Bistability and noise-enhanced velocity of rolling motion

Abstract

We investigate the motion of a hard cylinder rolling down a soft inclined plane. The cylinder is subjected to a viscous drag force and stochastic fluctuations due to the surrounding medium. In a wide range of parameters we observe bistability of the rolling velocity. In dependence on the parameters, increasing noise level may lead to increasing or decreasing average velocity of the cylinder. The approximative analytical theory agrees with numerical results.

A note on the violation of the Einstein relation in a driven moderately dense granular gas

“…First, as noted before in section 2, the expression for the fourth cumulant c 0 used here has been obtained by neglecting cumulants of higher order and considering only linear terms in c and c 0 . On the other hand, according to the previous results [33,34] obtained in the free cooling case for a monocomponent gas, the value of c 0 could change significantly for very strong dissipation when cumulants of higher order were taken into account in the form of the homogeneous distribution. In this context, the estimate of c 0 obtained in this paper could be unreliable for this range of values of inelasticity and so, the quantitative deviations of from 1 observed in figures 3 and 4 for the Gaussian thermostat when α 0 0.5 could be questionable.…”

“…In addition, although the expressions ( 6)-( 8) have been derived by neglecting non-linear terms in the coefficient c, the estimates ( 7) and ( 8) present quite a good agreement with Monte Carlo simulations of the Boltzmann equation [30,32] for moderate values of dissipation (say for instance, α 0.5). However, more recent results [33,34] for the homogeneous (undriven) cooling state have shown that for very large inelasticity (α 0.5), the higher order cumulants may not be neglected since they can be of the same order of magnitude as c. The breakdown of the Sonine polynomial expansion is caused by the increasing impact of the overpopulated high energy tail of the velocity distribution f [35].…”