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Thursday, October 18th 2007

1:25 pm:

An assembly of inelastically colliding hard spheres - the granular gas - is a simple model of °ow of granular materials. It provides a fascinating example of a complex system far from equilibrium. Granular gases exhibit a spontaneous clustering instability: development of clusters of particles and voids between them. A similar instability appears in gases and plasmas that cool by their own radiation. Nonlinear theory of the clustering instability has been a major unresolved problem of granular dynamics. We simplified this problem by considering a channel geometry, so that the coarse -grained °ow is one-dimensional. We found that, in the framework of idealized hydrodynamic equations, the gas exhibits a ¯nite-time density blowup. The \attempted" singularities are usually arrested only when the close packing density of hard spheres is reached. Molecular dynamics simulations support the hydrodynamic predictions until close to the time of attempted density blowup. In a certain limit of the instability, the dynamics is describable by a zero-viscosity Burgers equation which makes this system a distant cousin of a structure forming expanding Universe.

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