29 citations · 42 across the 8 of their papers we have counts for
9 papers
Euler's elastica functional as a large mass limit of a two-dimensional non-local isoperimetric problem
Cyrill B. Muratov, Matteo Novaga, Theresa M. Simon
We consider a large mass limit of the non-local isoperimetric problem with a repulsive Yukawa potential in two space dimensions. In this limit, the non-local term concentrates on t…
Existence of higher degree minimizers in the magnetic skyrmion problem
Cyrill B. Muratov, Theresa M. Simon, Valeriy V. Slastikov
We demonstrate existence of topologically nontrivial energy minimizing maps of a given positive degree from bounded domains in the plane to in a variational model des…
Theory of magnetic field-stabilized compact skyrmions in thin film ferromagnets
Anne Bernand-Mantel, Anaïs Fondet, Sarah Barnova +2
We present a micromagnetic theory of compact magnetic skyrmions under applied magnetic field that accounts for the full dipolar energy and the interfacial Dzyaloshinskii-Moryia int…
Local minimizers of the interface length functional based on a concept of local paired calibrations
Julian Fischer, Sebastian Hensel, Tim Laux +1
We establish that regular flat partitions are locally minimizing for the interface energy with respect to perturbations of the phases. Regular flat partitions are partitions…
On Rigidity for the Four-Well Problem Arising in the Cubic-to-Trigonal Phase Transformation
Angkana Rüland, Theresa M. Simon
We classify all exactly stress-free solutions to the cubic-to-trigonal phase transformation within the geometrically linearized theory of elasticity, showing that only simple lamin…
Magnetic skyrmions under confinement
Antonin Monteil, Cyrill B. Muratov, Theresa M. Simon +1
We present a variational treatment of confined magnetic skyrmions in a minimal micromagnetic model of ultrathin ferromagnetic films with interfacial Dzylashinksii-Moriya interactio…
Convergence rates of the Allen-Cahn equation to mean curvature flow: A short proof based on relative entropies
Julian Fischer, Tim Laux, Theresa M. Simon
We give a short and self-contained proof for rates of convergence of the Allen-Cahn equation towards mean curvature flow, assuming that a classical (smooth) solution to the latter…
A quantitative description of skyrmions in ultrathin ferromagnetic films and rigidity of degree harmonic maps from to
Anne Bernand-Mantel, Cyrill B. Muratov, Theresa M. Simon
We characterize skyrmions in ultrathin ferromagnetic films as local minimizers of a reduced micromagnetic energy appropriate for quasi two-dimensional materials with perpendicular…
Rigidity of branching microstructures in shape memory alloys
Thilo Simon
We analyze generic sequences for which the geometrically linear energy \[E_η(u,χ):= η^{-\frac{2}{3}}\int_{B_{0}(1)} \left| e(u)- \sum_{i=1}^3 χ_ie_i\right|^2 d x+η^\frac{1}{3} \sum…