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 Föppl-von Kármán equations from elasticity theory with techniques from out-of-equilibrium statistical physics to obtain a nonlinear strongly coupled φ4-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.
Bibliographical noteFunding Information:
The authors wish to thank one of the anonymous referees for insightful comments and analysis that helped to clarify the origin of the correction to the structure factor. This work was supported by the Israel Science Foundation Grant No. 1682/18.
© 2022 authors. Published by the American Physical Society.