Hostname: page-component-77c89778f8-m8s7h Total loading time: 0 Render date: 2024-07-18T06:50:46.973Z Has data issue: false hasContentIssue false
  • English
  • Français

Motion of spirals by crystalline curvature

Published online by Cambridge University Press:  15 August 2002

Hitoshi Imai ,
Naoyuki Ishimura  and
TaKeo Ushijima
Hitoshi Imai
Affiliation:
Department of Applied Physics and Mathematics, Faculty of Engineering, University of Tokushima, Tokushima 770-8506, Japan. imai@pm.tokushima-v.ac.jp.
Naoyuki Ishimura
Affiliation:
Department of Mathematics, Hitotsubashi University, Kunitachi, Tokyo 186-8601, Japan.
TaKeo Ushijima
Affiliation:
Graduate School of Mathematical Sciences, University of Tokyo, Komaba, Tokyo 153-8914, Japan.
Get access

Abstract

Modern physics theories claim that the dynamics of interfaces between the two-phase is described by the evolution equations involving the curvature and various kinematic energies. We consider the motion of spiral-shaped polygonal curves by its crystalline curvature, which deserves a mathematical model of real crystals. Exploiting the comparison principle, we show the local existence and uniqueness of the solution.

Keywords

Crystalline motionspiral-shaped polygonal curvesmaterial sciences.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 33 , Issue 4 , July 1999 , pp. 797 - 806
Copyright
© EDP Sciences, SMAI, 1999

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)