Nonlinear spectral-spatial control and localization of supercontinuum radiation

We present the first observation of spatiospectral control and localization of supercontinuum light through the nonlinear interaction of spectral components in extended periodic structures. We use an array of optical waveguides in a LiNbO3 crystal and employ the interplay between diffraction and nonlinearity to dynamically control the output spectrum of the supercontinuum radiation. This effect presents an efficient scheme for optically tunable spectral filtering of supercontinua.     

Model potentials in studies of atomic electron density distribution

In density functional theory (DFT ), a many-electron problem for the electron density in atoms may be reduced, according to the Kohn-Sham scheme, to a one-electron problem. In the present work, a variational model is proposed which leads, within some assumptions, to the set of equations describing the change of the electron density ρ and energy ϵ during the ionization process. It is shown that the one-electron density contributions are not necessarily spherically symmetric, but assume the symmetry which depends upon the symmetry of the positive field. A few nonspherically symmetric potentials are studied in the present article. The nonlinear differential equation for density r is formulated and solved for Coulombic, Fues-Kratzer, and Hartmann potentials. The solutions and some particular examples are presented. © 1996 John Wiley & Sons, Inc.     

Nonlocal elasticity in shape memory alloys modeled using peridynamics for solving dynamic problems

Nonlinear Dynamics - The work is primarily devoted to the peridynamic model elaborated for a solid body made of shape memory alloys (SMAs). The superelasticity effect is taken into consideration as...     

The third-order electric susceptibilities of NaCl and KCl monocrystals

The dispersion of the third-order electric susceptibilities(; , , –) and(; , 0, 0) of NaCl and KCl monocrystals has been calculated by means of experimental data on the electro-optic Kerr effect. The result has been obtained by using semi-classical models of anharmonic oscillators. An ionic contribution to the electro-optic coefficients has been presented. From the result obtained it follows that the third-order electric susceptibilities are of the order of 10^–22 m² V^–2.     

An efficient algorithm for a job shop problem

We study the problem of minimizing makespan in a two-machine job shop with unit processing time operations. An efficient algorithm with respect to a succinct encoding of the problem instances is proposed. The algorithm is an improvement of earlier algorithms proposed for the problem by Brucker [1,2], Hefetz and Adiri [7], and Timkovskiy [15]. The idea behind the algorithm has the potential of extension to job shops with parallel machines.This research is supported in part by NSERC Grants A4619, OGP0105675, OGP0104900, General Motors of Canada, and the Manufacturing Research Corporation of Ontario.     

Mixed symbolic–numerical computations with general DAEs II: An applications case study

A variety of theorems and properties of nonlinear DAEs were discussed in part I. This paper illustrates many of these ideas within the context of analyzing a specific nonlinear system that exhibits a variety of interesting features. This revised version was published online in June 2006 with corrections to the Cover Date.     

Two-dimensional state-space discrete models for hyperbolic partial differential equations

It is shown that the finite difference technique can be used to transform some important linear distributed processes described by partial differential equations into so-called Roesser discrete state-space models. Two illustrative examples of numerical solutions are given and compared with exact solutions.     

Nonlinear BLOCH-wave interaction and bragg scattering in optically induced lattices

We study, both theoretically and experimentally, the Bragg scattering of light in optically induced photonic lattices and reveal the key physical mechanisms which govern the nonlinear self-action of narrow beams under the combined effects of Bragg scattering and wave diffraction, allowing for selecting bands with different effective dispersion.