Advances in Kinetic Theory and Computing

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Publisher : World Scientific
ISBN 13 : 9789810216719
Total Pages : 232 pages
Book Rating : 4.2/5 (167 download)

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Book Synopsis Advances in Kinetic Theory and Computing by : B. Perthame

Download or read book Advances in Kinetic Theory and Computing written by B. Perthame and published by World Scientific. This book was released on 1994 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).

Advances in Kinetic Theory and Computing: Selected Papers

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Publisher : World Scientific
ISBN 13 : 9814502332
Total Pages : 228 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Advances in Kinetic Theory and Computing: Selected Papers by : B Perthame

Download or read book Advances in Kinetic Theory and Computing: Selected Papers written by B Perthame and published by World Scientific. This book was released on 1994-09-30 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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). Contents:Vlasov-Poisson in Plasma Physics:The Child-Langmuir Law in the Kinetic Theory of Charged-Particles. Part 1, Electron Flows in Vacuum (P Degond)Eulerian Codes for the Vlasov Equation (M R Feix et al.)Mathematical Models of Ion Extraction and Plasma Sheaths (S Mas-Gallic & P A Raviart)Quantum Mechanics and Semiconductors:Transport Equations for Quantum Plasmas (G Manfredi & M R Feix)Mathematical Theory of Kinetic Equations for Transport Modelling in Semiconductors (F Poupaud)Boltzmann Equations and Gas Dynamics:On Zero Pressure Gas Dynamics (F Bouchut)A Remark Concerning the Chapman-Enskog Asymptotics (L Desvillettes & F Golse)Introduction to the Theory of Random Particle Methods for Boltzmann Equation (B Perthame) Readership: Applied mathematicians. keywords:Semiconductor Modelling ;Plasma Physics;Boltzmann Equation;Monte-Carlo Method;Particle Methods;Quantum Mechanics;Vlasov Equation;Hypersonic Flows;Kinetic Theory;Multiscale Analysis

Singularly Perturbed Evolution Equations with Applications to Kinetic Theory

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Publisher : World Scientific
ISBN 13 : 9789810221256
Total Pages : 332 pages
Book Rating : 4.2/5 (212 download)

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Book Synopsis Singularly Perturbed Evolution Equations with Applications to Kinetic Theory by : J. R. Mika

Download or read book Singularly Perturbed Evolution Equations with Applications to Kinetic Theory written by J. R. Mika and published by World Scientific. This book was released on 1995 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years there appeared a large number of papers as well as chapters in more general monographs devoted to evolution equations containing small (or large) parameters. In this book it is intended to gather the existing results as well as to introduce new ones on the field of initial value problems for singularly perturbed evolution equations of the resonance type. Such equations are of great interest in the applied sciences, particularly in the kinetic theory which is chosen as the main field of application for the asymptotic theory developed in the monograph.

The Cauchy Problem in Kinetic Theory

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Publisher : SIAM
ISBN 13 : 0898713676
Total Pages : 246 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis The Cauchy Problem in Kinetic Theory by : Robert T. Glassey

Download or read book The Cauchy Problem in Kinetic Theory written by Robert T. Glassey and published by SIAM. This book was released on 1996-01-01 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: Studies the basic equations of kinetic theory in all of space, and contains up-to-date, state-of-the-art treatments of initial-value problems for the major kinetic equations. This is the only existing book to treat Boltzmann-type problems and Vlasov-type problems together. Although describing very different phenomena, these equations share the same streaming term.

Advances in Kinetic Theory and Continuum Mechanics

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Publisher :
ISBN 13 : 9780387539454
Total Pages : pages
Book Rating : 4.5/5 (394 download)

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Book Synopsis Advances in Kinetic Theory and Continuum Mechanics by : Renée Gatignol

Download or read book Advances in Kinetic Theory and Continuum Mechanics written by Renée Gatignol and published by . This book was released on 1991 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mathematical Topics in Nonlinear Kinetic Theory

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Publisher : World Scientific
ISBN 13 : 9789971507022
Total Pages : 248 pages
Book Rating : 4.5/5 (7 download)

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Book Synopsis Mathematical Topics in Nonlinear Kinetic Theory by : N. Bellomo

Download or read book Mathematical Topics in Nonlinear Kinetic Theory written by N. Bellomo and published by World Scientific. This book was released on 1988 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book has the aim of dealing with the Nonlinear evolution problems related to the spatially dependent Boltzmann and Enskog equations.

Advanced Mathematical & Computational Tools in Metrology VII

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Publisher : World Scientific
ISBN 13 : 9812566740
Total Pages : 386 pages
Book Rating : 4.8/5 (125 download)

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Book Synopsis Advanced Mathematical & Computational Tools in Metrology VII by : P. Ciarlini

Download or read book Advanced Mathematical & Computational Tools in Metrology VII written by P. Ciarlini and published by World Scientific. This book was released on 2006 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects the refereed contributions based on the presentations made at the Seventh Workshop on Advanced Mathematical and Computational Tools in Metrology, a forum for metrologists, mathematicians and software engineers that will encourage a more effective synthesis of skills, capabilities and resources. The volume contains articles by world renowned metrologists and mathematicians involved in measurement science and, together with the six previous volumes in this series, constitutes an authoritative source of the mathematical, statistical and software tools necessary in modern metrology. Contents: Modeling Measurement Processes in Complex Systems with Partial Differential Equations: From Heat Conduction to the Heart (M Baer et al.); Mereotipological Approach for Measurement Software (E Benoit & R Dapoigny); Data Evaluation of Key Comparisons Involving Several Artefacts (M G Cox et al.); Box-Cox Transformations Versus Robust Control Charts in Statistical Process Control (M I Gomes & F O Figueiredo); Decision Making Using Sensor's Data Fusion and Kohonen Self Organizing Maps (P S Girao et al.); Generic System Design for Measurement Databases Applied to Calibrations in Vacuum Metrology, Bio-Signals and a Template System (H Gro et al.); Repeated Measurements: Evaluation of Their Uncertainty from the Viewpoints of Classical and Bayesian Statistics (I Lira & W Woger); Detection of Outliers in Interlaboratory Testing and Some Thoughts About Multivariate Precision (C Perruchet); On Appropriate Methods for the Validation of Metrological Software (D Richter et al.); Data Analysis-A Dialogue (D S Sivia); Validation of a Virtual Sensor for Monitoring Ambient Parameters (P Ciarlini et al.); Evaluation of Standard Uncertainties in Nested Structures (E Filipe); Linking GUM and ISO 5725 (A B Forbes); Monte Carlo Study on Logical and Statistical Correlation (B Siebert et al.); Some Problems Concerning the Estimate of the Uncertainty of the Degree of Equivalence in MRA Key Comparisons (F Pavese); Preparing for a European Research Area Network in Metrology: Where are We Now? (M Kuhne et al.); and other papers. Readership: Researchers, graduate students, academics and professionals in metrology.

Multigroup Equations for the Description of the Particle Transport in Semiconductors

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Publisher : World Scientific
ISBN 13 : 9812563555
Total Pages : 247 pages
Book Rating : 4.8/5 (125 download)

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Book Synopsis Multigroup Equations for the Description of the Particle Transport in Semiconductors by : Martin Galler

Download or read book Multigroup Equations for the Description of the Particle Transport in Semiconductors written by Martin Galler and published by World Scientific. This book was released on 2005 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: Deterministic simulation of the particle transport in semiconductor devices is an interesting alternative to the common Monte Carlo approach. In this book, a state-of-the-art technique called the multigroup approach is presented and applied to a variety of transport problems in bulk semiconductors and semiconductor devices. High-field effects as well as hot-phonon phenomena in polar semiconductors are studied in detail. The mathematical properties of the presented numerical method are studied, and the method is applied to simulating the transport of a two-dimensional electron gas formed at a semiconductor heterostructure. Concerning semiconductor device simulation, several diodes and transistors fabricated of silicon and gallium arsenide are investigated. For all of these simulations, the numerical techniques employed are discussed in detail.This unique study of the application of direct methods for semiconductor device simulation provides the interested reader with an indispensable reference on this growing research area.

Dissipative Phase Transitions

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Publisher : World Scientific
ISBN 13 : 9812774297
Total Pages : 321 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis Dissipative Phase Transitions by : Pierluigi Colli

Download or read book Dissipative Phase Transitions written by Pierluigi Colli and published by World Scientific. This book was released on 2006 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Phase transition phenomena arise in a variety of relevant real world situations, such as melting and freezing in a solid-liquid system, evaporation, solid-solid phase transitions in shape memory alloys, combustion, crystal growth, damage in elastic materials, glass formation, phase transitions in polymers, and plasticity. The practical interest of such phenomenology is evident and has deeply influenced the technological development of our society, stimulating intense mathematical research in this area. This book analyzes and approximates some models and related partial differential equation problems that involve phase transitions in different contexts and include dissipation effects. Contents: Mathematical Models Including a Hysteresis Operator (T Aiki); Modelling Phase Transitions via an Entropy Equation: Long-Time Behavior of the Solutions (E Bonetti); Global Solution to a One Dimensional Phase Transition Model with Strong Dissipation (G Bonfanti & F Luterotti); A Global in Time Result for an Integro-Differential Parabolic Inverse Problem in the Space of Bounded Functions (F Colombo et al.); Weak Solutions for Stefan Problems with Convections (T Fukao); Memory Relaxation of the One-Dimensional CahnOCoHilliard Equation (S Gatti et al.); Mathematical Models for Phase Transition in Materials with Thermal Memory (G Gentili & C Giorgi); Hysteresis in a First Order Hyperbolic Equation (J Kopfovi); Approximation of Inverse Problems Related to Parabolic Integro-Differential Systems of Caginalp Type (A Lorenzi & E Rocca); Gradient Flow Reaction/Diffusion Models in Phase Transitions (J Norbury & C Girardet); New Existence Result for a 3-D Shape Memory Model (I Pawlow & W M Zajaczkowski); Analysis of a 1-D Thermoviscoelastic Model with Temperature-Dependent Viscosity (R Peyroux & U Stefanelli); Global Attractor for the Weak Solutions of a Class of Viscous Cahn-Hilliard Equations (R Rossi); Stability for Phase Field Systems Involving Indefinite Surface Tension Coefficients (K Shirakawa); Geometric Features of p -Laplace Phase Transitions (E Valdinoci). Readership: Applied mathematicians and researchers in analysis and differential equations."

Theory Of The Navier-Stokes Equations

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Publisher : World Scientific
ISBN 13 : 9814496782
Total Pages : 248 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Theory Of The Navier-Stokes Equations by : J G Heywood

Download or read book Theory Of The Navier-Stokes Equations written by J G Heywood and published by World Scientific. This book was released on 1998-05-30 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects the articles presented at the Third International Conference on “The Navier-Stokes Equations: Theory and Numerical Methods”, held in Oberwolfach, Germany. The articles are important contributions to a wide variety of topics in the Navier-Stokes theory: general boundary conditions, flow exterior to an obstacle, conical boundary points, the controllability of solutions, compressible flow, non-Newtonian flow, magneto-hydrodynamics, thermal convection, the interaction of fluids with elastic solids, the regularity of solutions, and Rothe's method of approximation. Contents: The 3D Stokes Systems in Domains with Conical Boundary Points (P Deuring)Weighted Estimates for the Oseen Equations and the Navier–Stokes Equations in Exterior Domains (R Farwig & H Sohr)On Boundary Zero Controllability of the Three-Dimensional Navier–Stokes Equations (A V Fursikov)Nonhomogeneous Navier–Stokes Problems in Lp Sobolev Spaces Over Exterior and Interior Domains (G Grubb)Lp-Decay Rates for Strong Solutions of a Perturbed Navier–Stokes–Systems in R3 (H Ch Grunau)On Two-Dimensional Equations of Thermal Convection in the Presence of the Dissipation Function (Y Kagei)On Decay Properties of Solutions to Stokes System in Exterior Domains (P Maremonti & V A Solonnikov)Compactness of Steady Compressible Isentropic Navier–Stokes Equations via the Decomposition Method (the Whole 3-D Space) (A Novotny)Convergence Rates in H2,r of Rothe's Method to the Navier–Stokes Equations (R Rautmann)On Equilibria in the Interaction of Fluids and Elastic Solids (M Rumpf)Regularity for Steady Solutions of the Navier–Stokes Equations (M Ruzicka & J Frehse)Decay of Non-Oscillating Solutions to the Magneto-Hydrodynamic Equations (M E Schonbeck)and other papers Readership: Applied mathematicians. keywords:Proceedings;Conference;Navier-Stokes Equations;Oberwolfach (Germany);Numerical Methods

Mathematical Methods in Electromagnetism

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Publisher : World Scientific
ISBN 13 : 9814525383
Total Pages : 396 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Mathematical Methods in Electromagnetism by : M Cessenat

Download or read book Mathematical Methods in Electromagnetism written by M Cessenat and published by World Scientific. This book was released on 1996-07-13 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the reader with basic tools to solve problems of electromagnetism in their natural functional frameworks thanks to modern mathematical methods: integral surface methods, and also semigroups, variational methods, etc., well adapted to a numerical approach. As examples of applications of these tools and concepts, we solve several fundamental problems of electromagnetism, stationary or time-dependent: scattering of an incident wave by an obstacle, bounded or not, by gratings; wave propagation in a waveguide, with junctions and cascades. We hope that mathematical notions will allow a better understanding of modelization in electromagnetism and emphasize the essential features related to the geometry and nature of materials. Contents:Mathematical Modelling of the Electromagnetic Field in Continuous Media: Maxwell Equations and Constitutive RelationsMathematical Framework for ElectromagnetismStationary Scattering Problems with Bounded ObstaclesWaveguide ProblemsStationary Scattering Problems on Unbounded ObstaclesEvolution ProblemsAppendix — Differential Geometry for ElectromagnetismReferencesIndexNotations Readership: Applied mathematicians. keywords:Electromagnetism;Mathematical Modeling;Maxwell Equations;Variational Methods;Differential Geometry;Hodge Decomposition;Impedance Operators;Calderon Operators;Waveguides;Scattering;Outgoing Waves;Causal Problems “I would recommend it to anyone interested in the analysis or numerical analysis of Maxwell's equations for its up-to-date and extensive treatment of the problem.” SIAM Reviews

Microscopic Theory of Condensation in Gases and Plasma

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Publisher : World Scientific
ISBN 13 : 9789810229078
Total Pages : 300 pages
Book Rating : 4.2/5 (29 download)

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Book Synopsis Microscopic Theory of Condensation in Gases and Plasma by : A. L. Itkin

Download or read book Microscopic Theory of Condensation in Gases and Plasma written by A. L. Itkin and published by World Scientific. This book was released on 1997 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book summarizes results on the creation of a new theory of condensation which has an impact on consideration of some microscopic effects left aside in the usual nucleation theories. In particular, the main idea of the authors' microscopic condensation theory is that it considers the violation of the equilibrium cluster distribution over the internal degrees of freedom due to co-occurring condensation and decay reactions of the clusters.

Mathematical Topics in Neutron Transport Theory

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Publisher : World Scientific
ISBN 13 : 981449819X
Total Pages : 364 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Mathematical Topics in Neutron Transport Theory by : M Mokhtar-Kharroubi

Download or read book Mathematical Topics in Neutron Transport Theory written by M Mokhtar-Kharroubi and published by World Scientific. This book was released on 1997-12-18 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents some recent mathematical developments about neutron transport equations. Several different topics are dealt with including regularity of velocity averages, spectral analysis of transport operators, inverse problems, nonlinear problems arising in the stochastic theory of neutron chain fissions, compactness properties of perturbed of c0-semigroups in Banach spaces with applications to transport theory, Miyadera perturbations of c0-semigroups in Banach spaces with applications to singular transport equations, a thorough analysis of the leading eigenelements of transport operators and their approximation, scattering theory. Besides the new problems addressed in this book a unification and extension of the classical spectral analysis of neutron transport equations is given. Contents:Compactness Properties of Perturbed c0-SemigroupsRegularity of Velocity AveragesSpectral Analysis of Transport Equations. A Unified TheoryOn the Leading Eigenelements of Transport OperatorsSpectral Theory of Transport of Operators with Form Positive Collision OperatorsOn Miyadera Perturbations of c0-SemigroupsOn Resolvent Positive Operators and Positive c0-Semigroups in L1(μ) SpacesOn Singular Neutron Transport Equations in L1 SpacesStochastic Formulations of Neutron Transport. Nonlinear ProblemsVelocity Averages and Inverse ProblemsLimiting Absorption Principles and Wave Operators in L1(μ) Spaces with Applications to Transport TheoryLin's Factorization Formalism and Applications to Transport TheoryInverse Scattering and Albedo Operator Readership: Applied mathematicians and mathematical physicists. keywords:Transport Operator;Spectral Theory;Compactness;Semigroup;Positive Operator;Irreducibility;Leading Eigenvalue;Neutron Chain Fissions;Inverse Problems;Scattering Theory

Lecture Notes On Mathematical Theory Of The Boltzmann Equation

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Publisher : World Scientific
ISBN 13 : 9814500844
Total Pages : 273 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Lecture Notes On Mathematical Theory Of The Boltzmann Equation by : Nicola Bellomo

Download or read book Lecture Notes On Mathematical Theory Of The Boltzmann Equation written by Nicola Bellomo and published by World Scientific. This book was released on 1995-08-31 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a collection of four lectures on some mathematical aspects related to the nonlinear Boltzmann equation. The following topics are dealt with: derivation of kinetic equations, qualitative analysis of the initial value problem, singular perturbation analysis towards the hydrodynamic limit and computational methods towards the solution of problems in fluid dynamics.

Lecture Notes On The Mathematical Theory Of Generalized Boltzmann Models

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Publisher : World Scientific
ISBN 13 : 9814494259
Total Pages : 356 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Lecture Notes On The Mathematical Theory Of Generalized Boltzmann Models by : Nicola Bellomo

Download or read book Lecture Notes On The Mathematical Theory Of Generalized Boltzmann Models written by Nicola Bellomo and published by World Scientific. This book was released on 2000-01-11 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on the idea that Boltzmann-like modelling methods can be developed to design, with special attention to applied sciences, kinetic-type models which are called generalized kinetic models. In particular, these models appear in evolution equations for the statistical distribution over the physical state of each individual of a large population. The evolution is determined both by interactions among individuals and by external actions.Considering that generalized kinetic models can play an important role in dealing with several interesting systems in applied sciences, the book provides a unified presentation of this topic with direct reference to modelling, mathematical statement of problems, qualitative and computational analysis, and applications. Models reported and proposed in the book refer to several fields of natural, applied and technological sciences. In particular, the following classes of models are discussed: population dynamics and socio-economic behaviours, models of aggregation and fragmentation phenomena, models of biology and immunology, traffic flow models, models of mixtures and particles undergoing classic and dissipative interactions.

Nonlinear Theory of Generalized Functions

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Publisher : CRC Press
ISBN 13 : 9780849306495
Total Pages : 396 pages
Book Rating : 4.3/5 (64 download)

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Book Synopsis Nonlinear Theory of Generalized Functions by : Michael Oberguggenberger

Download or read book Nonlinear Theory of Generalized Functions written by Michael Oberguggenberger and published by CRC Press. This book was released on 1999-03-16 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: Questions regarding the interplay of nonlinearity and the creation and propagation of singularities arise in a variety of fields-including nonlinear partial differential equations, noise-driven stochastic partial differential equations, general relativity, and geometry with singularities. A workshop held at the Erwin-Schrödinger International Institute for Mathematical Physics in Vienna investigated these questions and culminated in this volume of invited papers from experts in the fields of nonlinear partial differential equations, structure theory of generalized functions, geometry and general relativity, stochastic partial differential equations, and nonstandard analysis. The authors provide the latest research relevant to work in partial differential equations, mathematical physics, and nonlinear analysis. With a focus on applications, this books provides a compilation of recent approaches to the problem of singularities in nonlinear models. The theory of differential algebras of generalized functions serves as the central theme of the project, along with its interrelations with classical methods.

Differential Equations, Bifurcations, and Chaos in Economics

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Publisher : World Scientific Publishing Company
ISBN 13 : 9813106514
Total Pages : 512 pages
Book Rating : 4.8/5 (131 download)

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Book Synopsis Differential Equations, Bifurcations, and Chaos in Economics by : Wei-Bin Zhang

Download or read book Differential Equations, Bifurcations, and Chaos in Economics written by Wei-Bin Zhang and published by World Scientific Publishing Company. This book was released on 2005-07-18 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although the application of differential equations to economics is a vast and vibrant area, the subject has not been systematically studied; it is often treated as a subsidiary part of mathematical economics textbooks. This book aims to fill that void by providing a unique blend of the theory of differential equations and their exciting applications to dynamic economics. Containing not just a comprehensive introduction to the applications of the theory of linear (and linearized) differential equations to economic analysis, the book also studies nonlinear dynamical systems, which have only been widely applied to economic analysis in recent years. It provides comprehensive coverage of the most important concepts and theorems in the theory of differential equations in a way that can be understood by any reader who has a basic knowledge of calculus and linear algebra. In addition to traditional applications of the theory to economic dynamics, the book includes many recent developments in different fields of economics.