Kinetics of a frictional granular motor

TL;DR

This paper investigates the dynamics of a granular rotor with friction in a thermal bath, deriving exact solutions in different regimes and identifying two scaling behaviors at varying temperatures.

Contribution

It provides analytical solutions for the rotor's behavior in both large friction and small friction limits, advancing understanding of granular motor kinetics.

Findings

Identified two distinct scaling regimes at low and high bath temperatures.

Derived exact solutions for the rotor's dynamics in large friction and small rotor mass limits.

Established a Fokker-Planck equation describing the system's behavior in certain asymptotic regimes.

Abstract

Within the framework of a Boltzmann-Lorentz equation, we analyze the dynamics of a granular rotor immersed in a bath of thermalized particles in the presence of a frictional torque on the axis. In numerical simulations of the equation, we observe two scaling regimes at low and high bath temperatures. In the large friction limit, we obtain the exact solution of a model corresponding to asymptotic behavior of the Boltzmann-Lorentz equation. In the limit of large rotor mass and small friction, we derive a Fokker-Planck equation for which the exact solution is also obtained.