63 citations · 86 across the 4 of their papers we have counts for
5 papers
Unraveling the role of dipolar versus Dzyaloshinskii-Moriya interaction in stabilizing compact magnetic skyrmions
Anne Bernand-Mantel, Cyrill B. Muratov, Thilo M. Simon
Magnetic skyrmions have been the subject of extensive experimental studies in ferromagnetic thin films and multilayers, revealing a diversity in their size, stability and internal…
A nonlocal isoperimetric problem with dipolar repulsion
Cyrill B. Muratov, Thilo Simon
We study a geometric variational problem for sets in the plane in which the perimeter and a regularized dipolar interaction compete under a mass constraint. In contrast to previous…
Quantitative aspects of the rigidity of branching microstructures in shape memory alloys via H-measures
Thilo M. Simon
We quantify the rigidity of branching microstructures in shape memory alloys undergoing cubic-to-tetragonal transformations in the geometrically linearized theory by making use of…
Maximum palinstrophy amplification in the two-dimensional Navier-Stokes equations
Diego A. Ayala, Charles R. Doering, Thilo M. Simon
We derive and assess the sharpness of analytic upper bounds for the instantaneous growth rate and finite-time amplification of palinstrophy in solutions of the two-dimensional inco…
Convergence of the Allen-Cahn Equation to multi-phase mean-curvature flow
Tim Laux, Thilo Simon
We present a convergence result for solutions of the vector-valued Allen-Cahn Equation. In the spirit of the work of Luckhaus and Sturzenhecker we establish convergence towards a d…