Bose-Einstein condensation dynamics from the numerical solution of the Gross-Pitaevskii equation

We study certain stationary and time-evolution problems of trapped Bose-Einstein condensates using the numerical solution of the Gross-Pitaevskii (GP) equation with both spherical and axial symmetries. We consider time-evolution problems initiated by suddenly changing the interatomic scattering length or harmonic trapping potential in a stationary condensate. These changes introduce oscillations in the condensate which are studied in detail. We use a time iterative split-step method for the solution of the time-dependent GP equation, where all nonlinear and linear non-derivative terms are treated separately from the time propagation with the kinetic energy terms. Even for an arbitrarily strong nonlinear term this leads to extremely accurate and stable results after millions of time iterations of the original equation.

Numerical and variational solutions of the dipolar Gross-Pitaevskii equation in reduced dimensions

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

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)

Dynamics of a spacecraft and normalization around Lagrangian points in the Neptune-Triton system

The problem of a spacecraft orbiting the Neptune-Triton system is presented. The new ingredients in this restricted three body problem are the Neptune oblateness and the high inclined and retrograde motion of Triton. First we present some interesting simulations showing the role played by the oblateness on a Neptune's satellite, disturbed by Triton. We also give an extensive numerical exploration in the case when the spacecraft orbits Triton, considering Sun, Neptune and its planetary oblateness as disturbers. In the plane a x I (a = semi-major axis, I = inclination), we give a plot of the stable regions where the massless body can survive for thousand of years. Retrograde and direct orbits were considered and as usual, the region of stability is much more significant for the case of direct orbit of the spacecraft (Triton's orbit is retrograde). Next we explore the dynamics in a vicinity of the Lagrangian points. The Birkhoff normalization is constructed around L-2, followed by its reduction to the center manifold. In this reduced dynamics, a convenient Poincare section shows the interplay of the Lyapunov and halo periodic orbits, Lissajous and quasi-halo tori as well as the stable and unstable manifolds of the planar Lyapunov orbit. To show the effect of the oblateness, the planar Lyapunov family emanating from the Lagrangian points and three-dimensional halo orbits are obtained by the numerical continuation method. Published by Elsevier Ltd. on behalf of COSPAR.

Fixed points on torus fiber bundles over the circle

The main purpose of this work is to study fixed points of fiber-preserving maps over the circle S-1 for spaces which axe fibrations over S-1 and the fiber is the torus T. For the case where the fiber is a surface with nonpositive Euler characteristic, we establish general algebraic conditions, in terms of the fundamental group and the induced homomorphism, for the existence of a deformation of a map over S-1 to a fixed point, free map. For the case where the fiber is a torus, we classify all maps over S-1 which can be deformed fiberwise to a fixed point free map.

Coincidence points of fiber maps on S-n-bundles

In this note we study coincidence of pairs of fiber-preserving maps f, g : E-1 -> E-2 where E-1, E-2 are S-n-bundles over a space B. We will show that for each homotopy class vertical bar f vertical bar of fiber-preserving maps over B, there is only one homotopy class vertical bar g vertical bar such that the pair (f, g), where vertical bar g vertical bar = vertical bar tau circle f vertical bar can be deformed to a coincidence free pair. Here tau : E-2 -> E-2 is a fiber-preserving map which is fixed point free. In the case where the base is S-1 we classify the bundles, the homotopy classes of maps over S-1 and the pairs which can be deformed to coincidence free. At the end we discuss the self-coincidence problem. (C) 2010 Elsevier B.V. All rights reserved.

Abelianized obstruction for fixed points of fiber-preserving maps of surface bundles

Let f: M -> M be a fiber-preserving map where S -> M -> B is a bundle and S is a closed surface. We study the abelianized obstruction, which is a cohomology class in dimension 2, to deform f to a fixed point free map by a fiber-preserving homotopy. The vanishing of this obstruction is only a necessary condition in order to have such deformation, but in some cases it is sufficient. We describe this obstruction and we prove that the vanishing of this class is equivalent to the existence of solution of a system of equations over a certain group ring with coefficients given by Fox derivatives.

Fixed points on Klein bottle fiber bundles over the circle

The main purpose of this work is to study fixed points of fiber-preserving maps over the circle S(1) for spaces which are fiber bundles over S(1) and the fiber is the Klein bottle K. We classify all such maps which can be deformed fiberwise to a fixed point free map. The similar problem for torus fiber bundles over S(1) has been solved recently.

The natural radioactivity in water by gross alpha and beta measurements

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

Apical seal of root canals with gutta-percha points with calcium hydroxide

Foi propósito deste trabalho observar se o uso de cones de guta-percha contendo Ca(OH)2, promove melhora no selamento marginal apical e, também, se apenas o cone principal contendo essa droga produz esse efeito. Assim, dentes humanos extraídos foram preparados biomecânicamente e obturados pela técnica da condensação lateral com OZE e cones de guta-percha contendo ou não Ca(OH)2. Após imersão dos espécimes em azul de metileno a 2%, em ambiente com vácuo, observou-se diferença estatisticamente significante entre os espécimes obturados com cones contendo Ca(OH)2, comparativamente aos casos obturados com cones de guta percha comuns (p=0.01). Os resultados obtidos permitiram concluir que esses cones tornam as obturações mais herméticas e que esse efeito também pode ser obtido com o emprego do cone principal da mesma fórmula, aliado a cones acessórios comuns (p=0.05).

Gross anatomical study of the aortic ARC branches of the paca (Agouti paca, Linnaeus, 1766)

Foi descrita a distribuição do arco aórtico de oito animais da espécie Agouti paca, sendo duas fêmeas adultas e seis filhotes jovens (3 machos e 3 fêmeas) que foram obtidos no Setor de Animais Silvestres da Faculdade de Ciências Agrárias e Veterinárias -- Campus de Jaboticabal. Após morte natural, seus vasos arteriais foram injetados com Neoprene latex 650 (Du Pont do Brasil S.A.) coloridos e colocados em uma solução de formalina a 10%. Depois de dissecados, notou-se que o arco aórtico desses animais emite a artéria subclávia e o tronco braquiocefálico. Este último dá origem à artéria carótida comum esquerda e a um tronco, do qual surgem a artéria carótida comum direita e a artéria subclávia direita. Estas emitem, em cada antímero, a artéria vertebral, a artéria tronco costocervical, a artéria cervical superficial, a artéria axilar e a artéria torácica interna. em apenas um animal a artéria carótida comum esquerda apresenta-se na forma de um sifão, logo após sua origem na artéria subclávia direita. Nos demais animais, a artéria carótida comum esquerda apresenta um trajeto retilíneo.

Numerical study about natural escape and capture routes by the Moon via Lagrangian points L1 and L2

The lunar sphere of influence, whose radius is some 66,300 km, has regions of stable orbits around the Moon and also regions that contain trajectories which, after spending some time around the Moon, escape and are later recaptured by lunar gravity. Both the escape and the capture occur along the Lagrangian equilibrium points L1 and L2. In this study, we mapped out the region of lunar influence considering the restricted three-body Earth-Moon-particle problem and the four-body Sun-Earth-Moon-particle (probe) problem. We identified the stable trajectories, and the escape and capture trajectories through the L I and L2 in plots of the eccentricity versus the semi-major axis as a function of the time that the energy of the osculating lunar trajectory in the two-body Moon-particle problem remains negative. We also investigated the properties of these routes, giving special attention to the fact that they supply a natural mechanism for performing low-energy transfers between the Earth and the Moon, and can thus be useful on a great number of future missions. (C) 2007 Published by Elsevier Ltd on behalf of COSPAR.