Year: 2022
Type: article
Abstract: We propose a mathematical model to describe the athermal fluctuations of thin sheets driven by the type of random driving that might be experienced prior to weak crumpling. The model is obtained by merging the F\"oppl--von K\'arm\'an equations from elasticity theory with techniques from out-of-equilibrium statistical physics to obtain a nonlinear strongly coupled ${\ensuremath{\phi}}^{4}$-Langevin field equation with a spatially varying kernel. With the aid of the self-consistent expansion (SCE), this equation is analytically solved for the structure factor of a fluctuating sheet. In contrast to previous research which has suggested that the structure factor follows an anomalous power law, we find that the structure factor in fact obeys a logarithmically corrected rational function. Numerical simulations of our model confirm the accuracy of our analytical solution.
Source: Physical Review Research
Institution: Hebrew University of Jerusalem
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,625
Funder: Israel Science Foundation
Award: G3471219217
OpenAlex ID: W4289443633