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

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    Publications

    Scientific Articles (journals)

    • 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 239.
    • Simon TM. . ‘Rigidity of branching microstructures in shape memory alloys.’ Archive for Rational Mechanics and Analysis 241.
    • Simon TM. . ‘Quantitative aspects of the rigidity of branching microstructures in shape memory alloys via H-measures.’ SIAM Journal on Mathematical Analysis 53.
    • Bernand-Mantel A, Muratov CB, Simon TM. . ‘Unraveling the role of dipolar vs. Dzyaloshinskii-Moriya interaction in stabilizing compact magnetic skyrmions.’ Physical Review B 101.
    • 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 52.
    • Muratov CB, Simon TM. . ‘A nonlocal isoperimetric problem with dipolar repulsion.’ Communications in Mathematical Physics 372.
    • Ayala D, Doering CR, Simon TM. . ‘Maximum palinstrophy amplification in the two-dimensional Navier-Stokes equations.’ Journal of Fluid Mechanics 837: 839-857. doi: 10.1017/jfm.2017.874.
    • Laux T, Simon TM. . ‘Convergence of the Allen-Cahn equation to multi-phase mean curvature flow.’ Communications on Pure and Applied Mathematics 71.

    Theses (Doctoral or Post-Doctoral)

    • Simon TM. . Materials Science-inspired problems in the Calculus of Variations: Rigidity of shape memory alloys and multi-phase mean curvature flow Dissertation thesis, Universität Leipzig.

    Other Scientific Publications