Diffusion-generated motion by mean curvature for filaments
type: Item
instance of: scholarly article
title: Diffusion-generated motion by mean curvature for filaments
zbMATH Open document ID: 1037.35033
author: Steven J. Ruuth
author: Barry Merriman
author: Jack Xin
author: Stanley Osher
published in: Journal of Nonlinear Science
publication date: 2002-05-30T00:00:00Z
review text: This paper generalizes the well-studied and well-behaved algorithms for the diffusion-generated motion by mean curvature of surfaces to algorithms for diffusion-generated motion by curvature of filaments, i.e. curves in \(\mathbb R^3\). In addition, the initial configuration of links may be very complex. Motion of filaments occurs in many physical systems. ``Designing suitable algorithms is complicated by the fact that in many problems the filaments can merge or break up. It is particularly challenging to find algorithms that retain their simplicity, yet are robust enough to capture these topological transitions.'' The approach of this paper exploits basic features of the complex Ginzburg-Landau equation. It is shown that, asymptotically, the diffusion-generated filament motion gives motion by curvature in the normal direction. Several numerical experiments are presented. Finally, throughout the paper comparisons with other models are included and possible variations of the method under discussion are pointed out.
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35A35
Mathematics Subject Classification ID: 53C44
zbMATH DE Number: 1747954
zbMATH Keywords: topological transitions
zbMATH Keywords: numerical experiments
MaRDI profile type: Publication
full work available at URL: s00332-001-0404-x
OpenAlex ID: W2017670148
DOI: 10.1007/S00332-001-0404-X
description: scientific article; zbMATH DE number 1747954