Analysis Seminar

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Patterns in tri-block copolymers: droplets, double-bubbles and core-shells, and a “new” partitioning problem

Speaker: Lia Bronsard, McMaster University

Location: Warren Weaver Hall 1302

Date: Thursday, November 16, 2023, 11 a.m.

Synopsis:

We study the Nakazawa-Ohta ternary inhibitory system, which
describes domain morphologies in a triblock copolymer as a nonlocal
isoperimetric problem for three interacting phase domains.  The free
energy consists of two parts:  the local interface energy measures the
total perimeter of the phase boundaries, while a longer-range Coulomb
interaction energy reflects the connectivity of the polymer chains and
promotes splitting into micro-domains.  We consider global minimizers on
the two-dimensional torus, in a limit in which two of the species have
vanishingly small mass but the interaction strength is correspondingly
large.  In this limit there is splitting of the masses, and each
vanishing component rescales to a minimizer of an isoperimetric problem
for clusters in 2D.  Depending on the relative strengths of the
coefficients of the interaction terms we may see different structures
for the global minimizers, ranging from a lattice of isolated simple
droplets of each minority species to double-bubbles or core-shells.
These results have led to a new type of partitioning problem that I will
also introduce. These represent work with S. Alama, with X. Lu, and C.
Wang, as well as with S. Vriend.