| Research Interests | Micromagnetics and nonlocal isoperimetric problems Multi-phase mean curvature flow Dimension reduction in thin elastic bodies Microstructures in shape memory alloys |
| Selected Publications | • 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 |
| Topics in Mathematics Münster | T6: Singularities and PDEs T9: Multi-scale processes and effective behaviour |
| Current Talks | • Magnetic skyrmions under confinement. Queer in Computational and Applied Mathematics, Providence, Rhode Island Link to event • Nonlocal isoperimetric problems. Queer in Math Day, Leipzig Link to event • The elastica functional as the critical Gamma-limit of the screened Gamow model. Modeling and Analysis in Nanomagnetism and beyond, Parma Link to event • Magnetic skyrmions in extremely thin films. Graduate seminar IntComSin, Regensburg • The elastica functional as the critical Gamma-limit of the screened Gamow model. Applied Analysis Seminar, Heidelberg • The elastica functional as the critical Gamma limit of a nonlocal isoperimetric problem. Partial Differential Equations and their Applications Seminar, University of Warwick • The elastica functional as the critical Gamma limit of a nonlocal isoperimetric problem. Current challenges in complex materials: modelling and analysis, HIM, Bonn Link to event • The elastica functional as the critical Gamma limit of a nonlocal isoperimetric problem. Oberseminar Analysis, Bonn • The elastica functional as the critical Gamma limit of a nonlocal isoperimetric problem. Isoperimetric Problems, Pisa Link to event |
| Current Publications | • Fischer, J; Hensel, S; Laux, T; Simon, T.M. A weak-strong uniqueness principle for the Mullins-Sekerka equation. , 2024 online • Muratov, C.B.; Simon, T.M.; Slastikov, V.V. Existence of higher degree minimizers in the magnetic skyrmion problem. , 2024 online • Monteil, A; Muratov, C.B.; Simon, T.M.; Slastikov, V.V. Magnetic skyrmions under confinement. Communications in Mathematical Physics Vol. 404, 2023 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 • 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 • Fischer, J; Hensel, S; Laux, T; Simon, T.M. Local minimizers of the interface length functional based on a concept of local paired calibrations. , 2022 online • Muratov, C.B.; Simon, T.M. Correction to: A Nonlocal Isoperimetric Problem with Dipolar Repulsion. , 2022 online • Simon, T.M. Quantitative aspects of the rigidity of branching microstructures in shape memory alloys via H-measures. SIAM Journal on Mathematical Analysis Vol. 53 (4), 2021 online • Simon, T.M. Rigidity of branching microstructures in shape memory alloys. Archive for Rational Mechanics and Analysis Vol. 241, 2021 online |
| Current Projects | • EXC 2044 - T06: Singularities and PDEs Our goal is to utilise and further develop the theory of non-linear PDEs to understand singular phenomena arising in geometry and in the description of the physical world. Particular emphasis is put on the interplay of geometry and partial differential equations and also on the connection with theoretical physics. The concrete research projects range from problems originating in geometric analysis such as understanding the type of singularities developing along a sequence of four-dimensional Einstein manifolds, to problems in evolutionary PDEs, such as the Einstein equations of general relativity or the Euler equations of fluid mechanics, where one would like to understand the formation and dynamics (in time) of singularities. online • EXC 2044 - T09: Multiscale processes and effective behaviour Many processes in physics, engineering and life sciences involve multiple spatial and temporal scales, where the underlying geometry and dynamics on the smaller scales typically influence the emerging structures on the coarser ones. A unifying theme running through this research topic is to identify the relevant spatial and temporal scales governing the processes under examination. This is achieved, e.g., by establishing sharp scaling laws, by rigorously deriving effective scale-free theories and by developing novel approximation algorithms which balance various parameters arising in multiscale methods. online | theresa.simon@uni-muenster.de |
| Phone | +49 251 83-35090 |
| FAX | +49 251 83-32729 |
| Room | 130.019 |
| Secretary | Sekretariat Claudia Giesbert Frau Claudia Giesbert Telefon +49 251 83-33792 Fax +49 251 83-32729 Zimmer 120.002 |
| Address | Frau JProf. Dr. Theresa Simon Angewandte Mathematik Münster: Institut für Analysis und Numerik Fachbereich Mathematik und Informatik der Universität Münster Orléans-Ring 10 48149 Münster |
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