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Bridges 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
Addresses a functional equation for the nonequilibrium single-particle distribution function
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.
Content Level »Research
Keywords »Boltzmann equation theory - Grad’s moment method system - Navier-Stokes Fourier approximation - hydrodynamic equations, modes, fluctuations - kinetic theory models - the invariant manifold method