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Quasisteady patterns in interfaces: Folding and Faceting
Vinh Nguyen, Keith Promislow, Brian Wetton
We present a systematic derivation of the gradient flows associated to a broad class of interfacial energies, emphasizing the relation between intrinsic and extrinsic variations of…
Codimension One Minimizers of Highly Amphiphilic Mixtures
Shibin Dai, Keith Promislow
We present a modified form of the Functionalized Cahn Hilliard (FCH) functional which models highly amphiphilic systems in solvent. A molecule is highly amphiphilic if the energy o…
Manifolds of Amphiphilic Bilayers: Stability up to the Boundary
Yuan Chen, Keith Promislow
We consider the mass preserving -gradient flow of the strong scaling of the functionalized Cahn Hilliard gradient flow and establish the nonlinear stability of a manifold comp…
Gradient Invariance of Slow Energy Descent: Spectral Renormalization and Energy Landscape Techniques
Hayriye Guckir Cakir, Keith Promislow
For gradient flows of energies, both spectral renormalization (SRN) and energy landscape (EL) techniques have been used to establish slow motion of orbits near low-energy manifold.…
Robust Stability of Multicomponent Membranes: the Role of Glycolipids
Yuan Chen, Arjen Doelman, Keith Promislow +1
We present the multicomponent functionalized free energies that characterize the low-energy packings of amphiphilic molecules within a membrane through a correspondence to connecti…
Regularized Curve Lengthening from the Strong FCH Flow
Yuan Chen, Keith Promislow
We present a rigorous analysis of the transient evolution of nearly circular bilayer interfaces evolving under the thin interface limit, , of the mass preserving $…