An Eflective Heuristic Algorithm for the Traveling. THE SYMMETRIC traveling-salesman problem is: Given an n by n symmetric matrix of.symmetric traveling salesman problem. However, the design and implementation of an algorithm based on this heuristic is not trivial. There are many.This article is about the heuristic for the travelling salesman problem. An Effective Heuristic Algorithm for the Tr...

We study a sigmoidal version of the FitzHugh-Nagumo reaction-diffusion system based on an analytic description using piecewise linear approximations of the reaction kinetics. We completely describe the dynamics of wave fronts and discuss the properties of the speed equation. The speed diagrams show front bifurcations between branches with one, three, or five fronts that differ significantly fro...

Mathematical models have been widely used to describe the collective movement of bacteria by chemotaxis. In particular, bacterial concentration waves traveling in a narrow channel have been experimentally observed and can be precisely described thanks to a mathematical model at the macroscopic scale. Such model was derived in [1] using a kinetic model based on an accurate description of the mes...

High-speed transit (1300 km=hr) using pods traveling in evacuated tubes has been proposed. This Short Note addresses how earthquake ground shaking is changed when it is experienced by a high-speed pod that is confined to a track. In particular, earthquake motions can cause lateral deformations of the tube that cause centripetal forces in the pod. I discuss the nature of these forces for the cas...

Intracellular signaling induced by peptide growth factors can stimulate secretion of these molecules into the extracellular medium. In autocrine and paracrine networks, this can establish a positive feedback loop between ligand binding and ligand release. When coupled to intercellular communication by autocrine ligands, this positive feedback can generate constant-speed traveling waves. To demo...

In this paper the zero reaction limit of the hyperbolic conservation law with stiff source term of monostable type ∂tu+ ∂xf(u) = 1 u(1− u) is studied. Solutions of Cauchy problems of the above equation with initial value 0 ≤ u0(x) ≤ 1 are proved to converge, as → 0, to piecewise constant functions. The constants are separated by either shocks determined by the Rankine-Hugoniot jump condition, o...

Reaction-diffusion processes in two-dimensional percolating structures are investigated. Two different problems are addressed: reaction spreading on a percolating cluster and front propagation through a percolating channel. For reaction spreading, numerical data and analytical estimates show a power-law behavior of the reaction product as M(t)~t(d(l)), where d(l) is the connectivity dimension. ...

We explore a reaction-dispersal mechanism for the generation of wave fronts which consists of a set of particles traveling with random velocities (chosen from arbitrary distributions) which experience an autocatalytic reaction. The differences found between this mechanism and approaches based on the continuous-time random walks, where the particles are assumed to perform discrete jumps from one...

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 the modeling of Traveling-wave Amplification Photodetectors (TAP detectors). These novel monolithic devices combine optical gain and absorption in a distributed fashion along a traveling-wave structure, providing high...

This paper is chiefly concerned with qualitative properties of some reaction-diffusion fronts. The recently defined notions of transition fronts generalize the standard notions of traveling fronts. In this paper, we show the existence and the uniqueness of the global mean speed of bistable transition fronts in RN . This speed is proved to be independent of the shape of the level sets of the fro...