Related papers: Depinning transitions in discrete reaction-diffusi…
Previous work has established that the localized regime of wave transport in open media is characterized by a position-dependent diffusion coefficient. In this work we study how the concept of position-dependent diffusion affects the delay…
Traveling fronts describe the transition between two alternative states in a great number of physical and biological systems. Examples include the spread of beneficial mutations, chemical reactions, and the invasions by foreign species. In…
Metastable condensed matter typically fluctuates about local energy minima at the femtosecond time scale before transitioning between local minima after nanoseconds or microseconds. This vast scale separation limits the applicability of…
Near a parity breaking front bifurcation, small perturbations may reverse the propagation direction of fronts. Often this results in nonsteady asymptotic motion such as breathing and domain breakup. Exploiting the time scale differences of…
In this paper, we generalize the usual notions of waves, fronts and propagation speeds in a very general setting. These new notions, which cover all classical situations, involve uniform limits, with respect to the geodesic distance, to a…
We present three examples of delayed bifurcations for spike solutions of reaction-diffusion systems. The delay effect results as the system passes slowly from a stable to an unstable regime, and was previously analysed in the context of…
Spreading processes on top of active dynamics provide a novel theoretical framework for capturing emerging collective behavior in living systems. I consider run-and-tumble dynamics coupled with coagulation/decoagulation reactions that lead…
We prove existence of transition fronts for a large class of reaction-diffusion equations in one dimension, with inhomogeneous monostable reactions. We construct these as perturbations of corresponding front-like solutions to the…
We consider bistable reaction-diffusion equations in funnel-shaped domains of R N made up of straight parts and conical parts with positive opening angles. We study the large time dynamics of entire solutions emanating from a planar front…
The dynamics of capillary filling in the presence of chemically coated heterogeneous boundaries is investigated, both theoretically and numerically. In particular, by mapping the equations of front motion onto the dynamics of a dissipative…
We use a new method in the study of Fisher-KPP reaction-diffusion equations to prove existence of transition fronts for inhomogeneous KPP-type non-linearities in one spatial dimension. We also obtain new estimates on entire solutions of…
An analysis of traveling wave solutions of partial differential equation (PDE) systems with cross-diffusion is presented. The systems under study fall in a general class of the classical Keller-Segel models to describe chemotaxis. The…
We study of the formation of pattern-forming fronts in the presence of a rigidly-propagating parameter ramp which is slowly-varying in space. In the context of the prototypical supercritical complex Ginzburg-Landau equation, we show that…
We study the existence and stability of propagating fronts in Meinhardt's multivariable reaction-diffusion model of branching in one spatial dimension. We identify a saddle-node-infinite-period (SNIPER) bifurcation of fronts that leads to…
We consider a porous media equation with balanced bistable reactions, equipped with some general nonlinear boundary condition. When the coefficient of the reaction term is much larger than that of the diffusion term, we see that, besides…
In a companion paper, we established nonlinear stability with detailed diffusive rates of decay of spectrally stable periodic traveling-wave solutions of reaction diffusion systems under small perturbations consisting of a nonlocalized…
Using dynamical density functional theory we calculate the speed of solidification fronts advancing into a quenched two-dimensional model fluid of soft-core particles. We find that solidification fronts can advance via two different…
A wave front of Fisher and Kolmogorov, Petrovskii, and Piskunov type involving two species A and B with different diffusion coefficients $D_A$ and $D_B$ is studied using a master equation approach in dilute and concentrated solutions.…
In this paper, we investigate the existence and stability of random transition fronts of KPP-type lattice equations in random media, and explore the influence of the media and randomness on the wave profiles and wave speeds of such…
We consider a massive particle driven with a constant force in a periodic potential and subjected to a dissipative friction. As a function of the drive and damping, the phase diagram of this paradigmatic model is well known to present a…