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.

Surface morphology and molecular organization of lignins in Langmuir-Blodgett films

Atomic force microscopy (AFM) and Fourier transform infrared spectroscopy (FTIR) are used to investigate molecular organization in Langmuir-Blodgett (LB) films of two kinds of lignins. The lignins were extracted from sugar cane bagasse using distinct extraction processes and are referred to here as ethanol lignin (EL) and saccharification lignin (SAC). AFM images show that LB films from EL have a flat surface in comparison with those from SAC. For the latter, ellipsoidal aggregates are seen oriented perpendicularly to the substrate. This result is confirmed by a combination of transmission and reflection FTIR measurements, which also point to lignin aggregates preferentially oriented perpendicularly to the substrate. For LB films from EL, on the other hand, aggregates are preferentially oriented parallel to the substrate, again consistent with the flat surface observed in AFM data. The vibrational spectroscopy data for cast films from both lignins show random molecular organization, as one should expect.

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.

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.

Photoinduced birefringence at low temperatures in Langmuir-Blodgett films of azobenzene-functionalized copolymers

The temperature dependence has been investigated for the photoinduced birefringence in Langmuir-Blodgett (LB) films from the azocopolymer 4-[N- ethyl -N-(2-hydroxyethyl)] amino-2'-chloro-4'-nitroazobenzene (MMA-DR13) mixed with cadmium stearate. The buildup and relaxation of the birefringence in the range from 20 to 296 K were fitted with a Kohlrausch-Williams-Watts (KWW) function, with a beta-value of 0.78-0.98 for the build-up and 0.18-0.27 for the decay. This is consistent with a distribution of time constants for the kinetics of the birefringence processes. The maximum birefringence increased with increasing temperature up to 120 K because the free volume fluctuation also increased with temperature. Above 120 K, the birefringence decreased with temperature as thermal diffusion dominates. In the latter range of temperature, an Arrhenius behavior is inferred for both build-up and decay of birefringence. In each case two activation energies were obtained: 0.8 and 5 kJ/mol for the build-up and 10 and 30 kJ/mol for the decay. The energies for the build-up are much lower than those associated with motion of the polymer chain, which means that the dynamics is governed by the orientation of the chromophores. For the decay, local motion of lateral groups of the polymer chains becomes important as the activation energies are within the range of gamma-relaxation energies. (C) 2003 Elsevier B.V. B.V. All rights reserved.

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.

Dipole moments in Langmuir monolayers from aromatic carboxylic acids

The three-layer capacitor model proposed by Demchak and Fort [J. Colloid Interface Sci. 46 (1974) 191] is employed to relate measured surface potentials of Langmuir monolayers from a series of polyphenyl carboxylic acids to molecular dipole moments calculated using semiempirical quantum methods. The effective dielectric constant at the air/monolayer interface is 3.0 +/- 0.6, very close to that estimated for aliphatic compounds. Good agreement between theory and experiment is obtained by adopting a dielectric constant of 6.4 for the monolayer/water interface and a contribution from the water reorientation of -0.064 +/- 0.006 D, which shows that the parameters in the DF model are essentially the same as for aliphatic amphiphiles, such as esters, acids, alcohols and ethers. (C) 2000 Elsevier B.V. B.V. All rights reserved.

Using an effective surface charge to explain surface potentials of Langmuir monolayers from dialkyldimethylammonium halides with the Gouy-Chapman theory

The use of an effective surface charge density has allowed the Gouy-Chapman (CC) theory to explain surface potential isotherms of Langmuir monolayers of dioctadecyldimethylammonium bromide (DODAB). The effective surface charge density of DODAB monolayer increases with the electronegativity of the counterions in the subphase. The pressure-area isotherms indicate a very condensed monolayer for DODAB spread on an I--containing subphase, which exhibits the lowest surface charge density, whereas the monolayer on a F-containing subphase is extremely expanded owing to the high surface charge density or electrostatic repulsion between headgroups. (C) 2001 Published by Elsevier B.V. B.V.

Langmuir films of an amide extracted from Piperaceae and its interaction with phospholipids

In this work, we investigate Langmuir monolayers froth an amide extracted from dried roots of Ottonia propinqua, a native Brazilian plant believed to exhibit anesthetic and hallucinogen activities. In addition to producing monolayers from the amide itself, we probe the molecular-level action of the amide on phospholipids employed as simple membrane models. The surface pressure-molecular area (pi-A) isotherms for the amide were little affected by a number of subphase conditions. Almost no changes were observed upon varying the compression speed, spreading volume onto the surface, ions in the subphase, ionic strength and the solution solvent. However, stronger effects occurred when the subphase temperature and pH were altered, as the isotherms were shifted to larger areas with increasing temperatures and decreasing pHs. These results are discussed in terms of the molecular packing adopted by the amide at the air-water interface. In the mixed films with arachidic acid, the area per molecule varied linearly with the concentration of amide, probably due to phase separation. on the other hand, in the mixed films with dipalmitoyl phosphatidyl choline (DPPC), small amounts of the amide were sufficient to change the pi-A isotherms significantly. This points to a strong molecular-level interaction, probably between the phosphate group in the zwitterion of DPPC and the nitrogen from the amidic group. (c) 2004 Elsevier B.V. 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.