49 citations · 253 across the 59 of their papers we have counts for
7 papers · 1 filter
Wave train selection by invasion fronts in the FitzHugh--Nagumo equation
Paul Carter, Arnd Scheel
We study invasion fronts in the FitzHugh--Nagumo equation in the oscillatory regime using singular perturbation techniques. Phenomenologically, localized perturbations of the unsta…
Spatial Hamiltonian identities for nonlocally coupled systems
Bente Bakker, Arnd Scheel
We consider a broad class of systems of nonlinear integro-differential equations posed on the real line that arise as Euler-Lagrange equations to energies involving nonlinear nonlo…
Self-organized Clusters in Diffusive Run-and-Tumble Processes
Patrick Flynn, Quinton Neville, Arnd Scheel
We analyze a simplistic model for run-and-tumble dynamics, motivated by observations of complex spatio-temporal patterns in colonies of myxobacteria. In our model, agents run with…
Wavenumber selection via spatial parameter jump
Arnd Scheel, Jasper Weinburd
The Swift-Hohenberg equation describes an instability which forms finite-wavenumber patterns near onset. We study this equation posed with a spatial inhomogeneity; a jump-type para…
Pattern-forming fronts in a Swift-Hohenberg equation with directional quenching - parallel and oblique stripes
Ryan Goh, Arnd Scheel
We study the effect of domain growth on the orientation of striped phases in a Swift-Hohenberg equation. Domain growth is encoded in a step-like parameter dependence that allows st…
Bifurcation to coherent structures in nonlocally coupled systems
Arnd Scheel, Tianyu Tao
We show bifurcation of localized spike solutions from spatially constant states in systems of nonlocally coupled equations in the whole space. The main assumptions are a generic bi…