JProf. Dr. Theresa Simon

Topics in Mathematics Münster

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

• Bernand-Mantel, A.; Fondet, A; Barnova, S.; Simon, T.M.; Muratov C.B. Theory of magnetic field-stabilized compact skyrmions in thin film ferromagnets. Physical Review B Vol. 2023, 2023 online
• Bernand-Mantel, A.; Muratov, C.B.; Simon, T.M. Unraveling the role of dipolar vs. Dzyaloshinskii-Moriya interaction in stabilizing compact magnetic skyrmions. Physical Review B Vol. 101 (4), 2020 online
• Bernand-Mantel, A.; Muratov, C.B.; Simon, T.M. A quantitative description of skyrmions in ultrathin ferromagnetic films and rigidity of degree ±1 harmonic maps from from R² to S². Archive for Rational Mechanics and Analysis Vol. 239, 2021 online
• Hensel, S.; Fischer, J.; Laux, T.; Simon, T.M. The local structure of the energy landscape in multiphase mean curvature flow: Weak-strong uniqueness and stability of evolutions. Journal of the European Mathematical Society online
• Fischer, J.; Laux, T.; Simon, T.M. Convergence rates of the Allen-Cahn equation to mean curvature flow: A short proof based on relative entropies. SIAM Journal on Mathematical Analysis Vol. 52 (6), 2020 online
• Laux, T; Simon, T.M. Convergence of the Allen-Cahn equation to multi-phase mean curvature flow. Communications on Pure and Applied Mathematics Vol. 71 (8), 2018 online
• Monteil, A; Muratov, C.B.; Simon, T.M.; Slastikov, V.V. Magnetic skyrmions under confinement. Communications in Mathematical Physics Vol. 404, 2023 online
• Muratov, C.B.; Simon, T.M. A nonlocal isoperimetric problem with dipolar repulsion. Communications in Mathematical Physics Vol. 372, 2019 online
• Rüland, A.; Simon, T.M. On Rigidity for the Four-Well Problem Arising in the Cubic-to-Trigonal Phase Transformation. Journal of Elasticity Vol. 153, 2023 online
• Simon, T.M. Rigidity of branching microstructures in shape memory alloys. Archive for Rational Mechanics and Analysis Vol. 241, 2021 online

Recent Publications of JProf. Dr. Theresa Simon

$\bullet $ Cyrill B. Muratov, Theresa M. Simon, and Valeriy V. Slastikov. Existence of higher degree minimizers in the magnetic skyrmion problem. arXiv e-prints, September 2024. arXiv:2409.07205.

$\bullet $ Julian Fischer, Sebastian Hensel, Tim Laux, and Theresa M. Simon. A weak-strong uniqueness principle for the Mullins-Sekerka equation. arXiv e-prints, April 2024. arXiv:2404.02682.

$\bullet $ Antonin Monteil, Cyrill B. Muratov, Theresa M. Simon, and Valeriy V. Slastikov. Magnetic skyrmions under confinement. Communications in Mathematical Physics, 404(3):1571–1605, November 2023. doi:10.1007/s00220-023-04864-w.

$\bullet $ Anne Bernand-Mantel, Anaïs Fondet, Sarah Barnova, Theresa M. Simon, and Cyrill B. Muratov. Theory of magnetic field stabilized compact skyrmions in thin-film ferromagnets. Physical Review B, 108(16):L161405, October 2023. doi:10.1103/physrevb.108.l161405.

$\bullet $ Angkana Rüland and Theresa M. Simon. On rigidity for the four-well problem arising in the cubic-to-trigonal phase transformation. Journal of Elasticity, 153(3):455–475, April 2023. doi:10.1007/s10659-023-10011-2.

$\bullet $ Julian Fischer, Sebastian Hensel, Tim Laux, and Theresa M. Simon. Local minimizers of the interface length functional based on a concept of local paired calibrations. arXiv e-prints, December 2022. arXiv:2212.11840.

$\bullet $ Cyrill B. Muratov and Theresa M. Simon. Correction to: A nonlocal isoperimetric problem with dipolar repulsion. Commun. Math. Phys., 394(3):1361–1362, September 2022. doi:10.1007/s00220-022-04426-6.

$\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. Phys. Rev. B, 101(4):045416, January 2020. doi:10.1103/PhysRevB.101.045416.

$\bullet $ Cyrill B. Muratov and T. M. Simon. A nonlocal isoperimetric problem with dipolar repulsion. Commun. Math. Phys., 372(3):1059–1115, April 2019. doi:10.1007/s00220-019-03455-y.

$\bullet $ Tim Laux and T. M. Simon. Convergence of the Allen-Cahn equation to multiphase mean curvature flow. Commun. Pure Appl. Math., 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. J. Fluid Mech., 837:839–857, January 2018. doi:10.1017/jfm.2017.874.