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2013 | OriginalPaper | Chapter

3. Methods of Reduced Description

Author : Matteo Colangeli

Published in: From Kinetic Models to Hydrodynamics

Publisher: Springer New York

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Abstract

In this chapter, we will review some analytical methods that make it possible to determine approximate solutions of the Boltzmann equation. In particular, we will discuss the structure of the Hilbert and Chapman–Enskog perturbation techniques and will also outline the essential features of the invariant manifold method, which stems from the assumption of time scale separation and, unlike the former methods, is also applicable beyond the strict hydrodynamic limit. Before reviewing the wealth of different techniques, it is worth investigating in greater depth the role of the different time scales in a particle system, which is one of the main ingredients underlying the onset of collective behavior.

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previous chapter From the Phase Space to the Boltzmann Equation
next chapter Hydrodynamic Spectrum of Simple Fluids
Literature
1.
C. Cercignani, Theory and Application of the Boltzmann Equation (Scottish Academic Press, Edinburgh, 1975).
2.
D. Jou, J. Casas-Vázquez and G. Lebon, Extended Irreversible Thermodynamics (Springer, Berlin, 2010).
3.
H. C. Öttinger, Beyond Equilibrium Thermodynamics (Wiley, New York, 2005).
4.
H. Grad, On the kinetic theory of rarefied gases, Comm. Pure and Appl. Math. 2, 331 (1949).
5.
R. Liboff, Kinetic Theory Classical, Quantum and Relativistic Descriptions (Springer, New York, 2003).
6.
N. N. Bogoliubov, in Studies in statistical mechanics, vol. 1, J. de Boer and G. E. Uhlenbeck (Wiley, New York, 1962).
7.
R. Liboff, Generalized Bogoliubov hypothesis for dense fluids, Phys. Rev. A 31, 1883 (1985).
8.
R. Balescu, Equilibrium and nonequilibrium statistical mechanics (Wiley, New York, 1975).
9.
D. Forster, Hydrodynamic fluctuations, Broken Symmetry, and Corrrelation Functions (W. A. Benjamin, New York, 1975).
10.
S. Chapman and T. G. Cowling, The Mathematical Theory of Nonuniform Gases, (Cambridge University Press, New York, 1970).
11.
M. Lachowicz, From kinetic to Navier-Stokes-type equations, Appl. Math. Lett. 10, 19 (1997).
12.
A.N. Gorban and I.V. Karlin, Invariant Manifolds for Physical and Chemical Kinetics, Lect. Notes Phys. 660 (Springer, Berlin, 2005).
13.
M. Colangeli, I.V. Karlin and M. Kröger, From hyperbolic regularization to exact hydrodynamics for linearized Grad’s equations, Phys. Rev. E 75, 051204 (2007).
14.
M. Colangeli, I.V. Karlin and M. Kröger, Hyperbolicity of exact hydrodynamics for three-dimensional linearized Grad’s equations, Phys. Rev. E 76, 022201 (2007).
15.
A.V. Bobylev, Sov. Phys. Dokl. 27, 29 (1982).
16.
R. Zwanzig, Memory Effects in Irreversible Thermodynamics, Phys. Rev. 124, 983 (1961).
17.
D. N. Zubarev and V. P. Kalashnikov, Extremal properties of the nonequilibrium statistical operator, Theor. Math. Phys. 1, 108 (1969).
18.
H. Grabert, Projection Operator Techniques in Nonequilibrium statistical Mechanics (Springer, Berlin, 1982).
19.
H. Haken, Synergetics: an introduction: nonequilibrium phase transitions and self-organization in physics, chemistry and biology (Springer, Berlin, 1978).
20.
C. W. Gardiner, Handbook of stochastic methods (Springer, Berlin, 2004).
21.
I.V. Karlin, Exact summation of the Chapman-Enskog expansion from moment equations, J. Phys. A: Math. Gen. 33, 8037 (2000).
22.
I.V. Karlin and A.N. Gorban, Hydrodynamics from Grad’s equations: What can we learn from exact solutions?, Ann. Phys. (Leipzig) 11, 783 (2002).
Metadata
Title
Methods of Reduced Description
Author
Matteo Colangeli
Copyright Year
2013
Publisher
Springer New York
Book
From Kinetic Models to Hydrodynamics

Print ISBN: 978-1-4614-6305-4

Electronic ISBN: 978-1-4614-6306-1

Copyright Year: 2013

DOI
https://doi.org/10.1007/978-1-4614-6306-1_3

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