Impulse Spatial-Temporal Domains in Semiconductor Laser with Feedback

An initial value boundary problem for system of diffusion equations with delay arguments and dynamic nonlinear boundary conditions is considered. The problem describes evolution of the carrier density and the radiation density in the semiconductor laser or laser diodes with “memory” and with feedback. It is shown that the boundary problem can be reduced to a system of difference equations with continuous time. For large times, solutions of these equations tend to piecewise constant asymptotic periodic wave functions which represent chain of shock waves with finite or infinite points of discontinuities on a period. Applications to the optical systems with linear media and nonlinear surface optical properties with feedback have been done. The results are compared with the experiment.

Structure and Dynamics of Confined Polymer Melts from Attractive Interaction to Repulsive Interaction Between Polymer and Smooth Wall

We studied the static and dynamic properties of unentangled polymer chains which have a variable strength of interaction with the confining smooth walls by means of the lattice Monte Carlo simulation based on the bond-fluctuation model, that is, investigated the wall-polymer interactions which systematically vary from attraction to repulsion. A critical value of attractive potential（ewe） is found to be -0.6kilT, and only below it can the adsorption layer of monomers be formed near the wall. At the critical point of attraction ewe, attractive interaction counterba- lances the wall-polymer excluded volume effect, which minimizes the confinement effects on both chain dimension and mobility. Influences on both chain dimension and mobility increase with the increasing of either attraction or repulsion imposed by the walls. Despite of the nature and strength of the wall-polymer interaction, with the decrease of film thickness, configurations more parallelly aligned and flattened are adopted by confined chains, and a systematic trend of deceleration is found. Variations of chain dynamics with both film thickness and wall-polymer interaction can be well explained by the corresponding changes in the confinement of the nearest-neighboring particles that surround the chains. Besides, the thickness of the interfacial layer inside polymer films, where chains adopt a flattened ＂pancake＂ shape, is about two times the bulk radius of gyratioia and independent of the wall-polymer interaction.

THE STABILITY OF SCALAR AUTONOMOUS DIFFERENCE EQUATIONS

The general criteria of stability for equihbrium points of scalar autonomous difference equations are given, wich cover all the cases as long as the right-hand function has continuous derivatives up to the desired order. Thus, the stability problems of scalar autonomous difference equations are thoroughly solved. The proofs of the obtained criteria are mathematically rigorous and complete. Also, several exam pies are given to illustrate the obtained results.

Dynamic model of multi-agent social evolutionary algorithm and its convergence

With a typical and simple 2-bit problem, a dynamic model of multi-agent social evolutionary algorithm （MASEA） is constructed by dynamic method. Then, the global dynamic shape of MASEA is comprehensively analyzed and the common evolution operators are also formally described. Furthermore, the effect that every evolutionary operator has on the dynamic shape is discovered by attraction analysis of the fixed points in the models. The global convergence of MASEA is also proved.