Asymptotic soliton train solutions of the defocusing nonlinear Schrodinger equation

Asymptotic behavior of initially large and smooth pulses is investigated at two typical stages of their evolution governed by the defocusing nonlinear Schrodinger equation. At first, wave breaking phenomenon is studied in the limit of small dispersion. A solution of the Whitham modulational equations is found for the case of dissipationless shock wave arising after the wave breaking point. Then, asymptotic soliton trains arising eventually from a large and smooth initial pulse are studied by means of a semiclassical method. The parameter varying along the soliton train is calculated from the generalized Bohr-Sommerfeld quantization rule, so that the distribution of eigenvalues depends on two functions-intensity rho(0)(x) of the initial pulse and its initial chirp v(0)(x). The influence of the initial chirp on the asymptotic state is investigated. Excellent agreement of the numerical solution of the defocusing NLS equation with predictions of the asymptotic theory is found.

Fortran programs for the time-dependent Gross-Pitaevskii equation in a fully anisotropic trap

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Notes on the two-brane model with variable tension

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Short Comments on an Energy Pumping Levels in a MEMS Gyroscope Vibrating Problem, by Using of an Global and Local Optimal Linear Control Design

This paper deals with an energy pumping that occurs in a (MEMS) Gyroscope nonlinear dynamical system, modeled with a proof mass constrained to move in a plane with two resonant modes, which are nominally orthogonal. The two modes are ideally coupled only by the rotation of the gyro about the plane's normal vector. We also developed a linear optimal control design for reducing the oscillatory movement of the nonlinear systems to a stable point.

Stability of differential equations with piecewise constant argument via discrete equations

Lyapunov stability for a class of differential equation with piecewise constant argument (EPCA) is considered by means of the stability of a discrete equation. Applications to some nonlinear autonomous equations are given improving some linear known cases.

Relações lineares múltiplas entre deslocamentos químicos em RMN 13C de haletos alifáticos

Os deslocamentos químicos de RMN 13C de carbonos a , b , g e d de 17 conjuntos de haletos (F, Cl Br e I) alifáticos, inclusive compostos mono, bi e tricíclicos, podem ser reproduzidos por uma equação linear de duas constantes e duas variáveis do tipo : d R-X = A*d R-X1 + B*d R-X2 onde A e B são constantes obtidas por regressão multilinear a partir de deslocamentos químicos de 13C; d R-X, o deslocamento químico de 13C do composto com halogênio (R-X); d R-X1 e d R-X2 deslocamentos químicos de outros haletos. Para brometos (R-X) alifáticos a melhor correlação foi obtida com os dados de fluoretos (R-X1) e iodetos (R-X2) com R2 de 0,9989 e desvio médio absoluto (DM) de 0,39ppm. Para cloretos (R-X) a melhor correlação foi com dados de brometos (R-X1) e iodetos (R-X2) com R2 de 0,9960 e DM de 0,76ppm. Para fluoretos (R-X) a melhor correlação foi com brometos (R-X1) e iodetos (R-X2) com R2 de 0,9977 e DM de 1,10ppm e para iodetos (R-X) foi com fluoretos (R-X1) e brometos (R-X2) com R2 de 0,9972 e desvio médio absoluto de 0,60 ppm.

A MODEL OF THE DEUTERON BASED ON A BREIT TYPE EQUATION

A relativistic treatment of the deuteron and its observables based on a two-body Dirac (Breit) equation, with phenomenological interactions, associated to one-boson exchanges with cutoff masses, is presented. The 16-component wave function for the deuteron (J(pi) = 1+) solution contains four independent radial functions which obey a system of four coupled differential equations of first order. This radial system is numerically integrated, from infinity to the origin, by fixing the value of the deuteron binding energy and using appropriate boundary conditions at infinity. Specific examples of mixtures containing scalar, pseudoscalar and vector like terms are discussed in some detail and several observables of the deuteron are calculated. Our treatment differs from more conventional ones in that nonrelativistic reductions of the order c-2 are not used.

Generalised single-equation load flow method for unbalanced distribution systems

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Frequency upconversion in rare-earth doped fluoroindate glasses

We present recent results on frequency upconversion (UPC) obtained in fluoroindate glasses (FIG) doped with Ho3+, Tm3+ and Nd3+ ions and codoped with Pr3+/Nd3+ and Yb3+/Tb3+ ions. The results for the Ho3+-doped samples show strong evidence of energy transfer (ET) between Ho3+ ions resonantly excited at 640 nm. The origin of the blue-green upconverted fluorescence observed was identified and the dynamics of the signals revealed the pathways involved in the UPC process. In the case of Tm3+-doped FIG, the samples were resonantly excited at 650 nm and the main mechanism that contributes for the red-to-blue upconversion is excited-state absorption (ESA). The FIG samples codoped with Pr3+/Nd3+ were excited at 588 nm in resonance with transitions starting from the ground state of the Nd 3+ and the Pr3+ ions. It was observed that the presence of Nd3+ ions enhanced the Pr3+ emission at 480 nm by two orders of magnitude. Multiphonon (MP)-assisted upconversion is also discussed for Nd3+-doped FIG pumped at 866 nm. Emission at 750 nm with a peculiar linear dependence with the laser intensity was observed and explained. A rate-equation model that includes MP absorption via thermally coupled electronic excited states of Nd3+ was developed and describes well the experimental results. The role played by effective phonon modes is clearly demonstrated. MP-assisted UPC process was also studied in Yb3+/ Tb3+-codoped FIG samples excited at 1064 nm, which is off-resonance with electronic transitions starting from the ground state. It was determined that the mechanism leading to Tb3+ emission in the blue is due to ET from a pair of excited Yb3+ ions followed by ESA in the Tb 3+ ions. © 2002 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS.

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.

Eigenvalue analyses of two parallel lines using a single real transformation matrix

For a typical non-symmetrical system with two parallel three phase transmission lines, modal transformation is applied using some examples of single real transformation matrices. These examples are applied searching an adequate single real transformation matrix to two parallel three phase transmission line systems. The analyses are started with the eigenvector and eigenvalue studies, using Clarke's transformation or linear combinations of Clarke's elements. The Z C and parameters are analyzed for the case that presents the smallest errors between the exact eigenvalues and the single real transformation matrix application results. The single real transformation determined for this case is based on Clarke's matrix and its main characteristic is the use of a unique homopolar reference. So, the homopolar mode becomes a connector mode between the two three-phase circuits of the analyzed system. ©2005 IEEE.

Critical currents and melting temperature of a two-dimensional vortex lattice with periodic pinning

The critical current and melting temperature of a vortex system are analyzed. Calculations are made for a two-dimensional film at finite temperature with two kinds of periodic pinning: hexagonal and Kagomé. A transport current parallel and perpendicular to the main axis of the pinning arrays is applied and molecular dynamics simulations are used to calculate the vortex velocities to obtain the critical currents. The structure factor and displacements of vortices at zero transport current are used to obtain the melting temperature for both pinning arrays. The critical currents are higher for the hexagonal pinning lattice and anisotropic for both pinning arrays. This anisotropy is stronger with temperature for the hexagonal array. For the Kagomé pinning lattice, our analysis shows a multi stage phase melting; that is, as we increase the temperature, each different dynamic phase melts before reaching the melting temperature. Both the melting temperature and critical currents are larger for the hexagonal lattice, indicating the role for the interstitial vortices in decreasing the pinning strength. © 2012 Springer Science+Business Media New York.

Degree of conversion and hardness of two different systems of the vitrebond™ glass ionomer cement light cured with blue LED

This study investigated the physicochemical properties of the new formulation of the glass ionomer cements through hardness test and degree of conversion by infrared spectroscopy (FTIR). Forty specimens (n = 40) were made in a metallic mold (4 mm diameter × 2 mm thickness) with two resin-modified glass ionomer cements, Vitrebond™ and Vitrebond™ Plus (3M/ ESPE). Each specimen was light cured with blue LED with power density of 500 mW/cm2during 30 s. Immediately after light curing, 24h, 48h and 7 days the hardness and degree of conversion was determined. The Vickers hardness was performed by the MMT-3 microhardness tester using load of 50 gm force for 30 seconds. For degree of conversion, the specimens were pulverized, pressed with KBr and analyzed with FT-IR (Nexus 470). The statistical analysis of the data by ANOVA showed that the Vitrebond™ and Vitrebond™ Plus were no difference significant between the same storage times (p > 0.05). For degree of conversion, the Vitrebond™ and Vitrebond™ Plus were statistically different in all storage times after light curing. The Vitrebond™ showed higher values than Vitrebond™ Plus (p < 0.05). The performance of Vitrebond™ had greater results for degree of conversion than Vitrebond™ Plus. The correlation between hardness and degree of conversion was no evidence in this study.

O efeito da duração de pausa no exercício intermitente: um estudo pelo modelo da potência crítica

Pós-graduação em Ciências da Motricidade - IBRC

Sobre a produção de significados para a noção de transformação linear em álgebra linear

Pós-graduação em Educação Matemática - IGCE