TY - JOUR
T1 - Expanding selfsimilar solutions of a crystalline flow with applications to contour figure analysis
AU - Hontani, Hidekata
AU - Giga, Mi Ho
AU - Giga, Yoshikazu
AU - Deguchi, Koichiro
N1 - Funding Information:
The authors are grateful for referees for valuable remarks. The second author is grateful to Professor Hitoshi Imai for informative remarks. The third author is partly supported by the Grant in Aid for Scientific Research, No.14204011, No.1563408, the Japan Society for the Promotion of Science(JSPS). This work is also supported by COE ‘Mathematics of Nonlinear Structure via Singularities’ of JSPS.
PY - 2005/4/15
Y1 - 2005/4/15
N2 - A numerical method for obtaining a crystalline flow starting from a general polygon is presented. A crystalline flow is a polygonal flow and can be regarded as a discrete version of a classical curvature flow. In some cases, new facets may be created instantaneously and their facet lengths are governed by a system of singular ordinary differential equations (ODEs). The proposed method solves the system of the ODEs numerically by using expanding selfsimilar solutions for newly created facets. The computation method is applied to a multi-scale analysis of a contour figure.
AB - A numerical method for obtaining a crystalline flow starting from a general polygon is presented. A crystalline flow is a polygonal flow and can be regarded as a discrete version of a classical curvature flow. In some cases, new facets may be created instantaneously and their facet lengths are governed by a system of singular ordinary differential equations (ODEs). The proposed method solves the system of the ODEs numerically by using expanding selfsimilar solutions for newly created facets. The computation method is applied to a multi-scale analysis of a contour figure.
KW - Crystalline flow
KW - Evolving polygon
KW - Multi-scale analysis
KW - Selfsimilar solutions
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U2 - 10.1016/j.dam.2004.09.015
DO - 10.1016/j.dam.2004.09.015
M3 - Article
AN - SCOPUS:14744299462
VL - 147
SP - 265
EP - 285
JO - Discrete Applied Mathematics
JF - Discrete Applied Mathematics
SN - 0166-218X
IS - 2-3
ER -