Date: Friday, January 09, 2015
Location: 1084 East Hall (3:00 PM to 4:00 PM)
Title: Bifurcation and competitive evolution of network morphologies in the strong Functionalized CahnHilliard equation
Abstract: The Functionalized CahnHilliard (FCH) energy is a higherorder free energy for blends of amphiphillic polymers and solvent which balances solvation energy of ionic groups against elastic energy of the underlying polymer backbone. Its gradient flows describe the formation of solvent network structures which are essential to ionic conduction in polymer membranes. The FCH energy possesses stable, coexisting network morphologies and we characterize their geometric evolution, bifurcation and competition through a centerstable manifold reduction which encompasses a broad class of coexisting network morphologies. The stability of the different networks is characterized by the meandering and pearling modes associated to the linearized system. For the H^{1} gradient flow of the FCH energy, using functional analysis and asymptotic methods, we drive a sharpinterface geometric motion which couples the flow of codimension 1 and 2 network morphologies, through the farfield chemical potential. In particular, we derive expressions for the pearling and meander eigenvalues for a class of farfromselfintersection codimension 1 and 2 networks, and show that the linearization is uniformly elliptic off of the associated center stable space.
Files:
Speaker: Noa Kraitzman
Institution: Michigan State University
Event Organizer: Peter Miller millerpd@umich.edu
