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Atomistic and continuum models for phase change dynamics
KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
2006 (English)In: Proceedings of the International Congress of Mathematicians, 2006, 1563-1582 p.Conference paper, Published paper (Refereed)
Abstract [en]

The dynamics of dendritic growth of a crystal in an undercooled melt is determined by macroscopic diffusion-convection of heat and capillary forces acting on length scales compared to the nanometer width of the solid-liquid interface. Its modeling is useful for instance in processing techniques based on casting. The phase field method is widely used to study evolution of such microstructures of phase transformations on a continuum level; it couples the energy equation to a phenomenological Allen´┐ŻCahn/Ginzburg´┐ŻLandau equation modeling the dynamics of an order parameter determining the solid and liquid phases, including also stochastic fluctuations to obtain the qualitative correct result of dendritic side branching. This lecture presents some ideas to derive stochastic phase field models from atomistic formulations by coarse-graining molecular dynamics and kinetic Monte Carlo methods.

Place, publisher, year, edition, pages
2006. 1563-1582 p.
Keyword [en]
Phase transformation, phase-field, coarse-grained, molecular dynamics, Brownian
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-55367Scopus ID: 2-s2.0-84878067528ISBN: 978-3-03719-022-7 (print)OAI: oai:DiVA.org:kth-55367DiVA: diva2:471528
Conference
International Congress of Mathematicians. Madrid, Spain. August 22-30 2006
Note
QC 20120103Available from: 2012-01-02 Created: 2012-01-02 Last updated: 2012-02-25Bibliographically approved

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