Gradientflow through an energy landscape with a sharp lower bound.
© Sebastian Hensel

Research areas

Calculus of variations and nonlinear partial differential equations, in particular problems inspired by physics and materials science:

Micromagnetism and nonlocal isoperimteric problems
Multi-phase mean curvature flow
Dimension reduction in thin elastic bodies
Microstructures in shape memory alloys

Publications

Research Articles (Journals)
- Monteil, A; Muratov, CB; Simon, TM; Slastikov, VV. 2023. ‘Magnetic skyrmions under confinement.’ Communications in Mathematical Physics 404: 1571–2023. doi: 10.1007/s00220-023-04864-w.
- Rüland, A; Simon, TM. 2023. ‘On Rigidity for the Four-Well Problem Arising in the Cubic-to-Trigonal Phase Transformation.’ Journal of Elasticity 153: 455–475. doi: 10.1007/s10659-023-10011-2.
- Bernand-Mantel, A.; Fondet, A; Barnova, S.; Simon, T.M.; Muratov C.B. 2023. ‘Theory of magnetic field-stabilized compact skyrmions in thin film ferromagnets.’ Physical Review B 2023: L161405. doi: 10.1103/PhysRevB.108.L161405.
- Simon TM. 2021. ‘Quantitative aspects of the rigidity of branching microstructures in shape memory alloys via H-measures.’ SIAM Journal on Mathematical Analysis 53, No. 4. doi: 10.1137/18M1220017.
- Simon TM. 2021. ‘Rigidity of branching microstructures in shape memory alloys.’ Archive for Rational Mechanics and Analysis 241: 1707–1783. doi: 10.1007/s00205-021-01679-8.
- Bernand-Mantel A, Muratov CB, Simon TM. 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 239: 219–299. doi: 10.1007/s00205-020-01575-7.
- Fischer J, Laux T, Simon TM. 2020. ‘Convergence rates of the Allen-Cahn equation to mean curvature flow: A short proof based on relative entropies.’ SIAM Journal on Mathematical Analysis 52, No. 6. doi: 10.1137/20M1322182.
- Bernand-Mantel A, Muratov CB, Simon TM. 2020. ‘Unraveling the role of dipolar vs. Dzyaloshinskii-Moriya interaction in stabilizing compact magnetic skyrmions.’ Physical Review B 101, No. 4: 045416. doi: 10.1103/PhysRevB.101.045416.
- Muratov CB, Simon TM. 2019. ‘A nonlocal isoperimetric problem with dipolar repulsion.’ Communications in Mathematical Physics 372: 1059–1115. doi: 10.1007/s00220-019-03455-y.
- Laux T, Simon TM. 2018. ‘Convergence of the Allen-Cahn equation to multi-phase mean curvature flow.’ Communications on Pure and Applied Mathematics 71, No. 8: 1597–1647. doi: 10.1002/cpa.21747.
- Ayala D, Doering CR, Simon TM. 2018. ‘Maximum palinstrophy amplification in the two-dimensional Navier-Stokes equations.’ Journal of Fluid Mechanics 837: 839–857. doi: 10.1017/jfm.2017.874.
- 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.’ Journal of the European Mathematical Society (to appear). [accepted / in Press (not yet published)]
Theses (Doctoral or Postdoctoral)
- Simon TM. 2018. Materials Science-inspired problems in the Calculus of Variations: Rigidity of shape memory alloys and multi-phase mean curvature flow Dissertation thesis, Universität Leipzig. Leipzig: Selbstverlag / Eigenverlag.
Research Articles in Digital Collections
- Fischer, J; Hensel, S; Laux, T; Simon, TM. 2022. Local minimizers of the interface length functional based on a concept of local paired calibrations arXiv. doi: 10.48550/arXiv.2212.11840. [submitted / under review]
Errata
- Muratov, C.B.; Simon, T.M. 2022. Correction to: A Nonlocal Isoperimetric Problem with Dipolar Repulsion. doi: 10.1007/s00220-022-04426-6.

Research areas

Publications

Research Articles (Journals)

Theses (Doctoral or Postdoctoral)

Research Articles in Digital Collections

Errata