| 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 - C1: Evolution and asymptotics In this unit, we will use generalisations of optimal transport metrics to develop gradient flow descriptions of (cross)-diffusion-reaction systems, rigorously analyse their pattern forming properties, and develop corresponding efficient numerical schemes. Related transport-type- and hyperbolic systems will be compared with respect to their pattern-forming behaviour, especially when mass is conserved. Bifurcations and the effects of noise perturbations will be explored. Moreover, we aim to understand defect structures, their stability and their interactions. Examples are the evolution of fractures in brittle materials and of vortices in fluids. Our analysis will explore the underlying geometry of defect dynamics such as gradient descents or Hamiltonian structures. Also, we will further develop continuum mechanics and asymptotic descriptions for multiple bodies which deform, divide, move, and dynamically attach to each other in order to better describe the bio-mechanics of growing and dividing soft tissues. Finally, we are interested in the asymptotic analysis of various random structures as the size or the dimension of the structure goes to infinity. More specifically, we shall consider random polytopes and random trees.For random polytopes we would like to compute the expected number of faces in all dimensions, the expected (intrinsic) volume, and absorption probabilities, as well as higher moments and limit distributions for these quantities. online • EXC 2044 - C4: Geometry-based modelling, approximation, and reduction In mathematical modelling and its application to the sciences, the notion of geometry enters in multiple related but different flavours: the geometry of the underlying space (in which e.g. data may be given), the geometry of patterns (as observed in experiments or solutions of corresponding mathematical models), or the geometry of domains (on which PDEs and their approximations act). We will develop analytical and numerical tools to understand, utilise and control geometry, also touching upon dynamically changing geometries and structural connections between different mathematical concepts, such as PDE solution manifolds, analysis of pattern formation, and geometry. 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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