Related papers: Nucleation of reaction-diffusion waves on curved s…
For a substance diffusing on a curved surface, we obtain an explicit relation valid for very small values of the time, between the local concentration, the diffusion coefficient, the intrinsic spatial curvature and the time. We recover the…
Propagation failure (pinning) of traveling waves is studied in a discrete scalar reaction-diffusion equation with a piecewise linear, bistable reaction function. The critical points of the pinning transition, and the wavefront profile at…
A propagation method for the scattering of a quantum wave packet from a potential surface is presented. It is used to model the quantum reflection of single atoms from a corrugated (metallic) surface. Our numerical procedure works well in…
In two-dimensional reaction-diffusion systems, local curvature perturbations in the shape of traveling waves are typically damped out and disappear in the course of time. If, however, the inhibitor diffuses much faster than the activator,…
The reaction-diffusion waves of proteins are known to be involved in fundamental cellular functions, such as cell migration, cell division, and vesicular transportation. In some of these phenomena, pattern formation on the membranes is…
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…
It is not fully understood how electromagnetic waves propagate through plasma density fluctuations when the size of the fluctuations is comparable with the wavelength of the incident radiation. In this paper, the perturbing effect of a…
This paper is devoted to study the wave propagation and its stability for a class of two-component discrete diffusive systems. We first establish the existence of positive monotone monostable traveling wave fronts. Then, applying the…
A number of equations is deduced which describe propagation of excitations along $n$-dimensional surfaces in $R^N$. Usual excitations in wave theory propagate along 1-dimensional trajectories. The role of the medium of propagation of…
We examine traveling-wave solutions on a regular ring network with one additional long-range link that spans a distance d. The nodes obey the FitzHugh-Nagumo kinetics in the excitable regime. The additional shortcut induces a plethora of…
We study a system of differential equation simulating transport phenomena in active structured media. The model is a generalization of the McKean s modification of the celebrated FitzHugh--Nagumo system, describing the nerve impulse…
We investigate the propagation of transverse elastic waves in crumpled media. We set up the wave equation for transverse waves on a generic curved, strained surface via a Langrangian formalism and use this to study the scaling behaviour of…
The propagation of detonation waves in reactive media bounded by an inert, compressible layer is examined via computational simulations in two different geometries, axisymmetric cylinders and two dimensional, planar slabs. For simplicity,…
The propagation of a narrow-band signal radiated by a point source in a randomly layered absorbing medium is studied asymptotically in the weak-scattering limit. It is shown that in a disordered stratified medium that is homogeneous on…
Fundamental biological and biomimetic processes, from tissue morphogenesis to soft robotics, rely on the propagation of chemical and mechanical surface waves to signal and coordinate active force generation. The complex interplay between…
We investigate the propagation of surface waves along a spatially dispersive graphene sheet, including substrate effects. The proposed analysis derives the admittances of an equivalent circuit of graphene able to handle spatial dispersion,…
The description of gravity waves propagating on the water surface is considered from a historical point of view, with specific emphasis on the development of a theoretical framework and equations of motion for long waves in shallow water.…
It has been known that gravitational waves (GWs) transfer energy to viscous matter through which they propagate, but the effect is too weak to be astrophysically significant. Using linearized perturbations about a Minkowski background, we…
One of the main characteristics of blood coagulation is the speed of clot growth. This parameter strongly depends on the speed of propagation of the thrombin concentration in blood plasma. In the current work we consider mathematical model…
We study the diffusion phenomena on the negatively curved surface made up of congruent heptagons. Unlike the usual two-dimensional plane, this structure makes the boundary increase exponentially with the distance from the center, and hence…