April 1, 2018 at 8:00 pm

Math-Biology Seminar | Pattern Formation in Amphiphilic Mixtures, April 17

Dr. Qiliang Wu

Dr. Qiliang Wu

The Mathematical Biology and Dynamical Systems Seminar series presents Dr. Qiliang Wu discussing “Pattern Formation in Amphiphilic Mixtures” on Tuesday, April 17, from 3:05 to 4 p.m. in Morton 326.

Wu is Assistant Professor of Mathematics at Ohio University.

Abstract: We introduce the functionalized Cahn-Hilliard (FCH) free energy as a model for amphiphilic mixtures, and illustrate their history, derivation, merits and physical interpretation. In the context of single-component FCH (sFCH) free energy, we show via spatial dynamics that the onset of the pearling bifurcation—a co-dimensional morphological bifurcation—coincides with the creation of a two-parameter family of pearled equilibria which are periodic in the in-plane direction and exponentially localized in the transverse direction. In the context of multi-component FCH (mFCH) free energy, we create a submanifold of quasi-bilayers on which the mFCH free energy reduces to a Canham-Helfrich sharp interface energy, and connect the intrinsic curvature to a Melnikov parameter associated to amphiphilic molecule’s aspect ratio. We also construct asymmetric homoclinic bilayer profiles via a billiard limit potential and show that co-dimensional bifurcation is driven by the experimentally observed layer-by-layer pearling mechanism. We conclude with ongoing and future work on coexistence of bilayers with various compositions and the generic inhibition of pearling in multicomponent bilayers.

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