JournalsifbVol. 4 , No. 4DOI 10.4171/ifb/67

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

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.