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Hard Ball Systems and the Lorentz Gas pp 279–314Cite as

Simulation of Billiards and of Hard Body Fluids

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Part of the book series: Encyclopaedia of Mathematical Sciences ((EMS,volume 101))

Abstract

Recent computer simulations have contributed significantly to our understanding of the Lyapunov instability of hard particle systems in equilibrium and in nonequilibrium steady states. We discuss a very general method for the computation of the full Lyapunov spectra and apply it to billiards and to many-body hard disk and hard sphere systems. The velocity correlation function of billiard flows is also discussed. For hard disk and hard sphere systems the perturbed states associated with the smallest Lyapunov exponents (in absolute magnitude) are shown to reveal collective dynamic modes. We study the properties of these modes and provide examples for hard disk systems in two dimensions. It is suggested that there is a connection with the dynamic modes familiar from fluctuating hydrodynamics. The largest Lyapunov exponent, however, is associated with localized perturbations in the fluid.

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Authors
  1. H. A. Posch
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  2. R. Hirschl
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Editor information

Editors and Affiliations

  1. Institute of Mathematics, Budapest University of Technology and Economics, 91, 1521, Budapest, Hungary

    D. Szász

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© 2000 Springer-Verlag Berlin Heidelberg

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Posch, H.A., Hirschl, R. (2000). Simulation of Billiards and of Hard Body Fluids. In: Szász, D. (eds) Hard Ball Systems and the Lorentz Gas. Encyclopaedia of Mathematical Sciences, vol 101. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04062-1_11

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  • DOI: https://doi.org/10.1007/978-3-662-04062-1_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-08711-0

  • Online ISBN: 978-3-662-04062-1

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