Energy scaling and domain branching in type-I superconductors

January 29th, 2007 at 17:15 in HG G19.2

Given by: Sergio Conti (Duisburg)

Abstract: Many problems in material sciences are characterized by the
spontaneous formation of fine-scale structures,
whose topology changes when the control parameters are varied. The different
patterns can be understood using nonconvex functionals with a singular
perturbation, which physically represents surface energy terms.
Focusing on two specific examples (shape-memory alloys and flux
penetration in type-I superconductors), I shall show how a
combination of interpolation inequalities and explicit constructions
permits to determine the scaling of the minimal energy
with respect to the relevant material parameters, and therefore to
predict a phase diagram for the observed microstructure.