Harnessing fluctuations to discover dissipative evolution equations

Xiaoguai Li, Nicolas Dirr, Peter Embacher, Johannes Zimmer, Celia Reina

Research output: Contribution to journalArticle

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.
Original languageEnglish
Pages (from-to)240-251
JournalJournal of the Mechanics and Physics of Solids
Early online date18 Jun 2019
DOIs
Publication statusE-pub ahead of print - 18 Jun 2019

Cite this

Harnessing fluctuations to discover dissipative evolution equations. / Li, Xiaoguai; Dirr, Nicolas; Embacher, Peter; Zimmer, Johannes; Reina, Celia.

In: Journal of the Mechanics and Physics of Solids, 31.10.2019, p. 240-251.

Research output: Contribution to journalArticle

Li, Xiaoguai ; Dirr, Nicolas ; Embacher, Peter ; Zimmer, Johannes ; Reina, Celia. / Harnessing fluctuations to discover dissipative evolution equations. In: Journal of the Mechanics and Physics of Solids. 2019 ; pp. 240-251.
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