Studies on Spatial and Temporal solitons with varying dispersion,diffraction and nonlinearity

Department of Physics, Cochin University of Science and Technology

Diagnostic tools in beta regression with varying dispersion

We consider the issue of performing residual and local influence analyses in beta regression models with varying dispersion, which are useful for modelling random variables that assume values in the standard unit interval. In such models, both the mean and the dispersion depend upon independent variables. We derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes. An application using real data is presented and discussed.

Stable two-dimensional dispersion-managed soliton

The existence of a dispersion-managed soliton in two-dimensional nonlinear Schrodinger equation with periodically varying dispersion has been explored. The averaged equations for the soliton width and chirp are obtained which successfully describe the long time evolution of the soliton. The slow dynamics of the soliton around the fixed points for the width and chirp are investigated and the corresponding frequencies are calculated. Analytical predictions are confirmed by direct partial differential equation (PDE) and ordinary differential equation (ODE) simulations. Application to a Bose-Einstein condensate in optical lattice is discussed. The existence of a dispersion-managed matter-wave soliton in such system is shown.

Skovgaard`s adjustment to likelihood ratio tests in exponential family nonlinear models

Likelihood ratio tests can be substantially size distorted in small- and moderate-sized samples. In this paper, we apply Skovgaard`s [Skovgaard, I.M., 2001. Likelihood asymptotics. Scandinavian journal of Statistics 28, 3-321] adjusted likelihood ratio statistic to exponential family nonlinear models. We show that the adjustment term has a simple compact form that can be easily implemented from standard statistical software. The adjusted statistic is approximately distributed as X(2) with high degree of accuracy. It is applicable in wide generality since it allows both the parameter of interest and the nuisance parameter to be vector-valued. Unlike the modified profile likelihood ratio statistic obtained from Cox and Reid [Cox, D.R., Reid, N., 1987. Parameter orthogonality and approximate conditional inference. journal of the Royal Statistical Society B49, 1-39], the adjusted statistic proposed here does not require an orthogonal parameterization. Numerical comparison of likelihood-based tests of varying dispersion favors the test we propose and a Bartlett-corrected version of the modified profile likelihood ratio test recently obtained by Cysneiros and Ferrari [Cysneiros, A.H.M.A., Ferrari, S.L.P., 2006. An improved likelihood ratio test for varying dispersion in exponential family nonlinear models. Statistics and Probability Letters 76 (3), 255-265]. (C) 2008 Elsevier B.V. All rights reserved.

Mixing-cell boundary conditions and apparent mass balance errors for advective-dispersive solute transport

In many field or laboratory situations, well-mixed reservoirs like, for instance, injection or detection wells and gas distribution or sampling chambers define boundaries of transport domains. Exchange of solutes or gases across such boundaries can occur through advective or diffusive processes. First we analyzed situations, where the inlet region consists of a well-mixed reservoir, in a systematic way by interpreting them in terms of injection type. Second, we discussed the mass balance errors that seem to appear in case of resident injections. Mixing cells (MC) can be coupled mathematically in different ways to a domain where advective-dispersive transport occurs: by assuming a continuous solute flux at the interface (flux injection, MC-FI), or by assuming a continuous resident concentration (resident injection). In the latter case, the flux leaving the mixing cell can be defined in two ways: either as the value when the interface is approached from the mixing-cell side (MC-RT -), or as the value when it is approached from the column side (MC-RT +). Solutions of these injection types with constant or-in one case-distance-dependent transport parameters were compared to each other as well as to a solution of a two-layer system, where the first layer was characterized by a large dispersion coefficient. These solutions differ mainly at small Peclet numbers. For most real situations, the model for resident injection MC-RI + is considered to be relevant. This type of injection was modeled with a constant or with an exponentially varying dispersion coefficient within the porous medium. A constant dispersion coefficient will be appropriate for gases because of the Eulerian nature of the usually dominating gaseous diffusion coefficient, whereas the asymptotically growing dispersion coefficient will be more appropriate for solutes due to the Lagrangian nature of mechanical dispersion, which evolves only with the fluid flow. Assuming a continuous resident concentration at the interface between a mixing cell and a column, as in case of the MC-RI + model, entails a flux discontinuity. This flux discontinuity arises inherently from the definition of a mixing cell: the mixing process is included in the balance equation, but does not appear in the description of the flux through the mixing cell. There, only convection appears because of the homogeneous concentration within the mixing cell. Thus, the solute flux through a mixing cell in close contact with a transport domain is generally underestimated. This leads to (apparent) mass balance errors, which are often reported for similar situations and erroneously used to judge the validity of such models. Finally, the mixing cell model MC-RI + defines a universal basis regarding the type of solute injection at a boundary. Depending on the mixing cell parameters, it represents, in its limits, flux as well as resident injections. (C) 1998 Elsevier Science B.V. All rights reserved.

Dispersion properties of surface waves in a two-layer plasma structure bounded by a metal

The effect of the nonuniformity of the electron density on the dispersion properties of surface waves propagating in a direction transverse to an external magnetic field is studied for the model of a two-layer plasma structure bounded by a metal. It is shown that the spectra of the waves can be effectively controlled by varying the degree of nonuniformity of the density and the dimensions of the layers.

A note on the analysis of the dispersion equation for surface magnetoplasmons in the Faraday configuration

The analysis of the dispersion equation for surface magnetoplasmons in the Faraday configuration for the degenerate case of decaying constants being equal is given from the point of view of understanding the non-existence of the “degenerate modes”. This analysis also shows that there exist well defined “degenerate points” on the dispersion curve with electromagnetic fields varying linearly over small distances taken away from the interface.

Damage-tolerant design optimization of laminated composite structures using dispersion of ply angles by genetic algorithm

This article aims to obtain damage-tolerant designs with minimum weight for a laminated composite structure using genetic algorithm. Damage tolerance due to impacts in a laminated composite structure is enhanced by dispersing the plies such that too many adjacent plies do not have the same angle. Weight of the structure is minimized and the Tsai-Wu failure criterion is considered for the safe design. Design variables considered are the number of plies and ply orientation. The influence of dispersed ply angles on the weight of the structure for a given loading conditions is studied by varying the angles in the range of 0 degrees-45 degrees, 0 degrees-60 degrees and 0 degrees-90 degrees at intervals of 5 degrees and by using specific ply angles tailored to loading conditions. A comparison study is carried out between the conventional stacking sequence and the stacking sequence with dispersed ply angles for damage-tolerant weight minimization and some useful designs are obtained. Unconventional stacking sequence is more damage tolerant than the conventional stacking sequence is demonstrated by performing a finite element analysis under both tensile as well as compressive loading conditions. Moreover, a new mathematical function called the dispersion function is proposed to measure the dispersion of ply angles in a laminate. The approach for dispersing ply angles to achieve damage tolerance is especially suited for composite material design space which has multiple local minima.

Dispersion copolymerization of acrylamide with quaternary ammonium cationic monomer in aqueous salts solution

Dispersion copolymerization of acrylamide (AM) with 2-methylacryloylxyethyl trimethyl ammonium chloride (DMC) has been carried out in aqueous salts solution containing ammonium sulfate and sodium chloride with poly(acryloylxyethyl trimethyl ammonium chloride) (PDAC) as the stabilizer and 2,2'-azobis[2-(2-inidazolin-2-yl)propane]-dihydro chloride (VA-044) as the initiator. A new particle formation mechanism of the dispersion polymerization for the present system has been proposed. The effects of inorganic salts and stabilizer concentration on dispersion polymerization have been investigated. The results show that varying the salt concentration could affect the morphology and molecular weight of the resultant copolymer particles significantly. With increasing the stabilizer concentration, the particle size decreased at first and then increased, meanwhile the effect on the copolymer molecular weight was the contrary. These results had been rationalized based on the proposed mechanism.

Dispersion copolymerization of acrylamide with acrylic acid in an aqueous solution of ammonium sulfate: Synthesis and characterization

Dispersion copolymerization of acrylamide with acrylic acid in an aqueous solution of ammonium sulfate using poly(2-acrylamido-2-methylpropanesulfonic acid sodium) as the stabilizer and ammonium persulfate (APS) as the initiator was investigated. The influence of initiator concentration, stabilizer concentration, ammonium sulfate concentration, chain-transfer agent concentration, and polymerization temperature on the copolymerization was discussed. The results showed that varying the ammonium sulfate concentration could affect the particle size and the intrinsic viscosity of the copolymer significantly. With increasing the stabilizer concentration, the particle size of the copolymer decreased first, and then increased, meanwhile the intrinsic viscosity of the copolymer decreased. The increase of initiator concentration, chain-transfer agent concentration, and polymerization temperature resulted in the increase in the particle size. Polydisperse spherical particles were formed in the system, and the kinetics for the dispersion copolymerization were discussed.

Iterative Multiuser Detection and Decoding for DS-CDMA System With Space-Time Linear Dispersion

This paper considers a Q-ary orthogonal direct-sequence code-division multiple-access (DS-CDMA) system with high-rate space-time linear dispersion codes (LDCs) in time-varying Rayleigh fading multiple-input-multiple-output (MIMO) channels. We propose a joint multiuser detection, LDC decoding, Q-ary demodulation, and channel-decoding algorithm and apply the turbo processing principle to improve system performance in an iterative fashion. The proposed iterative scheme demonstrates faster convergence and superior performance compared with the V-BLAST-based DS-CDMA system and is shown to approach the single-user performance bound. We also show that the CDMA system is able to exploit the time diversity offered by the LDCS in rapid-fading channels.

Electronically controlled surface plasmon dispersion and optical transmission through metallic hole arrays using liquid crystal.

The enhanced optical properties of metal films periodically perforated with an array of sub-wavelength size holes have recently been widely studied in the field of surface plasmon optics. The ability to design the optical transmission of such nanostructures, which act as plasmonic crystals, by varying their geometrical parameters gives them great flexibility for numerous applications in photonics, opto-electronics, and sensing. Transforming these passive optical elements into devices that may be actively controlled has presented a new challenge. Here, we report on the realization of an electrically controlled nanostructured optical system based on the unique properties of surface plasmon polaritonic crystals in contact with a liquid crystal (LC) layer. We discuss the effect of LC layer modulation on the surface plasmon dispersion, the related optical transmission and the underlying mechanism. The reported effect may be used to achieve active spectral tuneability and switching in a wide range of applications.

Enhancing the Efficiency of Slit-Coupling to Surface-Plasmon Polariton via Dispersion Engineering

We describe a simple method for enhancing the efficiency of coupling from a free-space transverse-magnetic (TM) plane-wave mode into a surface-plasmon-polariton (SPP) mode. The coupling structure consists a metal film with a dielectric-filled slit and a planar, dielectric layer on the slit-exit side of the metal film. By varying the dielectric layer thickness, the wavevector of the SPP mode on the metal surface can be tuned to match the wavevector magnitude of the modes emanating from the slit exit, enabling high-efficiency radiation coupling into the SPP mode at the slit exit. An optimal dielectric layer thickness of approximately 100 nm yields a visible-frequency SPP coupling efficiency approximately 4 times greater than the SPP coupling efficiency without the dielectric layer. Commensurate coupling enhancement is observed spanning the free-space wavelength range 400 nm < or = lambda(0) < or = 700 nm. We map the dependence of the SPP coupling efficiency on the slit width, the dielectric-layer thickness, and the incident wavelength to fully characterize this SPP coupling methodology

Time-Varying Liquidity and Momentum Profits

A basic intuition is that arbitrage is easier when markets are most liquid. Surprisingly, we find that momentum profits are markedly larger in liquid market states. This finding is not explained by variation in liquidity risk, time-varying exposure to risk factors, or changes in macroeconomic condition, cross-sectional return dispersion, and investor sentiment. The predictive performance of aggregate market illiquidity for momentum profits uniformly exceed that of market return and market volatility states. While momentum strategies are unconditionally unprofitable in US, Japan, and Eurozone countries in the last decade, they are substantial following liquid market states.

Evaluation of the reconstruction limits of a frequency-independent crosshole georadar waveform inversion scheme in the presence of dispersion

Waveform tomographic imaging of crosshole georadar data is a powerful method to investigate the shallow subsurface because of its ability to provide images of pertinent petrophysical parameters with extremely high spatial resolution. All current crosshole georadar waveform inversion strategies are based on the assumption of frequency-independent electromagnetic constitutive parameters. However, in reality, these parameters are known to be frequency-dependent and complex and thus recorded georadar data may show significant dispersive behavior. In this paper, we evaluate synthetically the reconstruction limits of a recently published crosshole georadar waveform inversion scheme in the presence of varying degrees of dielectric dispersion. Our results indicate that, when combined with a source wavelet estimation procedure that provides a means of partially accounting for the frequency-dependent effects through an "effective" wavelet, the inversion algorithm performs remarkably well in weakly to moderately dispersive environments and has the ability to provide adequate tomographic reconstructions.