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

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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

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

Mean-field model for Josephson oscillation in a Bose-Einstein condensate on an one-dimensional optical trap

Using the axially-symmetric time-dependent Gross-Pitaevskii equation we study the phase coherence in a repulsive Bose-Einstein condensate (BEC) trapped by a harmonic and an one-dimensional optical lattice potential to describe the experiment by Cataliotti et al. on atomic Josephson oscillation [Science 293, 843 (2001)]. The phase coherence is maintained after the BEC is set into oscillation by a small displacement of the magnetic trap along the optical lattice. The phase coherence in the presence of oscillating neutral current across an array of Josephson junctions manifests in an interference pattern formed upon free expansion of the BEC. The numerical response of the system to a large displacement of the magnetic trap is a classical transition from a coherent superfluid to an insulator regime and a subsequent destruction of the interference pattern in agreement With the more recent experiment by Cataliotti et al. [New J. Phys. 5, 71 (2003)].

Relaxation algorithm to hyperbolic states in Gross-Pitaevskii equation

A new version of the relaxation algorithm is proposed in order to obtain the stationary ground-state solutions of nonlinear Schrodinger-type equations, including the hyperbolic solutions. In a first example, the method is applied to the three-dimensional Gross-Pitaevskii equation, describing a condensed atomic system with attractive two-body interaction in a non-symmetrical trap, to obtain results for the unstable branch. Next, the approach is also shown to be very reliable and easy to be implemented in a non-symmetrical case that we have bifurcation, with nonlinear cubic and quintic terms. (c) 2006 Elsevier B.V. All rights reserved.

Evolution of a collapsing and exploding Bose-Einstein condensate in different trap symmetries

Based on the time-dependent Gross-Pitaevskii equation we study the evolution of a collapsing and exploding Bose-Einstein condensate in different trap symmetries to see the effect of confinement on collapse and subsequent explosion, which can be verified in future experiments. We make a prediction for the evolution of the shape of the condensate and the number of atoms in it for different trap symmetries (cigar to pancake) as well as in the presence of an optical lattice potential. We also make a prediction for the jet formation in different cases when the collapse is suddenly terminated by changing the scattering length to zero via a Feshbach resonance. In addition to the usual global collapse to the center of the condensate, in the presence of an optical-lattice potential one could also have in certain cases independent collapse of parts of the condensate to local centers, which could be verified in experiments.

Numerical solution of the two-dimensional Gross-Pitaevskii equation for trapped interacting atoms

We present a numerical scheme for solving the time-independent nonlinear Gross-Pitaevskii equation in two dimensions describing the Bose-Einstein condensate of trapped interacting neutral atoms at zero temperature. The trap potential is taken to be of the harmonic-oscillator type and the interaction both attractive and repulsive. The Gross-Pitaevskii equation is numerically integrated consistent with the correct boundary conditions at the origin and in the asymptotic region. Rapid convergence is obtained in all cases studied. In the attractive case there is a limit Co the maximum number of atoms in the condensate. (C) 2000 Published by Elsevier B.V. B.V. All rights reserved.

Mean-field model for the interference of matter-waves from a three-dimensional optical trap

Using the mean-field time-dependent Gross-Pitaevskii equation we study the formation of a repulsive Bose-Einstein condensate on a combined optical and harmonic traps in two and three dimensions and subsequent generation of the interference pattern upon the removal of the combined traps as in the experiment by, Greiner et al. [Nature (London 415 (2002) 39]. For optical traps of moderate strength, interference pattern of 27 (9) prominent bright spots is found to be formed in three. (two) dimensions on a cubic (square) lattice in agreement with experiment. Similar interference pattern can also be formed upon removal of the optical lattice trap only. The pattern so formed can oscillate for a long time in the harmonic trap which can be observed experimentally. (C) 2003 Elsevier B.V. B.V. All rights reserved.

Collapse of attractive Bose-Einstein condensed vortex states in a cylindrical trap

The quantized vortex states of a weakly interacting Bose-Einstein condensate of atoms with attractive interatomic interaction in an axially symmetric harmonic oscillator trap are investigated using the numerical solution of the time-dependent Gross-Pitaevskii equation obtained by the semi-implicit Crank-Nicholson method. The collapse of the condensate is studied in the presence of deformed traps with the larger frequency along either the radial or the axial direction. The critical number of atoms for collapse is calculated as a function of the vortex quantum number L. The critical number increases with increasing angular momentum L of the cortex state but tends to saturate for large L.

Numerical study of the spherically symmetric Gross-Pitaevskii equation in two space dimensions

The Gross-Pitaevskii equation for Bose-Einstein condensation (BEC) in two space dimensions under the action of a harmonic oscillator trap potential for bosonic atoms with attractive and repulsive interparticle interactions was numerically studied by using time-dependent and time-independent approaches. In both cases, numerical difficulty appeared for large nonlinearity. Nonetheless, the solution of the time-dependent approach exhibited intrinsic oscillation with time iteration which is independent of space and time steps used in discretization.

The dynamics of bright matter wave solitons in a quasi one-dimensional Bose-Einstein condensate with a rapidly varying trap

The dynamics of a bright matter wave soliton in a quasi one-dimensional Bose-Einstein condensate (BEC) with a periodically rapidly varying time trap is considered. The governing equation is based on averaging the fast modulations of the Gross-Pitaevskii (GP) equation. This equation has the form of a GP equation with an effective potential of a more complicated structure than an unperturbed trap. In the case of an inverted (expulsive) quadratic trap corresponding to an unstable GP equation, the effective potential can be stable. For the bounded space trap potential it is showed that bifurcation exists, i.e. the single-well potential bifurcates to the triple-well effective potential. The stabilization of a BEC cloud on-site state in the temporary modulated optical lattice is found. This phenomenon is analogous to the Kapitza stabilization of an inverted pendulum. The analytical predictions of the averaged GP equation are confirmed by numerical simulations of the full GP equation with rapid perturbations.

Gross and microscopic observations on the lingual structure of the franciscana (Pontoporia blainvillei-gervais and d'orbigny, 1844)

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Laparoscopic ovum collection in sheep: Gross and microscopic evaluation of the ovary and influence on ooctye production

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

Comparison of four trap types for ambrosia beetles (Coleoptera, Scolytidae) in Brazilian Eucalyptus stands

Eucalyptus spp. plantations represent >60% of the reforested area in Brazil. Although ambrosia beetle attacks on live trees were at first nonexistent, they have begun to appear with greater frequency. Monitoring for pest insects is a key factor in integrated pest management, and baited traps are one of the most widely used methods for insect population detection and survey. We compared the efficiency of the most widely used trap in Brazil to survey for ambrosia beetles and other Scolytidae, the ESALQ-84 type, with other traditionally employed traps: the multiple funnel (Lindgren trap); drainpipe; and slot (Theyson) traps, in a Eucalyptus grandis Hill ex Maiden stand in Brazil. The ESALQ-84 trap was the most efficient in trapping Hypothenemus eruditus Westwood and Hypothenemus obscurus (F.); the multiple funnel trap caught significantly more Cryptocarenus diadematus Eggers; whereas the slot trap caught more Premnobius cavipennis Eichhoff and Xyleborus affinis Eichhoff than the other traps. The drainpipe trap was the least effective trap overall. When corrected for number of beetles caught per trap surface area, catches were significantly higher on the ESALQ-84 trap for the majority of the species analyzed, probably because of a smaller trap surface area. The slot trap was recommended for it caught overall more beetles of the three most economically important scolytid species in eucalypt plantations in Brazil, P. cavipennis, X. affinis, and X, ferrugineus.

Combined cycle versus one thousand diesel power plants: pollutant emissions, ecological efficiency and economic analysis

The increase in the use of natural gas in Brazil has stimulated public and private sectors to analyse the possibility of using combined cycle systems for generation of electrical energy. Gas turbine combined cycle power plants are becoming increasingly common due to their high efficiency, short lead times, and ability to meet environmental standards. Power is produced in a generator linked directly to the gas turbine. The gas turbine exhaust gases are sent to a heat recovery steam generator to produce superheated steam that can be used in a steam turbine to produce additional power. In this paper a comparative study between a 1000 MW combined cycle power plant and 1000 kW diesel power plant is presented. In first step, the energetic situation in Brazil, the needs of the electric sector modification and the needs of demand management and integrated means planning are clarified. In another step the characteristics of large and small thermoelectric power plants that use natural gas and diesel fuel, respectively, are presented. The ecological efficiency levels of each type of power plant is considered in the discussion, presenting the emissions of particulate material, sulphur dioxide (SO2), carbon dioxide (CO2) and nitrogen oxides (NOx). (c) 2006 Elsevier Ltd. All rights reserved.

Numeric simulation of pollutant dispersion by a control-volume based on finite element method

The dispersion of pollutants in the environment is an issue of great interest as it directly affects air quality, mainly in large cities. Experimental and numerical tools have been used to predict the behavior of pollutant species dispersion in the atmosphere. A software has been developed based on the control-volume based on the finite element method in order to obtain two-dimensional simulations of Navier-Stokes equations and heat or mass transportation in regions with obstacles, varying position of the pollutant source. Numeric results of some applications were obtained and, whenever possible, compared with literature results showing satisfactory accordance. Copyright (C) 2010 John Wiley & Sons, Ltd.