Lecturer:  Mr. Chanania Steinbock, HUJI
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 particular, we focus on two kinds of random forcing, ordinary thermal white noise [1] and previously unconsidered “conservative noise” which conserves linear momentum and thus leaves the sheet’s centre of mass stationary [2,3]. While ordinary thermal noise is the natural choice for sheets coupled to a thermal bath, such as freely suspended graphene, we argue that the novel model with conserved noise has important applications to understanding the physics of sheet crumpling and active sheets. For each type of noise, 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. In the thermal noise case, the structure of such sheets is found to belong to one of three classes depending on the size of the non-linear coupling while in the conservative noise case, all sheets are found to belong to a single class in which a non-trivial logarithmic correction needs to be accounted for. Additionally, a particularly important finding is that in both cases, 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, Thermally driven elastic membranes are quasi-linear across all scales (Accepted to J. Phys. A, arXiv:2304.03603)
[2] Steinbock, Katzav & Boudaoud, Structure of fluctuating thin sheets under random forcing, Phys. Rev. Research 4, 033096 (2022)
[3] Steinbock & Katzav, Dynamics of fluctuating thin sheets under random forcing, Phys. Rev. E 107, 025002 (2023)