Related papers: Traveling Waves in Bistable Reaction-Diffusion Cel…
We present experimental results on hydrothermal traveling-waves dynamics in long and narrow 1D channels. The onset of primary traveling-wave patterns is briefly presented for different fluid heights and for annular or bounded channels,…
Autocatalytic reaction between reacted and unreacted species may propagate as solitary waves, namely at a constant front velocity and with a stationary concentration profile, resulting from a balance between molecular diffusion and chemical…
We establish rigorous lower bounds on the speed of traveling fronts and on the bulk burning rate in reaction-diffusion equation with passive advection. The non-linearity is assumed to be of either KPP or ignition type. We consider two main…
In this work we revisit the existence, stability and dynamics of unstable traveling solitary waves in the context of lattice dynamical systems. We consider a nonlinear lattice of an $\alpha$-Fermi-Pasta-Ulam type with the additional feature…
We study multiplicity of the supercritical traveling front solutions for scalar reaction-diffusion equations in infinite cylinders which invade a linearly unstable equilibrium. These equations are known to possess traveling wave solutions…
In this paper, a comprehensive examination of the temperature- and bias-dependent diffusion regimes of underdamped Brownian particles is presented. A temperature threshold for a transition between anomalous and normal diffusive behaviors is…
Understanding how patterns and travelling waves form in chemical and biological reaction-diffusion models is an area which has been widely researched, yet is still experiencing fast development. Surprisingly enough, we still do not have a…
We theoretically study the transport properties of self-propelled particles on complex structures, such as motor proteins on filament networks. A general master equation formalism is developed to investigate the persistent motion of…
We study molecular dynamics within populations of diffusively coupled cells under the assumption of fast diffusive exchange. As a technical tool, we propose conditions on boundedness and ultimate boundedness for systems with a singular…
We investigate the inside structure of one-dimensional reaction-diffusion traveling fronts. The reaction terms are of the monostable, bistable or ignition types. Assuming that the fronts are made of several components with identical…
We consider principal properties of various wave regimes in two selected excitable systems with linear cross-diffusion in one spatial dimension observed at different parameter values. This includes fixed-shape propagating waves, envelope…
The structure of spiral waves is investigated in super-excitable reaction-diffusion systems where the local dynamics exhibits multi-looped phase space trajectories. It is shown that such systems support stable spiral waves with broken…
We consider the Vlasov--Poisson system describing a two-species plasma with spatial dimension $1$ and the velocity variable in $\mathbb{R}^n$. We find the necessary and sufficient conditions for the existence of solitary waves, shock waves,…
We present a family of one-dimensional cellular automata modeling the diffusion of an innovation in a population. Starting from simple deterministic rules, we construct models parameterized by the interaction range and exhibiting a…
We classify traveling waves and stationary solutions of a reaction-diffusion equation arising in population dynamics with Allee-type effects. The reaction term is given by a quadratic polynomial with a discontinuity at zero, which captures…
Cellular tissue behavior is a multiscale problem. At the cell level, out of equilibrium, biochemical reactions drive physical cell-cell interactions in a typical active matter process. Cell modeling computer simulations are a robust tool to…
Demixing of binary fluids subjected to slow temperature ramps shows repeated waves of nucleation which arise as a consequence of the competition between generation of supersaturation by the temperature ramp and relaxation of supersaturation…
In this paper the travelling wave solutions in the adiabatic model with two-step chain branching reaction mechanism are investigated both numerically and analytically in the limit of equal diffusivity of reactant, radicals and heat. The…
We consider positive travelling fronts of the time-delayed reaction-diffusion equation with the monostable birth function. Our main result says that for every fixed and sufficiently large velocity c, the positive travelling front is unique…
Transition waves in mechanical metamaterials manifest themselves as propagating interfaces between different stable states in lattices composed of arrays of coupled, intrinsically bistable elements. Here, we show experimentally and…