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A Stochastic Phase-Field Model Derived from Molecular Dynamics

  • Anders Szepessy (KTH Stockholm, Stockholm, Sweden)
G3 10 (Lecture hall)

Abstract

The phase-field method is widely used to study evolution of microstructural phase transformations on a continuum level; it couples the energy equation to a phenomenological Allen-Cahn/Ginzburg-Landau equation modeling 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 derive stochastic phase-field models from atomistic formulations by coarse-graining molecular dynamics. It has four steps: (1) derivation of stochastic molecular dynamics from the time-indepedent SchrÃdinger equation; (2) a precise quantitative atomistic definition of the phase-field variable, based on the local potential energy; (3) derivation of its coarse-grained dynamics model, from microscopic Smoluchowski molecular dynamics; and (4) numerical computation of the coarse-grained model functions.

Katja Bieling

Max Planck Institute for Mathematics in the Sciences Contact via Mail

Patrick Dondl

Max-Planck-Institut für Mathematik in den Naturwissenschaften

Stephan Luckhaus

Universität Leipzig

Max von Renesse

Technische Universität Berlin