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A Level Set Approach Reflecting Sheet Structure with Single Auxiliary Function for Evolving Spirals on Crystal Surfaces
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA. The University of Texas at Austin, United States .ORCID iD: 0000-0001-8441-3678
2015 (English)In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 62, no 3, 831-874 p.Article in journal (Refereed) Published
Abstract [en]

We introduce a new level set method to simulate motion of spirals in a crystal surface governed by an eikonal-curvature flow 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 theta, which reflects the strength of spirals (screw dislocation centers). The level set equation used in our method for u - theta is the same as that of the eikonal-curvature flow 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 final 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 et al. (Philos Trans R Soc Lond Ser A Math Phys Sci 243, 299-358, 1951) but also to find several new phenomena.

Place, publisher, year, edition, pages
2015. Vol. 62, no 3, 831-874 p.
Keyword [en]
Evolution of spirals, Level set method, Sheet structure function, Eikonal and curvature flow, Finite difference scheme
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-161096DOI: 10.1007/s10915-014-9877-2ISI: 000348984100009Scopus ID: 2-s2.0-84922337748OAI: oai:DiVA.org:kth-161096DiVA: diva2:797642
Note

QC 20150324

Available from: 2015-03-24 Created: 2015-03-09 Last updated: 2017-12-04Bibliographically approved

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Tsai, Yen-Hsi Richard

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