This project addresses topics at the interface between mathematics, physics, and materials science, particularly (a) energy-driven pattern formation in crystalline grain boundaries, and (b) energy-driven coarsening of phase mixtures and defects. Concerning the former: the PI will investigate pattern formation in twist grain boundaries, using a new viewpoint based on minimization of incoherence energy. Concerning the latter: the PI will investigate problems from phase separation, grain growth, and vortex annihilation, using a new viewpoint based on dissipation and isoperimetric inequalities.
Energy-driven pattern formation occurs in many different physical systems; examples include vortex lattices in type-II superconductors, dislocation patterns in grain boundaries, and labyrinthine structures created by phase separation. This project seeks an understanding -- for specific, widely studied systems -- why certain patterns form rather than others. Such understanding is crucial for interpreting experimental observations, i.e. for drawing inferences about the physics of a system from observations of the patterns it forms.
