Harnessing fluctuations to discover dissipative evolution equations

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:	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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