Effects of Thermal Noise on Pattern Onset in Continuum Simulations of Shaken Granular Layers

TL;DR

This paper examines how thermal noise influences the onset of pattern formation in shaken granular layers, demonstrating that incorporating noise into continuum models aligns critical acceleration predictions with molecular dynamics results.

Contribution

It introduces fluctuating hydrodynamics into continuum simulations of granular layers, improving accuracy in predicting pattern onset compared to noise-free models.

Findings

Continuum simulations without noise underestimate critical acceleration by ~10%.

Adding noise aligns continuum results with molecular dynamics.

Pattern wavelengths match experimental observations even without friction modeling.

Abstract

The author investigates the onset of patterns in vertically oscillated layers of dissipative particles using numerical solutions of continuum equations to Navier-Stokes order. Above a critical accelerational amplitude of the cell, standing waves form stripe patterns which oscillate subharmonically with respect to the cell. Continuum simulations neglecting interparticle friction yield pattern wavelengths consistent with experiments using frictional particles. However, the critical acceleration for standing wave formation is approximately 10% lower in continuum simulations without added noise than in molecular dynamics simulations. This report incorporates fluctuating hydrodynamics theory into continuum simulations by adding noise terms with no fit parameters; this modification yields a critical acceleration in agreement with molecular dynamics simulations.