This paper investigates traveling wave solutions of the spatially discrete reaction-diffusion systems whose kinetics are modeled by the McKean caricature of the FitzHugh-Nagumo model. In the limit of a weak coupling strength, we construct the traveling wave solutions and obtain the critical coupling constant below which propagation failure occurs. We report the existence of two different pulse ...

The study of spatially explicit integro-difference systems when the local population dynamics are given in terms of discrete-time generations models has gained considerable attention over the past two decades. These nonlinear systems arise naturally in the study of the spatial dispersal of organisms. The brunt of the mathematical research on these systems, particularly, when dealing with cooper...

The purpose of this paper is to study traveling wave fronts of a two-dimensional (2D) lattice delayed differential equation with global interaction. Applying the comparison principle combined with the technical weighted-energy method, we prove that any given traveling wave front with large speed is time-asymptotically stable when the initial perturbation around the wave front need decay to zero...

We study the existence and nonexistence of traveling waves of general diffusive KermackMcKendrick SIR models with standard incidence where the total population is not constant. The three classes, susceptible S, infected I and removed R, are all involved in the traveling wave solutions. We show that the minimum speed for the existence of traveling waves for this three-dimensional non-monotonic s...

This paper is concerned with the determination of the traveling speed of a moving object of a video clip based on subsequent object detection techniques. After preprocessing of the original image sequence, which is sampled from the video camera, the target moving object is detected with the improved algorithm in which the moving object region can be extracted completely through several processi...

Vehicular speed has a two-fold influence on traffic accident risk: It affects both probability of involvement and severity of consequence. In terms of involvement, it was long ago suggested that deviation from the mean travel speed of surrounding traffic carried an increased risk fbr the “offending” vehicle.’ A vehicle traveling significantly faster or slower than surrounding traffic is either ...

We study the interplay between rotation and openness for mode coupling in wavelength-scale microcavities. In cavities deformed from a circular disk, the decay rates of a quasidegenerate pair of resonances may cross or anticross with increasing rotation speed. The standing-wave resonances evolve to traveling-wave resonances at high rotation speed, however both the clockwise (CW) and counterclock...

We revisit the classical problem of speed selection for the propagation of disturbances in scalar reaction-diffusion equations with one linearly stable and one linearly unstable equilibrium. For a wide class of initial data this problem reduces to finding the minimal speed of the monotone traveling wave solutions connecting these two equilibria in one space dimension. We introduce a variational...

This paper deals with entire solutions of a bistable reaction-diffusion equation for which the speed of the traveling wave connecting two constant stable equilibria is zero. Entire solutions which behave as two traveling fronts approaching, with super-slow speeds, from opposite directions and annihilating in a finite time are constructed by using a quasiinvariant manifold approach. Such solutio...

Tra c estimation has been a long-studied problem, but prior work has mostly provided coarse estimates over large areas. This work proposes e ective ne-grained tra c volume estimation using invehicle dashboard mounted cameras. Existing work on tra c estimation relies on static tra c cameras that are usually deployed at crowded intersections and at some tra c lights. For streets with no tra c cam...