Traveling waves for a four-compartment lattice epidemic system with exposed class and standard incidence

This paper is considering the problem of traveling wave solutions (TWS) for a susceptible-exposed-infectious-recovered (SEIR) epidemic model with discrete diffusion. The threshold condition for the existence and nonexistence of TWS is obtained. More specifically, such kind of solutions are governed by the threshold number ?₀. We can find a critical wave speed c^? if ?₀ > 1, by employing the Schauder's fixed point theorem, limiting argument and two-sided Laplace transform, we confirm that there exists TWS for c > c^?, while there exists no TWS for c < c^?. We also obtain the nonexistence of TWS for ?₀ ≤ 1. At last, we give some biological explanations from the epidemiological perspective.     

A Note on the Indirect Controls for a Coupled System of Wave Equations

By a procedure of successive projections, the authors decompose a coupled system of wave equations into a sequence of sub-systems. Then, they can clarify the indirect controls and the total number of controls. Moreover, the authors give a uniqueness theorem of solution to the system of wave equations under Kalman’s rank condition.     

Decay rates of energy of the 1D damped original nonlinear wave equation

We consider the decay rate of energy of the 1D damped original nonlinear wave equation. We first construct a new energy function. Then, employing the perturbed energy method and the generalized Young’s inequality, we prove that, with a general growth assumption on the nonlinear damping force near the origin, the decay rate of energy is governed by a dissipative ordinary differential equation. This allows us to recover the classical exponential, polynomial, or logarithmic decay rate for the linear, polynomial or exponentially degenerating damping force near the origin, respectively. Unlike the linear wave equation, the exponential decay rate constant depends on the initial data, due to the nonlinearity.     

Special solutions for an equation arising in sand ripple dynamics

We study a nonlinear fourth order evolution equation arising in the context of sand ripple dynamics. We analyse the set of stationary solutions and travelling waves in order to recover the observed phenomenology such as different wavelengths ripples, travelling waves, coarsening and time scales. Moreover, we construct an approximate solution which describes the early stages of the dynamics and which suggests the existence of coarsening and of time scales with different dynamical behaviour.     

Explicit Traveling Wave Solutions and Their Dynamical Behaviors for the Coupled Higgs Field Equation

In this paper, we focus on the traveling wave solutions of the coupled Higgs field equation from the perspective of dynamical systems. Through the phase portraits, in addition to periodic wave solutions and solitary wave solutions, we also obtain explicit periodic singular wave solutions, singular wave solutions and kink wave solutions, which were not found in the previous works. The dynamical behavior of these solutions and their internal relations are revealed through asymptotic analysis. The results will help supplement the study of field equation.     

Ground-state energy of a quantum chain with competing interactions

We show rigorously that the ground state of a quantum chain with competing ferromagnetic nearest and antiferromagnetic next nearest interactions undergoes a transition from ferromagnetic to helical type, in the isotropic case, for a certain value of the relevant ratio of coupling constants. Boundaries of the phase diagram are also determined in the anisotropic case. The stability of a special quantum state (corresponding to a classical modulated phase of =/3) is analyzed by an extension of Holstein-Primakoff arguments, along a line of constant ratio of couplings, showing in particular a sequence of (instability) gaps. Finally, a natural adaptation of a variational wave function due to Huse and Elser is used to study several portions of the phase diagram, with very good agreement with previous theoretical results.     

Migration of seismic data

Prospecting for oil and gas resources poses the problem of determining the geological structure of the earth's crust from indirect measurements. Seismic migration is an acoustic image reconstruction technique based on the inversion of the scalar wave equation. Extensive computation is necessary before reliable information can be extracted from large sets of recorded data. In this paper a collection of industrial migration techniques, each giving rise to a data parallel algorithm, is outlined. Computer simulations on synthetic seismic data illustrate the problem and the approach.     

The studies of the effect of photostimulated changes in thin carbon films

Photostimulated changes in thin carbon films deposited onto fused silica substrates by reactive magnetron sputtering and irradiated by the light of the first (1060nm) and the second (530nm) harmonics of a QW-switched Nd³⁺ AVG laser were investigated. The changes are supposed to be connected with the reordering of chemical bounds.     

Metastable fluid flow described via a discrete-velocity coagulation-fragmentation model

A discrete-velocity Boltzmann model is introduced. It is based on two principles: (i) clusters of particles move in ³ with seven fixed momenta; (ii) clusters may gain or lose particles according to the rules of Becker-Döring cluster equations. The model provides a kinetic representation of evaporation and condensation. The model is used to obtain macroscopic fluid equations which are valid into the metastable fluid regime, , where is any positive number, is the inelastic Knudsen number, and _s is the saturation density.     

Exact solutions for Belousov-Zhabotinskii reaction-diffusion system

Abstract. We consider the following simplified model for the Belousou-Zhabotinskii(B-Z)reaction: