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Crystalline motion of spiral-shaped polygonal curves with a tip motion. (English) Zbl 1273.82076

Summary: We propose a crystalline motion of spiral-shaped polygonal curves with a tip motion as a simple model of a step motion on a crystal surface under screw dislocation. We give a tip motion and discuss the behavior of the solution curves by crystalline curvature flow with a driving force. We show that the solution curve belongs to a suitable class of spiral-shaped curves and also show a time-global existence of the spiral-shaped solutions.

MSC:

82D25 Statistical mechanics of crystals
34A34 Nonlinear ordinary differential equations and systems
39A12 Discrete version of topics in analysis
74N05 Crystals in solids
74N20 Dynamics of phase boundaries in solids
53A04 Curves in Euclidean and related spaces
Full Text: DOI

References:

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