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Gamma‐convergence of gradient flows with applications to Ginzburg‐Landau
We present a method to prove convergence of gradient flows of families of energies that Γ‐converge to a limiting energy. It provides lower‐bound criteria to obtain the convergence that correspond to
Vortices in the Magnetic Ginzburg-Landau Model
With the discovery of type-II superconductivity by Abrikosov, the prediction of vortex lattices, and their experimental observation, quantized vortices have become a central object of study in
Bogoliubov Spectrum of Interacting Bose Gases
We study the large‐N limit of a system of N bosons interacting with a potential of intensity 1/N. When the ground state energy is to the first order given by Hartree's theory, we study the next
A deterministic‐control‐based approach motion by curvature
The level‐set formulation of motion by mean curvature is a degenerate parabolic equation. We show that its solution can be interpreted as the value function of a deterministic two‐person game. More
Gamma-convergence of gradient flows on Hilbert and metric spaces and applications
We are concerned with -convergence of gradient ows, which is a notion meant to ensure that if a family of energy functionals depending of a parameter -converges, then the solutions to the associated
Higher‐Dimensional Coulomb Gases and Renormalized Energy Functionals
We consider a classical system of n charged particles in an external confining potential in any dimension d ≥ 2. The particles interact via pairwise repulsive Coulomb forces and the coupling
From the Ginzburg-Landau Model to Vortex Lattice Problems
It is shown that the vortices of minimizer of Ginzburg-Landau, blown-up at a suitable scale, converge to minimizers of W, thus providing a first rigorous hint at the Abrikosov lattices, which is a next order effect compared to the mean-field type results.
Coulomb Gases and Ginzburg - Landau Vortices
These are the lecture notes of a "Nachdiplomvorlesung" course taught at ETH Zurich in the Spring of 2013. They appeared in the EMS series Zurich Lectures in Advanced Mathematics.
Néel and Cross-Tie Wall Energies for Planar Micromagnetic Configurations
We study a two-dimensional model for micromagnetics, which consists in an energy functional over S 2 -valued vector fields. Bounded-energy configurations tend to be planar, except in small regions