Structure of fluctuating thin sheets under random forcing
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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2022-08-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.4.033096 |
| _version_ | 1797210621291266048 |
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| author | Chanania Steinbock Eytan Katzav Arezki Boudaoud |
| author_facet | Chanania Steinbock Eytan Katzav Arezki Boudaoud |
| author_sort | Chanania Steinbock |
| collection | DOAJ |
| description | 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 ϕ^{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. |
| first_indexed | 2024-04-24T10:13:30Z |
| format | Article |
| id | doaj.art-09bb27e51d964ea489e36edb1d5b1bce |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:13:30Z |
| publishDate | 2022-08-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-09bb27e51d964ea489e36edb1d5b1bce2024-04-12T17:23:21ZengAmerican Physical SocietyPhysical Review Research2643-15642022-08-014303309610.1103/PhysRevResearch.4.033096Structure of fluctuating thin sheets under random forcingChanania SteinbockEytan KatzavArezki BoudaoudWe 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 ϕ^{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.http://doi.org/10.1103/PhysRevResearch.4.033096 |
| spellingShingle | Chanania Steinbock Eytan Katzav Arezki Boudaoud Structure of fluctuating thin sheets under random forcing Physical Review Research |
| title | Structure of fluctuating thin sheets under random forcing |
| title_full | Structure of fluctuating thin sheets under random forcing |
| title_fullStr | Structure of fluctuating thin sheets under random forcing |
| title_full_unstemmed | Structure of fluctuating thin sheets under random forcing |
| title_short | Structure of fluctuating thin sheets under random forcing |
| title_sort | structure of fluctuating thin sheets under random forcing |
| url | http://doi.org/10.1103/PhysRevResearch.4.033096 |
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