Related papers: Pinned, locked, pushed, and pulled traveling waves…

We study invasion fronts in the FitzHugh--Nagumo equation in the oscillatory regime using singular perturbation techniques. Phenomenologically, localized perturbations of the unstable steady-state grow and spread, creating temporal…

The encounter of diffusing entities underlies a wide range of natural phenomena. The dynamics of these first-passage dynamics are strongly influenced by confining geometries. Confinement modifies microscopic diffusion through conservative…

When animal groups move coherently in the form of a flock, their trajectories are not all parallel, the individuals exchange their position in the group. In this Letter we introduce a measure of this mixing dynamics, which we quantify as…

We have discovered a new, forerunning mode transition as the periodic transition wave propagating in a uniform continuous waveguide. The latter is represented by an elastic beam separating from the elastic foundation under the action of…

We study an individual-based model in which two spatially-distributed species, characterized by different diffusivities, compete for resources. We consider three different ecological settings. In the first, diffusing faster has a cost in…

We show the existence of traveling front solutions in a diffusive classical SIS epidemic model and the SIS model with a saturating incidence in the size of the susceptible population. We investigate the situation where both susceptible and…

The presence of temporal correlations in random movement trajectories is a widespread phenomenon across biological, chemical and physical systems. The ubiquity of persistent and anti-persistent motion in many natural and synthetic systems…

In this paper, we proposed a stochastic model which describes two species of particles moving in counterflow. The model generalizes the theoretical framework describing the transport in random systems since particles can work as mobile…

This paper is concerned with a lattice dynamical system modeling the evolution of susceptible and infective individuals at discrete niches. We prove the existence of traveling waves connecting the disease-free state to non-trivial leftover…

L\'evy walks are continuous time random walks with spatio-temporal coupling of jump lengths and waiting times, often used to model superdiffusive spreading processes such as animals searching for food, tracer motion in weakly chaotic…

The transition from stick to slip at a dry frictional interface occurs through the breaking of the junctions between the two contacting surfaces. Typically, interactions between the junctions through the bulk lead to rupture fronts…

We show that propagating switching fronts mediate directional state transmission and polarity selection in a passive many-body suspension. In confined trains of slipper-shaped deformable particles in Poiseuille flow, this behavior…

We consider spatially discrete bistable reaction-diffusion equations that admit wave front solutions. Depending on the parameters involved, such wave fronts appear to be pinned or to glide at a certain speed. We study the transition of…

Spatially extended systems can support local transient excitations in which just a part of the system is excited. The mechanisms reported so far are local excitability and excitation of a localized structure. Here we introduce an…

We experimentally, numerically and analytically explore the diffusive transport of active colloidal particles with sensory delay, navigating motility landscapes in which the self-propulsion speed depends on space. We show how the transport…

We consider the propagation of a flame front in a solid periodic medium. The model is governed by a free boundary system in which the front's velocity depends on the temperature via a kinetic rate which may degenerate. We show the existence…

The development and time evolution of a transport barrier in a magnetically confined plasma with non-monotonic, nonlinear dependence of the anomalous flux on mean gradients is analyzed. Upon consideration of both the spatial inhomogeneity…

We consider a free boundary model of epithelial cell migration with logistic growth and nonlinear diffusion induced by mechanical interactions. Using numerical simulations, phase plane and perturbation analysis, we find and analyse…

Using numerical simulations, we examine a simple model of two or more coupled one-dimensional channels of driven particles with repulsive interactions in the presence of quenched disorder. We find that this model exhibits a remarkably rich…

Dense monolayers of living cells display intriguing relaxation dynamics, reminiscent of soft and glassy materials close to the jamming transition, and migrate collectively when space is available, as in wound healing or in cancer invasion.…