On singular vortex patches, II: Long-time dynamics

On the stability of a singular vortex dynamics

In this paper we address the question of the singular vortex dynamics exhibited in [15], which generates a corner in finite time. The purpose is to prove that under some appropriate small regular perturbation the corner still remains. Our approach uses the Hasimoto transform and deals with the long range scattering properties of a GrossPitaevski equation with time-variable coefficients.

Multiscale Approximation of Vortex Patches

We propose an adaptive scheme, based on multiscale decomposition into interpolatory wavelet bases, to simulate the evolution of vortex patches associated to solutions of the two-dimensional Euler equations. This scheme is based on fast algorithms that relate the numerically signiicant wavelet coeecients with the irregular sampling of the boundary of the patch on an adaptive grid. This method al...

Scattering for 1d Cubic Nls and Singular Vortex Dynamics

In this paper we study the stability of the self-similar solutions of the binormal flow, which is a model for the dynamics of vortex filaments in fluids and super-fluids. These particular solutions χa(t, x) form a family of evolving regular curves of R that develop a singularity in finite time, indexed by a parameter a > 0. We consider curves that are small regular perturbations of χa(t0, x) fo...

Vortex dynamics for low- type-II superconductors

Metapopulation dynamics on ephemeral patches.

A challenge for conservation management is to understand how population and habitat dynamics interact to affect species persistence. In real landscapes, timing and duration of disturbances can vary, and species' responses to habitat changes will depend on how timing of dispersal and reproduction events relate to the landscape temporal structure. For instance, increasing disturbance frequency ma...