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A LEVEL SET APPROACH REFLECTING SHEET STRUCTURE WITH SINGLE AUXILIARY FUNCTION FOR EVOLVING SPIRALS ON CRYSTAL SURFACES

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/84171

Title: A LEVEL SET APPROACH REFLECTING SHEET STRUCTURE WITH SINGLE AUXILIARY FUNCTION FOR EVOLVING SPIRALS ON CRYSTAL SURFACES
Authors: Ohtsuka, Takeshi Browse this author
Tsai,Yen-Hsi R. Browse this author
Giga, Yoshikazu Browse this author
Keywords: Evolution of spirals
Level set method
Sheet structure function
Eikonal and curvature flow
Finite difference scheme.
Issue Date: 16-Dec-2012
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 1025
Start Page: 1
End Page: 36
Abstract: We introduce a new level set method to simulate motion of spirals in a crystal surface governed by an eikonal-curvature ow equation. Our formulation allows collision of several spirals and different strength (different modulus of Burgers vectors) of screw dislocation centers. We represent a set of spirals by a level set of a single auxiliary function u minus a pre-determined multi-valued sheet structure function , which re ects the strength of spirals (screw dislocation centers). The level set equation used in our method for u 􀀀 is the same as that of the eikonal-curvature ow equation. The multi-valued nature of the sheet structure function is only invoked when preparing the initial auxiliary function, which is nontrivial, and in the nal step when extracting information such as the height of the spiral steps. Our simulation enables us not only to reproduce all speculations on spirals in a classical paper by Burton, Cabrera and Frank (1951) but also to nd several new phenomena.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69830
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

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