Inhomogeneous Cooling of the Rough Granular Gas in Two Dimensions

We study the inhomogeneous clustered regime of a freely cooling granular gas of rough particles in two dimensions using large-scale event driven simulations and scaling arguments. During collisions, rough particles dissipate energy in both the normal and tangential directions of collision. In the inhomogeneous regime, translational kinetic energy and the rotational energy decay with time $t$ as power-laws $t^{-\theta_T}$ and $t^{-\theta_R}$. We numerically determine $\theta_T \approx 1$ and $\theta_R \approx 1.6$, independent of the coefficients of restitution. The inhomogeneous regime of the granular gas has been argued to be describable by the ballistic aggregation problem, where particles coalesce on contact. Using scaling arguments, we predict $\theta_T=1$ and $\theta_R=1$ for ballistic aggregation, $\theta_R$ being different from that obtained for the rough granular gas. Simulations of ballistic aggregation with rotational degrees of freedom are consistent with these exponents.Comment: 6 pages, 5 figure

Effect of Landauer's blowtorch on the equilibration rate in a bistable potential

Kinetic aspect of Landauer's blowtorch effect is investigated for a model double-well potential with localized heating. Using the supersymmetric approach, we derive an approximate analytical expression for the equilibration rate as function of the strength, width and the position of the hot zone, and the barrier height. We find that the presence of the hot zone enhances the equilibration rate, which is found to be an increasing function of the strength and width of the hot zone. Our calculations also reveal an intriguing result, namely, that placing the hot zone away from the top of the potential barrier enhances the rate more than when it is placed close to it. A physically plausible explanation for this is attempted. The above analytical results are borne out by detailed numerical solution of the associated Smoluchowski equation for the inhomogeneous medium.Comment: 15 pages in LaTeX format and 6 figures in postscript E-Mail : [email protected] [email protected]