JournalsifbVol. 4, No. 4pp. 395–421

Motion by curvature of a three-dimensional filament: similarity solutions

  • Giles W. Richardson

    University of Nottingham, United Kingdom
  • John R. King

    University of Nottingham, United Kingdom
Motion by curvature of a three-dimensional filament: similarity solutions cover
Download PDF

Abstract

We systematically classify and investigate fully three-dimensional similarity solutions to a system of equations describing the motion of a filament moving in the direction of its principal normal with velocity proportional to its curvature, [ngr] = [kgr]n, where n is the principal normal and [kgr] the curvature of the filament. Such formulations are relevant to superconducting vortices and disclinations.

Cite this article

Giles W. Richardson, John R. King, Motion by curvature of a three-dimensional filament: similarity solutions. Interfaces Free Bound. 4 (2002), no. 4, pp. 395–421

DOI 10.4171/IFB/67