3:00 am Tuesday, May 24, 2005
ICES-Applied Math: Kinetic Theory of Granular Gases by Thorsten Poeschel (Humbolt University-Charite- Berlin) in ACES 6.304
Dilute force-free systems of dissipatively colliding particles - Granular Gases - reveal interesting phenomena such as non-Maxwellian velocity distribution, anomalous diffusion, self-organized vortexes and, at late stages of their evolution, density inhomogeneities and clusters. Similar to molecular gases, Granular Gases may be described by the concepts of classical Statistical Mechanics, such as temperature, velocity distribution function etc. Once initialized with a certain velocity distribution, during their evolution Granular Gases cool down due to inelastic collisions of their particles, characterized by the coefficient of restitution $\varepsilon$. We consider the first step of the evolution of a Granular Gas, where no spatial structures have emerged yet, starting from an initially homogeneous distribution. For simplicity of the mathematical analysis, in most studies the coefficient of restitution is assumed to be constant. It is known, however, that this assumption contradicts experiments and even a dimension analysis. Instead, for realistic materials it is a function on the impact velocity, $\varepsilon=\varepsilon(g)$ It is shown that the model assumptions $\varepsilon=$const and $\varepsilon=\varepsilon(g)$ (viscoelastic particles) lead to qualitatively different results. Whereas the velocity distribution function for the case $\varepsilon=$const. has a simple scaling form, the distribution function of gases of viscoelastic particles depends explicitely on time. This property allows to assign a Granular Gas an age. Moreover, in the long-time behavior, for viscoelastic particles the formation of clusters is suppressed or may occur only as a transient phenomenon. Ref: N.V. Brilliantov and T. P\"oschel: "Kinetic Theory of Granular Gases", Oxford University Press (2004) Submitted by
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