Single Particle Brownian Motion with Solid Friction

Abstract

We study the Brownian dynamics of a solid particle on a vibrating solid surface. Phenomenologically, the interaction between the two solid surfaces is modeled by solid friction, and the Gaussian white noise models the vibration of the solid surface. The solid friction is proportional to the sign of relative velocity. We derive the Fokker-Planck (FP) equation for the time-dependent probability distribution to find the particle at a given location. We calculate analytically the steady state velocity distribution function, mean-squared velocity and diffusion coefficient in $d$ dimensions. We present a generic method of calculating the autocorrelations in $d$ dimensions. This results in one dimension in an exact evaluation of the steady state velocity autocorrelation. In higher dimensions, our exact general expression enables the analytic evaluation of the autocorrelation to any required approximation. We present approximate analytic expressions in two and three dimensions. Next, we numerically calculate the mean-square velocity and steady state velocity autocorrelation function up to $d=3$. Our numerical results are in good agreement with the analytically obtained results.

2 figs, 2 tables, accepted in EPJE

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Cited by in corpus (6)

• Granular Fluids with Solid Friction and Heating
• Stochastic motion under nonlinear friction representing shear thinning
• Numerical solutions of Fokker-Planck equations with drift-admitting jumps
• Intruder Dynamics in a Frictional Granular Fluid: A Molecular Dynamics Study
• Velocity Distribution and Diffusion of an Athermal Inertial Run-and-Tumble Particle in a Shear-Thinning Medium
• Field Theory of Active Brownian Particles with Dry Friction