Harnessing fluctuations to discover dissipative evolution equations

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

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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.
Original languageEnglish
Pages (from-to)240-251
Number of pages12
JournalJournal of the Mechanics and Physics of Solids
Volume131
Early online date18 Jun 2019
DOIs
Publication statusPublished - 1 Oct 2019

Keywords

  • Coarse-graining
  • Fluctuation-dissipation
  • Multiscale
  • Non-equilibrium thermodynamics

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

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Code for "Harnessing fluctuations to discover dissipative evolution equations"

Li, X. (Creator), Dirr, N. (Creator), Embacher, P. (Creator), Zimmer, J. (Creator) & Reina, C. (Creator), University of Bath, 18 Jun 2019

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