In this paper we study for small positive the slow motion of the solution for evolution equations of Burgers’ type with small diffusion, ut = uxx + f(u)ux , u(x, 0) = u0(x), u(±1, t) = ±1, (?) on the bounded spatial domain [−1, 1]; f is a smooth function satisfying f(1) > 0, f(−1) < 0 and ∫ 1 −1 f(t)dt = 0. The initial and boundary value problem (?) has a unique asymptotically stable equilibriu...

In the present work, we complement our earlier study on the subject of granular crystals in the purely nonlinear limit (no precompression) by considering the case where an underlying linear limit exists (finite precompression). In the latter context, we explicitly prove the existence of supersonic traveling waves, which are smooth, positive and exponentially localized. While numerical computati...

We consider a branching-selection system in R with N particles which give birth independently at rate 1 and where after each birth the leftmost particle is erased, keeping the number of particles constant. We show that, as N → ∞, the empirical measure process associated to the system converges in distribution to a deterministic measure-valued process whose densities solve a free boundary integr...

We examine numerically the transport of an assembly of active run-and-tumble disks interacting with a traveling-wave substrate. We show that as a function of substrate strength, wave speed, disk activity, and disk density, a variety of dynamical phases arise that are correlated with the structure and net flux of disks. We find that there is a sharp transition into a state in which the disks are...

The existence of traveling wave front solutions with a minimum speed selected for reaction-dispersal processes is studied. We obtain a general existence condition in terms of the waiting time and dispersal distance probability distribution functions and we detail this result for situations of ecological interest. In particular, when particles disperse according to jumps of short length and any ...

We propose a phase field model that approximates its limiting sharp interface model (free boundary problem) up to second order in interface thickness. A broad range of double-well potentials can be utilized so long as the dynamical coefficient in the phase equation is adjusted appropriately. This model thereby assures that computation with particular value of interface thickness ε, will differ ...

We introduce distributed axonal transmission speeds and a long-range constant feedback loop into the standard neural field model. We analyze the stability of spatially homogeneous equilibrium solutions for general connectivity kernels. By studying reduced models based on the assumption of small delays, we determine the effects of the delays on the stability and bifurcations. We show in a reduce...

A novel particle swarm optimization (PSO)-based algorithm for the traveling salesman problem (TSP) is presented. An uncertain searching strategy and a crossover eliminated technique are used to accelerate the convergence speed. Compared with the existing algorithms for solving TSP using swarm intelligence, it has been shown that the size of the solved problems could be increased by using the pr...

Abstract This paper presents wavelet based analysis for transmission line fault location. Faults in power transmission lines cause transients that travel at a speed close to the speed of light and propagate along the line as traveling waves (TWs). Traveling wave theory is utilized in capturing the travel time of the transients along the monitored lines between the fault point and the protective...

High speed, high efficiency, low noise and high saturation power are the characteristics desired for detectors in high bit-rate long-haul optical communication systems. We present modeling and initial experimental results on Traveling-wave Amplification Photodetectors (TAP detectors). These novel monolithic devices combine optical gain and absorption in a traveling-wave structure, providing hig...