Speaker: Dr. Qiliang Wu from Ohio University (invited by Helen Li)
Title: Pearling and Localized Undulation of Bilayers in Amphiphilic Morphology
Abstract: Amphiphiles, such as lipids and functionalized polymers, plays a central
role in the self-assembly of solvent accessible, intricately structured
nano-scaled network structures, which are vital in cell functionality and
offer wide applications to drug delivery, detergent production, emulsion
stabilization and energy conversion devices. We study amphiphilic
morphology in the framework of the functionalized Cahn-Hilliard (FCH)
energy. The FCH is a continuum model accommodating various co-dimensional
structures such as bilayers (co-dim 1), filaments (co-dim 2) and micelles
(co-dim 3). We focus on defect structures that break the dimensional
reduction and include endcaps that terminate filaments or bilayers and Y
junctions. More specifically, we show the existence of pearled bilayer
solutions via a spatial-dynamics formulation, in combination with center
manifold reduction and a fixed-point argument. In addition, we also show
via a functional analytic framework that in the presence of spatial
inhomogeneity, localized undulation appears under proper functionalization
terms. More interestingly, both the pearling and localized undulation are
shown to be a manifestation of a degenerate 1:1 resonance Hopf
bifurcation encoded in a reduced ODE system from the FCH energy.