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A Stochastic Phase-Field Model Computed From Coarse-Grained Molecular DynamicsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); (English)Manuscript (Other academic)
##### Abstract [en]

##### National Category

Mathematics
##### Identifiers

URN: urn:nbn:se:kth:diva-7421OAI: oai:DiVA.org:kth-7421DiVA: diva2:12444
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt455",{id:"formSmash:j_idt455",widgetVar:"widget_formSmash_j_idt455",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt461",{id:"formSmash:j_idt461",widgetVar:"widget_formSmash_j_idt461",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt467",{id:"formSmash:j_idt467",widgetVar:"widget_formSmash_j_idt467",multiple:true});
##### Note

QC 20100824Available from: 2007-08-31 Created: 2007-08-31 Last updated: 2010-08-24Bibliographically approved
##### In thesis

Results are presented from numerical experiments aiming at the computation ofstochastic phase-field models for phase transformations by coarse-graining moleculardynamics. The studied phase transformations occur between a solid crystal and aliquid. Nucleation and growth, sometimes dendritic, of crystal grains in a sub-cooledliquid is determined by diffusion and convection of heat, on the macroscopic level,and by interface effects, where the width of the solid–liquid interface is on an atomiclength-scale. Phase-field methods are widely used in the study of the continuum leveltime evolution of the phase transformations; they introduce an order parameter todistinguish between the phases. The dynamics of the order parameter is modelled byan Allen–Cahn equation and coupled to an energy equation, where the latent heat atthe phase transition enters as a source term. Stochastic fluctuations are sometimesadded in the coupled system of partial differential equations to introduce nucleationand to get qualitatively correct behaviour of dendritic side-branching. In this reportthe possibility of computing some of the Allen–Cahn model functions from a microscalemodel is investigated. The microscopic model description of the material bystochastic, Smoluchowski, dynamics is considered given. A local average of contributionsto the potential energy in the micro model is used to determine the local phase,and a stochastic phase-field model is computed by coarse-graining the molecular dynamics.Molecular dynamics simulations on a two phase system at the melting pointare used to compute a double-well reaction term in the Allen–Cahn equation and adiffusion matrix describing the noise in the coarse-grained phase-field.

1. Adaptivity for Stochastic and Partial Differential Equations with Applications to Phase Transformations$(function(){PrimeFaces.cw("OverlayPanel","overlay12445",{id:"formSmash:j_idt731:0:j_idt735",widgetVar:"overlay12445",target:"formSmash:j_idt731:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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