Memory effects in fluctuating dynamic density-functional theory: theory and simulations
File(s)
Published version
Author(s)
Russo, Antonio
Duran-Olivencia, Miguel A
Yatsyshin, Peter
Kalliadasis, Serafim
Type
Journal Article
Abstract
This work introduces a theoretical framework to describe the dynamics of reacting multi-species fluid systems in-and-out of equilibrium. Our starting point is the system of generalised Langevin equations which describes the evolution of the positions and momenta of the constituent particles. One particular difficulty that this system of generalised Langevin equations exhibits is the presence of a history-dependent (i.e. non-Markovian) term, which in turn makes the system's dynamics dependent on its own past history. With the appropriate definitions of the local number density and momentum fields, we are able to derive a non-Markovian Navier–Stokes-like system of equations constituting a generalisation of the Dean–Kawasaki model. These equations, however, still depend on the full set of particles phase-space coordinates. To remove this dependence on the microscopic level without washing out the fluctuation effects characteristic of a mesoscopic description, we need to carefully ensemble-average our generalised Dean–Kawasaki equations. The outcome of such a treatment is a set of non-Markovian fluctuating hydrodynamic equations governing the time evolution of the mesoscopic density and momentum fields. Moreover, with the introduction of an energy functional which recovers the one used in classical density-functional theory and its dynamic extension (DDFT) under the local-equilibrium approximation, we derive a novel non-Markovian fluctuating DDFT (FDDFT) for reacting multi-species fluid systems. With the aim of reducing the fluctuating dynamics to a single equation for the density field, in the spirit of classical DDFT, we make use of a deconvolution operator which makes it possible to obtain the overdamped version of the non-Markovian FDDFT. A finite-volume discretization of the derived non-Markovian FDDFT is then proposed. With this, we validate our theoretical framework in-and-out-of-equilibrium by comparing results against atomistic simulations. Finally, we illustrate the influence of non-Markovian effects on the dynamics of non-linear chemically reacting fluid systems with a detailed study of memory-driven Turing patterns.
Date Issued
2020-11-06
Date Acceptance
2020-06-11
Citation
Journal of Physics A: Mathematical and Theoretical, 2020, 53 (44)
ISSN
1751-8113
Publisher
IOP Publishing
Journal / Book Title
Journal of Physics A: Mathematical and Theoretical
Volume
53
Issue
44
Copyright Statement
© 2020 The Author(s). Published by IOP Publishing Ltd Printed in the UK. Original content from this work may be used under the terms of theCreative CommonsAttribution 4.0 licence. Any further distribution of this work must maintain attributionto the author(s) and the title of the work, journal citation and DOI.
License URL
Identifier
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000583405500001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
Subjects
Science & Technology
Physical Sciences
Physics, Multidisciplinary
Physics, Mathematical
Physics
non-Markovian fluctuating dynamical density-functional theory
multispecies
reacting species
finite-volume simulations
memory-driven Turing patterns
PATTERN-FORMATION
MODEL
EQUATIONS
SYSTEMS
FLOW
Publication Status
Published
Article Number
ARTN 445007
Date Publish Online
2020-10-12