A stochastic phase-field model determined from molecular dynamics

Handle URI:
http://hdl.handle.net/10754/561524
Title:
A stochastic phase-field model determined from molecular dynamics
Authors:
von Schwerin, Erik; Szepessy, Anders
Abstract:
The dynamics of dendritic growth of a crystal in an undercooled melt is determined by macroscopic diffusion-convection of heat and by capillary forces acting on the nanometer scale of the solid-liquid interface width. Its modelling is useful for instance in processing techniques based on casting. The phase-field method is widely used to study evolution of such microstructural phase transformations on a continuum level; it couples the energy equation to a phenomenological Allen-Cahn/Ginzburg-Landau equation modelling the dynamics of an order parameter determining the solid and liquid phases, including also stochastic fluctuations to obtain the qualitatively correct result of dendritic side branching. This work presents a method to determine stochastic phase-field models from atomistic formulations by coarse-graining molecular dynamics. It has three steps: (1) a precise quantitative atomistic definition of the phase-field variable, based on the local potential energy; (2) derivation of its coarse-grained dynamics model, from microscopic Smoluchowski molecular dynamics (that is Brownian or over damped Langevin dynamics); and (3) numerical computation of the coarse-grained model functions. The coarse-grained model approximates Gibbs ensemble averages of the atomistic phase-field, by choosing coarse-grained drift and diffusion functions that minimize the approximation error of observables in this ensemble average. © EDP Sciences, SMAI, 2010.
KAUST Department:
Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Publisher:
EDP Sciences
Journal:
ESAIM: Mathematical Modelling and Numerical Analysis
Issue Date:
17-Mar-2010
DOI:
10.1051/m2an/2010022
Type:
Article
ISSN:
0764583X
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorvon Schwerin, Eriken
dc.contributor.authorSzepessy, Andersen
dc.date.accessioned2015-08-02T09:13:26Zen
dc.date.available2015-08-02T09:13:26Zen
dc.date.issued2010-03-17en
dc.identifier.issn0764583Xen
dc.identifier.doi10.1051/m2an/2010022en
dc.identifier.urihttp://hdl.handle.net/10754/561524en
dc.description.abstractThe dynamics of dendritic growth of a crystal in an undercooled melt is determined by macroscopic diffusion-convection of heat and by capillary forces acting on the nanometer scale of the solid-liquid interface width. Its modelling is useful for instance in processing techniques based on casting. The phase-field method is widely used to study evolution of such microstructural phase transformations on a continuum level; it couples the energy equation to a phenomenological Allen-Cahn/Ginzburg-Landau equation modelling the dynamics of an order parameter determining the solid and liquid phases, including also stochastic fluctuations to obtain the qualitatively correct result of dendritic side branching. This work presents a method to determine stochastic phase-field models from atomistic formulations by coarse-graining molecular dynamics. It has three steps: (1) a precise quantitative atomistic definition of the phase-field variable, based on the local potential energy; (2) derivation of its coarse-grained dynamics model, from microscopic Smoluchowski molecular dynamics (that is Brownian or over damped Langevin dynamics); and (3) numerical computation of the coarse-grained model functions. The coarse-grained model approximates Gibbs ensemble averages of the atomistic phase-field, by choosing coarse-grained drift and diffusion functions that minimize the approximation error of observables in this ensemble average. © EDP Sciences, SMAI, 2010.en
dc.publisherEDP Sciencesen
dc.subjectCoarse grainingen
dc.subjectMolecular dynamicsen
dc.subjectPhase-fielden
dc.subjectSmoluchowski dynamicsen
dc.subjectStochastic differential equationen
dc.titleA stochastic phase-field model determined from molecular dynamicsen
dc.typeArticleen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalESAIM: Mathematical Modelling and Numerical Analysisen
dc.contributor.institutionDepartment of Mathematics, Royal Institute of Technology (KTH), Stockholm, Swedenen
kaust.authorvon Schwerin, Eriken
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