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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