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 Cluster Publications

Current Cluster Publications of JProf. Dr. Theresa Simon

$\bullet $ Gerold Alsmeyer, Alin Bostan, Kilian Raschel, and Thomas Simon. Persistence for a class of order-one autoregressive processes and Mallows-Riordan polynomials. Advances in Applied Mathematics, 150:102555, September 2023. doi:10.1016/j.aam.2023.102555.

$\bullet $ Anne Bernand-Mantel, Sarah Barnova, Anaïs Fondet, Cyrill B. Muratov, and Theresa M. Simon. Theory of magnetic field-stabilized compact skyrmions in thin film ferromagnets. arXiv e-prints, June 2023. arXiv:2306.01413.

$\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 $ 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. doi:10.1103/PhysRevB.101.045416.

$\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. 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. 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.