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Harnessing fluctuations to discover dissipative evolution equations

Li, Xiaoguai, Dirr, Nicolas, 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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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: Mathematics
Publisher: Elsevier
ISSN: 0022-5096
Date of First Compliant Deposit: 16 July 2019
Date of Acceptance: 30 May 2019
Last Modified: 25 Nov 2020 06:59

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