Exciting hard spheres.
We investigate the collision cascade that is generated by a single moving particle in a static and homogeneous 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) , 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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Program for Evolutionary Dynamics, Harvard University, Cambridge, Massachusetts 02138, USA.
Krapivsky
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Redner
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D000465:Algorithms; D001703:Biophysics / Q000379:methods*; D003198:Computer Simulation; D004058:Diffusion; D005740:Gases; D006244:Hardness; D015233:Models, Statistical; D010316:Particle Size; D013499:Surface Properties
D005740:Gases