49 citations · 253 across the 59 of their papers we have counts for
63 papers
Oscillations in a scalar differential equation coupled to a diffusive field
Merlin Pelz, Arnd Scheel
We study the emergence of periodic oscillations through a Hopf bifurcation in a scalar diffusion equation on the half line coupled to a dynamic boundary condition. Our results quan…
Diffusive synchronization of phase waves in the FitzHugh-Nagumo system
Montie Avery, Paul Carter, Björn de Rijk +1
We analyze synchronization of relaxation oscillations in multiple-timescale reaction-diffusion systems. Interpreting synchronization as convergence to frequency-synchronized wave-t…
Selection mechanisms in front invasion
Montie Avery, Matt Holzer, Arnd Scheel
We review progress on questions related to front propagation into unstable states and point out open problems in the area. We strive to highlight different theoretical perspectives…
Pulled fronts are not (just) pulled
Montie Avery, Matt Holzer, Arnd Scheel
Front propagation into unstable states is often determined by the linearization, that is, propagation speeds agree with predictions from the linearized equation at the unstable sta…
Vacuum bubble and fissure formation in collective motion with competing attractive and repulsive forces
Olivia Clifton, Angel Chavez, Antonio Madrigal +3
We study the continuum limit of the motion of agents in the plane driven by competing short-range repulsion and long-range attractive forces. At a critical parameter value, we find…
Reversible switching due to attraction and repulsion: clusters, gaps, sorting, and mixing
Arnd Scheel, Angela Stevens
We describe a phase transition in continuum limits of interacting particle systems that exhibits a vertical bifurcation diagram. The transition is mediated by a competition short-r…