260 citations · 677 across the 25 of their papers we have counts for
25 papers
Curve Lengthening Bifurcations in Modally Filtered Nonlinear Schrödinger Systems
Keith Promislow, Abba Ramadan
Extensions of the parametric nonlinear Schrödinger equations (PNLS) for phase-sensitive optical resonance are developed that preserve the curve lengthening bifurcation seen in the…
Gradient Flows of Interfacial Energies: Curvature Agents and Incompressibility
Keith Promislow, Truong Vu, Brian Wetton
We present a framework for the gradient flow of sharp-interface surface energies that couple to embedded curvature active agents. We use a penalty method to develop families of loc…
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…
Curvature and Chaos in the Defocusing Parameteric Nonlinear Schrodinger System
Keith Promislow, Abba Ramadan
The parametric nonlinear Schrodinger equation models a variety of parametrically forced and damped dispersive waves. For the defocusing regime, we derive a normal velocity for the…
Parameterized Density Functional Models for Block Copolymer Melts
Sulin Wang, Yuan Chen, Zengqiang Tan +1
The derivation of density functional energies from the random phase approximation of self-consistent mean field theory is generalized and applied to a binary blend of diblock copol…
Defects and Frustration in the Packing of Soft Balls
Kenneth Jao, Keith Promislow, Samuel Sottile
This work introduces the Hookean-Voronoi energy, a minimal model for the packing of soft, deformable balls. This is motivated by recent studies of quasi-periodic equilibria arising…
Slow Migration of Brine Inclusions in First-Year Sea Ice
Noa Kraitzman, Keith Promislow, Brian Wetton
We derive a thermodynamically consistent model for phase change in sea ice by adding salt to the framework introduced by Penrose and Fife. Taking the salt entropy relative to the l…
Undulated Bilayer Interfaces in the Planar Functionalized Cahn-Hilliard Equation
Keith Promislow, Qiliang Wu
Experiments with diblock co-polymer melts display undulated bilayers that emanate from defects such as triple junctions and endcaps, \cite{batesjain_2004}. Undulated bilayers are c…
On nonnegative solutions for the Functionalized Cahn-Hilliard equation with degenerate mobility
Shibin Dai, Qiang Liu, Toai Luong +1
The Functionalized Cahn-Hilliard equation has been proposed as a model for the interfacial energy of phase-separated mixtures of amphiphilic molecules. We study the existence of a…
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…
Benchmark Computation of Morphological Complexity in the Functionalized Cahn-Hilliard Gradient Flow
Andrew Christlieb, Keith Promislow, Zengqiang Tan +3
Reductions of the self-consistent mean field theory model of amphiphilic molecules in solvent can lead to a singular family of functionalized Cahn-Hilliard energies. We modify thes…
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 $…
Asymptotic Behaviour of Time Stepping Methods for Phase Field Models
Xinyu Cheng, Dong Li, Keith Promislow +1
Adaptive time stepping methods for metastable dynamics of the Allen Cahn and Cahn Hilliard equations are investigated in the spatially continuous, semi-discrete setting. We analyse…
Competition and Complexity in Amphiphilic Polymer Morphology
Andrew Christlieb, Noa Kraitzman, Keith Promislow
We analyze the competitive evolution of codimension one and two morphologies within the gradient flow of the strong Functionalized Cahn-Hilliard equation. On a slow time s…
Pearling Bifurcations in the strong Functionalized Cahn-Hilliard Free Energy
Noa Kraitzman, Keith Promislow
The Functionalized Cahn-Hilliard free energy supports phase separated morphologies of distinct codimension, including codimension-one bilayer and codimension-two filament morpholog…
Existence, Bifurcation, and Geometric Evolution of Quasi-Bilayers in the Multicomponent Functionalized Cahn-Hilliard Equation
Keith Promislow, Qiliang Wu
Multicomponent bilayer structures arise as the ubiquitous plasma membrane in cellular biology and as blends of amphiphilic copolymers used in electrolyte membranes, drug delivery,…
Existence of pearled patterns in the planar Functionalized Cahn-Hilliard equation
Keith Promislow, Qiliang Wu
The functionalized Cahn-Hilliard (FCH) equation supports planar and circular bilayer interfaces as equilibria which may lose their stability through the pearling bifurcation: a per…
Adiabatic stability under semi-strong interactions: The weakly damped regime
Thomas Bellsky, Arjen Doelman, Tasso J. Kaper +1
We rigorously derive multi-pulse interaction laws for the semi-strong interactions in a family of singularly-perturbed and weakly-damped reaction-diffusion systems in one space dim…
Dependence of the dielectric constant of electrolyte solutions on ionic concentration - a microfield approach
Nir Gavish, Keith Promislow
We present a novel microfield approach for studying the dependence of the orientational polarization of the water in aqueous electrolyte solutions upon the salt concentration and t…
Localized breathing solutions for Bose-Einstein condensates in periodic traps
R. Carretero-González, K. Promislow
We demonstrate the existence of localized oscillatory breathers for quasi-one-dimensional Bose-Einstein condensates confined in periodic potentials. The breathing behavior correspo…
Stability of Attractive Bose-Einstein Condensates in a Periodic Potential
J. C. Bronski, L. D. Carr, R. Carretero-Gonzalez +3
Using a standing light wave trap, a stable quasi-one-dimensional attractive dilute-gas Bose-Einstein condensate can be realized. In a mean-field approximation, this phenomenon is m…