Critical size of crystals in the plane | Zendy

Przemysław Górka | Zendy

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Critical size of crystals in the plane

Author(s) -

Przemysław Górka

Publication year - 2005

Publication title -

interfaces and free boundaries mathematical analysis computation and applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.964

H-Index - 39

eISSN - 1463-9971

pISSN - 1463-9963

DOI - 10.4171/ifb/115

Subject(s) - polygon (computer graphics) , plane (geometry) , motion (physics) , mathematics , physics , materials science , geometry , mathematical analysis , classical mechanics , computer science , telecommunications , frame (networking)

We study a modified Stefan problem (and its quasi-steady approximation) for crystalline motion in the plane. We are interested in the behaviour of solution for a symmetric problem, in particular we assume that the Wulff shape W is a regular polygon withN sides. We describe two situations. In the first one we show that ice will be melting. In the second one we examine the properties of V (t) for small t assuming that V (0) = 0, whereV is the velocity of the interfacial curve.

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