Computing diffusivities from particle models out of equilibrium

Peter Embacher, Nicolas Dirr, Johannes Zimmer, Celia Reina

Research output: Contribution to journalArticle

2 Citations (Scopus)
1 Downloads (Pure)

Abstract

A new method is proposed to numerically extract the diffusivity of a (typically nonlinear) diffusion equation from underlying stochastic particle systems. The proposed strategy requires the system to be in local equilibrium and have Gaussian fluctuations but it is otherwise allowed to undergo arbitrary out-of-equilibrium evolutions. This could be potentially relevant for particle data obtained from experimental applications. The key idea underlying the method is that finite, yet large, particle systems formally obey stochastic partial differential equations of gradient flow type satisfying a fluctuation–dissipation relation. The strategy is here applied to three classic particle models, namely independent random walkers, a zero-range process and a symmetric simple exclusion process in one space dimension, to allow the comparison with analytic solutions.

Original languageEnglish
Article number20170694
JournalProceedings of the Royal Society A: Mathematical Physical and Engineering Sciences
Volume474
Issue number2212
DOIs
Publication statusPublished - 11 Apr 2018

Fingerprint

Particle System
Diffusivity
Zero-range Process
Fluctuations
Exclusion Process
Local Equilibrium
Nonlinear Diffusion Equation
Gradient Flow
Computing
Stochastic Partial Differential Equations
Analytic Solution
Stochastic Systems
Dissipation
Arbitrary
Model
Strategy

Keywords

  • Coarse-graining
  • Fluctuation–dissipation
  • Non-equilibrium thermodynamics
  • Transport coefficients

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)

Cite this

Computing diffusivities from particle models out of equilibrium. / Embacher, Peter; Dirr, Nicolas; Zimmer, Johannes; Reina, Celia.

In: Proceedings of the Royal Society A: Mathematical Physical and Engineering Sciences, Vol. 474, No. 2212, 20170694, 11.04.2018.

Research output: Contribution to journalArticle

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