Sudhir N. Pathak, Zahera Jabeen, Purusattam Ray, R. Rajesh
We analyze a recent experiment [Phys. Rev. Lett., {\bf103}, 224501 (2009)] in
which the shock, created by the impact of a steel ball on a flowing monolayer
of glass beads, is quantitatively studied. We argue that radial momentum is
conserved in the process, and hence show that in two dimensions the shock
radius increases in time $t$ as a power law $t^{1/3}$. This is confirmed in
event driven simulations of an inelastic hard sphere system. The experimental
data are compared with the theoretical prediction, and is shown to compare well
at intermediate times. At late times, the experimental data exhibit a crossover
to a different scaling behavior. We attribute this to the problem becoming
effectively three dimensional due to accumulation of particles at the shock
front, and propose a simple hard sphere model which incorporates this effect.
Simulations of this model capture the crossover seen in the experimental data.
View original:
http://arxiv.org/abs/1202.0413
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