Time: 12月21日 15:30—16:30
Title: Pattern formation – on the modeling of multi-constituent inhibitory systems
Abstract: Skin pigmentation, animal coats and block copolymers can be considered as multi-constituent inhibitory systems and studied as nonlocal geometric variational problems. The free energy functional consists of two parts: an interface energy and a long range Coulomb-type interaction energy which inhibits micro-domains from unlimited growth. We prove the existence of core-shell assemblies and the existence of disk assemblies in ternary systems and also the existence of a triple bubble in a quaternary system using the sharp interface model. Meanwhile, via the diffuse interface model, one open question related to the polarity direction of double bubble assemblies is answered. Moreover, it is shown that the average size of bubbles in a single bubble assembly depends on the sum of the minority constituent volumes and the long range interaction coefficients. One further identifies the ranges for volume fractions and the long range interaction coefficients for double bubble assemblies.