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A multiphase field concept: numerical simulations of moving phase boundaries and multiple junctions

Garcke, Harald; Nestler, Britta; Stoth, Barbara

We present numerical simulations which support the formal asymptotic analysis relating a multiorder parameter Allen-Cahn system to a multiphase interface problem with curvaturedependent evolution of the interfaces and angle conditions at triple junctions. Within the gradient energy of the Allen-Cahn system, the normal to an interface between phases i and j is modeled by the irreducible representations (uiruj ¡ujrui)=juiruj ¡ ujruij, where ui and uj are the ith and jth components of the vectorial order parameter u 2 RN. In the vectorial case, the dependence of the limiting surface tensions and mobilities on the bulk potentials of the Allen{Cahn system is not given explicitly but in terms of all the N components of the planar stationary wave solutions. One of the issues of this paper is to find bulk potentials which allow a rather easy access to the resulting surface tensions and mobilities. We compare numerical computations for planar and circular phase boundaries in two- and threephase systems. The difference is that in a three-phase system, the third phase generally will be present in the interfacial region between two other phases. ... mehr

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DOI: 10.5445/IR/1000019281
DOI: 10.1137/S0036139998334895
Zitationen: 147
Web of Science
Zitationen: 134
Zitationen: 135
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Zuverlässigkeit von Bauteilen und Systemen (IZBS)
Publikationstyp Zeitschriftenaufsatz
Publikationsjahr 1999
Sprache Englisch
Identifikator ISSN: 0036-1399, 0368-4245, 1095-712X
KITopen-ID: 1000019281
Erschienen in SIAM journal on applied mathematics
Verlag Society for Industrial and Applied Mathematics (SIAM)
Band 60
Heft 1
Seiten 295-315
Schlagwörter phase field models, multiphase diffusion, Allen-Cahn systems, triple junction dynamics, numerical simulations
Nachgewiesen in Scopus
Web of Science
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