Power-law velocity distributions in granular gases
E. Ben-Naim, B. Machta, and J. Machta
We report a general class of steady and transient states of granular
gases. We find that the kinetic theory of inelastic gases admits
stationary solutions with a power-law velocity distribution,
f(v)~v^(-sigma). The exponent sigma is found analytically and depends
on the spatial dimension, the degree of inelasticity, and the
homogeneity degree of the collision rate. Driven steady-states, with
the same power-law tail and a cut-off can be maintained by injecting
energy at a large velocity scale, which then cascades to smaller
velocities where it is dissipated. Associated with these steady-states
are freely cooling time-dependent states for which the cut-off
decreases and the velocity distribution is self-similar.
source,
ps,
pdf