Nonlinear Sciences – Chaotic Dynamics
Scientific paper
1999-06-24
NATO Science Series E, Vol. 317. Ed. J. Karkheck, 131-168 (Kluwer 2000)
Nonlinear Sciences
Chaotic Dynamics
35 pages, 10 figures (eps) + 1 LaTeX figure. Part of the proceedings of the 1998 NATO-ASI "Dynamics: Models and Kinetic Method
Scientific paper
It is generally believed that the dynamics of simple fluids can be considered to be chaotic, at least to the extent that they can be modeled as classical systems of particles interacting with short range, repulsive forces. Here we give a brief introduction to those parts of chaos theory that are relevant for understanding some features of non-equilibrium processes in fluids. We introduce the notions of Lyapunov exponents, Kolmogorov-Sinai entropy and related quantities using some simple low-dimensional systems as "toy" models of the more complicated systems encountered in the study of fluids. We then show how familiar methods used in the kinetic theory of gases can be employed for explicit, analytical calculations of the largest Lyapunov exponent and KS entropy for dilute gases composed of hard spheres in d dimensions. We conclude with a brief discussion of interesting, open problems.
Beijeren Henk van
Dorfman Robert J.
Zon Ramses van
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