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Hokkaido University Preprint Series in Mathematics >
A LEVEL SET APPROACH REFLECTING SHEET STRUCTURE WITH SINGLE AUXILIARY FUNCTION FOR EVOLVING SPIRALS ON CRYSTAL SURFACES
| 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 |
| Publisher: | Department of Mathematics, Hokkaido University |
| 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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Submitter: 数学紀要登録作業用
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