Outputs (7)

An effective model for boundary vortices in thin-film micromagnetics (2023)
Journal Article
Kurzke, M., & Ignat, R. (2023). An effective model for boundary vortices in thin-film micromagnetics. Mathematical Models and Methods in Applied Sciences, 33(9), 1929-1973. https://doi.org/10.1142/S021820252350046X

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
Golovaty, D., Kurzke, M., Montero, J. A., & Spirn, D. (2023). Tetrahedral Frame Fields via Constrained Third-Order Symmetric Tensors. Journal of Nonlinear Science, 33(3), Article 48. https://doi.org/10.1007/s00332-023-09898-x

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 Γ-convergence in a two-dimensional Ginzburg-Landau model for boundary vortices (2021)
Journal Article
Ignat, R., & Kurzke, M. (2021). Global Jacobian and Γ-convergence in a two-dimensional Ginzburg-Landau model for boundary vortices. Journal of Functional Analysis, 280(8), Article 108928. https://doi.org/10.1016/j.jfa.2021.108928

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 Γ-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
Ignat, R., Kurzke, M., & Lamy, X. (2020). Global Uniform Estimate for the Modulus of Two-Dimensional Ginzburg-Landau Vortexless Solutions with Asymptotically Infinite Boundary Energy. SIAM Journal on Mathematical Analysis, 52(1), 524-542. https://doi.org/10.1137/19m1262978

For ε > 0, let uε : Ω → R 2 be a solution of the Ginzburg-Landau system −∆uε = 1 ε 2 uε(1 − |uε| 2) in a Lipschitz bounded domain Ω. In an energy regime that excludes interior vortices, we prove that 1 − |uε| 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
Kurzke, M. (2019). The correlation coefficient for vortices in the plane. Journal of Mathematical Analysis and Applications, 479(1), 333-336. https://doi.org/10.1016/j.jmaa.2019.06.029

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.

Gross-Pitaevskii vortex motion with critically scaled inhomogeneities (2017)
Journal Article
Kurzke, M., Marzuola, J. L., & Spirn, D. (2017). Gross-Pitaevskii vortex motion with critically scaled inhomogeneities. SIAM Journal on Mathematical Analysis, 49(1), 471-500. https://doi.org/10.1137/15M1049014

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
Kurzke, M., & Spirn, D. (2014). Vortex liquids and the Ginzburg-Landau equation. Forum of Mathematics, Sigma, 2, Article e11. https://doi.org/10.1017/fms.2014.6

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.