Analysis of Nonlinear Optical Properties of Photonic Crystal Beam-splitters

The paper analyses electromagnetic wave propagation through nonlinear photonic crystal beam-splitters. Different lattice configurations of Y-junction beam-splitters are simulated and propagation properties are investigated with introducing nonlinearity with varying the rod size in crystal lattice. It is seen that nonlinear photonic crystal shows a considerable band-gap even at low refractive contrast. The division of power in both arms of beam-splitters can be controlled by varying the nonlinearity.

Formation and propagation of bands in jerky flow:a coupled lattice map description

There has been revival of interest in Jerky flow from the point of view of dynamical systems. The earliest attempt in this direction was from our group. One of the predictions of the theory is that Jerky flow could be chaotic. This has been recently verified by us. We have recently extended the earlier model to account for the spatial aspect as well. Both these models are in the form of coupled set of nonlinear differential equations and hence, they are complicated in their structure. For this reason we wish to devise a model based on the results of these two theories in the form of coupled lattice map for the description of the formation and propagation of dislocation bands. We report here one such model and its results.

Growth and characterization of single crystal cored fibers of organic nonlinear optical materials

The recent development of several organic materials with large nonlinear susceptibilities, high damage threshold and low melting points encouraged researchers to employ these materials in fiber form to efficiently couple diode laser pumps and obtain enhanced second harmonic generation (SHG). In this paper we report the growth of single crystal cored fibers of 4-nitro-4'-methylbenzylidene aniline, ethoxy methoxy chalcone and (-)2-((alpha) -methylbenzylamino)-5- nitropyridine by inverted Bridgman-Stockbarger technique. The fibers were grown in glass capillaries with varying internal diameters and lengths and were characterized using x-ray and polarizing microscope techniques. The propagation loss at 632.8 nm and 1300 nm were measured and SHG was studied using 1064 nm pump.

A Numerical Scheme for Three-Dimensional Front Propagation and Control of Jordan Mode

As an example of a front propagation, we study the propagation of a three-dimensional nonlinear wavefront into a polytropic gas in a uniform state and at rest. The successive positions and geometry of the wavefront are obtained by solving the conservation form of equations of a weakly nonlinear ray theory. The proposed set of equations forms a weakly hyperbolic system of seven conservation laws with an additional vector constraint, each of whose components is a divergence-free condition. This constraint is an involution for the system of conservation laws, and it is termed a geometric solenoidal constraint. The analysis of a Cauchy problem for the linearized system shows that when this constraint is satisfied initially, the solution does not exhibit any Jordan mode. For the numerical simulation of the conservation laws we employ a high resolution central scheme. The second order accuracy of the scheme is achieved by using MUSCL-type reconstructions and Runge-Kutta time discretizations. A constrained transport-type technique is used to enforce the geometric solenoidal constraint. The results of several numerical experiments are presented, which confirm the efficiency and robustness of the proposed numerical method and the control of the Jordan mode.

Wave propagation in a porous composite beam: Porosity determination, location and quantification

A wave-based method is developed to quantify the defect due to porosity and also to locate the porous regions, in a composite beam-type structure. Wave propagation problem for a porous laminated composite beam is modeled using spectral finite element method (SFEM), based on the modified rule of mixture approach, which is used to include the effect of porosity on the stiffness and density of the composite beam structure. The material properties are obtained from the modified rule of mixture model, which are used in a conventional SFEM to develop a new model for solving wave propagation problems in porous laminated composite beam. The influence of the porosity content on the group speed and also the effect of variation in theses parameters on the time responses are studied first, in the forward problem. The change in the time responses with the change in the porosity of the structure is used as a parameter to find the porosity content in a composite beam. The actual measured response from a structure and the numerically obtained time responses are used for the estimation of porosity, by solving a nonlinear optimization problem. The effect of the length of the porous region (in the propagation direction), on the time responses, is studied. The damage force indicator technique is used to locate the porous region in a beam and also to find its length, using the measured wave propagation responses. (C) 2012 Elsevier Ltd. All rights reserved.

Comparative study of different nonconserving time integrators for wave propagation in hyperelastic waveguides

This paper addresses the formulation and numerical efficiency of various numerical models of different nonconserving time integrators for studying wave propagation in nonlinear hyperelastic waveguides. The study includes different nonlinear finite element formulations based on standard Galerkin finite element model, time domain spectral finite element model, Taylor-Galerkin finite element model, generalized Galerkin finite element model and frequency domain spectral finite element model. A comparative study on the computational efficiency of these different models is made using a hyperelastic rod model, and the optimal computational scheme is identified. The identified scheme is then used to study the propagation of transverse and longitudinal waves in a Timoshenko beam with Murnaghan material nonlinearity.

Shock propagation in gas dynamics: explicit form of higher order compatibility conditions

With the use of tensor analysis and the method of singular surfaces, an infinite system of equations can be derived to study the propagation of curved shocks of arbitrary strength in gas dynamics. The first three of these have been explicitly given here. This system is further reduced to one involving scalars only. The choice of dependent variables in the infinite system is quite important, it leads to coefficients free from singularities for all values of the shock strength.

Nonlinear Enzyme Kinetics Can Lead to High Metabolic Flux Control Coefficients: Implications for the Evolution of Dominance

In a classic study, Kacser & Burns (1981, Genetics 97, 639-666) demonstrated that given certain plausible assumptions, the flux in a metabolic pathway was more or less indifferent to the activity of any of the enzymes in the pathway taken singly. It was inferred from this that the observed dominance of most wild-type alleles with respect to loss-of-function mutations did not require an adaptive, meaning selectionist, explanation. Cornish-Bowden (1987, J. theor. Biol. 125, 333-338) showed that the Kacser-Burns inference was not valid when substrate concentrations were large relative to the relevant Michaelis constants. We find that in a randomly constructed functional pathway, even when substrate levels are small, one can expect high values of control coefficients for metabolic flux in the presence of significant nonlinearities as exemplified by enzymes with Hill coefficients ranging from two to six, or by the existence of oscillatory loops. Under these conditions the flux can be quite sensitive to changes in enzyme activity as might be caused by inactivating one of the two alleles in a diploid. Therefore, the phenomenon of dominance cannot be a trivial ''default'' consequence of physiology but must be intimately linked to the manner in which metabolic networks have been moulded by natural selection.

Finite volume evolution Galerkin method for hyperbolic conservation laws with spatially varying flux functions

We present a generalization of the finite volume evolution Galerkin scheme [M. Lukacova-Medvid'ova,J. Saibertov'a, G. Warnecke, Finite volume evolution Galerkin methods for nonlinear hyperbolic systems, J. Comp. Phys. (2002) 183 533-562; M. Luacova-Medvid'ova, K.W. Morton, G. Warnecke, Finite volume evolution Galerkin (FVEG) methods for hyperbolic problems, SIAM J. Sci. Comput. (2004) 26 1-30] for hyperbolic systems with spatially varying flux functions. Our goal is to develop a genuinely multi-dimensional numerical scheme for wave propagation problems in a heterogeneous media. We illustrate our methodology for acoustic waves in a heterogeneous medium but the results can be generalized to more complex systems. The finite volume evolution Galerkin (FVEG) method is a predictor-corrector method combining the finite volume corrector step with the evolutionary predictor step. In order to evolve fluxes along the cell interfaces we use multi-dimensional approximate evolution operator. The latter is constructed using the theory of bicharacteristics under the assumption of spatially dependent wave speeds. To approximate heterogeneous medium a staggered grid approach is used. Several numerical experiments for wave propagation with continuous as well as discontinuous wave speeds confirm the robustness and reliability of the new FVEG scheme.

Wave propagation in elastic solids undergoing damage and growth process

Modeling and analysis of wave propagation in elastic solids undergoing damage and growth process are reported in this paper. Two types of diagnostic problems, (1) the propagation of waves in the presence of a slow growth process and (2) the propagation of waves in the presence of a fast growth process, are considered. The proposed model employs a slow and a fast time scale and a homogenization technique in the wavelength scale. A detailed analysis of wave dispersion is carried out. A spectral analysis reveals certain low-frequency bands, where the interaction between the wave and the growth process produces acoustic metamaterial-like behavior. Various practical issues in designing an efficient method of acousto-ultrasonic wave based diagnostics of the growth process are discussed. Diagnostics of isotropic damage in a ductile or quasi-brittle solid by using a micro-second pulsating signal is considered for computer simulations, which is to illustrate the practical application of the proposed modeling and analysis. The simulated results explain how an estimate of signal spreading can be effectively employed to detect the presence of a steady-state damage or the saturation of a process.

Einstein Relation in n-Channel Inversion Layers of Nonlinear Optical, Optoelectronic and Related Materials: Simplified Theory, Relative Comparison and Suggestion for an Experimental Determination

In this paper, we study the Einstein relation for the diffusivity to mobility ratio (DMR) in n-channel inversion layers of non-linear optical materials on the basis of a newly formulated electron dispersion relation by considering their special properties within the frame work of k.p formalism. The results for the n-channel inversion layers of III-V, ternary and quaternary materials form a special case of our generalized analysis. The DMR for n-channel inversion layers of II-VI, IV-VI and stressed materials has been investigated by formulating the respective 2D electron dispersion laws. It has been found, taking n-channel inversion layers of CdGeAs2, Cd(3)AS(2), InAs, InSb, Hg1-xCdxTe, In1-xGaxAsyP1-y lattice matched to InP, CdS, PbTe, PbSnTe, Pb1-xSnxSe and stressed InSb as examples, that the DMR increases with the increasing surface electric field with different numerical values and the nature of the variations are totally band structure dependent. The well-known expression of the DMR for wide gap materials has been obtained as a special case under certain limiting conditions and this compatibility is an indirect test for our generalized formalism. Besides, an experimental method of determining the 2D DMR for n-channel inversion layers having arbitrary dispersion laws has been suggested.

Field imperfection induced axial secular frequency shifts in nonlinear ion traps

This article develops a simple analytical expression that relates ion axial secular frequency to field aberration in ion trap mass spectrometers. Hexapole and octopole aberrations have been considered in the present computations. The equation of motion of the ions in a pseudopotential well with these superpositions has the form of a Duffing-like equation and a perturbation method has been used to obtain the expression for ion secular frequency as a function of field imperfections. The expression indicates that the frequency shift is sensitive to the sign of the octopole superposition and insensitive to the sign of the hexapole superposition. Further, for weak multipole superposition of the same magnitude, octopole superposition causes a larger frequency shift in comparison to hexapole superposition.

A probabilistic constrained nonlinear optimization framework to optimize RED parameters

The random early detection (RED) technique has seen a lot of research over the years. However, the functional relationship between RED performance and its parameters viz,, queue weight (omega(q)), marking probability (max(p)), minimum threshold (min(th)) and maximum threshold (max(th)) is not analytically availa ble. In this paper, we formulate a probabilistic constrained optimization problem by assuming a nonlinear relationship between the RED average queue length and its parameters. This problem involves all the RED parameters as the variables of the optimization problem. We use the barrier and the penalty function approaches for its Solution. However (as above), the exact functional relationship between the barrier and penalty objective functions and the optimization variable is not known, but noisy samples of these are available for different parameter values. Thus, for obtaining the gradient and Hessian of the objective, we use certain recently developed simultaneous perturbation stochastic approximation (SPSA) based estimates of these. We propose two four-timescale stochastic approximation algorithms based oil certain modified second-order SPSA updates for finding the optimum RED parameters. We present the results of detailed simulation experiments conducted over different network topologies and network/traffic conditions/settings, comparing the performance of Our algorithms with variants of RED and a few other well known adaptive queue management (AQM) techniques discussed in the literature.

The Parallel Complexity Of Propagation In Boolean Circuits

We consider the problem of deciding whether the output of a boolean circuit is determined by a partial assignment to its inputs. This problem is easily shown to be hard, i.e., co-Image Image -complete. However, many of the consequences of a partial input assignment may be determined in linear time, by iterating the following step: if we know the values of some inputs to a gate, we can deduce the values of some outputs of that gate. This process of iteratively deducing some of the consequences of a partial assignment is called propagation. This paper explores the parallel complexity of propagation, i.e., the complexity of determining whether the output of a given boolean circuit is determined by propagating a given partial input assignment. We give a complete classification of the problem into those cases that are Image -complete and those that are unlikely to be Image complete.

In search of inorganic nonlinear optical materials for second harmonic generation

In a search for inorganic oxide materials showing second-order nonlinear optical (NLO) susceptibility, we investigated several berates, silicates, and a phosphate containing trans-connected MO6, octahedral chains or MO5 square pyramids, where, M = d(0): Ti(IV), Nb(V), or Ta(V), Our investigations identified two new NLO structures: batisite, Na2Ba(TiO)(2)Si4O12, containing trans-connected TiO5 octahedral chains, and fresnoite, Ba2TiOSi2O7, containing square-pyramidal TiO5. Investigation of two other materials containing square-pyramidal TiO5 viz,, Cs2TiOP2O7 and Na4Ti2Si8O22. 4H(2)O, revealed that isolated TiO5, square pyramids alone do not cause a second harmonic generation (SHG) response; rather, the orientation of TiO5 units to produce -Ti-O-Ti-O- chains with alternating long and short Ti-O distances in the fresnoite structure is most likely the origin of a strong SHG response in fresnoite,