Author: B. Perthame
Publisher: World Scientific
ISBN: 9789810216719
Category : Mathematics
Languages : en
Pages : 232
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Book Description
This selection of 8 papers discusses ?Equations of Kinetic Physics? with emphasis on analysis, modelling and computing. The first 3 papers are on numerical methods for Vlasov-Poisson and Vlasov-Maxwell Equations ? Comparison between Particles and Eulerian Methods (G Manfredi and M R Feix), Computing BGK Instability with Eulerian Codes (M R Feix, Pertrand & A Ghieco) and Coupling Particles and Eulerian Methods (S Mas-Gallic and P A Raviart) ? Followed by a survey of kinetic and macroscopic models for semiconductor devices ? Boltzmann Equation, Drift-Diffusion Models (F Poupaud). In addition, there are 2 papers on the modelling and analysis of singular perturbation problems arising in plasma physics ? Derivation of the Child-Lagmuyr Emission Laws (P Degond) and Euler Models with Small Pressure Terms (F Bouchut) ? followed by two papers on the analysis and numerical analysis of the Boltzmann equations ? Symmetry Properties in the Polynomials Arising in Chapman-Enskog Expansion (L Desvillettes and F Golse) and A General Introduction to Computing the Boltzmann Equations with Random Particle Methods (B Perthame).
Author: Benoit Perthame
Publisher: World Scientific
ISBN: 9814502332
Category : Mathematics
Languages : en
Pages : 228
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Book Description
This selection of 8 papers discusses “Equations of Kinetic Physics” with emphasis on analysis, modelling and computing. The first 3 papers are on numerical methods for Vlasov-Poisson and Vlasov-Maxwell Equations — Comparison between Particles and Eulerian Methods (G Manfredi and M R Feix), Computing BGK Instability with Eulerian Codes (M R Feix, Pertrand & A Ghieco) and Coupling Particles and Eulerian Methods (S Mas-Gallic and P A Raviart) — Followed by a survey of kinetic and macroscopic models for semiconductor devices — Boltzmann Equation, Drift-Diffusion Models (F Poupaud). In addition, there are 2 papers on the modelling and analysis of singular perturbation problems arising in plasma physics — Derivation of the Child-Lagmuyr Emission Laws (P Degond) and Euler Models with Small Pressure Terms (F Bouchut) — followed by two papers on the analysis and numerical analysis of the Boltzmann equations — Symmetry Properties in the Polynomials Arising in Chapman-Enskog Expansion (L Desvillettes and F Golse) and A General Introduction to Computing the Boltzmann Equations with Random Particle Methods (B Perthame).
Author: Henryk Gzyl
Publisher: World Scientific
ISBN: 9814501921
Category : Mathematics
Languages : en
Pages : 161
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Book Description
This monograph is an outgrowth of a set of lecture notes on the maximum entropy method delivered at the 1st Venezuelan School of Mathematics. This yearly event aims at acquainting graduate students and university teachers with the trends, techniques and open problems of current interest. In this book the author reviews several versions of the maximum entropy method and makes its underlying philosophy clear.
Author: Drumi D Bainov
Publisher: World Scientific
ISBN: 9814501883
Category : Mathematics
Languages : en
Pages : 246
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Book Description
The question of the presence of various asymptotic properties of the solutions of ordinary differential equations arises when solving various practical problems. The investigation of these questions is still more important for impulsive differential equations which have a wider field of application than the ordinary ones.The results obtained by treating the asymptotic properties of the solutions of impulsive differential equations can be found in numerous separate articles. The systematized exposition of these results in a separate book will satisfy the growing interest in the problems related to the asymptotic properties of the solutions of impulsive differential equations and their applications.
Author: Carlo Cattani
Publisher: World Scientific
ISBN: 981447505X
Category : Mathematics
Languages : en
Pages : 473
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Book Description
This seminal book unites three different areas of modern science: the micromechanics and nanomechanics of composite materials; wavelet analysis as applied to physical problems; and the propagation of a new type of solitary wave in composite materials, nonlinear waves. Each of the three areas is described in a simple and understandable form, focusing on the many perspectives of the links among the three.All of the techniques and procedures are described here in the clearest and most open form, enabling the reader to quickly learn and use them when faced with the new and more advanced problems that are proposed in this book. By combining these new scientific concepts into a unitary model and enlightening readers on this pioneering field of research, readers will hopefully be inspired to explore the more advanced aspects of this promising scientific direction. The application of wavelet analysis to nanomaterials and waves in nanocomposites can be very appealing to both specialists working on theoretical developments in wavelets as well as specialists applying these methods and experiments in the mechanics of materials.
Author: Ekaterina Ivanova Kozlova
Publisher: World Scientific
ISBN: 9814497533
Category : Science
Languages : en
Pages : 448
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Book Description
This is a memorial volume in honor of Serguei Kozlov, one of the founders of homogenization, a new branch of mathematical physics. This volume contains original contributions of leading world experts in the field.
Author: Kumbakonam Ramamani Rajagopal
Publisher: World Scientific
ISBN: 9810215851
Category : Science
Languages : en
Pages : 220
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Book Description
This book presents a unified treatment of the mechanics of mixtures of several constituents within the context of continuum mechanics. After an introduction to the basic theory in the first few chapters, the book deals with a detailed exposition of the mechanics of a mixture of a fluid and an elastic solid, which is either isotropic or anisotropic and is capable of undergoing large deformations. Issues regarding the specification of boundary conditions for mixtures are discussed in detail and several boundary value and initial-boundary value problems are solved. The status of some special theories like those of Darcy and Biot are discussed. Such a study has relevance to several technologically significant problems in geomechanics, biomechanics, diffusion of contaminants and the swelling and absorption of fluids in polymers and polymer composites, to mention a few.
Author: Remigio Russo
Publisher: World Scientific
ISBN: 9814499277
Category : Mathematics
Languages : en
Pages : 206
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Book Description
In this volume, five papers are collected that give a good sample of the problems and the results characterizing some recent trends and advances in this theory. Some of them are devoted to the improvement of a general abstract knowledge of the behavior of elastic bodies, while the others mainly deal with more applicative topics.
Author: Marek Capi?ski
Publisher: World Scientific
ISBN: 9789810217105
Category : Science
Languages : en
Pages : 256
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Book Description
This book is an exposition of a new approach to the Navier-Stokes equations, using powerful techniques provided by nonstandard analysis, as developed by the authors. The topics studied include the existence and uniqueness of weak solutions, statistical solutions and the solution of general stochastic equations.The authors provide a self-contained introduction to nonstandard analysis, designed with applied mathematicians in mind and concentrated specifically on techniques applicable to the Navier-Stokes equations. The subsequent exposition shows how these new techniques allow a quick and intuitive entrance into the mathematical theory of hydrodynamics, as well as provide a research tool that has proven useful in solving open problems concerning stochastic equations.
Author: Yevgeny Mamontov
Publisher: World Scientific
ISBN: 9810243855
Category : Mathematics
Languages : en
Pages : 322
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Book Description
This book is the first one devoted to high-dimensional (or large-scale) diffusion stochastic processes (DSPs) with nonlinear coefficients. These processes are closely associated with nonlinear Ito's stochastic ordinary differential equations (ISODEs) and with the space-discretized versions of nonlinear Ito's stochastic partial integro-differential equations. The latter models include Ito's stochastic partial differential equations (ISPDEs).The book presents the new analytical treatment which can serve as the basis of a combined, analytical-numerical approach to greater computational efficiency in engineering problems. A few examples discussed in the book include: the high-dimensional DSPs described with the ISODE systems for semiconductor circuits; the nonrandom model for stochastic resonance (and other noise-induced phenomena) in high-dimensional DSPs; the modification of the well-known stochastic-adaptive-interpolation method by means of bases of function spaces; ISPDEs as the tool to consistently model non-Markov phenomena; the ISPDE system for semiconductor devices; the corresponding classification of charge transport in macroscale, mesoscale and microscale semiconductor regions based on the wave-diffusion equation; the fully time-domain nonlinear-friction aware analytical model for the velocity covariance of particle of uniform fluid, simple or dispersed; the specific time-domain analytics for the long, non-exponential “tails” of the velocity in case of the hard-sphere fluid.These examples demonstrate not only the capabilities of the developed techniques but also emphasize the usefulness of the complex-system-related approaches to solve some problems which have not been solved with the traditional, statistical-physics methods yet. From this veiwpoint, the book can be regarded as a kind of complement to such books as “Introduction to the Physics of Complex Systems. The Mesoscopic Approach to Fluctuations, Nonlinearity and Self-Organization” by Serra, Andretta, Compiani and Zanarini, “Stochastic Dynamical Systems. Concepts, Numerical Methods, Data Analysis” and “Statistical Physics: An Advanced Approach with Applications” by Honerkamp which deal with physics of complex systems, some of the corresponding analysis methods and an innovative, stochastics-based vision of theoretical physics.To facilitate the reading by nonmathematicians, the introductory chapter outlines the basic notions and results of theory of Markov and diffusion stochastic processes without involving the measure-theoretical approach. This presentation is based on probability densities commonly used in engineering and applied sciences.