Stationary states and energy cascades in inelastic gases
E. Ben-Naim and J. Machta
We find a general class of nontrivial stationary states in inelastic
gases where, due to dissipation, energy is transfered from large
velocity scales to small velocity scales. These steady-states exist
for arbitrary collision rules and arbitrary dimension. Their signature
is a stationary velocity distribution f(v) with an algebraic
high-energy tail, f(v) ~ v^{-sigma}. The exponent sigma is obtained
analytically and it varies continuously with the spatial dimension,
the homogeneity index characterizing the collision rate, and the
restitution coefficient. We observe these stationary states in
numerical simulations in which energy is injected into the system by
infrequently boosting particles to high velocities. We propose that
these states may be realized experimentally in driven granular
systems.
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