The partition of energy for air-fluidized grains

TL;DR

This study investigates the applicability of statistical mechanics to air-fluidized grains by testing various perturbations, revealing conditions under which the Langevin description holds or fails.

Contribution

It systematically explores the limits of the Langevin and Fluctuation-Dissipation framework in describing air-fluidized grains under different experimental modifications.

Findings

Velocity distributions remain circularly symmetric despite asymmetrical traps.

All grains of different densities share the same effective temperature.

The thermal analogy weakens with increasing size disparity.

Abstract

The dynamics of one and two identical spheres rolling in a nearly-levitating upflow of air obey the Langevin Equation and the Fluctuation-Dissipation Relation [Ojha et al. Nature 427, 521 (2004) and Phys. Rev. E 71, 01631 (2005)]. To probe the range of validity of this statistical mechanical description, we perturb the original experiments in four ways. First, we break the circular symmetry of the confining potential by using a stadium-shaped trap, and find that the velocity distributions remain circularly symmetric. Second, we fluidize multiple spheres of different density, and find that all have the same effective temperature. Third, we fluidize two spheres of different size, and find that the thermal analogy progressively fails according to the size ratio. Fourth, we fluidize individual grains of aspherical shape, and find that the applicability of statistical mechanics depends on whether or not the grain chatters along its length, in the direction of airflow.