Diffusion-Generated Motion by Mean Curvature for Filaments

Steady motion of hairpin-shaped vortex filaments in excitable systems.

We demonstrate the existence of steadily translating filaments in the Belousov-Zhabotinsky reaction. The filaments have self-reinforcing shapes tracing planar hairpins and constant velocities that are inversely proportional to their width. These features are well described by an analytical solution of the mean curvature flow problem. Using numerical simulations based on an excitable reaction-di...

Curvature-driven diffusive and dynamo actions in vortex unstretched filaments from solar prominences data

Examples of the use of Frenet curvature-driven motion of vortex unstretched filamentary diffusion processes in plasmas are investigated. The first example addresses the unstretched filaments which are embedded in a steady plasma flow. The particle number density of a weakly ionized plasma is shown to be proportional to the total Frenet curvature. The particle number does not decays in plasma al...

A Morphological Scheme for Mean Curvature Motion and Applications to Anisotropic Diffusion and Motion of Level Sets

This paper introduces a discrete scheme for mean curvature motion using a morphological image processing approach. After brieey presenting an axiomatic approach of image processing and the mean curvature PDE, the properties of the proposed scheme are studied, in particular consistency and convergence are proved. The applications of mean curvature motion in image denoising and form evolution are...

Effective dynamics of twisted and curved scroll waves using virtual filaments.

Scroll waves are three-dimensional excitation patterns that rotate around a central filament curve; they occur in many physical, biological, and chemical systems. We explicitly derive the equations of motion for scroll wave filaments in reaction-diffusion systems with isotropic diffusion up to third order in the filament's twist and curvature. The net drift components define at every instance o...

Modified Mean Curvature Motion For Multispectral Anisotropic Diffusion