Modeling and Computational Methods for Kinetic Equations

ISBN-13: 9780817632540 / Angielski / Twarda / 2004 / 356 str.

Pierre Degond; Lorenzo Pareschi; Giovanni Russo

Opis

In recent years kinetic theory has developed in many areas of the physical sciences and engineering, and has extended the borders of its traditional fields of application. This monograph is a self-contained presentation of such recently developed aspects of kinetic theory, as well as a comprehensive account of the fundamentals of the theory. Emphasizing modeling techniques and numerical methods, the book provides a unified treatment of kinetic equations not found in more focused works. Specific applications presented include plasma kinetic models, traffic flow models, granular media models, and coagulation-fragmentation problems. The work may be used for self-study, as a reference text, or in graduate-level courses in kinetic theory and its applications.

Recenzje

From the reviews:

"Kinetic models can be used to describe the behaviour of gases and fluids in applications ... . The structure is different from a classical book, as it is actually a collection of scientific papers. ... it is recommended primarily for mathematicians with a high interest in physics, or for theoretical physicists, both of which at least at graduate level, but for those who understand the presented ideas, it might be a highly valuable tool or an inspiration for further research." (Simon Seichter, Simulation News Europe, Vol. 16 (1), 2006)

Spis treści

Preface Part I: Rarefied Gases Macroscopic Limits of the Boltzmann Equation: A Review Moment Equations for Charged Particles: Global Existence Results Monte-Carlo Methods for the Boltzmann Equation Accurate Numerical Methods for the Boltzmann Equation Finite-Difference Methods for the Boltzmann Equation for Binary Gas Mixtures Part II: Applications Plasma Kinetic Models: The Fokker-Planck-Landau Equation On Multipole Approximations of the Fokker-Planck-Landau Operator Traffic Flow: Models and Numerics Modelling and Numerical Methods for Granular Gases Quantum Kinetic Theory: Modelling and Numerics for Bose--Einstein Condensation On Coalescence Equations and Related Models

Blurb

In recent years kinetic theory has developed in many areas of the physical sciences and engineering, and has extended the borders of its traditional fields of application. New applications in traffic flow engineering, granular media modeling, and polymer and phase transition physics have resulted in new numerical algorithms which depart from traditional stochastic Monte--Carlo methods.

This monograph is a self-contained presentation of such recently developed aspects of kinetic theory, as well as a comprehensive account of the fundamentals of the theory. Emphasizing modeling techniques and numerical methods, the book provides a unified treatment of kinetic equations not found in more focused theoretical or applied works.

The book is divided into two parts. Part I is devoted to the most fundamental kinetic model: the Boltzmann equation of rarefied gas dynamics. Additionally, widely used numerical methods for the discretization of the Boltzmann equation are reviewed: the Monte--Carlo method, spectral methods, and finite-difference methods. Part II considers specific applications: plasma kinetic modeling using the Landau--Fokker--Planck equations, traffic flow modeling, granular media modeling, quantum kinetic modeling, and coagulation-fragmentation problems.

Modeling and Computational Methods of Kinetic Equations will be accessible to readers working in different communities where kinetic theory is important: graduate students, researchers and practitioners in mathematical physics, applied mathematics, and various branches of engineering. The work may be used for self-study, as a reference text, or in graduate-level courses in kinetic theory and its applications.