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Computing diffusivities from particle models out of equilibrium

Embacher, Peter, Dirr, Nicolas, Zimmer, Johannes and Reina, Celia 2018. Computing diffusivities from particle models out of equilibrium. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 474 (2212) , 0694. 10.1098/rspa.2017.0694

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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.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Publisher: Royal Society, The
ISSN: 1364-5021
Date of First Compliant Deposit: 27 April 2018
Date of Acceptance: 7 March 2018
Last Modified: 31 Jul 2020 01:23
URI: http://orca.cf.ac.uk/id/eprint/110754

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