Dr. Giacomo Del Nin (University of Warwick): Pattern formation in optimal planar partitions
Mittwoch, 15.01.2020 16:00 im Raum M5
Given a fixed open set $\Omega$ in the plane we focus on optimal partitions, that is, partitions of $\Omega$ into $N$ equal-area subsets that minimize the total perimeter. Hales proved in 1999 that the asymptotic optimal energy for large $N$ is given by the hexagonal honeycomb, and thus hexagonal patterns are expected. However, since $\Omega$ may not accomodate a perfectly hexagonal partition, a polycrystalline structure may emerge, where different zones of constant orientation ("grains") are separated by "grain boundaries", similarly to what happens with dislocations in materials. In this talk I will present some ongoing work on the mathematical description of such structures.