implemented in terrestrial control flight centre (CFC) in order to ensure the ADCS reliability and survivability at faults of onboard devices. Moreover a telemetric information of operative diagnosis is applied where the measured data have been contained on the satellite kinematic parameters both motion of mass center and angular motion. For the ADCS in-flight supporting the CFC operators have been applied a computer supporting system. In this system the localization is carried out on faults of onboard devices and by dialog with operators the recommendations are forming on needed operations by the solving rules in the knowledge base data.
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Time-Optimal Control of the Spacecraft Trajectories in the Earth-Moon System Fain Approved This paper outlines the multiparametric optimization of the L1-L2 and L2-L1 missions in the Earth-Moon system using electric propulsion. The optimal control laws are obtained using the Fedorenko succe . . .ssful linearization method to estimate the derivatives and the gradient method to optimize the control laws. The study of the transfers is based on the restricted circular three-body problem. The mathematical model of the missions is described within the barycentric system of coordinates. The optimization criterion is the total flight time. The perturbation from the Earth, the Moon and the Sun are taking into account. The impact of the shaded areas, induced by the Earth and the Moon, is also accounted. As the results of the optimization we obtained optimal control laws, corresponding trajectories and minimal total flight times.
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Methods for Predicting Unsteady Takeoff and Landing Trajectories of the Aircraft Shevchenko Approved Processes takeoff roll and ground braking on the runway are essentially nonlinear and nonstationary. These phases of the flight mission are performed with the participation of the pilot. Being under t . . .ime pressure and in the absence of information support, the pilot is experiencing high psychological stress. Therefore, there are prerequisites for taking improper or wrong decisions
To improve situational awareness of the pilot the methods of predict future events are offered. The methods are based on the energy approach to motion control. The mathematical formulation of the approach is the energy balance equation. In our works this approach was extended to ground segments of trajectory. Our own energy balance equation is written in the increment the total specific energy:
This equation makes it possible to determine the distance required for variation of the total energy at the amount of .
With regard to the braking on landing the final value of the energy is the energy at the speed of taxiing. At the stage of takeoff in the presence of tall obstacles the final value of energy is determined by the obstacle height and the minimum steady flight speed. Based on these values of final energy, we have found the length of the ahead segment sufficient to reach the required state of the aircraft.
On the takeoff run we have found the distance to the point of decision making about possibility of safe overfly the obstacle. On the landing roll we got the algorithm to predict the braking distance.
In the braking process a different devices such as thrust reverse, spoilers and wheel brakes usually are used. The rate of deceleration depends from them on and off. Therefore, correction circuits have been added to the prediction algorithms to adapt the algorithms in accordance with the used braking devices. These facilities ensure high likelihood of the prediction.
Prediction algorithms were tested on a nonlinear model of modern liner over the entire range of operating flight conditions. Integrated prediction errors are within 20m.
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Nonlinear Modeling and Study for Control of the Research Spacecraft with Solar Sail Khabibullin Approved This paper outlines the mathematical motion model of the research spacecraft that uses solar sail instead of an engine and a propellant. The mathematical motion model for solar sail spacecraft is form . . .ulated and described. The work considers the mathematical motion model within the heliocentric system of coordinates. The best way to assess the reasonableness of the mathematical model is the using model in motion simulation process. On the basis of the formulated mathematical model the special software complex for interplanetary transfer simulation is developed. Especially, the mission of the transfer of the spacecraft from the Earth’s orbit to the potentially hazardous asteroid is simulated. The obtained results during simulation demonstrate correctness and feasibility of the considered mathematical motion model.
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Nonlinear Algorithm for Navigation of a Moving Object in Magnetic Field Shevchenko Approved Consideration was given to the problem of relative positioning with the use of alternating magnetic field. The problem was shown to be solvable using a system of three magnetic dipoles emitting magneti . . .c field at different frequencies. Ambiguity of its solution was discussed, and ways to resolve it were proposed. An algorithm for relative positioning based on the solution of this problem was proposed. Error equations of the positioning algorithm and the results of their analysis were presented. Calibration procedures, improving accuracy of relative positioning, are also considered. One of these procedures, based on nonlinear optimization techniques, was presented in greater details. Particularly,the problem of avoiding local minima during minimization of non-convex cost function was considered carefully. The paper was supplied with several numerical examples demonstrating effectiveness of proposed algorithms in relative positioning.
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An analytic approach to the relation between GPS attitude determination accuracy and antenna configuration geometry Kozlov Approved The reliability and accuracy of GPS attitude determination are still the main relevant theoretical questions. While the first one derives from the probabilistic nature of phase ambiguity resolution al . . .gorithms and effectiveness of multipath reduction, the second is additionally affected by geometric properties of GNSS antenna configuration. Being trivial in two-antenna system, the relation between GPS attitude determination accuracy and antenna spatial layout becomes much less intuitive for multi-antenna configurations, and seems to have been examined analytically in some specific cases only. For example, most of research papers in the field use Euler angles as attitude representation, which have singularity in some cases, and consider the number of antennas of not more than four. We present some further investigation in this area.
In our study we obtain a polynomial representation for the relation between attitude determination accuracy factors, i.e. the singular values of some certain measurement matrix, and antenna baseline vector coordinates. An examination of several specific cases show that our representation can be used to determine the optimal antenna configuration under conventional geometry limitations.
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Block Design of Tracking Systems under Unmatched Disturbances via Sigmoidal Feedbacks Kochetkov Approved The paper deals with the tracking output variables of quasi-canonical system for given signals under unmatched external disturbances and functional uncertainties within the restrictions on state varia . . .bles. A new approach, based on the block control principle via sigmuidal local feedbacks is designed. In contrast to the commonly used linear local feedbacks with high gains required for the suppression of disturbances, S-shaped sigma-function is nonlinear, smooth and bounded everywhere, which allows us to take into account the restrictions on the phase variables at the synthesis stage. It is shown that properties similar to the properties of systems with discontinuous controls operating in the sliding mode, are provided in the closed-loop system via smooth and bounded signals in the prelimit case. Namely, the decomposition of the total motion on multirate components and invariance with respect to disturbances with a given accuracy are provided. Decomposition procedure for selecting the parameters of sigmoidal local feedbacks based inequalities is developed. This approach extends the class of admissible systems by nonlinear systems with non-smooth disturbances, where special requirements for the arguments composition of functional uncertainties not needed.
Also systems with uncertain input channels of controls are studied. We consider the general case, when matrix front of controls is non-singular, does not have a dominant diagonal, analytical view of its elements is known, their current values are unknown, and limited. For this case, the decomposing synthesis procedure of sigmoidal control actions, based on the method of the hierarchy of controls, is developed. The developed approach is promising and expanding class of robust systems, since in contrast to the known algorithms does not require of constancy (low drift) of unknown parameters.
As an example, block procedure of feedback synthesis for controlling the position of the endpoint of a manipulator with electric actuators is designed. Local feedbacks and corrective actions of the states observer in the form of smooth sigma-functions provide tracking of trajectories defined in the coordinate system of the manipulator endpoint. Tracking system is provided the invariance with a given accuracy with respect to the existing uncertainties subject to the restrictions on the variables of the mechanical subsystem. The simulation results of a three-link manipulator in a cylindrical coordinate system show the effectiveness of the developed method.
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Application of GNSS-INS simulator for testing algorithms of the airborne vector gravimetry problem. Bogdanov Approved Laboratory of Control and Navigation of Lomonosov Moscow State University in cooperation with several Russian companies is involved into the project of GNSS-INS simulator elaboration. The first versio . . .n of the above-mentioned simulator deals with simulation of GNSS (GPS, Galileo, GLONASS) radio signals and was used for testing GNSS users navigation equipment (UNE). The idea of synchronous computer modeling of algorithms of strapdown inertial navigation system (INS) and GNSS radio signals simulation represents an evident development of simulator functional capabilities. GNSS-INS simulator represents a universal tool for testing and investigation of a wide range of navigation applications for land, marine, airborne and space vehicles in case when INS inertial sensors – angular rate sensors, accelerometers – can have different accuracy: from precise laser or FOG gyros to MEMS sensors.
There are two parts in the proposed report. In the first part the basic principles, models, algorithms used in the GNSS-INS simulator are briefly described. The second part of the report deals with the usage of the GNSS-INS simulator for investigation and testing algorithms of the airborne vector gravimetry problem. The issues are: modeling typical gravity survey trajectories; models of normal and anomalous gravity field, simulation of measurements of inertial sensors, integrated models for dead reckoning algorithms, algorithms of the gravity anomaly vector estimation. Some simulation results will be presented.
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Tracking problem for electromechanical system under influence of unknown unmatched perturbation Kochetkov Approved The theory of relay systems is widely used for design of electromechanical systems. In particular, modern electric drives are supplied by power electronic converters that have switching nature, and us . . .ing bang-bang control actions is most convenient from practical point of view. Also, the relay control algorithms can be used for synthesis of closed loop systems on the base of sliding mode. The main advantages of closed loop systems with sliding mode are:
In the case of unmatched perturbations, direct using of sliding mode theory does not provide an invariance property. Under assumption, that disturbances model is known, the control algorithms are developed with dynamical compensators and observers in the feedback. For arbitrary disturbances (unknown model) the block control algorithms with differentiators are used.
In this paper alternative approach (vortex algorithms) is proposed to provide asymptotical disturbances rejection. The main idea is to create nonlinear oscillation modes in the closed-loop system by applying bang-bang controls in the case of unmatched disturbances of a broad class. The properties of nonlinear oscillations are frequently employed in control theory, for example, in algorithm with second order sliding, which ensure that second order systems with matched disturbances converge in a finite time. At a physical level, the basic idea of this work is based on the vibrolinearization of relay characteristics by applying a high frequency signal to the relay input. It is well known, that the vibrolinearization coefficient of the relay increases unlimitedly with decreasing amplitude of the high-frequency signal. Based on this fact, damped eigenoscillations with respect to the output coordinate can be generated in the closed-loop system by applying a bang-bang control and, as a consequence, an infinitely large vibrolinearization coefficient can be obtained. As a result, the asymptotic invariance problem for output variables can be solved in the case of unmatched disturbances from a broad class. Note that the unlimited growth of the vibrolinearization coefficient is then caused not by applying an external high-frequency signal, but rather by damped high-frequency eigenoscillations in the closed-loop system. The efficiency of the proposed algorithm is demonstrated on DC motor control example.
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Estimation of Land Remote Sensing Satellites Operational Efficiency Kucherov Approved One of the most advanced approaches in spacecraft designing is based on regard for required efficiency indices.
As to land remote sensing satellites (LRSS), these indices are surveillance frequency, g . . .round resolution, swath
width, field of view width, operational efficiency, productivity, operating lifetime and some others.
One of the main indices crucial for LRSS efficiency is operational efficiency – an interval between the moment
of any object survey and the moment when the object picture may be send to the ground receiving center (GRC).
The last operation is possible when the satellite is within the radio coverage zone (RCZ) of the ground receiving
center.
Complex model for estimation of periodicity index includes:
– model for determination of a LRSS being inside the radio coverage zone of the GRC;
– model for plotting of the radio coverage zone boundary in cylindrical equal-­spaced projection;
– model for statistical estimation of operational efficiency index on the assumption of random coordinates of
survey objects.
The algorithm of operational efficiency estimation includes the next items.
1. The software, simulating the satellite operation is started. Computing time t is set equal to zero.
2. Computing time is incremented by the step of simulation d.
3. When a survey object falls within the LRSS field of view, this time point t1 is remembered.
4. When the LRSS enters the GRC radio coverage zone, this time point t2 is remembered.
5. The index of operational efficiency t0 is determined: t0=t2-t1.
6. Jump to item 2 is fulfilled, unless the calculation is stopped by the user.
7. Obtained data are treated for determination of the minimum, mean, and maximum values of operational efficiency
index, as well as its distribution law over all the period of the LRSS operating simulation.
The above algorithm was implemented in the software, developed in Delphi programming support environment.
Illustrating examples are cited.
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Arrangement of spacecraft onboard equipment with minimizing the influence of external factors Shulepov Approved We consider actual problems on protection of the spacecraft onboard equipment for decreasing influence of external environment. The problems are studied at design of spacecraft and a flight support of . . . its control system with respect to meteoric particles, electromagnetic radiation and other external factors. We have suggested constructive mathematical methods for increasing the spacecraft survivability during its long-term operation and present some results on the efficiency of the developed methods.
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Nonlinear research of an image motion stabilization system embedded in a space land-survey telescope Somov Approved Unique requirements are presented to an attitude control system of a large-scale maneuvering land-survey satellite on accuracy of its attitude motion stabilization at a scanning optoelectronic observa . . .tion. For solving of this problem we usually apply an astro-inertial satellite attitude determination system and a gyro moment cluster based on a redundant number of gyrodines. A radically different method is known for an image motion stabilization in space engineering for optoelectronic observation. This method is based on the use of an image motion compensator (IMC) embedded into the telescope optical scheme, moreover, variation of the IMC position causes a displacement of rays at the image formation.
In the paper we first study the image motion stabilization system embedded into the space telescope for scanning optoelectronic observation of terrestrial objects. Here the principal problems are (i) synthesis of the signal processing algorithms for an offset guiding by an image velocity in the center of the telescope focal plane and (ii) development of a structure and mathematical model of piezo-ceramic driver for precise displacements of the IMC. We have designed algorithms for discrete filtering of signal information and digital control laws for the piezo-ceramic driver taking into account a time delay. We have presented the numerical results on the efficiency of the image motion stabilization system embedded into a space telescope for a scanning optoelectronic land-survey.
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NONLINEAR MODELING OF AN AEROSPACE OBJECT DYNAMICS Davydov Approved We present the results on modeling of a complicated aerospace object system motion with consideration of nonlinearities. We have developed a computerized panel that allows to measure mutual influence . . .of the object motion and stabilization device with consideration of its real characteristics. Analysis of the system stability in general was carried out and the time relationships are presented for the system taking into account nonlinearities.
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Liquid oscillations in the tanks’ level sensors of aerospace objects Davydov Approved We have considered reasons on appearance of longitudinal oscillations in the system of fuel consumption control and the methods for reducing of these oscillations. Valuation of the most significant f . . .actors and them influence on accuracy of the system’s operation in general has been carried out. We have presented recommendations for installation of the system’s sensitive elements.
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A VLF-based technique for analysis and synthesis of nonlinear digital control systems and its applications Ul’yanov Approved In this paper, the development of a computational technology for rigorous analysis and design of nonlinear digital control systems on the basis of the reduction method and sublinear vector Lyapunov fu . . .nctions is given. The digital control system under consideration incorporates the continuous-time dynamics of the plant and the discrete-time dynamics of the controller, i.e. it is hybrid in nature. Unlike most known approaches to analysis of such systems, the proposed technique does not consider the preliminary reduction of the system to the discrete one, which allows us to eliminate the errors associated with discretization and improve the accuracy of the analysis. The technology is applied to the attitude control of a flexible spacecraft in the fine stabilization mode and to the formation control problem for a fleet of autonomous underwater vehicles. Simulation results are provided to demonstrate the performance of the designed control systems.
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Automation of Multi-Agent Control for Complex Dynamic Systems in Heterogeneous Computational Network Oparin Approved Currently, the organization of multi-agent control is one of the most actually problems in the field for research of complex dynamic systems. Within the framework of such control, system objects are p . . .resented by the specialized applications (agents), which interact with other objects based on their self-organization in the system control process. This problem becomes much more complicated when agents interact in a heterogeneous computational network and distributed computing is needed for forming control actions by these agents. Analysis of researches in this field shows that nowadays there are no all necessary methods and tools to solve this problem completely. In this regard there is a need to develop new models, methods, algorithms and tools for organizing multi-agent control in a heterogeneous computational network. These developments will provide the fundamentals and high-level tools for creating control systems in various subject areas. In this report the most important aspects for the automation technology of creating self-organizing multi-agent control system are considered. The special attention is paid to the information-logical scheme of a multi-agent control system, the simulation modeling system for analysis of a heterogeneous computational network, the network monitoring system and the algorithms that provide the reliability and effectiveness of control processes. Some features of the technology use are illustrated by the example of solving problems of an automated analysis and parametric synthesis of control systems for variety complex dynamic objects.
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On the problem of discrete-event systems properties preservation Nadezhda Approved We present a novel approach to solving a problem generally arising in studying dynamical systems, namely the problem of a system’s properties preservation under some transformation. For example, since . . . XIX century the problem of stability property preservation during coordinate transformations of differential equations systems is known: stability of the solution in one variables does not imply stability in other variables (A.M. Lyapunov, 1892). On the other hand, properties preservation is the important problem in studying algebraic systems. A number of statements of classical model theory, so called stability theorems, or characteristic theorems, determine a connection between semantic and syntactic properties of the formulas of the first order logic language. Combining algebra, logic and dynamics, the method of logical-algebraic equations (LAE-method) is developed, serving to synthesize criteria for preservation properties of systems connected by special type of morphisms.
The LAE-method is applicable to various systems, but we focus on the case of discrete-event systems (DESs), which are the systems that evolve in time due to the occurrence of some event sequences. The development of DESs theory is driven by the rapid progress of manufacturing systems and communication networks, technological processes, transportation networks, automated and robotic systems, and others, primarily man-made systems. We consider the issues of the LAE-method application to the reduction of supervisor for DESs, the problems of DESs basic properties, such as observability and controllability, preservation when sensor readings provide information about system’s state and it is available to a supervisor. Decentralized supervisory control is also addressed, in particular, the question whether local supervisors properties are inherited in a global supervisor.
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Total Abstracts: 20

M1: Functional Analysis and Related Topics with Applications

Abstract:
Functional Analysis and its interaction with PDE are increasingly important areas for mathematical modelling in various kinds of applications both to other fields of Mathematics and to other . . . sciences, e.g. physics, material science, numerical analysis, geophysics etc. The main aim of the symposium is to bring together researchers involved to share ideas, recognising the common thread in the recent developments in all aspects of these areas of mathematics and plan for future cooperation and new directions of joint research. As background the participants will present the “state of art” of their research fields. The topics of interest include (but are not limited to): Harmonic Analysis, Operators Theory, Function spaces, Inequalities, Real Analysis, Interpolation Theory, Homogenization Theory, PDE. Summing up, we invite all interested researchers in the areas described above to participate.
Organizers:
Lars-Erik Persson , LTU, Sweden, E-mail: Lars-Erik.Persson@ltu.se
Natasha Samko, LTU, Sweden, E-mail: nsamko@gmail.com
Alessandra Ragusa, UniCt, Italy. E-mail: maragusa@dmi.unict.it
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Title Author Status Abstract
The dual spaces of new lambda^m-sequence spaces and their matrix maps ERCAN Approved In this paper, we compute alpha-, beta- and gamma- duals of the new BK-spaces. We also give some classes of matrix transformations from these spaces to the spaces of convergent, null-convergent, bound . . .ed, almost convergent and almost null convergent.
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On spectral properties and invertibility of some operators of Mathematical Physics Rabinovich Approved The main aim of the talk is the Fredholm property,
essential spectrum, and invertibility of some operators of the Mathematical
Physics, such that the Schrödinger and Dirac operators with complex ele . . .c-
tric potentials, and the Maxwell operators in absorbing at infinity media.
This investigation is based on the limit operators method, and the uniqueness con-
tinuation property for the operators under consideration.
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On Weighted Sub-linear Operators in Generalized Morrey Spaces and their applications Samko Approved We prove point-wise estimates of Weighted Sub-linear Operators of a certain class via the sum of the non-weighted such operator, and a combination of Hardy and potential operators. By use of known res . . .ults for the operators in this sum, we obtain conditions on the boundedness of sub-linear operators in weighted generalized Morrey spaces for a class of radial weights.
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Homogenization and thin film flow Wall Approved Homogenization is the branch of mathematics where partial differential equations with rapidly oscillating coefficients are studied. We will discuss how homogenization can be used to model and analyze . . .the effects of surface roughness in lubrication between surfaces in sliding and/or rolling contact (as in bearings, gears or hip joints).
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A convexity approach to consider and prove Hardy type inequalities with sharp constants Persson Approved As background I fist give some remarkable details concerning the prehistory before Hardy discovered his famous inequality.
After that I will present a fairly new convexity approach to prove Hardy typ . . .e inequalities with sharp constants, which was not discovered by Hardy himself.
I will give some results which can be obtained by using this technique, results which can not be found e.g. in standard books on this subject
(see e.g. [2]-[4]). Especially, I will present some recent results I obtained jointly with S. Barza and N. Samko (see [1] and c.f. also [6]).
[1] S. Barza, L.E. Persson and N. Samko, Some new Hardy-type inequalities via convexity, J. Inequal. Appl. 2014:6, 10 pp.
[2] A. Kufner and L.E. Persson, Weighted Inequalities of Hardy Type, World Scientific publishing Co. Inc., river edge, NJ, 2003.
[3] A Kufner, L. Maligranda and L.E. Persson, The Hardy Inequality. About its History and Some related results, Vydavatelsky Servis publishing House, Pilsen, 2007.
[4] V. Kokilashvili, A. Meskhi and L.E. Persson, Weighted Norm Inequalities for Integral Transforms with Product Weights, Nova Scientific Publishers, Inc., New York, 2010
[5] L.E. Persson, Lecture Notes, Collège de France, Paris, November 2015.
[6] L.E. Persson and N. Samko, Classical and New Inequalities via Convexity and Interpolation, book manuscript, in preparation.
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On the boundedness of Hardy-type operators in Hölder-type spaces Lundberg Approved We present theorems on boundedness of Hardy type operator in Hölder type spaces in multidimensional case. We also discuss the Hölder spaces with compactification and present the corresponding theorems . . . on the boundedness of Hardy operators in such spaces.
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SIO in non-standard spaces Burtseva Approved We discuss Singular Integral Operators on closed contours in different function spaces.
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The concept of very weak multiscale convergence and some applications to homogenization of evolution problems Holmbom Approved We give a brief introduction to two-scale convergence and multiscale convergence. Then we define the notion of very weak multiscale convergence [1], [2] and demonstrate its applicability to various ev . . .olution problems of parabolic and hyperbolic type. Very weak multiscale convergence is particularly well suited to treat evolution problems with different combinations of rapid spatial and temporal scales.
[1] L. Flodén, A. Holmbom, M. Olsson, J. Persson; Very weak multiscale convergence. Appl. Math. Lett., 23 (10): 1170-1173 (2010).
[2] L. Flodén, A. Holmbom, M. Olsson, J. Persson; Homogenization of parabolic equations with an arbitrary number of scales in both space and time. J. Appl. Math., Vol. 2014 (2014).
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Several estimates for generalized fractional integrals on $\lambda$-$\mathrm{CMO}$ spaces Matsuoka Approved Rencetly, we generalized the modified fractional integrals
${\tilde{I}}_{\alpha}$, whicn modify the fractional integrals $I_{\alpha}$,
and showed the boundedness results of generalized fractional inte . . .grals
${\tilde{I}}_{\alpha,d}$ on the central Morrey spaces $B^{p,\lambda}$,
which extend the boundedness results of $I_{\alpha}$ and ${\tI}_{\alpha}$ on
$B^{p,\lambda}$, and moreover, $L^p$. In order to prove these boundedness
results, we introduced the generalized $\lambda$-central mean oscillation
($\lambda$-$\mathrm{CMO}$) spaces $\Lambda^{(d)}_{p,\lambda}$,
the generalized weak $\lambda$-$\CMO$ spaces $W\Lambda^{(d)}_{p,\lambda}$
and the generalized $\sigma$-Lipschitz spaces $\mathrm{Lip}^{(d)}_{\beta,\sigma}$.
In this paper, we will investigate several estimates of boundedness of
${\tilde{I}}_{\alpha,d}$ on the $\lambda$-$\mathrm{CMO}$ spaces $\mathrm{CMO}^{p,\lambda}$, which
extend the boundedness results on $B^{p,\lambda}$, and moreover, the
boundedness results of ${\tilde{I}}_{\alpha}$ on $\mathrm{CMO}^{p,\lambda}$ and $\mathrm{BMO}$.
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Homogenization of a mathematical model of thin film flow Tsandzana Approved We derive a mathematical model of thin film flow between two close rough
surfaces which are in relative motion. In particular, the model takes
cavitation, surface roughness and pressure dependent dens . . .ity into
account. For example such flows take place in different kinds of bearings
and gears when a lubricant is used to reduce friction and wear. For
some surface geometries shapes of the surfaces and boundary conditions
the pressure in the fluid will become so low that the continuous liquid
film ruptures and air bubbles are formed. This phenomenon is known
as cavitation and has a huge impact on the hydrodynamic performance.
A second effect which should be taken into account in the mathematical
modeling is that in many situations the pressure becomes so high that
the fluid density varies. The distance between the surfaces, $h$,
are in typical applications very small and therefore the roughness
of the surfaces can not be neglected. This leads to that $h$, which
appears as a coefficient in the governing differential equations,
will be a rapidly oscillating function. A direct numerical computation
is therefore very heavy, since an extremely dense mesh is needed to
resolve the oscillations due to the surface roughness. A natural approach
for analyzing such problems is to do some type of averaging. The mathematical theory which has
been developed to handle such problems is known as homogenization.
We use two-scale convergence to homogenize the model.
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Elliptic PDE, and SIO in non-standard spaces Burtseva Approved We discuss Singular Integral Operators and their commutators in some non-standard function spaces, and their applications to partial differential equations.
We also discuss Singular Integral Operator . . .s on closed contours in different function spaces.
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On a new space of defined by using Orlicz functions A. BEKTAŞ Approved In this paper, we introduce a new paranormed sequence space defined by a sequence of Orlicz functions over a seminormed sequence space. We investigated some properties of this space.
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Regularity of solutions to linear elliptic equations in Generalized Morrey Spaces Scapellato Approved The author shows some results obtained in cooperation with Maria Alessandra Ragusa. We prove regularity results, in some Generalized Morrey Spaces, for highest order derivatives of solutions of second . . .-order elliptic equations. We would like to extend some known local regularity results in the case that the coefficients of the principal part of the differential operator under consideration are discontinuous and the source term belongs to certain Generalized Morrey Spaces.
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Layer potentials on rough boundaries and fractals Guseynov Approved Oqtay Q. Azizov
Azerbaycan Technical Universitu Riyaziyyat kafedrası, Baku, Azerbaijan
Yevgeniy Guseynov
Policy Research and Analysis Department, PBGC, Washington, DC, USA
Layer potentials on rough bo . . .undaries and fractals
In layer potentials theory, the new surface integral introduced by the second author allows extend layer potentials properties to highly irregular boundaries. This surface integral was defined over boundary of open bounded sets in d-dimensional Euclidean space, d > 1 and a criterion based on geometry of boundary was provided that completely describes all boundaries where this integral exists for (d – 1)-differential forms from Holder classes. This integration process substantially extends class boundaries where surface integrals were previously defined for Holder classes and includes highly irregular surfaces like non-rectifiable Jordan curves, fractals, sets of finite perimeter boundaries and flat chains. Such surfaces could have the normal to boundary nowhere, and in the current presentation we define single and double layer potentials for continuous differential forms over a boundary of open bounded set that does not require a notion of boundary smoothness. Meanwhile, we show that for piecewise smooth boundaries the introduced layer potentials equal classical single and double layer potentials.
The properties of new layer potentials are studied in d-dimensional Euclidean space, d > 1 for Holder classes and for domains that satisfy the condition which was introduced to describe the boundary integral existence for Holder classes, particularly, we prove the Green’s identity and the Holder continuity of single and double layer potentials in the closure of domains. We use these layer potentials to construct “generalized” solutions to the Dirichlet and Neumann problems for Laplace’s equation in Holder classes and very rough domains.
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Perturbation methods for nonlinear elliptic problems Ragusa Approved
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Total Abstracts: 15

M6: Studies on Mathematical Methods and Models in Engineering, Sciences and Technology

Abstract: This special session is focused on the mathematical methods and models which need to be constructed by using the tools of mathematics. Generally, it is the most attraction to obtain the rea . . .sonable results by solving the unsolved problems placed in the different fields of engineering, sciences and technology. This special session is to give an opportunity for getting together with the colleagues, graduate and undergraduate students who are working on these special topics.
The proposed special session will seek to assemble the leading experts in the field to present the latest methods, compare them and discuss new avenues of research. The main goal of the special session would be to stimulate interesting new ideas for future research.
Authors are invited to submit original unpublished results which are not under review in any other conference or journal, to the peer review for publication and presentation. The special session covers the following topics areas but is not limited to:
• Improvement of analytical approaches and their applications in science and engineering problems
• Analytical or semi-analytical techniques for solving ordinary or partial differential equations
• Fractional ordinary and partial differential equations with applications
• Stability and convergence of numerical methods
• Numerical methods in engineering
• Mathematical modelling and analysis for lasers in nanoscience
• Analysis of models in sciences and engineering
• Computational techniques for applications in engineering, science, and other disciplines
• Computational Geometry and Topology
Organizers:
Prof. Dr. Necdet Bildik, Celal Bayar University, Faculty of Art & Sciences, Department of Mathematics, 45047, Manisa, Turkey, necdet.bildik@cbu.edu.tr
Ass. Prof. Dr. Duygu Dönmez Demir, Celal Bayar University, Faculty of Art & Sciences, Department of Mathematics, 45047, Manisa, Turkey, duygu.donmez@cbu.edu.tr
Ass. Prof. Dr. Yusuf Pandir, Bozok University, Faculty of Art & Sciences, Department of Mathematics, 66100, Yozgat, Turkey, yusufpandir@gmail.com
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Title Author Status Abstract
Applicability Extent of 2-D Heat Equation for Numerical Analysis of Multiphysics Problems Khawaja Approved This work focuses on thermal problems solvable using the Heat Equation. The fundamental question being answered here is what are the limits of the dimensions that will allow a 3-D thermal problem to b . . .e accurately modelled using a 2-D Heat Equation. The presented work solves 2-D and 3-D Heat Equations using Finite Difference Method also known as ‘Forward Time Central Space (FTCS)’ method in MATLAB®. For this study, a cuboidal shape domain with a square cross-section is assumed. The boundary conditions are set such that there is a constant temperature in its centre and outside its boundaries. The 2-D and 3-D Heat Equations are solved in time dimension to develop a steady state temperature profile. The method is tested for its stability using Courant Friedrichs Lewy (CFL) criteria. The results are compared in the space dimension not taken into consideration in 2-D solution. The maximum error is calculated and recommendations are given on the applicability of 2-D Heat Equation.
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New Complex and Hyperbolic Function Solutions to the Generalized Double Combined Sinh-Cosh-Gordon Equation Baskonus Approved In this study, we have applied the improved Bernoulli sub-equation function method to the generalized double
combined Sinh-Cosh-Gordon equation. This method gives new analytical solutions such as comp . . .lex and hyperbolic function
solutions to the problem considered in this paper. Then, we plot the three and two dimensional surfaces of analytical solutions by
using Wolfram Mathematica 9.
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Application of the Modified Exponential Function Method to the Cahn-Allen Equation Bulut Approved In this study, we have applied the modified exp (-Ω(ξ))-expansion function method to the Cahn-Allen equation. We have obtained some new analytical solutions such hyperbolic function solutions. Then, w . . .e have constructed the two and three dimensional surfaces for all analytical solutions obtained in this paper by using Wolfram Mathematica 9.
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Analytical Study of Sandwich Structures using Euler-Bernoulli Beam Equation Khawaja Approved This paper presents an analytical study of sandwich structures. In this study, Euler–Bernoulli beam equation is solved analytically for a four-point bending problem. Appropriate initial and boundary c . . .onditions are specified to enclose the problem. In addition, the balance coefficients are calculated and the rule of mixture is applied. The focus of this study to determine the effective material properties and geometric features such as the moment of inertia of a sandwich beam. The effective parameters help in the development of a generic analytical correlation for complex sandwich structures for the perspective of four-point bending calculations. The main outcomes of these analytical calculations are the lateral displacements and longitudinal stresses for each particular material in the sandwich structure.
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Dark Soliton Solutions of Klein-Gordon-Zakharov Equation in (1+2) Dimensions Bulut Approved This study base on dark soliton solutions of Klein-Gordon-Zakharov (KGZ) equation in (1+2) dimensions. The generalized Kudryashov method (GKM) which is one of the analytical methods has been handled f . . .or finding exact solutions of KGZ equation in (1+2) dimensions. By using this method, dark soliton solutions of this equation have been obtained. Also, by using Mathematica Release 9, some graphical simulations were done to see the behavior of these solutions.
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Modification of perturbation-iteration method to solve different types of nonlinear differential equations Bildik Approved Perturbation iteration method has been recently constructed by Pakdemirli and co-workers. It has been also proven that this technique is very effective and applicable for solving some nonlinear differ . . .ential equations. In this study we suggest a modification to expedite the solution process of perturbation-iteration algorithms. This work might greatly improve the computational efficiency of the perturbation iteration method and also its Mathematica package to solve nonlinear equations. Numerical illustrations are also given to show how modified method eliminates cumbersome computational work needed by perturbation iteration method.
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Determining Critical Load in the Multispan Beams with the Nonlinear Model Dönmez Demir Approved In this study, the buckling behaviors of beams are investigated. The general nonlineer mathematical of the beams are derived for multi support case. For some span numbers such as one, two and three, t . . .he nonlinear mathematical model is presented. To be able to obtain the independent of the material and the geometry, the presented model are became dimensionless. The analytical solution for fixed–fixed supported beam gives the critical axial load and bifurcation diagrams. Effect of the multisupport on the critical axial load is found. For this pusposes, the nonlinear models are analytically solved. It is found that the support number and support location have an effect on the critical axial load. Since the engineering practice of this kind of problems is very common, determining the critical load is quite important.
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Rationality of Large Mass Method for Frequency Response Analysis Mehmood Approved Most of previous work on Large Mass (LM) Method by Kim Y.-W. and Jhung, M. J.for dynamic problems is related to the study of transient responses. This paper discusses the numerical effectiveness of La . . .rge Mass Method for frequency response problems in truss structures. The results achieved are of great importance for design of launch vehicle structures which must be capable of withstanding a wide range of frequencies for smooth operation of sensors. The paper also presents a very simple technique for developing an LM analysis model through programming language e.g. MATLAB.
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Properties of Soft Homotopy in Digital Images Öztunç Approved In this paper first of all it is aimed to define the soft continuity in digital images. Also soft homeomorphism and soft homotopy in digital images is defined by determining soft continuity in digital . . . images. Then some results of soft set theory dealing with soft continuity and soft homotopy in digital images is obtained. In addition to this, we give new examples of soft continuity in digital images and soft homotopy in digital images. Since this paper contains important examples and results, it becomes a usuful tool for mathematicians especially working in digital topology.
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Numerical simulations to the nonlinear model of interpersonal Relationships with time fractional derivative Gencoglu Approved The main aim of this manuscript is to obtain numerical solutions for the nonlinear model of interpersonal relationships with time fractional derivative. The variational iteration method is theoretical . . .ly implemented and numerically conducted only to yield the desired solutions. Numerical simulations of desired solutions are plotted by using Wolfram Mathematica 9.
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Applications of Optimal Perturbation Iteration Method for solving Nonlinear Differential Equations Deniz Approved Perturbation iteration method has been recently constructed and it has been also proven that this technique is very effective and applicable for solving some nonlinear differential equations. In this . . .study, we develop the new optimal perturbation iteration method based on the perturbation iteration algorithms for the approximate solutions of nonlinear differential equations of many types. This work might greatly improve the computational efficiency of the perturbation iteration method. Applications also show that only a few terms are required to get an approximate solution which is more accurate and efficient than many other methods in literature.
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Nonlinear Stability and Optimization Techniques: Modeling, Analysis and Computational Methods Cave Approved Nonlinear stability and optimization techniques are modified and briefly outlined in terms of their inherent relationships with one another. This is done by making use of the interrelationships among . . . modeling, analysis and computational methodologies. Then modification of existing methods in aerospace, land and marine vehicles,engineering, physical sciences and biotechnology are used to illustrate the techniques.The specific areas considered are Variational Principle Modeling, Control, Estimation, Energy and Power Requirements,Computational Methods directly derivable from formal solutions, Langevin Enhancements in molecular modeling, Variational Principles in Error Analysis, and Standard Error Analysis Approach of previously enhanced endo and exoatmospheric techniques.
ALL RIGHTS RESERVED.
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A general method for the study of systems of rigid bodies interconnected with the aid of elastic links and the rod Mizhidon Approved As far as investigations of mechanical vibrations of elements of different constructions, parts and mechanisms are concerned, the computational schemes to be investigated are in many cases represented . . . by rigid bodies (or systems of rigid bodies) interconnected with the aid of elastic links and the rod. Application of the Hamilton variation principle for constructing such systems necessitates consideration of hybrid systems of differential equations. A hybrid system of differential equations is understood as a system of differential equations composed of ordinary differential equations and partial differential equations. The report discusses a generalized mathematical model of a system of rigid bodies mounted on the Euler-Bernoulli beam in the form of a hybrid system of differential equations of a given structure, on whose basis a universal method of investigation of the natural oscillations for a given class of mechanical systems is developed. Note the issues of investigation of the natural oscillations for a given class of mechanical systems under certain specific types of typical computational schemes can be found in a sufficient number of publications, for example in the journal “Sound and Vibration”. In all these publications special analytical and numerical-analytical methods are developed or method of finite elements is used. Unfortunately, the majority of the mathematical models of the typical computational schemes are the case models elaborated for particular case studies. Meanwhile, the natural vibrations of mechanical systems considered in these papers, you can explore on the basis of a generalized mathematical model with universal analytical-numerical method proposed in the report.
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Solutions of Young-Laplace equation for capillary bridges and stability analysis Millet Approved We revisit from an inverse problem method the exact resolution of the Young-Laplace equation
for capillary doublets. The missing information on the pressure deficiency (which is often an
unknown of th . . .e problem) will be restored without experimental device of suction control.
We establish a simple criterion based on the observation of the contact point, of the wetting angle
and the gorge radius, to classify in an exhaustive way the nature of the surface of revolution:
portion of nodoid, of unduloid, both with concave or convex meridian, of catenoid, of cylinder
or of circular profiles (toroid). In every case, we propose an exact parametric representation of
the meridian based on the observed geometry of the boundary conditions and on a first integral of
Young-Laplace equation that traduces a conservation energy principle. Moreover, we prove that
the inter-particle force my be evaluated on any section of the capillary bridge and constitutes a
kind of specific invariant for surfaces of revolution. The proposed method leads to very
convenient analytical expressions easy to use.
The pertinence of the addressed approach will be put in a prominent position on several experimental
results obtained on various geometries of capillary bridges. Moreover, the stability of
solutions of Young-Laplace equations will be analyzed, based on the second variation criterion of
the associated potential (minimization problem under constraints), revisited through Vogel’s stability
criteria. A theoretical stability criterion and conjectures on breakage will be proposed and
discussed.
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THE PREDICTION OF BRICK WALL STRENGTHS WITH ARTIFICIAL NEURAL NETWORKS MODEL Demir Approved The aim of this study is to predict with Artificial Neural Networks (ANN) compressive and shear strengths of brick walls plastered with specific stuccos. It is very difficult to determine strengths of . . . brick walls with experimental procedures. Therefore, an Artificial Neural Networks model was developed with data obtained by investigating many papers from literature and experiments carried out by authors. Finally, a good degree of coherency was obtained between the experimental and predicted data. The model that was developed makes it possible to easily predict the compressive and shear strengths of the brick walls. Additionally, this model can be continuously trained with new data and its practicability range can easily be extended.
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A new version of the generalized F-expansion method and its applications Pandir Approved In this study, a new version of the generalized F-expansion method is suggested to search exact solutions of nonlinear partial differential equations. We find many new and interesting results for Kort . . .eweg-de Vries(KdV) equation by use of the proposed method. The solutions acquired from the proposed method are single and combined non-degenerate Jacobi elliptic function solutions. The new method allows a more systematic, easiness use of the solution process of nonlinear equations.
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Extended (G’/G)-Expansion Method for non lineer partial equations Tuz Approved In this study, we present a new version of (G’/G)- expansion method by using extended (G’/G)-expansion method which is suggested in [1]. By this method, we find traveling wave solutions of Burgers, . . . KdV and Hirota-Satsuma equations.
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Numerical modelling and experimentation of curtain containing floating oil pollution in harbor MUTTIN Approved Numerical modelling and experimentation of curtain containing floating oil pollution in harbor
Frédéric MUTTIN*, Abdellatif OUANSAFI**, Youssef BENELMOSTAFA**
*EIGSI La Rochelle and ** EIGSICA Casabla . . .nca
Marine water pollution is a most challenging problem for coastal environment.
Apart from the large oil spills many smaller incidents happen in many ports which generate loss of time, money and polluted waste.
The main challenges faced by port authorities are the optimization of the deployment of resources, both in men power and technical barriers to limit the pollution extent,
according to local and real time parameters value such as hydrodynamic, meteorological and tidal conditions.
Our research works aim to provide those managers decision aid tools to accelerate the implementation of the best adequate technical and preorganization solutions.
Models of flexible barriers have been developed using a thin shell membrane finite-element in large displacements and small strains.
The flexible barrier named curtain dedicated to calm water is composed of set of a rigid tube and a submersible skirt.
The boundary condition applied to the tube/skirt junction is a rigid condition on the sea-surface.
The boundary condition applied to the barrier extremity is rigid displacement.
The hydrodynamic pressure on the curtain skirt results from the sea current velocity and it is assumed as a uniform pressure on the vertical.
These models have been implemented in simulation software and experimented in real life situation in the fishing port of La Rochelle located in the Chef de Baie district.
Every year this harbor faces small pollution incident involving floating oil and uses barrier to contain the pollutant fluid.
A real case exercise has been simulated and experimented on the basis of a triangular barrier deployment.
The rigid boundary condition is applied at each corner of the triangle. The hydrodynamic pressure is limited to the drifting water surface resulting from the South and South-East wind direction.
Wave and current motion are supposed negligible where and when the exercise has been performed: the fuelling pontoon and a small tide amplitude.
A comparison is given between the experiment results (in the port with real barrier) and the numerical computations showing major issues in term of mathematical modelling and pollution containment.
From the numerical point of view the limit to zero of the mechanical forcing will result in a steady sate of the barrier,
while the experiment shows that an infinite number of positions are possible with rigid motion displacement of the barrier.
From the operational point of view the main findings concern the necessary numerical prediction of the wave and marine current motion and the atmospheric state to assure a safe barrier deployment.
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Total Abstracts: 18

Keynote talks of ICNPAA 2016:

Prof. Jan AWREJCEWICZ, Technical University of Lódz, Poland
Title: Novel non-linear phenomena exhibited by interacting structural members

Prof. Stefan BALINT, West University of Timisoara, Romania
Title: Space-Time Evolution of the Perturbations of a Spatially Developing Constant Gas Flow

Prof. José Manoel BALTHAZAR, ITA-Aeronautics Technological Institute, Mechanical-Aeronautics Division, Brazil
Title:A tour of nonlinear dynamic analysis of a flexible slewing structures, excited by non-ideal sources (nis),using sma actuators and including parameter sensibility analysis


Dr. Itzhak BARKANA, Barkana Consulting, 11 Hashomer St., Ramat Hasharon, Israel
Title: Can Stability Analysis be really simplified? (Revisiting Lyapunov, Barbalat, LaSalle and all that)


Prof Francesco Dell'isola, University of Rome, Italy
Title: “TBA”

Prof. Metin DEMIRALP, Istanbul Technical University, Turkey
Title: Enhanced multivariance products representation (empr) from scratch to its most recent status

Prof Marc Garbey, University of Houston, USA
Title: “TBA”

Prof. Rudolf HILFER, Institut für Computerphysik, Universität Stuttgart, Germany
Title: ""Experimental implications of Bochner-Levy-Riesz diffusion""

Prof. Harry H. HILTON, University of Illinois at Urbana-Champaign, USA
Title: The influence of time dependent flight and maneuver velocities and elastic or viscoelastic flexibilities on aerodynamic and stability derivatives

Prof Naira Hovakimyan, University of Illinois at Urbana-Champaign, USA
Title: “Cooperative Control of UAVs”

Prof. Gangaram S. LADDE, University of South Florida, USA
Title: "TBA"

Prof Irena Lasiecka, The University of Memphis, USA
Title: “How to control flutter arising in flow structure interactions”

Dr. Jiro NAKAMICHI, Japan Aerospace Exploration Agency (JAXA), Japan
Title: Some Considerations on Prandtl Lifting-Line Theory

Prof. Ruggero Maria Santilli, Thunder Energies Corporation , USA
Title: outline of the new era in mathematics and its applications

Prof Sergei Silvestrov, Mälardalen University, Sweden
Title: "Engineering Mathematics for big data networks and computational electromagnetics. ”

Dr. Toshiya Nakamura, Japan Aerospace Exploration Agency (JAXA), Japan
Title: Operational Loads Identification for Aerospace Structures

Prof.Takeshi Tsuchiya, University of Tokyo, Japan
Title: Research on Advanced Flight Control System Using UAV

Prof..Aghalaya Vatsala, Lousiana State University, USA
Title: Riemann Liouville Dynamic systems versus sequential Caputo dynamic systems with applications

Prof. S.N. VASSILYEV, Trapeznikov Insitute of Control Sciences of RAS, Moscow, Russia
Title: Differential equations, Invariants and Qualitative Properties of Solutions

General Sessions

General Sessions
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Title Author Status Abstract
Optimization of Wall Thickness and Lay-Up for the Shell-Like Composite Structure Loaded by Non-Uniform Pressure Field Shevtsov Approved S. Shevtsov1,2,a), I. Zhilyaev1,2,b), P. Oganesyan2,c), I, Tarasov3,d, V. Axenov4,5,e)
1 South Center of Russian Academy, 344006, Tchekhov str., 41, Rostov on Don, Russia
2 Southern Federal University . . ., 344090, Milchakov str., 8A, Rostov on Don, Russia
3 AP Group “Carbon Studio”, 192236, Saint-Petersburg, Sophiiskaya, 8/1
4 Mil Moscow Helicopter Plant, Rostov Branch, 344038, Novatorov str., 5, Rostov on Don, Russia
5 Don State Technical University, 344000, Gagarin sq., 1, Rostov on Don, Russia
a) Corresponding author: sergnshevtsov@gmail.com
b) zhilyaev@mail.com
c) gwolwer1ne@gmail.com
d) ilya.tarasov@carbonstudio.ru
e) vnaxenov@mail.ru
Abstract. The glass/carbon fiber composites are widely used in the design of such aircraft and rotorcraft components such as wing-body fairings, engine pylon fairings, engine and radar cowlings due to increased specific and fatigue strength or stiffness, better weight saving of composite materials that are sufficiently exceed the same properties of metallic light weight alloys. All these components made of quasi-isotropic laminates have predominantly a shell-like geometry. The term quasi-isotropic means that such laminates have different properties in the out-of-plane direction. In order to achieve these quasi-isotropic properties of laminates need to adopt a lay-up having an equal number of plies oriented parallel to the sides of an equilateral triangle. For example, a quasi-isotropic 24-ply laminate could be made with 8 plies oriented at each of 0 °, + 60 °, and – 60 °, or by use equal numbers of plies oriented at 0 °, +45 °, -45 °, and 90 ° [1].
The main requirements to such the composite parts are the specified mechanical stiffness to withstand the non-uniform air pressure at the different flight conditions and reduce a level of noise caused by the airflow-induced vibrations at the constrained weight of the part. The main objective of present study is the optimization of wall thickness and lay-up of composite shell-like cowling, which is installed on a helicopter airframe. In order to attain the purpose of this problem we first convert the CAD model of the cowling to finite element (FE) representation of its external surface assumed as stiff shell, and air blasting in a wind tunnel of this shell was simulated at the different orientation of airflow to find the most stressed mode of flight. This problem was solved numerically using Navier-Stokes equations averaged by Reynolds technique and supplemented by k-w turbulence model. The results of the FE model transient analysis were the spatial distributions of air pressure applied to the shell surface.
The maximum of strain energy calculated within the optimized shell was assumed as the objective. Thickness distribution of the shell had to change over its surface to minimize the objective at the constrained weight. Our attempts to use known topology optimization methods (SIMP, ESO, BESO), which were “softened” to eliminate the emergence of void areas, were unsuccessful due to low numerical stability, and due to delivery the “stillborn” structures. We proposed the simple parameterization of the problem, which assumed an initiation of auxiliary sphere with varied radius and coordinates of the center, which all four parameters were the design variables. Curve that formed by the intersection of the shell with sphere defined boundary of area, which should be reinforced by local thickening the shell walls. To eliminate a local stress concentration this increment was defined as the smooth function defined on the shell surface. As a result of structural optimization we obtained the thickness of shell’s wall distribution, which then was used to design the scanning and lay-up of composite prepreg layers. The maximum strain energy in the optimized cowling was reduced by 27% at the weight growth up to 15%, whereas the eigenfrequencies at the 6 first natural vibration modes have been increased by 5-15%.
The present approach and developed programming tools that demonstrated a good efficiency and stability at the acceptable computational costs can be used to optimize a fairly wide range of shell-like structures made of quasy-isotropic composites.
[1] A. Baker, S. Dutton, D. Kelly, Composite Materials for Aircraft Structures. Reston, Virginia: AIAA ltd., 2004, pp. 597.
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Nasedkin A.V. Models and finite element approximations for interacting nanosized piezoelectric bodies and acoustic medium Nasedkin Approved This research presents the new size-dependent models of piezoelectric materials oriented to finite element applications. The proposed models include the facilities of taking into account different mec . . .hanisms of damping for mechanical and electric fields. The coupled models also incorporate the equations of the theory of acoustics for viscous fluids. In particular cases, these models permit to use the mode superposition method with full separation of the finite element systems into independent equations for the independent modes for transient and harmonic problems.
The main boundary conditions were supplemented with the facilities of taking into account the surface effects, allowing to explore the nanoscale piezoelectric materials in the framework of theories of continuous media with surface stresses and their generalizations. We have paid special attention to the boundary conditions for the piezoelectric bodies with surface effects, interacting with the acoustic medium.
For all the problems we have implemented the finite element technologies based on the generalized statements. Here we have used various numerical algorithms to maintain a symmetrical structure of the finite element quasi-definite matrices (matrix structure for the problems with a saddle point) for modal, harmonic and transient problems, as well as the algorithms of the mode superposition methods.
To increase the accuracy of calculations, especially for nanoscale and nonlinear problems, we have provided the ability of automatic transfer to the dimensionless problem statements.
Analysis of the well-known finite element software shows that the proposed models and technologies significantly increase the facilities for analyzing complex active materials and provide the methods of solving new problems with coupled physico-mechanical fields, including the problems for nanoscale and composite bodies.
This work was supported by the Russian Science Foundation (grant number 15-19-10008).
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Second Law considerations for Fourier Heat Conduction in relation to intermolecular potentials Jesudason Approved %the form I am submitting a latex document
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\titulo{ Second Law considerations for Fourier Heat Conduction in relation to intermolecular potentials}
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%\autores{Gabriel Aguilera, Jos\’e Luis Gal\’an, Pedro Rodr\'{\i}guez \\ %
% University of M\’alaga (Spain) \\ \\ % Affiliation 1
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Benofy and Quay (BQ)\cite[p.11]{bq} have claimed that the Fourier law is essentially local in nature whenever a temperature gradient is present whereas the second law statements of Kelvin and Clausius are global, so that with compensation, there can be transfer of heat from cold to hot. Recently, on the other hand, it was demonstrated \cite{cgj1} from simulation of heat conduction of a lattice chain with an anharmonic interparticle potential that one can model the process as one that conforms to a zero entropy trajectory, where there is movement of energy from hot to cold, in agreement with the Clausius statement of the Second law, where we envisage the processes between the reservoirs and the lattice to be in the limit cyclical. It was inferred also \cite{cgj1} , that heat energy as defined in thermodynamics was equivalent to the energy conveyed by Fourier conduction. Fourier, in his development \cite[as cited by BQ in their p.9 , pp. 41-45 of Fourier’s Dover reprint]{bq} claimed that heat flow cannot occur when no temperature gradient exists, and furthermore, heat can only flow from a hotter to a colder region in heat conduction. Using the anharmonic potential \cite{cgj1} seems to verify this claim. On the other hand, the seminal work by Lebowitz et al. \cite{lebo1} created a model of heat conduction for the case of a purely harmonic potential $\frac{\mathbf{q}^2}{2}$ ($\mathbf{q}$ is the coordinate vector of the equilibrium position) where the temperature profile $T(j,\nu)=T[1-\eta \nu (\varphi_1)^{2j-1}], \,\,1 < j < \frac{1}{2}N, \,T(j,\nu)=T[1+\eta \nu (\varphi_1)^{2j^\prime-1}], \,\,1 < j^\prime = N-j < \frac{1}{2}N$, where $\eta, \nu$ and $\varphi_1$ may be considered to be small parameters ($|\eta|\leq 1 $) about a mean temperature T . The mean profile shows a slight gradient that does not correspond to the Fourier law: in particular the gradients seem to be contrary to Fourier's claims; it is explicitly stated that the hot thermal reservoir on the left hand side of Fig 1 (\cite{lebo1} has a temperature profile that dips below the mean temperature $T$ whilst conducting heat to the colder reservoir on the right hand side. This contradicts the BQ and Fourier assumption at least, and perhaps the Clausius assumption of the Second law. Although many simulations seemed to have verified the profile of Fig. 1, we find that depending on the thermostats used and the accuracy of the MD algorithm, different chaotic profiles can be generated, where no clear gradients seem to obtain, even if close to zero. We will explore the pathological outcomes of using a harmonic potential for various thermodynamical systems relative to different MD algorithms and temperature conditions, and suggest whether violations to the standard statements of the thermodyanamical laws are implied. The possible consequences of such violations will be discussed. \end{abstract} % Write down at least 3 Keywords % \section{Introduction} %%\bibliographystyle{model1a-num-names} \bibliographystyle{unsrt} % or "unsrt", "alpha", "abbrv", etc. %%\bibliography{mpbib} %%\bibliography{mpbib} %\begin{thebibliography}{100} % 100 is a random guess of the total number of %references \begin{thebibliography}{100} \bibitem{bq} S.~J. Benofy and P.~M. \mbox{Quay, S.J.} \newblock Fourier inequality as a principle of thermodynamics, with applications to magnetothermoelectric effects. \newblock In L.~Tisza, A.~Shimony, and H.~Feshbach, editors, {\em Physics as natural philosophy : essays in honor of Laszlo Tisza on his seventy-fifth birthday}, pages 7--24. M.I.T. Press, 1982. \bibitem{cgj1} C.~G. Jesudason. \newblock One-Particle Representation of Heat Conduction Described within the Scope of the Second Law. PLoS ONE 11(1): e0145026. doi:10.1371/journal.pone.0145026, 2016. \bibitem{lebo1} Rieder Z, Lebowitz JL and Lieb E. C.~G. Jesudason. \newblock Properties of a Harmonic crystal in a stationary Nonequilibrium State \newblock J Math Phys. 8(5):1073–1078. doi: 10.1063/1.1705319, 1967 \end{thebibliography} %%%%%%%%%%%%% end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \end{document}
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Atmospheric Icinig Intensity on Slowly Rotating Hexagonal Prism and Cylinder with Fins Mughal Approved Atmospheric ice accretion intensities on constantly slowly rotating hexagonal prism with six fins and constantly slowly rotating cylinder with four fins were studied using experimental and mathematica . . .l analysis. The experimental intensities were compared with the existing ice accretion intensity models of Makkonen. Based upon this study a forced rotation constant and generalized windward area ratio is proposed to be added in the existing intensity models, in order to validate the experimental observations.
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Total Abstracts: 4

Tutorial session on Monday July 4th, a full day 9AM-5PM


The Beauty of Simple Adaptive Control and Old and New results in Stability Analysis of Nonlinear Systems

Intructors: Itzhak Barkana. Haim Weiss, Ilan Rusnak
Keywords: Control, Adaptive Control, Positive Realness and Passivity, Lyapunov methods; Barbalat’s Lemma, LaSalle’s Invariance Principle, New Theorem of Stability
Abstract Simple Adaptive Control (SAC) techniques have initially been conceived because of the need for adaptive control methods in large-scale systems, where the use of models and controllers of the order of the plant was naturally excluded. While initially SAC was considered (even by its own developers) to be just a modest version of the standard MRAC, the workshop shows that it was only before appropriate mathematical tools of analysis (that could reveal its real potential yet were missing at the time) had been developed. Further developments showed that they can easily be applied to such applications as robots, planes, missiles, satellites, fine motion control, etc. The talk explains how various drawbacks related to the classical Model Reference Adaptive Control (MRAC) methodology have been addressed and eliminated. To this end, it will be shown that the conditions needed for robust stability have been significantly mitigated. Recent developments in nonlinear systems stability analysis tools lead to clear proofs of SAC stability in real-world application and realistic environments. Previously unstable “counterexamples” to MRAC are revisited and shown to be just simple, successful, and stable applications of SAC. Realistic examples from various domains of flight control, guidance and aerospace are also used to show that indeed SAC is the Stable Direct MRAC methodology. A non-minimum-phase and unstable UAV will be used as a detailed case-study to illustrates show the simplicity of implementation of SAC as an Add-On to classical control design towards improving performance beyond anything that could be obtained otherwise.
To this end, although Lyapunov stability theory is the customary basis of any modern stability analysis, its direct application requires fitting to the system a Positive Definite function whose derivative ”along all trajectories of the system” is Negative Definite. If this is the case, it is easy to see that both the Lyapunov function and its derivative ultimately vanish and therefore, one can reach the desired conclusion of asymptotic stability. However, because in most non-trivial problems the derivative is at most Negative Semi-Definite, various extensions to the basic Lyapunov stability theory have been sought. Because early extensions of Lyapunov stability theory were only covering autonomous systems of the form , various alternatives were sought for nonautonomous systems of the form . In particular, a successful alternative has been provided by Barbalat Lemma that under some conditions allowed concluding that the Lyapunov derivative ultimately vanishes and therefore, as many examples illustrated, asymptotic stability conclusions could be drawn. Texts on Nonlinear Control gave various formulations intending to mitigate prior conditions that would facilitate application of Barbalat Lemma to stability analysis. However, Barbalat Lemma that deals with function theory and not necessarily with theory of systems stability imposes conditions of uniform continuity of functions and even continuity of derivatives that again could limit its applicability. Besides, even when applicable, it only ends with partial results. As even recent publications illustrate, although extensions of LaSalle's Invariance Principle to nonautonomous systems have been available at least since 1976, they have remained surprisingly unknown for large circles of the nonlinear control community. Moreover, even if assumably known, misinterpretations of its larger mathematical scope (that covers much more than mere asymptotic stability) may have misled the prospective users with respect to its usefulness. It is hoped that the review of LaSalle’s Invariance Principle along with a new extended Invariance Principles and the comparative parallel presentation of various alternatives to stability analysis may help showing the extreme efficiency of the new Theorems of Stability to nonlinear systems stability analysis.
Outline Review of need for adaptation Life is with uncertainty: need various gains for various situation, either change in nominal parameters or various operational conditions Nonstationary gains: right gains at right times. Good idea, yet… must be careful. Example: The danger of “safe” fixed control in nonstationary environments Model Reference Adaptive Control (MRAC) First Adaptive Control ideas: ingenious and failure Basic MRAC: First rigorous proofs, problematic SPR conditions “Classical” MRAC: Stability in ideal situations , problems otherwise:- Persistent excitation - Bursting, etc. - Unmodeled dynamics Simple Adaptive Control (SAC) From MRAC towards Simple Adaptive Control (SAC) - Can Adaptive Control use and extend ideas from Optimization to the world of uncertainty? The Simple Adaptive Control (SAC)-Minimum Phase and conditions on CB-Claim and Proof: Same conditions that allow LTI design also guarantee stability with SAC. Advantage: the guarantee of stability allows reaching superior performance.-Nonstationary and Nonlinear systems-On Robustness
and Perfect Tracking -Robustness with Noise -Discrete-time systems -Continuous mitigation of stability conditions -Gentle introduction of Stability conditions in Engineering terms Brief review of stability analysis for nonlinear systems. Lyapunov stability approach: examples and limitations Simple example and LTI example First extensions: Krasovskii and LaSalle, The Invariance Principle for Autonomous systems only First extension for Nonautonomous systems: Barbalat’s Lemma: the apparent need for uniform continuity (and the implied ‘threat” of discontinuity). Further extensions: (The real and ignored) LaSalle’s Invariance Principle for Nonautonomous systems The new Invariance Principle The new Theorem of Stability: simple and safe tool for proofs of stability Example problems Application of SAC Approach Unstable MRAC “counterexamples” become simple examples for SAC Explicit design case: Combining Classical LTI design and SAC guarantee stability and lead to superior performance for Non-minimum Phase UAV. Missile Flexible structures: new developments relax the need for collocation Example Problems Advanced issues (time permitting): gain convergence, participants proposed examples

RECOMENDED REFERENCES
1) H. Kaufman, I. Barkana, K. Sobel: Direct Adaptive Control Algorithms, Springer 1998 (2nd edition)
2) I. Barkana: "Parallel Feedforward and Simplified Adaptive Control," International Journal of Adaptive Control and Signal Processing, Vol. 1, No. 2, pp. 95-109, 1987.
3) I. Barkana: "Classical and Simple Adaptive Control Design for a Non-Minimum Phase Autopilot," AIAA Journal of Guidance, Control and Dynamics, Vol. 28, No. 4, pp. 631-638, 2005.
4) I. Barkana: “Extensions on Adaptive Model Tracking with Mitigated Passivity Conditions,” Chinese Journal of Aeronautics, Vol. 26, No. 1, 2013, pp. 136-150.
5) I. Barkana: “Simple Adaptive Control - A Stable Direct Model Reference Adaptive Control Methodology- Brief Survey,” International Journal of Adaptive Control and Signal Processing, Vol. 28, No. 7-8, pp. 567-603, July 2014, (Published On-Line 17 June 2013) DOI: 10.1002/acs.2411.
6) I. Barkana: “Robustness and Perfect Tracking in Simple Adaptive Control,” International Journal of Adaptive Control and Signal Processing, Published On-Line in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/acs.2411.
7) I. Barkana: “Parallel Feedforward and Simple Adaptive Control of Flexible Structures: First order-pole instead of collocated velocity sensors?,” ASCE’s Journal of Aerospace Engineering (Published On-Line). DOI: 10.1061/(ASCE)AS.1943-5525.0000538.
8) LaSalle JP: “Stability of Nonautonomous systems,” Nonlinear Analysis, Theory, Methods and Applications 1976; 1(1): 83–90.
7) LaSalle JP. The Stability of Dynamical Systems, 2nd ed. SIAM: New York, 1976.
9) Z. Artstein: “Limiting equations and stability of nonautonomous ordinary differential equations,” Appendix A in: LaSalle, The Stability of Dynamical Systems, 2nd ed., SIAM, New York, 1976.
10) Z. Artstein: "Uniform asymptotic stability via the limiting equations," J. Differential Equations, vol. 25, pp. 184–202, 1977.
11) Z. Artstein: "Uniform asymptotic stability via the limiting equations," J. Differential Equations, vol. 27, pp. 172â˘A ¸ S-189, 1978.
12) I. Barkana: “Defending the Beauty of the Invariance Principle," International Journal of Control, Vol. 87, No. 1, pp. 186-206, 2014.
13) Ilan Rusnak, Haim Weiss and Itzhak Barkana: “Improving the Performance of Existing Missile Autopilot using Simple Adaptive Control,” International Journal of Adaptive Control and Signal Processing, Vol. 28, No. 7-8, pp. 732-759, July 2014. DOI: 10.1002/acs.2457.
14) Ulrich, S., and Sasiadek, J. Z., “Decentralized Simple Adaptive Control for Nonlinear Systems,” International Journal of Adaptive Control and Signal Processing, Vol. 28, No. 7-8, pp. 750-763, 2014. doi:10.1002/acs.2446
15) I. Barkana: The new Theorem of Stability – Direct Extension of Lyapunov Theorem. Mathematics in Engineering, Science and Aerospace (MESA), Vol. 6, no. 3, pp. 519-535, 2015.
16) I. Barkana: The Beauty of Simple Adaptive Control and New Results in Stability Analysis of Nonlinear Systems. ICNPAA 2014.
17) I. Barkana: “Parallel Feedforward and Simple Adaptive Control of Flexible Structures: First order-pole instead of collocated velocity sensors?” ASCE’s Journal of Aerospace Engineering (Published On-Line) DOI: 10.1061/(ASCE)AS.1943-5525.0000538.
18) I. Barkana: “Robustness and Perfect Tracking in Simple Adaptive Control,” International Journal of Adaptive Control and Signal Processing (2015). Published online in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/acs.2573).
19) I. Barkana: Barbalat’s Lemma and Stability - Misuse of a correct mathematical result? BARKANA Consulting Technical Report, 2015.

  Lecturers: Itzhak Barkana Itzhak Barkana received his B.Sc. and M.Sc. degrees in electrical engineering from Technion—Israel Institute of Technology and his PhD degree in 1983 from Rensselaer Polytechnic Institute (RPI). He presently is a Consulting for high-tech industry, after retiring from his job as a Fellow with Kulicke and Soffa Industries, Inc., Fort Washington, PA, USA. In this job he had been an internal technical consultant and authority for all problems related to systems and controls of fine machines motion control, design of optimal trajectories of motion, system analysis for both power consumption and performance. Between 1988 and 2000 has also been Visiting and Adjunct Professor with Drexel University in Philadelphia. Has developed self-tuning algorithms and specialized feedback and feedforward control techniques that had pushed forward and permanently maintained the K&S bonding machines as the fastest and the most precise in the world. Has been a leading developer of the Simple Adaptive Control (SAC) methodology and has developed the fine theoretical points needed to guarantee robust stability of the adaptive control systems. Has defined and clarified the underlying theoretical “almost strictly positive real (ASPR)” and “almost strict passivity (ASP)” conditions needed for stable adaptation and has invented the so called “Parallel Feedforward Configuration (PFC) that has become the main tool that allows implementation of Adaptive Control in real-world systems. Has continued to develop the theory related to implications of adaptive control techniques, including extensions and modified versions of the LaSalle’s Invariance Principle, with new and valuable implications for the guarantee of stability of adaptive controllers and of general nonlinear systems in practical applications.
In 2002 has received the Benjamin Franklin Key Award from Philadelphia Chapter of IEEE for “advancing the theory and practice of adaptive control, and in so doing, making major contributions to improving the speed and accuracy of specialty robotics for the semiconductor industry.” These techniques helped to extend the life of wire bonding technology. As a result of this work, the challenge of portability – the ability to repeatedly perform the same task on different machines – was solved. The time duration of bond table motion was reduced by more than 60%, dramatically increasing productivity, and the accuracy limit was lowered from more than 100 microns in the late 1990s to 35 microns in the current generation of bonders. The robustness of the algorithms has been proven over the last 17 years by its successful implementation in tens of thousands of machines representing various platforms. It is one of the major innovations that have made these wire bonders the world industry leaders. Is co-author of the book: “Direct Adaptive Control Algorithms – Theory and Applications” and has published 3 chapters in books and more than 100 papers in Journals and major Technical Conferences.  
Ilan Rusnak Ilan Rusnak holds B.Sc. and M.Sc. in electrical engineering from Technion Haifa, Israel, and Ph.D. in ECE from Drexel University, Philadelphia, USA. He is currently with RAFAEL, Israel, holding the position of senior research fellow, and holding position of adjunct senior lecturer at Technion, Haifa, Israel. His current interests are Systems Engineering, Guidance, Control Theory, Motion Control, Estimation Theory, Architecture of the Feedback, Simulation and Signal Processing.  
Haim Weiss Haim Weiss received his B.Sc. and M.Sc. degrees in electrical engineering, in 1966 and 1971, respectively, both from Technion—Israel Institute of Technology. In 1979 he received Ph.D. degree from University of Newcastle, Australia, also in electrical engineering. From 1966 to 1970 he served as an electronic engineer in the Israeli Air Force. In 1972 he joined RAFAEL where he is now a research fellow. From 1999–2001 he was Lady Davis visiting scientist at Faculty of Aerospace Engineering, Technion, Israel. Currently he holds the position of adjunct senior teaching fellow. His research interests include estimation, guidance, adaptive control and spacecraft attitude determination and control.

Registration: Tutorial session fee 70 Euros should be added to regular conference registration fee

Multivariate Function Decomposition and Data Analysis with a Basic Focus on HDMR and EMPR


Lecturers: (oral presentations) Metin Demiralp, İstanbul Technical University, (Chairman)
Süha Tuna, İstanbul Technical University, (Organizing Assistant to Chairman)
Alper Tunga, Bahçeşehir University
Burcu Tunga, İstanbul Technical University
Evrim Korkmaz Özay, Aydın University
  Lecturers: (focusing on certain specific topics in core sessions composed of oral presentations)
Zeynep Gündoğar, İstanbul Technical University
Ayla Okan, İstanbul Technical University
Derya Bodur, İstanbul Technical University
  Implementative Session(s) Devoted to Only (Poster Presentations)
Evrim Korkmaz Özay, Zeynep Gündoğar, Ayla Okan, and, Derya Bodur
Assistive instructors:
Berfin Kalay, İstanbul Technical University
Melike Ebru Kırkın, İstanbul Technical University
Elif Tataroğlu, İstanbul Technical University
  If any application comes from outside the above team for the announcement
of special expertises then some of instructively important ones will be
selected to be presented in this session via poster(s).
The original findings including one will be redirected to the special ICNPAA 2016
session organized by Demiralp.  
ABSTRACT: The topics of this pre-ICNPAA 2016 organization will be focused on the following areas:
* ANOVA and basic conceptualism of High Dimensional Model Representation (HDMR). Sobol's definition and related works.
* Weights and orthogonal geometry in HDMR, the works of Rabitz and his group. Cut-HDMR, Random Sampling HDMR, Multicut HDMR.
* Orthogonality, truncation approximants, quality measurers. How to increase truncation approximation quality.
* Other HDMR varieties from Demiralp Group: HDMR with Generalized Weights, Factorized HDMR, Hybrid HDMR, Discrete and discretized HDMR applications.
* Further HDMR developments from Demiralp group: Logarithmic HDMR, Transformational HDMR (under various transformations like affine, quadratic, cubic, Moebius type).
* Ascending approximation quality via multivariance enhancement. Supporting element concept. Enhanced Multivariance Products Representation (EMPR = Supported HDMR) as introduced in Demiralp group works.
* EMPR in practical applications. EMPR varieties as extended counterparts of HDMR. What does EMPR bring new extension and capabilities against HDMR's limited structure.
* Support function and support array optimisation. Integral equations related issues. Multiway array related issues.
* Supportive hybridization in EMPR. Developments outside Sobol's, Rabitz group's, and, Demiralp group's studies. Future work possibilities.
Core Sessions Devoted to Oral Presentations  
DOCUMENTATION and WEB SITE: The construction of a tutorial/textbook type book has been started and will be, at least, ready to the online access of participants. The distribution of the printed version of this book is also under consideration. The ultimate status will be announced quite before of the tutorial/workshop day.
Almost all of the abovementioned contributors will give certain level of support to this documentation in both printed and online versions.
Event support to the documentation. * N. Abdülbaki Baykara, Marmara University
* Coşar Gözükırmızı, İstanbul Technical University
* Muzaffer Ayvaz, İstanbul Technical University
* Semra Bayat, İstanbul Technical University
  Organizers: Metin Demiralp, İstanbul Technical University, (Chairman) Informatics Institute, Computational Science and Engineering Department. Süha Tuna, İstanbul Technical University, (Organizing Assistant to Chairman) Alper Tunga, Bahçeşehir University, Burcu Tunga, İstanbul Technical University, Evrim Korkmaz Özay, Aydın University
URL for further information about this activity in english and turkish (choose and click on relevant flag therein): bebbyt.be.itu.edu.tr/empr. You can also leave a message in that site if you need.

Registration: Tutorial session fee 70 Euros should be added to regular conference registration fee