Stochastic discs that roll
Miranda Holmes-Cerfon

TL;DR
This paper models stochastic rolling particles, deriving their equilibrium distributions and revealing that rolling constraints alter thermodynamic properties, with implications for understanding friction and modeling in microscopic systems.
Contribution
It introduces a formal framework for stochastic rolling particles, deriving their dynamics as Brownian motion on (sub-)Riemannian manifolds and analyzing the impact of rolling constraints on equilibrium distributions.
Findings
Rolling constraints change the equilibrium distribution of the system.
The dynamics can be described as Brownian motion on a Riemannian or sub-Riemannian manifold.
Different distributions arise with and without rolling constraints, indicating a fundamental impact on thermodynamics.
Abstract
We study a model of rolling particles subject to stochastic fluctuations, which may be relevant in systems of nano- or micro-scale particles where rolling is an approximation for strong static friction. We consider the simplest possible non-trivial system: a linear polymer of three of discs constrained to remain in contact, and immersed in an equilibrium heat bath so the internal angle of the polymer changes due to stochastic fluctuations. We compare two cases: one where the discs can slide relative to each other, and the other where they are constrained to roll, like gears. Starting from the Langevin equations with arbitrary linear velocity constraints, we use formal homogenization theory to derive the overdamped equations that describe the process in configuration space only. The resulting dynamics have the formal structure of a Brownian motion on a Riemannian or sub-Riemannian…
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Taxonomy
TopicsSports Dynamics and Biomechanics · Advanced Thermodynamics and Statistical Mechanics · Material Dynamics and Properties
