Numerical study of the coupled time-dependent Gross-Pitaevskii equation: Application to Bose-Einstein condensation

The Bose-Einstein condensate of several types of trapped bosons at ultralow temperature was described using the coupled time dependent Gross-Pitaevskii equation. Both the stationary and time evolution problems were analyzed using this approach. The ground state stationary wave functions were found to be sharply peaked near the origin for attractive interatomic interaction for larger nonlinearity while for a repulsive interatomic interaction the wave function extends over a larger region of space.

Renormalization of the ladder light-front Bethe-Salpeter equation in the Yukawa model

The reduction of the two-fermion Bethe-Salpeter equation in the framework of light-front dynamics is studied for the Yukawa model. It yields auxiliary three-dimensional quantities for the transition matrix and the bound state. The arising effective interaction can be perturbatively expanded in powers of the coupling constant gs allowing a defined number of boson exchanges; it is divergent and needs renormalization; it also includes the instantaneous term of the Dirac propagator. One possible solution of the renormalization problem of the boson exchanges is shown to be provided by expanding the effective interaction beyond single boson exchange. The effective interaction in ladder approximation up to order g4 s is discussed in detail. It is shown that the effective interaction naturally yields the box counterterm required to be introduced ad hoc previously. The covariant results of the Bethe-Salpeter equation can be recovered from the corresponding auxiliary three-dimensional quantities.

Envelhecimento acelerado em sementes de Eucalyptus grandis Hill ex Maiden classificadas por tamanho

Two experiments of seed ageing of Eucalyptus grandis Hill ex Maiden were carried out at laboratory conditions. In the first experiment, two seed lots were classified in two square mesh screens (< 0.84 to ≥ 0.71 mm and < 0.71 mm to ≥ 0.59 mm), submitted to 42 °C and 100% relative humidity, for 0, 8, 12, 24, and 32 hours of stress treatments. Seed germination tests were done with just aged seeds. The results showed that the stress period was not sufficient for ageing the seeds. In the second experiment, the best quality seed lot was separated in the same two sizes. The seeds were submitted under the same stress conditions of the first experiment but for 0, 48, 72, and 96 hours. The germination test was done right after the seeds were taken from the stress conditions, and with stored seeds at dry chamber (2 weeks and 26 months). It was concluded that both seed sizes reached 30% of moisture content under 72 hours of ageing conditions and showed significant germination losses when compared with seeds without ageing (control), as the moist seeds as the stored ones at dry chamber, for both 2 weeks and 26 months.

Efeito da densidade de plantas de Bracharia decumbens Stapf sobre o crescimento inicial de mudas de Eucalyptus grandis W. Hill ex Maiden

In order to verify the effect of Brachiaria decumbens plant density on the initial growth of Eucalyptus grandis plants, one assay was conducted under semi-controlled conditions of soil fertility and humidity. Dark red Latossol, collected from the arable layer, was used as substrate in 50 liters amianthus cement boxes. One seedling of Eucalyptus was planted in each box. Fifteen days later, seedlings of B. decumbens were transplanted on the same box. The treatments consisted of 0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 60, 80, 100, and 120 plants of B. decumbens. The experimental design was the complete randomized design, with 15 treatments and four replicates. The Eucalyptus plants that lived with B. decumbens were evaluated for stem diameter, plant high, leaf area, and dry weight of stem, branches and leaves. B. decumbens plants were evaluated for dry weight of aerial parts. B. decumbens, at the density level of four plants per m 2 and over, reduced of the initial growth of the Eucalyptus plants. B. decumbens reduced on average 27.78% stem diameter, 18.47% plant high, 70.56% leaf number, 63.26% leaf area, and 55.22%, 77.29% and 55.30% of stem, branch and leaf dry weight, respectively. Plant high was not a good parameter to evaluate the B. decumbens interference.

Efeito da densidade de plantas de Panicum maximum Jacq. sobre o crescimento inicial de Eucalyptus grandis W.Hill ex Maiden

In order to verify the effect of Panicum maximum plant density on the initial growth of Eucalyptus grandis plants, one assay was conducted under semi-controlled conditions of soil fertility and humidity. Dark red Latossol, collected from the arable layer, was used as substrate in 50 liters amianthus cement boxes. One seedling of Eucalyptus was planted in each box. Fifteen days later, seedlings of P. maximum were transplanted on the same box. The treatments consisted of 0, 4, 8, 12, 16 and 20 plants of P. maximum per m 2. The experimental design was the complete randomized design, with six treatments and eight replicates for P. maximum. One hundred and ten and 190 days after transplanting, Eucalyptus plants grown among P. maximum showed an average reduction of 30.80 and 46.55% stem diameter, 25.10 and 22.50 plant high, 40.18 and 31.29% stem dry weight, 61.32 and 54.06% branch dry weight, 53.72 and 51.82% root dry weight, 44.62 and 38.50% leaf dry weight, 22.51 and 23.16 branch number, 20.72 and 19.97% leaf number, and 33.88 and 17.05% leaf area, respectively.

The Dirac-Hestenes equation for spherical symmetric potentials in the spherical and Cartesian gauges

In this paper, using the apparatus of the Clifford bundle formalism, we show how straightforwardly solve in Minkowski space-time the Dirac-Hestenes equation - which is an appropriate representative in the Clifford bundle of differential forms of the usual Dirac equation - by separation of variables for the case of a potential having spherical symmetry in the Cartesian and spherical gauges. We show that, contrary to what is expected at a first sight, the solution of the Dirac-Hestenes equation in both gauges has exactly the same mathematical difficulty. © World Scientific Publishing Company.

On a negative flow of the AKNS hierarchy and its relation to a two-component Camassa-Holm equation?

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

Antinucleon spectra in the Dirac equation with scalar and vector Wood-Saxon potentials

We analyze here the spin and pseudospin symmetry for the antinucleon spectra solving the Dirac equation with scalar and vector Wood-Saxon potentials. In relativistic nuclear mean field theories where these potentials have large magnitudes and opposite signs we show that contrary to the nucleon case where pseudospin interaction is never very small and cannot be treated perturbatively, for antinucleon systems this interaction is perturbative and an exact pseudospin symmetry is possible. This result manifests the relativistic nature of the nuclear pseudospin symmetry. © 2009 American Institute of Physics.

Darboux-Bäcklund transformations and rational solutions of the painlevé IV equation

Rational solutions of the Painlevé IV equation are constructed in the setting of pseudo-differential Lax formalism describing AKNS hierarchy subject to the additional non-isospectral Virasoro symmetry constraint. Convenient Wronskian representations for rational solutions are obtained by successive actions of the Darboux-Bäcklund transformations. ©2010 American Institute of Physics.

Pharmacognostical evaluation of fruits of Solanum lycocarpum A. St.-Hill. (Solanaceae)

This study describes the chemical and physical-chemical profile of plant drug and ethanolic extract obtained from fruits of Solanum lycocarpum A. St.-Hill. (Solanaceae). The physical and chemical analysis involved the granulometry determination, non-compacted apparent density, loss on drying in oven and in infrared scale, pH, ash values and extractive values. The results determined the physical-chemical characteristics of the drug plant. It was also carried out the microbiological control of the plant drug. The preliminary phytochemical screening featured the presence of tannins, flavonoids and saponins in the plant drug and alkaloids and steroids in the ethanolic exctract. The solamargine and solasonine glycoalkaloids were identified through TLC and GC/ MS. The levels of total phenols and tannins were quantified in the extract (8.90% and 6,85% respectively). Such studies contribute to the chemical identification and quality control of S. lycocarpum fruits. © 2010 Phcog.net.

Estudo fitoquímico preliminar e bioensaio toxicológico frente a larvas de Artemia salina Leach. de extrato obtido de frutos de Solanum lycocarpum A. St.-Hill (Solanaceae)

The phytochemical profile of ethanolic extract of Solanum lycocarpum fruits was analyzed and preliminary toxicity tests were performed against brine shrimp larvae. The extract was subjected to preliminary phytochemical analysis to identify the main classes of secondary metabolites and tested against the larvae of A. salina to obtain the median lethal concentrations (LC50%). The phytochemical tests showed the presence of phenols, tannins, saponins, alkaloids and free steroids. The extract was fractionated with various solvents for toxicity testing against the larvae and the hydroalcoholic fraction showed considerable cytotoxicity (CL50% = 285.546 g/mL).

Stability of the null solution of the equation ẋ(t) = -a(t)x(t) + b(t)x([t])

The asymptotic stability of the null solution of the equation ẋ(t) = -a(t)x(t)+b(t)x([t]) with argument [t], where [t] designates the greatest integer function, is studied by means of dichotomic maps. © 2010 Academic Publications.

Qualidade fisiológica de sementes de diferentes árvores matrizes de Corymbia citriodora (Hook.) K.D.Hill & L.A.S. Johnson

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

State Dependent Riccati Equation (SDRE) control method applied in cancellation of a parametric resonance in a magnetically levitated body

Here, a simplified dynamical model of a magnetically levitated body is considered. The origin of an inertial Cartesian reference frame is set at the pivot point of the pendulum on the levitated body in its static equilibrium state (ie, the gap between the magnet on the base and the magnet on the body, in this state). The governing equations of motion has been derived and the characteristic feature of the strategy is the exploitation of the nonlinear effect of the inertial force associated, with the motion of a pendulum-type vibration absorber driven, by an appropriate control torque [4]. In the present paper, we analyzed the nonlinear dynamics of problem, discussed the energy transfer between the main system and the pendulum in time, and developed State Dependent Riccati Equation (SDRE) control design to reducing the unstable oscillatory movement of the magnetically levitated body to a stable fixed point. The simulations results showed the effectiveness of the (SDRE) control design. Copyright © 2011 by ASME.

Geometrical wave equation and the cauchy-like theorem for octonions

Riemann surfaces, cohomology and homology groups, Cartan's spinors and triality, octonionic projective geometry, are all well supported by Complex Structures [1], [2], [3], [4]. Furthermore, in Theoretical Physics, mainly in General Relativity, Supersymmetry and Particle Physics, Complex Theory Plays a Key Role [5], [6], [7], [8]. In this context it is expected that generalizations of concepts and main results from the Classical Complex Theory, like conformal and quasiconformal mappings [9], [10] in both quaternionic and octonionic algebra, may be useful for other fields of research, as for graphical computing enviromment [11]. In this Note, following recent works by the autors [12], [13], the Cauchy Theorem will be extended for Octonions in an analogous way that it has recentely been made for quaternions [14]. Finally, will be given an octonionic treatment of the wave equation, which means a wave produced by a hyper-string with initial conditions similar to the one-dimensional case.