The Structure and Dynamics of Fluctuating Elastic Thin Sheets

by Prof. Eytan Katzav

Racah Institute of Physics, The Hebrew University of Jerusalem

at Biological and soft-matter physics

Thu, 28 Nov 2024, 12:10
Sacta-Rashi Building for Physics (54), room 207 & ZOOM hybrid

Abstract

Thin sheets and membranes are ubiquitous at all scales and yet while the static behaviour of fluctuating elastic sheets has been extensively studied over the last 35 years, the dynamics of such sheets has barely been considered. With the recent development of ultra-thin materials such as graphene, this inattentiveness has become sorely felt. By combining techniques from elasticity and statistical physics, we model such sheets out-of-equilibrium with a nonlinear Langevin equation – the overdamped dynamic Föppl-von Kármán equation. Using a self-consistent methodology known as the Self-Consistent Expansion (SCE), we are able to study the equal-time and dynamic structure factors of elastic sheets under various kinds of random forcing. In all cases, we are able to successfully obtain precise analytic predictions for the equal-time and dynamic structure factors, even in the presence of strong nonlinear coupling. Interestingly, the decay rate of the dynamic structure factor is related to the static structure as if the system were completely linear and this so-called “quasi-linearity” is present at all length scales. All results are confirmed by numerical simulations.

[1] Steinbock, Katzav & Boudaoud, Structure of fluctuating thin sheets under random forcing, Phys. Rev. Research 4, 033096 (2022).
[2] Steinbock & Katzav, Dynamics of fluctuating thin sheets under random forcing, Phys. Rev. E 107, 025002 (2023).
[3] Steinbock & Katzav, Thermally driven elastic membranes are quasi-linear across all scales, J. Phys. A 56, 215002 (2023).

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Created on 13-10-2024 by Granek, Rony (rgranek)
Updaded on 28-11-2024 by Granek, Rony (rgranek)