عنوان

Modeling and Computational Methods for Kinetic Equations

(Number (ISBN

9780817682002

(Number (ISBN

9781461264873

Number

b402585

Title Proper

Modeling and Computational Methods for Kinetic Equations

General Material Designation

[Book]

First Statement of Responsibility

edited by Pierre Degond, Lorenzo Pareschi, Giovanni Russo.

Place of Publication, Distribution, etc.

Boston, MA :

Name of Publisher, Distributor, etc.

Imprint: Birkhäuser,

Date of Publication, Distribution, etc.

2004.

Series Title

Modeling and Simulation in Science, Engineering and Technology,

ISSN of Series

2164-3679

Text of Note

I. Geometric Operators and the Inde -- Spectral invariants of operators of Dirac type on partitioned manifolds -- Index theory of Dirac operators on manifolds with corners up to codimension two -- Index defects in the theory of spectral boundary value problems -- Cyclic homology and pseudo differential operators, a survey -- Index and secondary index theory for flat bundles with duality -- II. Elliptic Boundary Value Problems -- Toeplitz operators, and ellipticity of boundary value problems with global projection conditions -- On the tangential oblique derivative problem - methods, results, open problems -- A note on boundary value problems on manifolds with cylindrical ends -- Relative elliptic theory -- Appendix. Fourier Integral Operators -- A.1. Homogeneous Lagrangian manifolds -- A.2. Local description of homogeneous Lagrangian manifolds -- A.3. Composition of homogeneous Lagrangian manifolds -- A.4. Definition of Fourier integral operators -- A.5. Pseudodifferential operators as Fourier integral operators -- A.6. Boundedness theorems -- A.7. Composition theorems -- References.

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Text of Note

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.

International Standard Book Number

9781461264873

Title

Springer eBooks

Computer science-- Mathematics.

Engineering mathematics.

Mathematics.

Degond, Pierre.

Pareschi, Lorenzo.

Russo, Giovanni.

SpringerLink (Online service)

Date of Transaction

20190307155800.0

Electronic name

[Book]

Y