49 citations · 253 across the 59 of their papers we have counts for
5 papers · 2 filters
Depinning asymptotics in ergodic media
Arnd Scheel, Sergey Tikhomirov
We study speeds of fronts in bistable, spatially inhomogeneous media at parameter regimes where speeds approach zero. We provide a set of conceptual assumptions under which we can…
Phase separation patterns from directional quenching
Rafael Monteiro, Arnd Scheel
We study the effect of directional quenching on patterns formed in simple bistable systems such as the Allen-Cahn and the Cahn-Hilliard equation on the plane. We model directional…
Linear spreading speeds from nonlinear resonant interaction
Gregory Faye, Matt Holzer, Arnd Scheel
We identify a new mechanism for propagation into unstable states in spatially extended systems, that is based on resonant interaction in the leading edge of invasion fronts. Such r…
Continuation and Bifurcation of Grain Boundaries in the Swift-Hohenberg Equation
David J. B. Lloyd, Arnd Scheel
We study grain boundaries between striped phases in the prototypical Swift-Hohenberg equation. We propose an analytical and numerical far-field-core decomposition that allows us to…
Universal wavenumber selection laws in apical growth
Ryan Goh, Rajendra Beekie, Daniel Matthias +2
We study pattern-forming dissipative systems in growing domains. We characterize classes of boundary conditions that allow for defect-free growth and derive universal scaling laws…