TY - JOUR
T1 - Structure of fluctuating thin sheets under random forcing
AU - Steinbock, Chanania
AU - Katzav, Eytan
AU - Boudaoud, Arezki
N1 - Publisher Copyright:
© 2022 authors. Published by the American Physical Society.
PY - 2022/7
Y1 - 2022/7
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85135880191&partnerID=8YFLogxK
U2 - 10.1103/PhysRevResearch.4.033096
DO - 10.1103/PhysRevResearch.4.033096
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AN - SCOPUS:85135880191
SN - 2643-1564
VL - 4
JO - Physical Review Research
JF - Physical Review Research
IS - 3
M1 - 033096
ER -