Formation and evolution of density singularities in hydrodynamics of inelastic gases

Details Formation and evolution of density singularities in hydrodynamics of inelastic gases Formation and evolution of density singularities in hydrodynamics of inelastic gases

2006-10-22

arxiv.org/abs/cond-mat/0610603v3

Phys. Rev. E 75, 050301(R) (2007)

Physics

Condensed Matter

Soft Condensed Matter

4 pages, 3 figures, final version

Scientific paper

10.1103/PhysRevE.75.050301

We use ideal hydrodynamics to investigate clustering in a gas of inelastically colliding spheres. The hydrodynamic equations exhibit a new type of finite-time density blowup, where the gas pressure remains finite. The density blowups signal formation of close-packed clusters. The blowup dynamics are universal and describable by exact analytic solutions continuable beyond the blowup time. These solutions show that dilute hydrodynamic equations yield a powerful effective description of a granular gas flow with close-packed clusters, described as finite-mass point-like singularities of the density. This description is similar in spirit to the description of shocks in ordinary ideal gas dynamics.

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