Linearizability of the perturbed Burgers equation

We show in this report that the perturbed Burgers equation ut = 2uux + uxx + ε(3 α1u2ux + 3 α2uuxx + 3 α3u2 x + α4uxxx) is equivalent, through a near-identity transformation and up to O(ε), to a linearizable equation if the condition 3 α1 - 3 α3 - 3/2α2 + 3/2α4 = 0 is satisfied. In the case this condition is not fulfilled, a normal form for the equation under consideration is given. We show, furthermore, that nonlinearizable cases lead to perturbative expansions with secular-type behavior. Then, to illustrate our results, we make a linearizability analysis of the equations governing the dynamics of a one-dimensional gas.

Gel'fand-Levitan equation for deletion of states from Coulomb spectra

The Gel'fand-Levitan formalism is used to study how a selected set of bound states can be eliminated from the spectrum of the Coulomb potential and also how to construct a bound state in the Coulomb continuum. It is demonstrated that a sizeable quantum well can be produced by deleting a large number of levels from the s spectral series and the edge of the Coulomb potential alone can support the von Neumann-Wigner states in the continuum. © 1998 Elsevier Science B.V.

Two-body Dirac equation approach to the deuteron

The two-body Dirac(Breit) equation with potentials associated to one-boson-exchanges with cutoff masses is solved for the deuteron and its observables calculated. The 16-component wave-function for the Jπ = 1+ state contains four independent radial functions which satisfy a system of four coupled differential equations of first order. This system is numerically integrated, from infinity towards the origin, by fixing the value of the deuteron binding energy and imposing appropriate boundary conditions at infinity. For the exchange potential of the pion, a mixture of direct plus derivative couplings to the nucleon is considered. We varied the pion-nucleon coupling constant, and the best results of our calculations agree with the lower values recently determined for this constant.

Two-dimensional integrable generalization of the Camassa-Holm equation

In this letter we discuss the (2 + 1)-dimensional generalization of the Camassa-Holm equation. We require that this generalization be, at the same time, integrable and physically derivable under the same asymptotic analysis as the original Camassa-Holm equation. First, we find the equation in a perturbative calculation in shallow-water theory. We then demonstrate its integrability and find several particular solutions describing (2 + 1) solitary-wave like solutions. © 1999 Published by Elsevier Science B.V. All rights reserved.

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.

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.

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.