Improved numerical approach for the time-independent Gross-Pitaevskii nonlinear Schrödinger equation

In the present work, we improve a numerical method, developed to solve the Gross-Pitaevkii nonlinear Schrödinger equation. A particular scaling is used in the equation, which permits us to evaluate the wave-function normalization after the numerical solution. We have a two-point boundary value problem, where the second point is taken at infinity. The differential equation is solved using the shooting method and Runge-Kutta integration method, requiring that the asymptotic constants, for the function and its derivative, be equal for large distances. In order to obtain fast convergence, the secant method is used. © 1999 The American Physical Society.

Treatment of mucus retention phenomena in children by the micro-marsupialization technique: case reports

The purpose of the present study was to emphasize the technique of micro-marsupialization as an alternative for the treatment of mucus retention phenomena. Out of 41 patients, 14 were selected for treatment by the micro-marsupialization technique on the basis of clinical criteria. Patient age ranged from 5-9 years. The technique was performed as follows: the area was disinfected with 0.1% iodine; a topical anesthetic was applied to cover the entire lesion for approximately 3 min; a 4.0 silk suture was passed through the internal part of the lesion along its widest diameter; and a surgical knot was made. Of the original 14 patients treated by the micro-marsupialization technique, 12 presented full regression one week after treatment. Recurrence occurred in two cases. It was possible to conclude that the micro-marsupialization technique is an alternative to be considered, especially in pediatric dentistry.

On the integrable perturbations of the Camassa-Holm equation

We present an investigation of the nonlinear partial differential equations (PDE) which are asymptotically representable as a linear combination of the equations from the Camassa-Holm hierarchy. For this purpose we use the infinitesimal transformations of dependent and independent variables of the original PDE. This approach is helpful for the analysis of the systems of the PDE which can be asymptotically represented as the evolution equations of polynomial structure. © 2000 American Institute of Physics.

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.

Galilean covariance and the Duffin-Kemmer-Petiau equation

We use a five-dimensional approach to Galilean covariance to investigate the non-relativistic Duffin-Kemmer-Petiau first-order wave equations for spinless particles. The corresponding representation is generated by five 6 × 6 matrices. We consider the harmonic oscillator as an example.

Exact solutions of the dirac equation for modified coulombic potentials

Exact solutions are found for the Dirac equation for a combination of Lorentz scalar and vector Coulombic potentials with additional non-Coulombic parts. An appropriate linear combination of Lorentz scalar and vector non-Coulombic potentials, with the scalar part dominating, can be chosen to give exact analytic Dirac wave functions. The method works for the ground state or for the lowest orbital state with l = j - 1/2 , for any j.

The influence of ultrasound on the retention of cast posts cemented with different agents

Aim: The aim of this study was to evaluate the influence of ultrasound during the removal of posts cemented with either zinc phosphate cement, glass ionomer cement or resin cement. Methodology: Eighty-four single-rooted teeth were prepared and after cementation of cast posts, they were randomly divided into six groups of 14. Groups 1, 2 and 3 did not receive ultrasonic vibration, whilst groups 4, 5 and 6 received ultrasonic vibration for 10 min. The force necessary for post removal was determined using a universal testing machine. Results were statistically analysed using ANOVA and Tukey tests (5%). Results: The application of ultrasonic vibration reduced the retention provided by zinc phosphate and glass ionomer cements by 39% and 33%, respectively. Conclusions: A statistically significant reduction in the force necessary to remove posts cemented with zinc phosphate and glass ionomer cements occurred following application of ultrasound. The application of ultrasonic vibration did not influence the retention of cast posts cemented with resin cement.

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.

The influence of diabetes mellitus and insulin therapy on biomechanical retention around dental implants: a study in rabbits.

The oral rehabilitation by dental implants in patients with diabetes remains a controversial issue. The aim of this study was to evaluate the influence of diabetes mellitus and insulin therapy on the bone healing around dental implants using torque removal. Twenty-seven rabbits were randomly divided into 3 groups with 9 animals each: control (C) group, induced diabetic (D) group, and insulin-treated diabetic (ITD) group (10 U/day). After 1 week, one implant was inserted at the tibial metaphysis of the animals. The glucose levels were periodically evaluated through the glucose-oxidase enzymatic method. The animals were killed at 4, 8, and 12 weeks after surgery and the biomechanical test was performed using a torque manometer. Statistically significant differences regarding the removal torque of the implant could not be found at 4 weeks (P = 0.2) among groups. Group C showed statistically higher values than groups D and ITD at the experimental periods of 8 (P = 0.0001 and P = 0.0002, respectively) and 12 weeks (P = 0.0053 and P = 0.001, respectively). There were no statistical differences between D and ITD groups in any of the experimental periods. Diabetes mellitus has negatively influenced the mechanical retention of implants placed at the tibial metaphysis of rabbits. Therapy with insulin did not induce any changes.

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.

Oxidative stability and α-tocopherol retention in soybean oil with lemon seed extract (Citrus limon) under thermoxidation

The synergistic effect of lemon seed extract with tert-butylhydroquinone (TBHQ) in soybean oil subjected to thermoxidation by Rancimat was investigated, and the influence of these antioxidants on α-tocopherol degradation in thermoxidized soybean oil. Control, LSE (2,400 mg/kg Lemon Seed Extract), TBHQ (50 mg/kg), Mixture 1 (LSE + 50 mg/kg TBHQ) and Mixture 2 (LSE + 25 mg/kg TBHQ) were subjected to 180°C for 20 h. Samples were taken at time 0, 5, 10, 15 and 20 h intervals and analysed for oxidative stability and α-tocopherol content. LSE and Mixtures 1 and 2 showed the capacity of retarding lipid oxidation when added to soya oil and also contributed to α-tocopherol retention in oil heated at high temperatures. However, Mixtures 1 and 2 added to the oil presented a greater antioxidant power, consequently proving the antioxidants synergistic effect.

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.