Search results for: Nonlinear advection-diffusion equation.

Authors: I. Otete, A. I. Ejere, I. S. Okunzuwa

Abstract:

In this work, we used the Hulthen-Yukawa potential to obtain the bound state energy eigenvalues of the Schrödinger equation in D-dimensions within the frame work of the Nikiforov-Uvarov (NU) method. We demonstrated the graphical behaviour of the Hulthen and the Yukawa potential and investigated how the screening parameter and the potential depth affected the structure and the nature of the bound state eigenvalues. The results we obtained showed that increasing the screening parameter lowers the energy eigenvalues. Also, the eigenvalues acted as an inverse function of the potential depth. That is, increasing the potential depth reduces the energy eigenvalues.

Keywords: Schrödinger's equation, bound state, Hulthen-Yukawa potential, Nikiforov-Uvarov, D-dimensions

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Authors: E. Sobhani-Tehrani, K. Khorasani, N. Meskin

Abstract:

This paper presents a novel integrated hybrid approach for fault diagnosis (FD) of nonlinear systems. Unlike most FD techniques, the proposed solution simultaneously accomplishes fault detection, isolation, and identification (FDII) within a unified diagnostic module. At the core of this solution is a bank of adaptive neural parameter estimators (NPE) associated with a set of singleparameter fault models. The NPEs continuously estimate unknown fault parameters (FP) that are indicators of faults in the system. Two NPE structures including series-parallel and parallel are developed with their exclusive set of desirable attributes. The parallel scheme is extremely robust to measurement noise and possesses a simpler, yet more solid, fault isolation logic. On the contrary, the series-parallel scheme displays short FD delays and is robust to closed-loop system transients due to changes in control commands. Finally, a fault tolerant observer (FTO) is designed to extend the capability of the NPEs to systems with partial-state measurement.

Keywords: Hybrid fault diagnosis, Dynamic neural networks, Nonlinear systems.

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Authors: Ampon Dhamacharoen, Kanittha Chompuvised

Abstract:

In this work, we solve multipoint boundary value problems where the boundary value conditions are equations using the Newton-Broyden Shooting method (NBSM).The proposed method is tested upon several problems from the literature and the results are compared with the available exact solution. The experiments are given to illustrate the efficiency and implementation of the method.

Keywords: Boundary value problem; Multipoint equation boundary value problems, Shooting Method, Newton-Broyden method.

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Authors: Minghui Wang, Luping Xu, Juntao Zhang

Abstract:

Based on the conjugate gradient (CG) algorithm, the constrained matrix equation AXB=C and the associate optimal approximation problem are considered for the symmetric arrowhead matrix solutions in the premise of consistency. The convergence results of the method are presented. At last, a numerical example is given to illustrate the efficiency of this method.

Keywords: Iterative method, symmetric arrowhead matrix, conjugate gradient algorithm.

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Authors: Delfim Soares Jr., Webe J. Mansur

Abstract:

The Time-Domain Boundary Element Method (TDBEM) is a well known numerical technique that handles quite properly dynamic analyses considering infinite dimension media. However, when these analyses are also related to nonlinear behavior, very complex numerical procedures arise considering the TD-BEM, which may turn its application prohibitive. In order to avoid this drawback and model nonlinear infinite media, the present work couples two BEM formulations, aiming to achieve the best of two worlds. In this context, the regions expected to behave nonlinearly are discretized by the Domain Boundary Element Method (D-BEM), which has a simpler mathematical formulation but is unable to deal with infinite domain analyses; the TD-BEM is employed as in the sense of an effective non-reflexive boundary. An iterative procedure is considered for the coupling of the TD-BEM and D-BEM, which is based on a relaxed renew of the variables at the common interfaces. Elastoplastic models are focused and different time-steps are allowed to be considered by each BEM formulation in the coupled analysis.

Keywords: Boundary Element Method, Dynamic Elastoplastic Analysis, Iterative Coupling, Multiple Time-Steps.

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Authors: M. G. M. Khan, V. D. Prasad, D. K. Rao

Abstract:

In this manuscript, we discuss the problem of determining the optimum stratification of a study (or main) variable based on the auxiliary variable that follows a uniform distribution. If the stratification of survey variable is made using the auxiliary variable it may lead to substantial gains in precision of the estimates. This problem is formulated as a Nonlinear Programming Problem (NLPP), which turn out to multistage decision problem and is solved using dynamic programming technique.

Keywords: Auxiliary variable, Dynamic programming technique, Nonlinear programming problem, Optimum stratification, Uniform distribution.

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Authors: D.Elleuch, T.Damak

Abstract:

In this paper, the performance of two adaptive observers applied to interconnected systems is studied. The nonlinearity of systems can be written in a fractional form. The first adaptive observer is an adaptive sliding mode observer for a Lipchitz nonlinear system and the second one is an adaptive sliding mode observer having a filtered error as a sliding surface. After comparing their performances throughout the inverted pendulum mounted on a car system, it was shown that the second one is more robust to estimate the state.

Keywords: Adaptive observer, Lipchitz system, Interconnected fractional nonlinear system, sliding mode.

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Authors: Roozbeh Keshmiri, Alireza Mohamad Shahri

Abstract:

Fuzzy controllers are potential candidates for the control of nonlinear, time variant and also complicated systems. Anti lock brake system (ABS) which is a nonlinear system, may not be easily controlled by classical control methods. An intelligent Fuzzy control method is very useful for this kind of nonlinear system. A typical antilock brake system (ABS) by sensing the wheel lockup, releases the brakes for a short period of time, and then reapplies again the brakes when the wheel spins up. In this paper, an intelligent fuzzy ABS controller is designed to adjust slipping performance for variety of roads. There are tow major sections in the proposing control system. First section consists of tow Fuzzy-Logic Controllers (FLC) providing optimal brake torque for both front and rear wheels. Second section which is also a FLC provides required amount of slip and torque references properties for different kind of roads. Simulation results of our proposed intelligent ABS for three different kinds of road show more reliable and better performance in compare with two other break systems.

Keywords: Fuzzy Logic Control, ABS, Anti lock BrakingSystem.

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Authors: B. S. Raghavendra, D. Narayana Dutt

Abstract:

Many recent electrophysiological studies have revealed the importance of investigating meditation state in order to achieve an increased understanding of autonomous control of cardiovascular functions. In this paper, we characterize heart rate variability (HRV) time series acquired during meditation using nonlinear dynamical parameters. We have computed minimum embedding dimension (MED), correlation dimension (CD), largest Lyapunov exponent (LLE), and nonlinearity scores (NLS) from HRV time series of eight Chi and four Kundalini meditation practitioners. The pre-meditation state has been used as a baseline (control) state to compare the estimated parameters. The chaotic nature of HRV during both pre-meditation and meditation is confirmed by MED. The meditation state showed a significant decrease in the value of CD and increase in the value of LLE of HRV, in comparison with premeditation state, indicating a less complex and less predictable nature of HRV. In addition, it was shown that the HRV of meditation state is having highest NLS than pre-meditation state. The study indicated highly nonlinear dynamic nature of cardiac states as revealed by HRV during meditation state, rather considering it as a quiescent state.

Keywords: Correlation dimension, Embedding dimension, Heartrate variability, Largest Lyapunov exponent, Meditation, Nonlinearity score.

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Authors: Karuppsamy K., Eswara Prasad C. R.

Abstract:

In this paper analysis of an infinite beam resting on tensionless extensible geosynthetic reinforced granular bed overlying soft soil strata under moving load with constant velocity is presented. The beam is subjected to a concentrated load moving with constant velocity. The upper reinforced granular bed is modeled by a rough elastic membrane embedded in Pasternak shear layer overlying a series of compressible nonlinear Winkler springs representing the under-lied very poor soil. The tensionless extensible geosynthetic layer has been assumed to deform such that at interface the geosynthetic and the soil have some deformation. Nonlinear behavior of granular fill and the very poor soil has been considered in the analysis by means of hyperbolic constitutive relationships. Detailed parametric study has been conducted to study the influence of various parameters on the response of soil foundation system under consideration by means of deflection and bending moment in the beam and tension mobilized in the geosynthetic layer. This study clearly observed that the comparisons of tension and tensionless foundation and magnitude of applied load, relative compressibility of granular fill and ultimate resistance of poor soil has significant influence on the response of soil foundation system.

Keywords: Infinite Beams, Tensionless Extensible Geosynthetic, Granular layer, Moving Load and Nonlinear behavior of poor soil

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Authors: Yanling Zhu, Kai Wang

Abstract:

By means of Mawhin’s continuation theorem, we study a kind of third-order p-Laplacian functional differential equation with distributed delay in the form: ϕp(x (t)) = g  t,  0 −τ x(t + s) dα(s)  + e(t), some criteria to guarantee the existence of periodic solutions are obtained.

Keywords: p–Laplacian, distributed delay, periodic solution, Mawhin's continuation theorem.

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Authors: Vishwesh Kulkarni, Nikhil Bellarykar

Abstract:

Cellular complexity stems from the interactions among thousands of different molecular species. Thanks to the emerging fields of systems and synthetic biology, scientists are beginning to unravel these regulatory, signaling, and metabolic interactions and to understand their coordinated action. Reverse engineering of biological networks has has several benefits but a poor quality of data combined with the difficulty in reproducing it limits the applicability of these methods. A few years back, many of the commonly used predictive algorithms were tested on a network constructed in the yeast Saccharomyces cerevisiae (S. cerevisiae) to resolve this issue. The network was a synthetic network of five genes regulating each other for the so-called in vivo reverse-engineering and modeling assessment (IRMA). The network was constructed in S. cereviase since it is a simple and well characterized organism. The synthetic network included a variety of regulatory interactions, thus capturing the behaviour of larger eukaryotic gene networks on a smaller scale. We derive a new set of algorithms by solving a nonlinear optimization problem and show how these algorithms outperform other algorithms on these datasets.

Keywords: Synthetic gene network, network identification, nonlinear modeling, optimization.

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Authors: Nopparat Pochai, Rujira Deepana

Abstract:

Water pollution assessment problems arise frequently in environmental science. In this research, a finite difference method for solving the one-dimensional steady convection-diffusion equation with variable coefficients is proposed; it is then used to optimize water treatment costs.

Keywords: Finite difference, One-dimensional, Steady state, Waterpollution control, Optimization, Convection-diffusion equation.

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Authors: J. Kala, P. Hradil, V. Salajka

Abstract:

Reinforced concrete crash barriers used in road traffic must meet a number of criteria. Crash barriers are laid lengthwise, one behind another, and joined using specially designed steel locks. While developing BSV reinforced concrete crash barriers (type ŽPSV), experiments and calculations aimed to optimize the shape of a newly designed lock and the reinforcement quantity and distribution in a crash barrier were carried out. The tension carrying capacity of two parallelly joined locks was solved experimentally. Based on the performed experiments, adjustments of nonlinear properties of steel were performed in the calculations. The obtained results served as a basis to optimize the lock design using a computational model that takes into account the plastic behaviour of steel and the influence of the surrounding concrete [6]. The response to the vehicle impact has been analyzed using a specially elaborated complex computational model, comprising both the nonlinear model of the damping wall or crash barrier and the detailed model of the vehicle [7].

Keywords: Crash Barrier, impact, static analysis, concrete nonlinear model.

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Authors: Babesse Saad, Ameddah Djameleddine

Abstract:

In this paper, a learning algorithm using neuronal networks to improve the roll stability and prevent the rollover in a single unit heavy vehicle is proposed. First, LQR control to keep balanced normalized rollovers, between front and rear axles, below the unity, then a data collected from this controller is used as a training basis of a neuronal regulator. The ANN controller is thereafter applied for the nonlinear side force model, and gives satisfactory results than the LQR one.

Keywords: Rollover, single unit heavy vehicle, neural networks, nonlinear side force.

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Authors: Ram N. Singh, Abraham K. George, Dawood N. Al-Namaani

Abstract:

The Euler-s equation of motion is extended to include the viscosity stress tensor leading to the formulation of Navier– Stokes type equation. The latter is linearized and applied to investigate the rotational motion or vorticity in a viscous fluid. Relations for the velocity of viscous waves and attenuation parameter are obtained in terms of viscosity (μ) and the density (¤ü) of the fluid. μ and ¤ü are measured experimentally as a function of temperature for two different samples of light and heavy crude oil. These data facilitated to determine the activation energy, velocity of viscous wave and the attenuation parameter. Shear wave velocity in heavy oil is found to be much larger than the light oil, whereas the attenuation parameter in heavy oil is quite low in comparison to light one. The activation energy of heavy oil is three times larger than light oil.

Keywords: Activation Energy, Attenuation, Crude Oil, Navier- Stokes Equation, Viscosity.

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Authors: Jiashang Jiang, Hao Liu, Yongxin Yuan

Abstract:

In this paper the gradient based iterative algorithms are presented to solve the following four types linear matrix equations: (a) AXB = F; (b) AXB = F, CXD = G; (c) AXB = F s. t. X = XT ; (d) AXB+CYD = F, where X and Y are unknown matrices, A,B,C,D, F,G are the given constant matrices. It is proved that if the equation considered has a solution, then the unique minimum norm solution can be obtained by choosing a special kind of initial matrices. The numerical results show that the proposed method is reliable and attractive.

Keywords: Matrix equation, iterative algorithm, parameter estimation, minimum norm solution.

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Authors: R.K. Behera, S.Behera

Abstract:

In a wind power generator using doubly fed induction generator (DFIG), the three-phase pulse width modulation (PWM) voltage source converter (VSC) is used as grid side converter (GSC) and rotor side converter (RSC). The standard linear control laws proposed for GSC provides not only instablity against comparatively large-signal disturbances, but also the problem of stability due to uncertainty of load and variations in parameters. In this paper, a nonlinear controller is designed for grid side converter (GSC) of a DFIG for wind power application. The nonlinear controller is designed based on the input-output feedback linearization control method. The resulting closed-loop system ensures a sufficient stability region, make robust to variations in circuit parameters and also exhibits good transient response. Computer simulations and experimental results are presented to confirm the effectiveness of the proposed control strategy.

Keywords: Doubly fed Induction Generator, grid side converter, machine side converter, dc link, feedback linearization.

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Authors: Vivekanandan C., Prabhakar .R., Prema D.

Abstract:

This paper presents the application of discrete-time variable structure control with sliding mode based on the 'reaching law' method for robust control of a 'simple inverted pendulum on moving cart' - a standard nonlinear benchmark system. The controllers designed using the above techniques are completely insensitive to parametric uncertainty and external disturbance. The controller design is carried out using pole placement technique to find state feedback gain matrix , which decides the dynamic behavior of the system during sliding mode. This is followed by feedback gain realization using the control law which is synthesized from 'Gao-s reaching law'. The model of a single inverted pendulum and the discrete variable structure control controller are developed, simulated in MATLAB-SIMULINK and results are presented. The response of this simulation is compared with that of the discrete linear quadratic regulator (DLQR) and the advantages of sliding mode controller over DLQR are also presented

Keywords: Inverted pendulum, Variable Structure, Sliding mode control, Discrete-time systems, Nonlinear systems.

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Authors: N. Fusun Oyman Serteller

Abstract:

In this paper, the techniques to solve time dependent electromagnetic wave propagation equations based on the Finite Difference Method (FDM) are proposed by comparing the results with Finite Element Method (FEM) in 2D while discussing some special simulation examples.  Here, 2D dynamical wave equations for lossy media, even with a constant source, are discussed for establishing symbolic manipulation of wave propagation problems. The main objective of this contribution is to introduce a comparative study of two suitable numerical methods and to show that both methods can be applied effectively and efficiently to all types of wave propagation problems, both linear and nonlinear cases, by using symbolic computation. However, the results show that the FDM is more appropriate for solving the nonlinear cases in the symbolic solution. Furthermore, some specific complex domain examples of the comparison of electromagnetic waves equations are considered. Calculations are performed through Mathematica software by making some useful contribution to the programme and leveraging symbolic evaluations of FEM and FDM.

Keywords: Finite difference method, finite element method, linear-nonlinear PDEs, symbolic computation, wave propagation equations.

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Authors: M. Karami Khorramabadi, A. R. Nezamabadi

Abstract:

This paper studies free vibration of functionally graded beams Subjected to Axial Load that is simply supported at both ends lies on a continuous elastic foundation. The displacement field of beam is assumed based on Engesser-Timoshenko beam theory. The Young's modulus of beam is assumed to be graded continuously across the beam thickness. Applying the Hamilton's principle, the governing equation is established. Resulting equation is solved using the Euler's Equation. The effects of the constituent volume fractions and foundation coefficient on the vibration frequency are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data.

Keywords: Functionally Graded Beam, Free Vibration, Elastic Foundation, Engesser-Timoshenko Beam Theory.

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Authors: Huei-Fu Lu

Abstract:

This study links up the theories of social psychology, economics and sport management to assess the impact of sport participation on subjective well-being (SWB) and use a simple statistic method to estimate the relative monetary value that sport participation derives SWB for Taiwan-s college students. By constructing proper measurements on sport participation and SWB respectively, a structural equation model (SEM) is developed to perform a confirmatory factory analysis, and the causal relationship between sport participation and SWB as well as the effect of the demographic variables on these two concepts are also discussed.

Keywords: Demographics, Economic value, Sport participation, Structural equation modeling (SEM), Subjective well-being.

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Authors: Fatma Ghangir, Andrzej F. Nowakowski, Franck C. G. A. Nicolleau, Thomas M. Michelitsch

Abstract:

The performance of high-resolution schemes is investigated for unsteady, inviscid and compressible multiphase flows. An Eulerian diffuse interface approach has been chosen for the simulation of multicomponent flow problems. The reduced fiveequation and seven equation models are used with HLL and HLLC approximation. The authors demonstrated the advantages and disadvantages of both seven equations and five equations models studying their performance with HLL and HLLC algorithms on simple test case. The seven equation model is based on two pressure, two velocity concept of Baer–Nunziato [10], while five equation model is based on the mixture velocity and pressure. The numerical evaluations of two variants of Riemann solvers have been conducted for the classical one-dimensional air-water shock tube and compared with analytical solution for error analysis.

Keywords: Multiphase flow, gas-liquid flow, Godunov schems, Riemann solvers, HLL scheme, HLLC scheme.

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Authors: Gulgassyl Nugmanova, Zhanat Zhunussova, Kuralay Yesmakhanova, Galya Mamyrbekova, Ratbay Myrzakulov

Abstract:

In this paper, we consider some integrable Heisenberg Ferromagnet Equations with self-consistent potentials. We study their Lax representations. In particular we derive their equivalent counterparts in the form of nonlinear Schr¨odinger type equations. We present the integrable reductions of the Heisenberg Ferromagnet Equations with self-consistent potentials. These integrable Heisenberg Ferromagnet Equations with self-consistent potentials describe nonlinear waves in ferromagnets with some additional physical fields.

Keywords: Spin systems, equivalent counterparts, integrable reductions, self-consistent potentials.

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Authors: Alexandra Leukauf, Alexander Schirrer, Emir Talic

Abstract:

Numerical computation of wave propagation in a large domain usually requires significant computational effort. Hence, the considered domain must be truncated to a smaller domain of interest. In addition, special boundary conditions, which absorb the outward travelling waves, need to be implemented in order to describe the system domains correctly. In this work, the linear one dimensional wave equation is approximated by utilizing the Fourier Galerkin approach. Furthermore, the artificial boundaries are realized with absorbing boundary conditions. Within this work, a systematic work flow for setting up the wave problem, including the absorbing boundary conditions, is proposed. As a result, a convenient modal system description with an effective absorbing boundary formulation is established. Moreover, the truncated model shows high accuracy compared to the global domain.

Keywords: Absorbing boundary conditions, boundary control, Fourier Galerkin approach, modal approach, wave equation.

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Authors: Azizollah Khormali, Seyyed Shahab Tabatabaee Moradi, Dmitry Petrakov

Abstract:

One of the most important parameters in petroleum reservoirs is the pressure distribution along the reservoir, as the pressure varies with the time and location. A popular method to determine the pressure distribution in a reservoir in the unsteady state regime of flow is applying Darcy’s equation and solving this equation numerically. The numerical simulation of reservoirs is based on these numerical solutions of different partial differential equations (PDEs) representing the multiphase flow of fluids. Pressure profile has obtained in a one dimensional system solving Darcy’s equation explicitly. Changes of pressure profile in three situations are investigated in this work. These situations include section length changes, step time changes and time approach to infinity. The effects of these changes in pressure profile are shown and discussed in the paper.

Keywords: Explicit solution, Numerical simulation, Petroleum reservoir, Pressure distribution.

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Authors: A.Tajaddini

Abstract:

In this paper, two matrix iterative methods are presented to solve the matrix equation A1X1B1 + A2X2B2 + ... + AlXlBl = C the minimum residual problem l i=1 AiXiBi−CF = minXi∈BRni×ni l i=1 AiXiBi−CF and the matrix nearness problem [X1, X2, ..., Xl] = min[X1,X2,...,Xl]∈SE [X1,X2, ...,Xl] − [X1, X2, ..., Xl]F , where BRni×ni is the set of bisymmetric matrices, and SE is the solution set of above matrix equation or minimum residual problem. These matrix iterative methods have faster convergence rate and higher accuracy than former methods. Paige’s algorithms are used as the frame method for deriving these matrix iterative methods. The numerical example is used to illustrate the efficiency of these new methods.

Keywords: Bisymmetric matrices, Paige’s algorithms, Least square.

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Authors: Roozbeh Molavi, Davood A. Khaburi

Abstract:

The permanent magnet synchronous motor (PMSM) is very useful in many applications. Vector control of PMSM is popular kind of its control. In this paper, at first an optimal vector control for PMSM is designed and then results are compared with conventional vector control. Then, it is assumed that the measurements are noisy and linear quadratic Gaussian (LQG) methodology is used to filter the noises. The results of noisy optimal vector control and filtered optimal vector control are compared to each other. Nonlinearity of PMSM and existence of inverter in its control circuit caused that the system is nonlinear and time-variant. With deriving average model, the system is changed to nonlinear time-invariant and then the nonlinear system is converted to linear system by linearization of model around average values. This model is used to optimize vector control then two optimal vector controls are compared to each other. Simulation results show that the performance and robustness to noise of the control system has been highly improved.

Keywords: Kalman filter, Linear quadratic Gaussian (LQG), Linear quadratic regulator (LQR), Permanent-Magnet synchronousmotor (PMSM).

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Authors: Kaoutar Lamrini Uahabi, Mohamed Atounti

Abstract:

In the present work, we consider one category of curves denoted by L(p, k, r, n). These curves are continuous arcs which are trajectories of roots of the trinomial equation zn = αzk + (1 − α), where z is a complex number, n and k are two integers such that 1 ≤ k ≤ n − 1 and α is a real parameter greater than 1. Denoting by L the union of all trinomial curves L(p, k, r, n) and using the box counting dimension as fractal dimension, we will prove that the dimension of L is equal to 3/2.

Keywords: Feasible angles, fractal dimension, Minkowski sausage, trinomial curves, trinomial equation.

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Authors: Mauricio Pe˜na, Adriana Luna, Carol Rodr´ıguez

Abstract:

In the following article we begin from a multi-parameter unstable nonlinear model of a Quadrotor. We design a control to stabilize and assure the attitude of the device, starting off a linearized system at the equilibrium point of the null angles of Euler (hover), which provides us a control with limited capacities at small angles of rotation of the vehicle in three dimensions. In order to clear this obstacle, we propose the identification of models in different angles by means of simulations and the design of a controller specifically implemented for the identification task, that in future works will allow the development of controllers according to fast and agile angles of Euler for Quadrotor.

Keywords: Quadrotor, model, control, identification.

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