26 citations · 41 across the 8 of their papers we have counts for
9 papers
A Heterogeneous FitzHugh-Nagumo Model Exhibiting Local and Regional Dynamics that Mimic Spontaneous Atrial Fibrillation
Alexander Hattoum, Camden Kilton, Martin Mohlenkamp +3
We study two-dimensional networks of FitzHugh-Nagumo oscillators in regimes that mimic cardiac tissue. The networks include small layers of cells that have fast-recovery characteri…
Pinning and dipole asymptotics of locally deformed striped phases
Arnd Scheel, Qiliang Wu
We investigate the effect of spatial inhomogeneity on perfectly periodic, self-organized striped patterns in spatially extended systems. We demonstrate that inhomogeneities select…
Weak Diffusive Stability of Roll Solutions at the Zigzag Boundary
Abhijit Chowdhary, Mason Haberle, William Ofori-atta +1
Roll solutions at the zigzag boundary, typically selected by patterns and defects in numerical simulations, are shown to be nonlinearly stable. This result also serves as an exampl…
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…
Nonlinear Stability at the Zigzag Boundary
Mason Haberle, Abhijit Chowdhary, Qiliang Wu
We investigate the dynamics of roll solutions at the zigzag boundary of the planar Swift-Hohenberg equation. Linear analysis shows an algebraic decay of small perturbation with a $…
The Effect of Impurities on Striped Phases
Gabriela Jaramillo, Arnd Scheel, Qiliang Wu
We study the effect of algebraically localized impurities on striped phases in one space-dimension. We therefore develop a functional-analytic framework which allows us to cast the…
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…
Diffusive stability of Turing patterns via normal forms
Arnd Scheel, Qiliang Wu
We investigate dynamics near Turing patterns in reaction-diffusion systems posed on the real line. Linear analysis predicts diffusive decay of small perturbations. We construct a "…