Random Motion with Interfacial Contact: Driven Diffusion vis-a-vis Mechanical Activation

TL;DR

This paper investigates how non-linear friction and external noise influence the motion and effective temperature of a sphere rolling on a substrate, revealing complex fluctuation behaviors and barrier crossing dynamics.

Contribution

It introduces a new experimental approach to measure effective temperature in systems with non-linear friction and noise, challenging the notion of a unique temperature value.

Findings

Fluctuation ratios decrease monotonically over time.

Diffusivity and mobility increase with noise strength, with diffusivity increasing super-linearly.

Barrier crossing rates follow classical transition state theory.

Abstract

Rolling of a small sphere on a solid support is governed by a non-linear friction that is akin to the Coulombic dry fiction. No motion occurs when the external field is weaker than the frictional resistance. However, with the intervention of an external noise, a viscous friction like property emerges; thus the sphere rolls with an uniform drift velocity that is proportional to the applied field. As the sphere rolls, it rocks forward and backward resulting in substantial fluctuation of displacement opposite to the net drift. The ratio of the integrated probabilities of the negative to positive work fluctuations decreases monotonically with the time of observation, from which a temperature like intensive parameter can be estimated. This parameter conforms to the Einstein's ratio of diffusivity and mobility that increases almost linearly, even though the diffusivity increases super-linearly, with the strength of the noise. A new barrier crossing experiment is introduced that can be performed either with a hard (e.g. a steel ball) or with a soft (e.g. a water drop) sphere in contact with a periodically undulated substrate. The frequency of barrier crossing follows the classical transition state equation allowing a direct estimation of the effective temperature. These experiments as well as certain numerical simulations suggest that the effective temperature of a system controlled by a non-linear friction may not have a unique value.