Date/Time Date(s) - 06/02/20261:30 pm - 2:30 pm
Speaker: Xin Yang Lu (Lakehead University)
Location: Hamilton Hall, Room 410
Title: Core-shell formation in ternary systems
Abstract: Ternary systems are governed by energies consisting of a local, sublinear term, which dominates at smaller masses, and a long range superlinear term, dominating at large masses. Optimal configurations strike a balance between these two classes of forces. The perimeter is one classical choice for the local term. We consider the case where perimeters between different phases are weighted, i.e., some perimeters are penalized more than others. This creates two very distinct situations: if the weights satisfy the triangular inequality, then the analysis is similar to the case with equally weighted perimeters; if, on the other hand, the weights do not satisfy the triangular inequality, then the energy is not lower semicontinuous anymore, making the analysis significantly more involved. We will present some results regarding this latter case, and show how the core-shell configurations arise as optimal ones.