Graduate Student Seminar- Core shells and double bubbles in a weighted nonlocal isoperimetric problem

Date and Time: Tuesday, February 13, 2023 2:15-3:15 p.m.

Place: Rome 206 and Mandatory for Graduate students

Speaker: Professor Chong Wang(former PhD student, GWU), Washington & Lee University

Title: Core shells and double bubbles in a weighted nonlocal isoperimetric problem

Abstract: We consider a sharp-interface model of ABC triblock copolymers, for which the surface tension σij across the interface separating phase i from phase j may depend on the components. We study global minimizers of the associated ternary local isoperimetric problem in R2 and show how the geometry of minimizers changes with the surface tensions σij , varying from symmetric double-bubbles for equal surface tensions, through asymmetric double bubbles, to core shells as the values of σij become more disparate. Then we consider the effect of nonlocal interactions in a droplet scaling regime, in which vanishingly small particles of two phases are distributed in a sea of the third phase. We are particularly interested in a degenerate case of σij in which minimizers exhibit core shell geometry, as this phase configuration is expected on physical grounds in nonlocal ternary systems.