Related papers: Pinned, locked, pushed, and pulled traveling waves…
We study the dynamics of waves in a system of diffusively coupled discrete nonlinear sources. We show that the system exhibits burst waves which are periodic in a traveling-wave reference frame. We demonstrate that the burst waves are…
A phase-separation front will leave in its wake a phase-separated morphology that differs markedly from homogeneous phase-separation morphologies. For a purely diffusive system such a front, moving with constant velocity, will generate very…
We analyze the transition between pulled and pushed fronts both analytically and numerically from a model-independent perspective. Based on minimal conceptual assumptions, we show that pushed fronts bifurcate from a branch of pulled fronts…
We study the stochastic motion of active particles that undergo spontaneous transitions between two distinct modes of motion. Each mode is characterized by a velocity distribution and an arbitrary (anti-)persistence. We present an…
We consider a partial differential equation model for the growth of heterogeneous cell populations subdivided into multiple distinct discrete phenotypes. In this model, cells preferentially move towards regions where they feel less…
We scrutinize the temporally-resolved speed of active cargo transport in living cells, and show intermittent bursting motions. These nonlinear fluctuations follow a scaling law over several decades of time and space, the statistical…
The transition from static to dynamic friction when an elastic body is slid over another is now known to result from the motion of interface rupture fronts. These fronts may be either crack-like or pulse-like, with the latter involving…
A wide variety of interacting particle assemblies driven by an external force are characterized by a transition between a blocked and a moving phase. The origin of this deblocking transition can be traced back to the presence of either…
Stochastic particle--based models are useful tools for describing the collective movement of large crowds of pedestrians in crowded confined environments. Using descriptions based on the simple exclusion process, two populations of…
Driven suspensions, where energy is input at a particle scale, are a framework for understanding general principles of out-of-equilibrium organization. A large number of simple interacting units can give rise to non-trivial structure and…
The relevant parameters at the microstructure scale that govern the macroscopic toughness of disordered brittle materials are investigated theoretically. We focus on planar crack propagation and describe the front evolution as the…
Environmental variations can significantly influence how populations compete for resources, and hence shape their evolution. Here, we study population dynamics subject to a fluctuating environment modeled by a varying carrying capacity…
We study the random walk of a particle in a compartmentalized environment, as realized in biological samples or solid state compounds. Each compartment is characterized by its length $L$ and the boundaries transmittance $T$. We identify two…
We study a singular diffusive prey-predator system with nonlocal dispersal for which the carrying capacity of the predator is proportional to the density of prey. We show the existence of positive one-dimensional traveling waves connecting…
The cohesive collective motion (flocking, swarming) of autonomous agents is ubiquitously observed and exploited in both natural and man-made settings, thus, minimal models for its description are essential. In a model with continuous space…
In pattern-forming systems, localized patterns are states of intermediate complexity between fully extended ordered patterns and completely irregular patterns. They are formed by stationary fronts enclosing an ordered pattern inside an…
Front propagation in two dimensional steady and unsteady cellular flows is investigated in the limit of very fast reaction and sharp front, i.e., in the geometrical optics limit. In the steady case, by means of a simplified model, we…
Motivated by various recent experimental findings, we propose a dynamical model of intermittently self-propelled particles: active particles that recurrently switch between two modes of motion, namely an active run-state and a turn state,…
Human mobility and activity patterns mediate contagion on many levels, including the spatial spread of infectious diseases, diffusion of rumors, and emergence of consensus. These patterns however are often dominated by specific locations…
The theory of traveling waves and spreading speeds is developed for time-space periodic monotone semiflows with monostable structure. By using traveling waves of the associated Poincar\'e maps in a strong sense, we establish the existence…