From Kinetic Models to Hydrodynamics
Some Novel Results
Seiten
2013
Springer-Verlag New York Inc.
978-1-4614-6305-4 (ISBN)
Springer-Verlag New York Inc.
978-1-4614-6305-4 (ISBN)
From Kinetic Models to Hydrodynamics serves as an introduction to the asymptotic methods necessary to obtainhydrodynamic equations from a fundamental description using kinetic theory models and the Boltzmann equation.
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.
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.
1. Introduction.- 2. From the Phase Space to the Boltzmann Equation.- 3. Methods of Reduced Description.- 4. Hydrodynamic Spectrum of Simple Fluids.- 5. Hydrodynamic Fluctuations from the Boltzmann Equation.- 6. 13 Moment Grad System.- 7. Conclusions.- References.
| Reihe/Serie | SpringerBriefs in Mathematics |
|---|---|
| Zusatzinfo | 9 Illustrations, color; 12 Illustrations, black and white; X, 96 p. 21 illus., 9 illus. in color. |
| Verlagsort | New York, NY |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Angewandte Mathematik |
| Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik | |
| Naturwissenschaften ► Physik / Astronomie ► Thermodynamik | |
| ISBN-10 | 1-4614-6305-X / 146146305X |
| ISBN-13 | 978-1-4614-6305-4 / 9781461463054 |
| Zustand | Neuware |
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