Shape-changing Collisions of Coupled Bright Solitons in Birefringent Optical Fibers

Wecritically review the recent progress in understanding soliton propagation in birefringent optical fibers.By constructing the most general bright two-soliton solution of the integrable coupled nonlinear Schroedinger equation (Manakov model) we point out that solitons in birefringent fibers can in general change their shape after interaction due to a change in the intensity distribution among the modes even though the total energy is conserved. However, the standard shape-preserving collision (elastic collision) property of the (1+1)-dimensional solitons is recovered when restrictions are imposed on some of the soliton parameters. As a consequence the following further properties can be deduced using this shape-changing collision. (i) The exciting possibility of switching of solitons between orthogonally polarized modes of the birefringent fiber exists. (ii) When additional effects due to periodic rotation of birefringence axes are considered, the shape changing collision can be used as a switch to suppress or to enhance the periodic intensity exchange between the orthogonally polarized modes. (iii) For ultra short optical soliton pulse propagation in non-Kerr media, from the governing equation an integrable system of coupled nonlinear Schroedinger equation with cubic-quintic terms is identified. It admits a nonlocal Poisson bracket structure. (iv) If we take the higher-order terms in the coupled nonlinear Schroedinger equation into account then their effect on the shape-changing collision of solitons, during optical pulse propagation, can be studied by using a direct perturbational approach.Comment: 14 pages, ROMP31, 4 EPS figure

Physical and numerical sources of computational inefficiency in integration of chemical kinetic rate equations: Etiology, treatment and prognosis

The design of a very fast, automatic black-box code for homogeneous, gas-phase chemical kinetics problems requires an understanding of the physical and numerical sources of computational inefficiency. Some major sources reviewed in this report are stiffness of the governing ordinary differential equations (ODE's) and its detection, choice of appropriate method (i.e., integration algorithm plus step-size control strategy), nonphysical initial conditions, and too frequent evaluation of thermochemical and kinetic properties. Specific techniques are recommended (and some advised against) for improving or overcoming the identified problem areas. It is argued that, because reactive species increase exponentially with time during induction, and all species exhibit asymptotic, exponential decay with time during equilibration, exponential-fitted integration algorithms are inherently more accurate for kinetics modeling than classical, polynomial-interpolant methods for the same computational work. But current codes using the exponential-fitted method lack the sophisticated stepsize-control logic of existing black-box ODE solver codes, such as EPISODE and LSODE. The ultimate chemical kinetics code does not exist yet, but the general characteristics of such a code are becoming apparent

CREKID: A computer code for transient, gas-phase combustion of kinetics

A new algorithm was developed for fast, automatic integration of chemical kinetic rate equations describing homogeneous, gas-phase combustion at constant pressure. Particular attention is paid to the distinguishing physical and computational characteristics of the induction, heat-release and equilibration regimes. The two-part predictor-corrector algorithm, based on an exponentially-fitted trapezoidal rule, includes filtering of ill-posed initial conditions, automatic selection of Newton-Jacobi or Newton iteration for convergence to achieve maximum computational efficiency while observing a prescribed error tolerance. The new algorithm was found to compare favorably with LSODE on two representative test problems drawn from combustion kinetics

Molecules to materials. 1. An overview of functional molecular solids

With the advent of modern physics and chemistry, fundamentally new types of materials have been created in this century. Various types of forces operating in different classes of solids are exploited in the design of molecular materials. A variety of fabrication techniques have been developed to make materials with the desired properties. An overview of these aspects is provided in this article

Molecule matters. Carbon dioxide: molecular states and beyond

Carbon dioxide is a fascinating molecule; its gaseous, liquid, solid and even supercritical fluid states have unique properties and applications. The linear triatomic structure of carbon dioxide molecule with two carbon-oxygen double bonds is all too familiar. However a whole new world has been opened up by high pressure-high temperature experiments that effected the polymerization of this small molecule into a covalent network structure with carbon-oxygen single bonds. The crystalline and amorphous forms of carbonia are built up of linked tetrahedral CO4 units

Molecules to materials. 3. Molecular magnetic materials

Molecular materials represent an area of fruitful interaction between synthetic chemistry, solid state physics and materials science. This article discusses the development of magnetic materials based on metal complexes, organometallic compounds and organic radicals

Performance of a Farmer Interest Group in Tamil Nadu

The present study was undertaken with an objective to find out the performance of Old Ayakudi guava Farmers’ Interest Group (FIG), Dindigul district, Tamil Nadu. The overall performance of the FIG were analysed using six variables viz., mobilizing support, exploitation resistance, identifying market opportunities, business orientation, marketing network and responsibility sharing The study revealed that majority of the FIG members perceive the performance of FIG at moderate level performance followed by high and low level performance