Stabilization of a (3+1)-dimensional soliton in a Kerr medium by a rapidly oscillating dispersion coefficient

Using the numerical solution of the nonlinear Schrodinger equation and a variational method it is shown that (3 + 1)-dimensional spatiotemporal optical solitons can be stabilized by a rapidly oscillating dispersion coefficient in a Kerr medium with cubic nonlinearity. This has immediate consequence in generating dispersion-managed robust optical soliton in communication as well as possible stabilized Bose-Einstein condensates in periodic optical-lattice potential via an effective-mass formulation. We also critically compare the present stabilization with that obtained by a rapid sinusoidal oscillation of the Kerr nonlinearity parameter.

Relic abundance of mass-varying cold dark matter particles

In models of coupled dark energy and dark matter the mass of the dark matter particle depends on the cosmological evolution of the dark energy field. In this Letter we exemplify in a simple model the effects of this mass variation on the relic abundance of cold dark matter. (c) 2005 Elsevier B.V. All rights reserved.

Cooper pair dispersion relation for weak to strong coupling

Cooper pairing in two dimensions is analyzed with a set of renormalized equations to determine its binding energy for any fermion number density and all coupling assuming a,generic pairwise residual interfermion interaction. Also considered are Cooper pairs (CP's) with nonzero center-of-mass momentum (CMM) and their binding energy is expanded analytically in powers of the CMM up to quadratic terms. A Fermi-sea-dependent linear term in the CMM dominates the pair excitation energy in weak coupling (also called the BCS regime) while the more familiar quadratic term prevails in strong coupling (the Bose regime). The crossover, though strictly unrelated to BCS theory per se, is studied numerically as it is expected to play a central role in a model of superconductivity as a Bose-Einstein condensation of CPs where the transition temperature vanishes for all dimensionality d less than or equal to 2 for quadratic dispersion, but is nonzero for all d greater than or equal to 1 for linear dispersion.

Resonances in a trapped 3D Bose-Einstein condensate under periodically varying atomic scattering length

Nonlinear oscillations of a 3D radial symmetric Bose-Einstein condensate under periodic variation in time of the atomic scattering length have been studied. The time-dependent variational approach is used for the analysis of the characteristics of nonlinear resonances in the oscillations of the condensate. The bistability in oscillations of the BEC width is investigated. The dependence of the BEC collapse threshold on the drive amplitude and parameters of the condensate and trap is found. Predictions of the theory are confirmed by numerical simulations of the full Gross-Pitaevskii equation.

Linear to quadratic crossover of Cooper-pair dispersion relation

Cooper pairing is studied in three dimensions to determine its binding energy for all coupling using a general separable interfermion interaction. Also considered are Cooper pairs (CPs) with nonzero center-of-mass momentum (CMM). A coupling-independent linear term in the CMM dominates the pair excitation energy in weak coupling and/or high fermion density, while the more familiar quadratic term prevails only in the extreme low-density (i.e., vacuum) limit for any nonzero coupling. The linear-to-quadratic crossover of the CP dispersion relation is analyzed numerically, and is expected to play a central role in a model of superconductivity (and superfluidity) simultaneously accommodating a Bardeen-Cooper-Schrieffer condensate as well as a Bose-Einstein condensate of CP bosons. (C) 2001 Elsevier B.V. B,V. All rights reserved.

Cooper pair dispersion relation in two dimensions

The Cooper pair binding energy vs. center-of-mass-momentum dispersion relation for Bose-Einstein condensation studies of superconductivity is found in two dimensions for a renormalized attractive delta interaction. It crosses over smoothly from a linear to a quadratic form as coupling varies from weak to strong.

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.

Mass varying neutrinos in supernovae

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

Recurrence of particles in static and time varying oval billiards

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Rapidly varying boundaries in equations with nonlinear boundary conditions. The case of a Lipschitz deformation

We analyze the behavior of solutions of nonlinear elliptic equations with nonlinear boundary conditions of type partial derivative u/partial derivative n + g( x, u) = 0 when the boundary of the domain varies very rapidly. We show that the limit boundary condition is given by partial derivative u/partial derivative n+gamma(x) g(x, u) = 0, where gamma(x) is a factor related to the oscillations of the boundary at point x. For the case where we have a Lipschitz deformation of the boundary,. is a bounded function and we show the convergence of the solutions in H-1 and C-alpha norms and the convergence of the eigenvalues and eigenfunctions of the linearization around the solutions. If, moreover, a solution of the limit problem is hyperbolic, then we show that the perturbed equation has one and only one solution nearby.

VERY RAPIDLY VARYING BOUNDARIES IN EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS. THE CASE of A NON UNIFORMLY LIPSCHITZ DEFORMATION

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

Coordination polymer adsorbent for matrix solid-phase dispersion extraction of pesticides during analysis of dehydrated Hyptis pectinata medicinal plant by GC/MS

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

High precision calculation of multipolar dynamic polarizabilities and two- and three-body dispersion coefficients of atomic hydrogen

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Behaviour of dispersion indices in pattern detection of a population of angico, Anadenanthera peregrina (Leguminosae)

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

Performance of a reciprocal shaker in mechanical dispersion of soil samples for particle-size analysis

A dispersão da amostra de solo é uma etapa fundamental da análise granulométrica, sendo realizada mediante o uso de dispersantes químicos e agitação mecânica. O objetivo deste trabalho foi avaliar a eficiência de mesa agitadora reciprocante de baixa rotação na dispersão mecânica de amostras de solos de diferentes classes texturais. Foram realizadas análises granulométricas em 61 amostras com quatro repetições, empregando o método da pipeta para determinação da fração argila e tamisagem para determinação das frações areia grossa, areia fina e areia total, sendo o silte determinado por diferença. Na avaliação de desempenho, os resultados obtidos com uso da mesa agitadora reciprocante (MAR) foram comparados com dados disponíveis para as mesmas amostras oriundos de relatórios do Ensaio de Proficiência IAC para Laboratórios de Análises de Solos - Prolab/IAC. Análises de acurácia foram realizadas com base nos valores dos intervalos de confiança definidos para cada fração granulométrica componente de cada amostra ensaiada. Indicadores gráficos também foram utilizados na comparação de dados, por meio de dispersão e ajuste linear. A estatística descritiva indicou preponderância de baixa variabilidade em mais de 90 % dos resultados obtidos para as amostras de texturas arenosa, média e argilosa e em 68 % dos obtidos para as amostras de textura muito argilosa, indicando boa repetibilidade dos resultados obtidos com a MAR. Média variabilidade foi mais frequentemente associada à fração silte, seguida da fração areia fina. Os resultados das análises de sensibilidade indicam acurácia de 100 % nas três frações granulométricas - areia total, silte e argila - para todas as amostras analisadas pertencentes às classes texturais muito argilosa, argilosa e média. Para as nove amostras de textura arenosa, a acurácia média foi de 85,2 %, e os maiores desvios ocorreram em relação à fração silte. Nas aproximações lineares, coeficientes de correlação igual (silte) ou superiores (areia total e argila) a 0,93, bem como diferenças menores do que 0,16 entre os coeficientes angulares das retas e o valor unitário, indicam alta correlação entre os resultados de referência (Prolab/IAC) e os obtidos nos ensaios com a MAR. Conclui-se pelo desempenho satisfatório da mesa agitadora reciprocante de baixa rotação para dispersão mecânica de amostras de solo de diferentes classes texturais para fins de análise granulométrica, permitindo recomendar o uso alternativo do equipamento quando se emprega agitação lenta. As vantagens do uso do equipamento nacional incluem o baixo custo, a possibilidade de análise simultânea de grande número de amostras e o uso de frascos comuns, de vidro ou de plástico, baratos e de fácil reposição.