All Outputs (8)

An effective model for boundary vortices in thin-film micromagnetics (2023)
Journal Article

Ferromagnetic materials are governed by a variational principle which is nonlocal, nonconvex and multiscale. The main object is given by a unit-length three-dimensional vector field, the magnetization, that corresponds to the stable states of the mic... Read More about An effective model for boundary vortices in thin-film micromagnetics.

Tetrahedral Frame Fields via Constrained Third-Order Symmetric Tensors (2023)
Journal Article

Tetrahedral frame fields have applications to certain classes of nematic liquid crystals and frustrated media. We consider the problem of constructing a tetrahedral frame field in three-dimensional domains in which the boundary normal vector is inclu... Read More about Tetrahedral Frame Fields via Constrained Third-Order Symmetric Tensors.

Global Jacobian and ?-convergence in a two-dimensional Ginzburg-Landau model for boundary vortices (2021)
Journal Article

In the theory of 2D Ginzburg-Landau vortices, the Jacobian plays a crucial role for the detection of topological singularities. We introduce a related distributional quantity, called the global Jacobian that can detect both interior and boundary vort... Read More about Global Jacobian and ?-convergence in a two-dimensional Ginzburg-Landau model for boundary vortices.

Global Uniform Estimate for the Modulus of Two-Dimensional Ginzburg-Landau Vortexless Solutions with Asymptotically Infinite Boundary Energy (2020)
Journal Article

For ? > 0, let u? : ? ? R 2 be a solution of the Ginzburg-Landau system ??u? = 1 ? 2 u?(1 ? |u?| 2) in a Lipschitz bounded domain ?. In an energy regime that excludes interior vortices, we prove that 1 ? |u?| is uniformly estimated by a positive powe... Read More about Global Uniform Estimate for the Modulus of Two-Dimensional Ginzburg-Landau Vortexless Solutions with Asymptotically Infinite Boundary Energy.

The correlation coefficient for vortices in the plane (2019)
Journal Article

For point vortices in the plane, we consider the correlation coefficient of Ovchinnikov and Sigal. Generalising a result by Esposito, we show that it vanishes for all vortex equilibria.

The effect of forest dislocations on the evolution of a phase-field model for plastic slip (2018)
Journal Article

We consider the gradient flow evolution of a phase-field model for crystal dislocations in a single slip system in the presence of forest dislocations. The model is based on a Peierls-Nabarro type energy penalizing non-integer slip and elastic stress... Read More about The effect of forest dislocations on the evolution of a phase-field model for plastic slip.

Gross-Pitaevskii vortex motion with critically scaled inhomogeneities (2017)
Journal Article

We study the dynamics of vortices in an inhomogeneous Gross--Pitaevskii equation iδtu = Δu + 1/ε²(ρ² ε(ᵡ) - |u|²). For a unique scaling regime |ρε(ᵡ) - 1 = O(logε¯¹), it is shown that vortices can interact both with the background perturbation and wi... Read More about Gross-Pitaevskii vortex motion with critically scaled inhomogeneities.

Vortex liquids and the Ginzburg-Landau equation (2014)
Journal Article

We establish vortex dynamics for the time-dependent Ginzburg–Landau equation for asymptotically large numbers of vortices for the problem without a gauge field and either Dirichlet or Neumann boundary conditions. As our main tool, we establish quanti... Read More about Vortex liquids and the Ginzburg-Landau equation.