Forschungsschwerpunkte

Forschungsartikel (Zeitschriften)

• Monteil, A, Muratov, C.B., Simon, T.M., und Slastikov, V.V. 2023. „Magnetic skyrmions under confinement.“ Communications in Mathematical Physics, Nr. 404: 1571–1605. doi: 10.1007/s00220-023-04864-w.
• Rüland, A., und Simon, T.M. 2023. „On Rigidity for the Four-Well Problem Arising in the Cubic-to-Trigonal Phase Transformation.“ Journal of Elasticity, Nr. 153: 455–475. doi: 10.1007/s10659-023-10011-2.
• Bernand-Mantel, A., Fondet, A, Barnova, S., Simon, T.M., und C.B., Muratov. 2023. „Theory of magnetic field-stabilized compact skyrmions in thin film ferromagnets.“ Physical Review B, Nr. 2023 L161405. doi: 10.1103/PhysRevB.108.L161405.
• Simon, und T.M.. 2021. „Quantitative aspects of the rigidity of branching microstructures in shape memory alloys via H-measures.“ SIAM Journal on Mathematical Analysis, Nr. 53 (4) doi: 10.1137/18M1220017.
• Simon, und T.M.. 2021. „Rigidity of branching microstructures in shape memory alloys.“ Archive for Rational Mechanics and Analysis, Nr. 241: 1707–1783. doi: 10.1007/s00205-021-01679-8.
• Bernand-Mantel, A., Muratov, C.B., und Simon, T.M. 2021. „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, Nr. 239: 219–299. doi: 10.1007/s00205-020-01575-7.
• Fischer, J., Laux, T., und Simon, T.M. 2020. „Convergence rates of the Allen-Cahn equation to mean curvature flow: A short proof based on relative entropies.“ SIAM Journal on Mathematical Analysis, Nr. 52 (6): 6222–6233. doi: 10.1137/20M1322182.
• Bernand-Mantel, A., Muratov, C.B., und Simon, T.M. 2020. „Unraveling the role of dipolar vs. Dzyaloshinskii-Moriya interaction in stabilizing compact magnetic skyrmions.“ Physical Review B, Nr. 101 (4) 045416. doi: 10.1103/PhysRevB.101.045416.
• Muratov, C.B., und Simon, T.M. 2019. „A nonlocal isoperimetric problem with dipolar repulsion.“ Communications in Mathematical Physics, Nr. 372: 1059–1115. doi: 10.1007/s00220-019-03455-y.
• Laux, T, und Simon, T.M. 2018. „Convergence of the Allen-Cahn equation to multi-phase mean curvature flow.“ Communications on Pure and Applied Mathematics, Nr. 71 (8): 1597–1647. doi: 10.1002/cpa.21747.
• Ayala, D, Doering, C.R., und Simon, T.M. 2018. „Maximum palinstrophy amplification in the two-dimensional Navier-Stokes equations.“ Journal of Fluid Mechanics, Nr. 837: 839–857. doi: 10.1017/jfm.2017.874.
• Hensel, S., Fischer, J., Laux, T., und Simon, T.M. im Druck. „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

Qualifikationsschriften (Dissertationen, Habilitationsschriften)

• Simon, und T.M.. 2018. „Materials Science-inspired problems in the Calculus of Variations: Rigidity of shape memory alloys and multi-phase mean curvature flow.“ Dissertationsschrift, Universität Leipzig.

Forschungsartikel in Online-Sammlungen

• Fischer, J, Hensel, S, Laux, T, und Simon, T.M. 2024. „A weak-strong uniqueness principle for the Mullins-Sekerka equation.“ arXiv doi: 10.48550/arXiv.2404.02682.
• Muratov, C.B., Simon, T.M., und Slastikov, V.V. 2024. „Existence of higher degree minimizers in the magnetic skyrmion problem.“ arXiv doi: 10.48550/arXiv.2409.07205.
• Fischer, J, Hensel, S, Laux, T, und Simon, T.M. 2022. „Local minimizers of the interface length functional based on a concept of local paired calibrations.“ arXiv doi: 10.48550/arXiv.2212.11840.

Errata

• Muratov, C.B., und Simon, T.M. 2022. Correction to: A Nonlocal Isoperimetric Problem with Dipolar Repulsion, doi: 10.1007/s00220-022-04426-6.