From Kinetic Models to Hydrodynamics
Subtitle: Some Novel Results
By: by Matteo Colangeli
Contributors: SpringerLink (Online service)
Series: SpringerBriefs in Mathematics
Publisher: Springer New York; Imprint: Springer
Published: 2013
Place of publication: New York, NY
Language: eng
Format: [electronic resource] :
Number of pages: 96
ISBN-13: 9781461463061
Subjects: Mathematical physics; Mathematical Applications in the Physical Sciences; Mathematics; Mathematical Modeling and Industrial Mathematics; Mathematical Methods in Physics; Mathematical and Computational Physics Theoretical; Dynamical Systems and Complexity Statistical Physics
Description: ​​From Kinetic Models to Hydrodynamics serves as an introduction to the asymptotic methods necessary to obtain hydrodynamic equations from a fundamental description using kinetic theory models and the Boltzmann equation.  The work is a survey of an active research area, which aims to bridge time and length scales from the particle-like description inherent in Boltzmann equation theory to a fully established “continuum” approach typical of macroscopic laws of physics.The author sheds light on a new method—using invariant manifolds—which addresses a functional equation for the nonequilibrium single-particle distribution function.  This method allows one to find exact and thermodynamically consistent expressions for: hydrodynamic modes; transport coefficient expressions for hydrodynamic modes; and transport coefficients of a fluid beyond the traditional hydrodynamic limit.  The invariant manifold method paves the way to establish a needed bridge between Boltzmann equation theory and a particle-based theory of hydrodynamics.  Finally, the author explores the ambitious and longstanding task of obtaining hydrodynamic constitutive equations from their kinetic counterparts.​ The work is intended for specialists in kinetic theory—or more generally statistical mechanics—and will provide a bridge between a physical and mathematical approach to solve real-world problems.​
Table of contents: title: ​​​ 1. Introduction; title: 2. From the Phase Space to the Boltzmann Equation; title: 3. Methods of Reduced Description; title: 4. Hydrodynamic Spectrum of Simple Fluids; title: 5. Hydrodynamic Fluctuations from the Boltzmann Equation; title: 6. 13 Moment Grad System; title: 7. Conclusions; title: References.   ​ ​​.