- Series
- PDE Seminar
- Time
- Tuesday, March 25, 2025 - 3:30pm for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Tobias Reid – Georgia Tech – tobias.ried@gatech.edu – https://sites.gatech.edu/tobiasried/
- Organizer
- Gong Chen
The Landau-Lifshitz model of micromagnetics is a powerful continuum theory that describes the occurrence of magnetization patterns in a ferromagnetic body. In this talk I will discuss domain branching in strongly uniaxial materials resulting from the competition between a short-range attractive interaction (surface energy), a long-range repulsive interaction (stray field energy), and a non-convex constraint coming from the strong uniaxiality.
On a mathematical level, we use modern tools from elliptic regularity theory, convex duality, ideas from statistical physics, and fine geometric constructions to describe the occurrence of domain branching through local energy estimates at the boundary of the sample (where the branching is infinitely fine). Our approach provides a robust framework for other domain branching problems and is the first step to prove self-similarity in a statistical sense.
(Joint work with Carlos Román)