Projects in Mathematics Muenster
Research Interests

Research Interests

$\bullet$ Micromagnetics and nonlocal isoperimetric problems
$\bullet$ Multi-phase mean curvature flow
$\bullet$ Dimension reduction in thin elastic bodies
$\bullet$ Microstructures in shape memory alloys

Current Publications

$\bullet$ Antonin Monteil, Cyrill B. Muratov, Theresa M. Simon, and Valeriy V. Slastikov. Magnetic skyrmions under confinement. arXiv e-prints, July 2022. arXiv:2208.00058.

$\bullet$ Anne Bernand-Mantel, Cyrill B. Muratov, and Theresa M. Simon. A quantitative description of skyrmions in ultrathin ferromagnetic films and rigidity of degree $\pm 1$ harmonic maps from $\mathbb R^2$ to $\mathbb S^2$. Arch. Ration. Mech. Anal., 239(1):219–299, September 2021. doi:10.1007/s00205-020-01575-7.

$\bullet$ Theresa M. Simon. Quantitative aspects of the rigidity of branching microstructures in shape memory alloys via H-measures. SIAM J. Math. Anal., 53(4):4537–4567, August 2021. doi:10.1137/18M1220017.

$\bullet$ Theresa M. Simon. Rigidity of branching microstructures in shape memory alloys. Arch. Ration. Mech. Anal., 241(3):1707–1783, June 2021. doi:10.1007/s00205-021-01679-8.

$\bullet$ Julian Fischer, Tim Laux, and Theresa M. Simon. Convergence rates of the Allen-Cahn equation to mean curvature flow: a short proof based on relative entropies. SIAM J. Math. Anal., 52(6):6222–6233, December 2020. doi:10.1137/20M1322182.

$\bullet$ Anne Bernand-Mantel, Cyrill B Muratov, and T. M. Simon. Unraveling the role of dipolar versus Dzyaloshinskii-Moriya interactions in stabilizing compact magnetic skyrmions. Physical Review B, 101(4):045416, January 2020.

$\bullet$ Cyrill B. Muratov and T. M. Simon. A nonlocal isoperimetric problem with dipolar repulsion. Communications in Mathematical Physics, 372(3):1059–1115, April 2019.

$\bullet$ Tim Laux and T. M. Simon. Convergence of the Allen-Cahn equation to multiphase mean curvature flow. Communications on Pure and Applied Mathematics, 71(8):1597–1647, August 2018. doi:10.1002/cpa.21747.

$\bullet$ T. M. Simon. Materials Science-inspired problems in the Calculus of Variations: Rigidity of shape memory alloys and multi-phase mean curvature flow. PhD thesis, University of Leipzig, May 2018.

$\bullet$ Diego Ayala, Charles R. Doering, and T. M. Simon. Maximum palinstrophy amplification in the two-dimensional Navier–Stokes equations. Journal of Fluid Mechanics, 837:839–857, January 2018. doi:10.1017/jfm.2017.874.