Research

 

Research interests

Calculus of variations and nonlinear partial differential equations, in particular problems in energy-driven pattern formation:

• Micromagnetics
• Nonlocal isoperimetric problems
• Microstructures in shape memory alloys
• Curvature-driven evolution equations

Publications

1. "The local structure of the energy landscape in multiphase mean curvature flow: Weak-strong uniqueness and stability of evolutions"
   S. Hensel, J. Fischer, T. Laux and T. M. Simon
2. "Quantitative aspects of the rigidity of branching microstructures in shape memory alloys via H-measures"
   T. M. Simon
   (submitted).
3. "Rigidity of branching microstructures in shape memory alloys"
   T. M. Simon
   (submitted).
4. "A quantitative description of skyrmions in ultrathin ferromagnetic films and rigidity of degree ±1 harmonic maps from  from R² to S²"
   A. Bernand-Mantel, C. B. Muratov and T. M. Simon
   Arch. Ration. Mech. Anal. 239, 219-299 (2021)
5. "Convergence rates of the Allen-Cahn equation to mean curvature flow: A short proof based on relative entropies"
   J. Fischer, T. Laux and T. M. Simon
   SIAM J. Math. Anal. 52, 6222-6233 (2020)
6. "Unraveling the role of dipolar vs. Dzyaloshinskii-Moriya interaction in stabilizing compact magnetic skyrmions"
   A. Bernand-Mantel, C. B. Muratov and T. M. Simon
   Phys. Rev. B. 101, 045416 (2020)
7. "A nonlocal isoperimetric problem with dipolar repulsion"
   C. B. Muratov and T. M. Simon
   Comm. Math. Phys. 372, 1059–1115 (2019).
8. "Convergence of the Allen-Cahn equation to multi-phase mean curvature flow"
   T. Laux and T. M. Simon 
   Comm. Pure Appl. Math. 71, 1597-1647 (2018).
9. "Maximum palinstrophy amplification in the two-dimensional Navier-Stokes equations"
   D. Ayala, C. R. Doering and T. M. Simon
   J. Fluid Mech. 837, 839-857 (2018).