Li, Xiaoguai, Dirr, Nicolas  ORCID: https://orcid.org/0000-0003-3634-7367, Embacher, Peter, Zimmer, Johannes and Reina, Celia
2019.
Harnessing fluctuations to discover dissipative evolution equations.
Journal of the Mechanics and Physics of Solids
131
, pp. 240-251.
10.1016/j.jmps.2019.05.017
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Abstract
Continuum modeling of dissipative processes in materials often relies on strong phenomenological assumptions, as their derivation from underlying atomistic/particle models remains a major long-standing challenge. Here we show that the continuum evolution equations of a wide class of dissipative phenomena can be numerically obtained (in a discretized form) from fluctuations via an infinite-dimensional fluctuation-dissipation relation. A salient feature of the method is that these continuum equations can be fully pre-computed, enabling macroscopic simulations of arbitrary admissible initial conditions, without the need of any further microscopic simulations. We test this coarse-graining procedure on a one-dimensional non-linear diffusive process with known analytical solution, and obtain an excellent agreement for the density evolution. This illustrative example serves as a blueprint for a new multiscale paradigm, where full dissipative evolution equations — and not only parameters — can be numerically computed from lower scale data.
| Item Type: | Article |
|---|---|
| Date Type: | Publication |
| Status: | Published |
| Schools: | Schools > Mathematics |
| Publisher: | Elsevier |
| ISSN: | 0022-5096 |
| Date of First Compliant Deposit: | 16 July 2019 |
| Date of Acceptance: | 30 May 2019 |
| Last Modified: | 04 Dec 2024 11:30 |
| URI: | https://orca.cardiff.ac.uk/id/eprint/124249 |
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