Dynamics of Fluctuating Thin Sheets Under Random Forcing

TL;DR

This paper investigates the dynamic behavior of fluctuating elastic thin sheets under random forcing, revealing exponential decay of correlations and quasi-linear behavior through analytical and numerical methods.

Contribution

It extends previous static analysis by characterizing the dynamic structure factor and decay rates using the self-consistent expansion method.

Findings

Dynamic structure factor decays exponentially over time.

Decay rate matches the effective coupling constant for static properties.

Numerical simulations confirm analytical predictions.

Abstract

We study the dynamic structure factor of fluctuating elastic thin sheets subject to conservative (athermal) random forcing. In Steinbock, Katzav & Boudaoud, Phys. Rev. Research 4, 033096 (2022), the static structure factor of such a sheet was studied. In this paper, we recap the model developed there and investigate its dynamic properties. Using the self-consistent expansion (SCE), the time dependent two-point function of the height profile is determined and found to decay exponentially in time. Despite strong nonlinear coupling, the decay rate of the dynamic structure factor is found to coincide with the effective coupling constant for the static properties which suggests that the model under investigation exhibits certain quasi-linear behaviour. Confirmation of these results by numerical simulations is also presented.