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From Kinetic Models to Hydrodynamics

Some Novel Results

Colangeli, Matteo

2013, X, 96 p. 21 illus., 9 illus. in color.

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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

Related subjects » Complexity - Mathematics - Theoretical, Mathematical & Computational Physics

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