Indirect Evidence for L\'evy Walks in Squeeze Film Damping

TL;DR

This study provides experimental evidence that molecular gas damping in confined geometries exhibits superdiffusive behavior consistent with L\'evy walks, challenging traditional Gaussian models and aligning with Monte Carlo simulations.

Contribution

It demonstrates that squeeze film damping follows a L\'evy walk model, offering new insights into molecular flow behavior in confined spaces.

Findings

Damping scales with a fractional power between 1/d and 1/d^2.

Experimental results align with L\'evy walk superdiffusion.

Monte Carlo simulations confirm the observed distance dependence.

Abstract

Molecular flow gas damping of mechanical motion in confined geometries, and its associated noise, is important in a variety of fields, including precision measurement, gravitational wave detection, and MEMS devices. We used two torsion balance instruments to measure the strength and distance-dependence of `squeeze film' damping. Measured quality factors derived from free decay of oscillation are consistent with gas particle superdiffusion in L\'evy walks and inconsistent with those expected from traditional Gaussian random walk particle motion. The distance-dependence of squeeze film damping observed in our experiments is in agreement with a parameter-free Monte Carlo simulation. The squeeze film damping of the motion of a plate suspended a distance d away from a parallel surface scales with a fractional power between 1/d and 1/d^2.