| Research Interests | Micromagnetics and nonlocal isoperimetric problems Multi-phase mean curvature flow Dimension reduction in thin elastic bodies Microstructures in shape memory alloys |
| Project membership Mathematics Münster | C: Models and Approximations C1: Evolution and asymptotics C4: Geometry-based modelling, approximation, and reduction |
| Current Talks | • Skyrmions and stability of degree 1 harmonic maps from the plane to the two-dimensional sphere. CNA Seminar, Carnegie Mellon University, Pittsburgh, USA • Skyrmions and stability of degree 1 harmonic maps from the plane to the two-dimensional sphere. Young Women in PDEs and Applications, Rheinische Friedrich-Wilhelms-Universtität Bonn, Bonn, Deutschland • Skyrmions and stability of degree 1 harmonic maps from the plane to the two-dimensional sphere. HCM Workshop: Geometric and Applied Analysis, Rheinische Friedrich-Wilhelms-Universtität Bonn, Bonn, Deutschland • Skyrmions and stability of degree 1 harmonic maps from the plane to the two-dimensional sphere. SIAM Conference on Mathematical Aspects of Materials Science, Basque Center for Applied Mathematics, Bilbao, Spain • Rigidity of branching microstructures in shape memory alloys. SIAM Conference on Mathematical Aspects of Materials Science, Basque Center for Applied Mathematics, Bilbao, Spain • Skyrmions and stability of degree ±1 harmonic maps from the plane to the two-dimensional sphere. Arbeitsgemeinschaft Angewandte Analysis, Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig, Deutschland • Skyrmions and stability of degree 1 harmonic maps from the plane to the two-dimensional sphere. Analysis and PDE Seminar, University of California, Berkeley, USA • A nonlocal isoperimetric problem with dipolar repulsion. The International Congress on Industrial and Applied Mathematics, Valencia, Spain • A nonlocal isoperimetric problem with dipolar repulsion. Mathematics and CS Seminar, Institute of Science and Technology Austria, Klosterneuburg, Österreich |
| Current Publications | • Monteil, A; Muratov, CB; Simon,TM; Slastikov, VV Magnetic skyrmions under confinement. , 2022 online • Rüland, A; Simon, TM On Rigidity for the Four-Well Problem Arising in the Cubic-to-Trigonal Phase Transformation. , 2022 online • Fischer, J; Hensel, S; Laux, T; Simon, TM Local minimizers of the interface length functional based on a concept of local paired calibrations. , 2022 online • Hensel S, Fischer J, Laux T, Simon TM The local structure of the energy landscape in multiphase mean curvature flow: Weak-strong uniqueness and stability of evolutions. Vol. ---, 2021 online • Simon TM Quantitative aspects of the rigidity of branching microstructures in shape memory alloys via H-measures. SIAM Journal on Mathematical Analysis Vol. 53, 2021 online • Simon TM Rigidity of branching microstructures in shape memory alloys. Archive for Rational Mechanics and Analysis Vol. 241, 2021 online • Bernand-Mantel A, Muratov CB, Simon TM 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 • Fischer J, Laux T, Simon TM 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, 2020 online • Bernand-Mantel A, Muratov CB, Simon TM Unraveling the role of dipolar vs. Dzyaloshinskii-Moriya interaction in stabilizing compact magnetic skyrmions. Physical Review B Vol. 101, 2020 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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