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A stochastic phase-field model determined from molecular dynamics
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2010 (English)In: Mathematical Modelling and Numerical Analysis, ISSN 0764-583X, E-ISSN 1290-3841, Vol. 44, no 4, 627-646 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2010. Vol. 44, no 4, 627-646 p.
Keyword [en]
Phase-field, molecular dynamics, coarse graining, Smoluchowski dynamics, stochastic differential equation
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-29468DOI: 10.1051/m2an/2010022ISI: 000280137500002Scopus ID: 2-s2.0-77956601375OAI: oai:DiVA.org:kth-29468DiVA: diva2:395864
Funder
Swedish e‐Science Research Center
Note
QC 20110208Available from: 2011-02-08 Created: 2011-02-02 Last updated: 2017-12-11Bibliographically approved

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Publisher's full textScopushttp://dx.doi.org/10.1051/m2an/2010022

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von Schwerin, Erik

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