Exciting Hard Spheres

T. Antal; P. L. Krapivsky; S. Redner

doi:10.1103/physreve.78.030301

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arXiv · 0805.3783

Exciting Hard Spheres

T. Antal·P. L. Krapivsky·S. Redner

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Abstract

We investigate the collision cascade that is generated by a single moving incident particle on a static hard-sphere gas. We argue that the number of moving particles at time t grows as t^{xi} and the number collisions up to time t grows as t^{eta}, with xi=2d/(d+2) and eta=2(d+1)/(d+2) and d the spatial dimension. These growth laws are the same as those from a hydrodynamic theory for the shock wave emanating from an explosion. Our predictions are verified by molecular dynamics simulations in d=1 and 2. For a particle incident on a static gas in a half-space, the resulting backsplatter ultimately contains almost all the initial energy.

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T. Antal, P. L. Krapivsky, S. Redner. 2008-05-25. Exciting Hard Spheres. https://doi.org/10.1103/physreve.78.030301

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