A MODEL OF THE DEUTERON BASED ON A BREIT TYPE EQUATION

A relativistic treatment of the deuteron and its observables based on a two-body Dirac (Breit) equation, with phenomenological interactions, associated to one-boson exchanges with cutoff masses, is presented. The 16-component wave function for the deuteron (J(pi) = 1+) solution contains four independent radial functions which obey a system of four coupled differential equations of first order. This radial system is numerically integrated, from infinity to the origin, by fixing the value of the deuteron binding energy and using appropriate boundary conditions at infinity. Specific examples of mixtures containing scalar, pseudoscalar and vector like terms are discussed in some detail and several observables of the deuteron are calculated. Our treatment differs from more conventional ones in that nonrelativistic reductions of the order c-2 are not used.

A note on the controllability for the wave equation in nonsmooth plane domains

We study exact boundary controllability for a two-dimensional wave equation in a region which is an angular sector of a circle or an angular sector of an annular region. The control, of Neumann type, acts on the curved part of the boundary, while in the straight part we impose homogeneous Dirichlet boundary condition. The initial state has finite energy and the control is square integrable. (c) 2005 Elsevier B.V. All rights reserved.

SURFACE PERTURBATIONS OF A SHALLOW VISCOUS-FLUID HEATED FROM BELOW AND THE (2+1)-DIMENSIONAL BURGERS-EQUATION

The (2 + 1)-dimensional Burgers equation is obtained as the equation of motion governing the surface perturbations of a shallow viscous fluid heated from below, provided the Rayleigh number of the system satisfies the condition R not-equal 30. A solution to this equation is explicitly exhibited and it is argued that it describes the nonlinear evolution of a nearly one-dimensional kink.

The thermohydrodynamical picture of Brownian motion via a generalized Smoluchowsky equation

Via an operator continued fraction scheme, we expand Kramers equation in the high friction limit. Then all distribution moments are expressed in terms of the first momemt (particle density). The latter satisfies a generalized Smoluchowsky equation. As an application, we present the nonequilibrium thermodynamics and hydrodynamical picture for the one-dimensional Brownian motion. (C) 2000 Elsevier B.V. B.V. All rights reserved.

SUPERSYMMETRIC SOLUTION FOR 2-DIMENSIONAL SCHRODINGER-EQUATION

We use a non usual realization of the superalgebra to resolve certain two-dimensional potentials. The Hartmann and an anisotropic ring-shaped oscillator are explicitly solved.

Hausdorff dimension of non-hyperbolic repellers. I: Maps with holes

This is the first paper in a two-part series devoted to studying the Hausdorff dimension of invariant sets of non-uniformly hyperbolic, non-conformal maps. Here we consider a general abstract model, that we call piecewise smooth maps with holes. We show that the Hausdorff dimension of the repeller is strictly less than the dimension of the ambient manifold. Our approach also provides information on escape rates and dynamical dimension of the repeller.

Solving Schrödinger equation for two dimensional potential using supersymmetry

The formalism of supersymmetric Quantum Mechanics can be extended to arbitrary dimensions. We introduce this formalism and explore its utility to solve the Schodinger equation for a bidimensional potential. This potential can be applied in several systens in physical and chemistry context, for instance, it can be used to study benzene molecule.

Fitting hyperbolic universes to Cayon-Smoot spots in COBE maps

On the possibility that the universe's matter density is low (Ohm(0) < 1), cosmologies can be considered with the metric of Friedmann's open universe but with closed hyperbolic manifolds as the physical three-space. These models have nontrivial spatial topology, with the property of producing multiple images of cosmic sources. Here a fit is attempted of 10 of these models to the physical cold and hot spots found by Cayon & Smoot in the COBE/DMR maps. These spots are interpreted as early, distant images of much nearer sources of inhomogeneity. The source for one of the cold spots is seen as the seed of a known supercluster.

Exact boundary control for the wave equation in a polyhedral time-dependent domain

We establish exact boundary controllability for the wave equation in a polyhedral domain where a part of the boundary moves slowly with constant speed in a small interval of time. The control on the moving part of the boundary is given by the conormal derivative associated with the wave operator while in the fixed part the control is of Neuman type. For initial state H-1 x L-2 we obtain controls in L-2. (C) 1999 Elsevier B.V. Ltd. All rights reserved.

A well-balanced flow equation for noise removal and edge detection

In this paper, an anisotropic nonlinear diffusion equation for image restoration is presented. The model has two terms: the diffusion and the forcing term. The balance between these terms is made in a selective way, in which boundary points and interior points of the objects that make up the image are treated differently. The optimal smoothing time concept, which allows for finding the ideal stop time for the evolution of the partial differential equation is also proposed. Numerical results show the proposed model's high performance.

Dirac equation in magnetic-solenoid field

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Bound states of the Dirac equation for a class of effective quadratic plus inversely quadratic potentials

The Dirac equation is exactly solved for a pseudoscalar linear plus Coulomb-like potential in a two-dimensional world. This sort of potential gives rise to an effective quadratic plus inversely quadratic potential in a Sturm-Liouville problem, regardless the sign of the parameter of the linear potential, in sharp contrast with the Schrodinger case. The generalized Dirac oscillator already analyzed in a previous work is obtained as a particular case. (C) 2004 Elsevier B.V. All rights reserved.