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Toward computational algorithm for time-fractional Fokker-Planck models

ADVANCES IN MECHANICAL ENGINEERING 2019年第10期11卷

作者： Freihet, Asad Hasan, Shatha Alaroud, Mohammad Al-Smadi, Mohammed Ahmad, Rokiah Rozita Din, Ummul Khair Salma Al Balqa Appl Univ Ajloun Coll Dept Appl Sci Ajloun Jordan Univ Kebangsaan Malaysia Fac Sci & Technol Sch Math Sci Bangi 43600 Selangor Malaysia

This article describes an efficient algorithm based on residual power series to approximate the solution of a class of partial differential equations of time-fractional Fokker-Planck model. The fractional derivative is assumed in the Caputo sense. The proposed algorithm gives the solution in a form of rapidly convergent fractional power series with easily computable coefficients. It does not require linearization, discretization, or small perturbation. To test simplicity, potentiality, and practical usefulness of the proposed algorithm, illustrative examples are provided. The approximate solutions of time-fractional Fokker-Planck equations are obtained by the residual power series method are compared with those obtained by other existing methods. The present results and graphics reveal the ability of residual power series method to deal with a wide range of partial fractional differential equations emerging in the modeling of physical phenomena of science and engineering.

关键词： Caputo fractional derivatives Fokker-Planck equation residual power series numerical algorithms

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CALCULATION OF OPTICAL-LINE SHAPES FOR GENERALIZED MULTILEVEL SYSTEMS

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JOURNAL OF CHEMICAL PHYSICS 1984年第12期81卷 5899-5905页

作者： LAGOS, RE FRIESNER, RA Department of Chemistry University of Texas Austin Austin Texas 78712

An approximate method for calculating the one‐exciton Green’s functions (and hence the linear response optical line shapes) of a multilevel excited electronic manifold is presented. Vibronic coupling to low and high frequency modes are treated by appropriate perturbative techniques; the resulting numerical algorithms are rapidly convergent and easily evaluated. For two excited levels and single vibrational mode, the method reduces (at lowest order) to previous approximations which have been extensively compared with basis set results.

关键词： Green&apos s function methods Manifolds numerical algorithms

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Tensile response of unidirectional ceramic minicomposites

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 2020年 138卷 103903-103903页

作者： Callaway, E. Benjamin Zok, Frank W. Univ Calif Santa Barbara Dept Mat Santa Barbara CA 93106 USA

Mechanical response of ceramic matrix composites is critically dependent on properties of fibers and fiber coatings. In the present study, we examine effects of these and other constituent properties on the tensile response of unidirectionally-reinforced composites through a combination of existing models of fiber fracture, Monte Carlo simulations of concurrent matrix and fiber fragmentation, and complementary experimental measurements. The results show that, contrary to prevailing understanding, the process of fiber fragmentation cannot go to completion in a uniaxial tensile test. At low stresses (before the maximum), fiber breaks are essentially random throughout the bundle;in contrast, at the stress maximum, all additional breaks are localized to regions close to the fracture plane (within a distance dictated by the characteristic transfer length). Therefore, the resulting distributions in fiber pullout length and strength of pulled-out fibers do not match predictions from existing models. Although the composite stress-strain response associated with fragmentation can be accurately predicted by existing fragmentation models, accurate prediction of the point of instability requires consideration of the local response of fibers in the most heavily strained regions (within matrix crack planes). The response in the latter regions leads to instability at stresses and strains that are lower than those obtained from the average stress-strain response. Additionally, the composite strength and failure strain are found to be sensitive to the fiber volume fraction and the matrix strength distribution. One implication is that the full potential of the fibers may not be realizable in composites of practical interest. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： Fracture Ceramic material Fiber-reinforced composite material numerical algorithms Mechanical testing

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Robust and Efficient Software for Control Problems: The SLICOT Library

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IFAC Proceedings Volumes 2000年第6期33卷 51-56页

作者： I. Blanquer V. Hernández A. Vidal E. Arias Universidad Politécnica de Valencia Dpto. de Sistemas Informáticos y Computación (DSIC). Camino de Vera s/n Valencia 46022

This article describes the library SLICOT (Software Library In COntrol Theory) [40] [7] [43] [2] that provides Fortran 77 implementation and also MATLAB and SciLAB [39] interfaces for numerical algorithms for computations in systems and control theory. The library is build up on an efficient kernel of basic numerical linear algebra subroutines and provides tools for solving matrix equations, model reduction, subspaceidentification, robust control and non-linear control. SLICOT is freely available and it has been tested on many industrial problems.

关键词： Computer-aided control systems design Parallel algorithms numerical algorithms Robust control Model reduction Nonlinear control systems Identification

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ROBUST POLE ASSIGNMENT BY STATE FEEDBACK CONTROL USING INTERVAL ANALYSIS

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IFAC Proceedings Volumes 2005年第1期38卷 48-53页

作者： Marcia L.M. Prado Alfredo D.S. Lordelo Paulo A.V. Ferreira University of Campinas School of Electrical and Computer Engineering Campinas SP 13083-852 Brazil

An interval analysis approach for the design of robust state feedback controllers is proposed. It is shown that when regional pole placement specifications are represented as spectral sets of interval polynomials, the robust state feedback design problem can be entirely formulated and solved in the context of the concepts and methods of interval analysis. Explicit convex polyhedral representations of a class of robust state feedback controllers satisfying an interval Ackerman's equation are derived. A design procedure based on nonlinear programming which aims at maximizing the non-fragility of the resulting robust controller is introduced. numerical examples illustrate the design of robust state feedback controllers through the interval analysis approach proposed.

关键词： Uncertain linear systems pole assignment intervals polynomials numerical algorithms

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High-Precision algorithms for Constructing Optimal Trajectories via Solving Hamiltonian Systems *

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IFAC Proceedings Volumes 2009年第2期42卷 70-75页

作者： Andrey A. Krasovskii Alexander M. Tarasyev Institute of Mathematics and Mechanics Ural Branch of RAS S. Kovalevskoi Str. 16 620219 Ekaterinburg Russia and Vienna Institute of Demography Austrian Academy of Sciences Wohllebengasse 12-14 1040 Vienna Austria Institute of Mathematics and Mechanics UrB RAS S. Kovalevskoi Str. 16 620219 Ekaterinburg Russia

The paper deals with analysis of optimal control problems arising in models of economic growth. The Pontryagin maximum principle is applied for analysis of the optimal investment problem. Specifically, the research is based on existence results and necessary conditions of optimality in problems with infinite horizon. Properties of Hamiltonian systems are examined for different regimes of optimal control. The existence and uniqueness result is proved for a steady state of the Hamiltonian system. Analysis of properties of eigenvalues and eigenvectors is completed for the linearized system in a neighborhood of the steady state. Description of behavior of the nonlinear Hamiltonian system is provided on the basis of results of the qualitative theory of differential equations. This analysis allows us to outline proportions of the main economic factors and trends of optimal growth in the model. A numerical algorithm for construction of optimal trajectories of economic growth is elaborated on the basis of constructions of backward procedures and conjugation of an approximation linear dynamics with the nonlinear Hamiltonian dynamics. High order precision estimates are obtained for the proposed algorithm. These estimates establish connection between precision parameters in the phase space and precision parameters for functional indices.

关键词： Nonlinear control systems numerical algorithms Precision measurements Economic design

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Rapid Model Selection and the Separability Index

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IFAC Proceedings Volumes 2000年第11期33卷 1151-1156页

作者： Stephen L. Campbell Kirk Horton Ramine Nikoukhah Francois Delebecque Dept. of Mathematics North Carolina State University Raleigh NC 27695-8205. USA Operations Research Program North Carolina State University Raleigh NC 27695-7913. USA INRIA Rocquencourt BP 105 78153 Le Chesnay Cedex France

Under the assumption that one of two given models is the real underlying model of the system, a proper auxiliary signal is defined as an input signal that allows one to select the correct model. It is assumed that there is no knowledge prior to the beginning of the application of the auxiliary signal and that detection is to be done within a specified detection horizon. Under the assumption that the noise energy is bounded, the separability index is defined as the least energy of a proper auxiliary signal. A method for computation of this index is presented.

关键词： Descriptor system Differential equations Identification Linear systems numerical algorithms

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A Structure Based Synthesis Method for Disturbance Rejection

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IFAC Proceedings Volumes 1998年第18期31卷 691-696页

作者： Jean-François Camart Basilio Del-Muro-Cuellar Michel Malabre Institut de Recherche en Cybernétique de Nantes UMR GNRS 6597 1 rue de la Noë B.P. 92101 44321 Nantes Gedex 03 France. Phone: (+33) 2 40 37 16 51. Fax: (+33) 2 40 37 25 22. ITESM-GEM Depto. de Ingeniera Mécanica Apdo. Postal 6-3 Atizapan Estado de México GP 52926 México

A new method for the synthesis of compensators which solve the disturbance rejection problem (either by state feedback or by output feedback) is presented. This method, based on structural and geometric approaches, provides solutions to the problem with the minimal number of unassignable poles (i.e. poles that are fixed due to the fact that this particular problem is been solved). Moreover, all the poles that remain assignable are relocated to values selected by a non expert user, without any required knowledge of the proposed programs. Une nouvelle méthode de synthèse de compensateurs solutions du problème du rejet de perturbation, soit par retour d'état soit par retour de mesure, est proposée. Cette méthode, basée sur les approches géométrique et structurelle, permet de résoudre le problème (s'il est soluble) avec le minimum de pôles imposés par cette résolution. De plus tous les autres pôles sont placés aux valeurs indiquées par un utilisateur non expert de ces méthodes.

关键词： Linear Systems Disturbance Rejection Dynamic Output Feedback State Feedback Geometric Approach Fixed Poles Pole Assignment numerical algorithms

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AN ALGORITHM FOR CONSISTENT LINEARIZATION OF SHIP MANOEUVRING MATHEMATICAL MODELS

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IFAC Proceedings Volumes 2007年第17期40卷 243-248页

作者： Serge Sutulo C. Guedes Soares Unit of Marine Technology and Engineering Technical University of Lisbon Instituto Superior Técnico Av. Rovisco Pais 1049-001 Lisbon Portugal

A numerical algorithm for flexible linearization of substantially nonlinear ship mathematical models described by ordinary differential equations is proposed. The linearization can be performed over any pre-defined domain in the state space or subspace in the least-square sense. A discrete set of points is created inside the domain of interest by means of a quasi-random sequence generator. Then, the exact model's responses are calculated on this set and a common least-square procedure is applied. Local or differential linearization can be performed with the same algorithm choosing an appropriately small domain around any point of interest in the state space. A numerical example for a typical directionally unstable vessel is given and studied is the influence of the number of the generated quasi-random points and of the linearization domain's dimensions.

关键词： Ship Manoeuvrability Nonlinear mathematical models Linearization Model approximation Least squares approximation Control applications numerical algorithms Random numbers State space

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Structure-preserving Computation of Stable Deflating Subspaces

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IFAC Proceedings Volumes 2010年第10期43卷 249-254页

作者： Vasile Sima National Institute for Research & Development in Informatics Bucharest 011455 Romania

Structure-preserving numerical techniques for computation of stable deflating subspaces, with applications in control systems design, are presented. The techniques use extended skew-Hamiltonian/Hamiltonian matrix pencils, and specialized algorithms to exploit their structure: the symplectic URV decomposition, periodic QZ algorithm, solution of periodic Sylvester-like equations, etc. The structure-preserving approach has the potential to avoid the numerical difficulties which are encountered for a traditional, non-structured solution, returned by the currently available software tools.

关键词： Computational methods Control systems design Eigenvalue problems Linear multivariable systems Matrix equations numerical algorithms

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