Diffusion-generated motion by mean curvature for filaments
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.
scientific article; zbMATH DE number 1747954