Slider on a Driven Substrate: Markovian Competition Between Two Limiting Attractors

TL;DR

This study investigates the motion of a slider on a shaken substrate, revealing the significant influence of static friction and modeling the dynamics with a Markovian approach to understand stick-slip behavior and walk-off phenomena.

Contribution

The paper introduces a Markovian model for slider motion under periodic driving, highlighting the role of static friction in low-acceleration regimes and explaining walk-off effects.

Findings

Static friction coefficient is crucial even when slightly higher than dynamic friction.

Markovian model captures stick-slip transitions in slider motion.

Walk-off occurs due to asymmetric periodic driving.

Abstract

We present experimental data of the motion of a rimmed checker's piece on a polished horizontal tray, in two specific conditions: with the substrate harmonically shaken at 20 Hz, and with a static substrate. The latter experiment immediately yields the dynamic friction coefficient. The harmonic experimental results are very sensitive on the static friction coefficient, which is not even a percent higher than the dynamic one. Due to the low harmonic acceleration of the driver, the static friction has enormous influence on the slider's motion. We modeled the slider's motion using a discrete Markovian progression model, which at every discrete time-step chooses between a sticking attempt and a return to the non-sticking trajectory. The present model does not take into account the driver's acceleration. In the final section, we explain the physical origin of walk-off, in case of periodic but asymmetric driving.