Self-trapping of a binary Bose-Einstein condensate induced by interspecies interaction

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Dimensional reduction of a binary Bose-Einstein condensate in mixed dimensions

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Symmetry breaking in a localized interacting binary Bose-Einstein condensate in a bichromatic optical lattice

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PULLBACK ATTRACTORS FOR A SINGULARLY NONAUTONOMOUS PLATE EQUATION

We consider the family of singularly nonautonomous plate equation with structural dampingu(tt) + a(t, x)u(t) - Delta u(t) + (-Delta)(2)(u) + lambda u = f(u),in a bounded domain Omega subset of R(n), with Navier boundary conditions. When the nonlinearity f is dissipative we show that this problem is globally well posed in H(0)(2)(Omega) x L(2)(Omega) and has a family of pullback attractors which is upper-semicontinuous under small perturbations of the damping a.

LOWER SEMICONTINUITY of PULLBACK ATTRACTORS FOR A SINGULARLY NONAUTONOMOUS PLATE EQUATION

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

Mass fractal characteristics of wet sonogels as determined by small-angle x-ray scattering and differential scanning calorimetry

Low density silica sonogels were prepared from acid sonohydrolysis of tetraethoxysilane. Wet gels were studied by small-angle x-ray scattering (SAXS) and differential scanning calorimetry (DSC). The DSC tests were carried out under a heating rate of 2 degrees C/min from -120 degrees C up to 30 degrees C. Aerogels were obtained by CO(2) supercritical extraction and characterized by nitrogen adsorption and SAXS. The DSC thermogram displays two distinct endothermic peaks. The first, a broad peak extending from about -80 degrees C up to practically 0 degrees C, was associated to the melting of ice nanocrystals with a crystal size distribution with pore diameter ranging from 1 or 2 nm up to about 60 nm, as estimated from Thomson's equation. The second, a sharp peak with onset temperature close to 0 degrees C, was attributed to the melting of macroscopic crystals. The DSC incremental nanopore volume distribution is in reasonable agreement with the incremental pore volume distribution of the aerogel as determined from nitrogen adsorption. No macroporosity was detected by nitrogen adsorption, probably because the adsorption method applies stress on the sample during measurement, leading to a underestimation of pore volume, or because often positive curvature of the solid surface is in aerogels, making the nitrogen condensation more difficult. According to the SAXS results, the solid network of the wet gels behaves as a mass fractal structure with mass fractal dimension D=2.20 +/- 0.01 in a characteristic length scale below xi=7.9 +/- 0.1 nm. The mass fractal characteristics of the wet gels have also been probed from DSC data by means of an earlier applied modeling for generation of a mass fractal from the incremental pore volume distribution curves. The results are shown to be in interesting agreement with the results from SAXS.

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.

Environmental coordination chemistry: Binary systems comprising some bivalent cations and monocarboxylates in aqueous solution. Ionic medium effects on equilibrium constants

The molar single activity coefficients associated with propionate ion (Pr) have been determined at 25 degrees C and ionic strengths comprised between 0.300 and 3.00 M, adjusted with NaClO4, as background electrolyte. The investigation was carried out potentiometrically by using a second class Hg/Hg2Pr2 electrode. It was found that the dependence of propionate activity coefficients as a function of ionic strength (I) can be assessed through the following empirical equation: log y(Pr) = -0.185 I-3/2 + 0.104 I-2. Next, simple equations relating stoichiometric protonation constants of several monocarboxylates and formation constants associated with 1:1 complexes involving some bivalent cations and selected monocarboxylates, in aqueous solution, at 25 degrees C, as a function of ionic strength were derived, allowing the interconversion of parameters from one ionic strength to another, up to I = 3.00 M. In addition, thermodynamic formation constants as well as parameters associated with activity coefficients of the complex species in the equilibria are estimated. The body of results shows that the proposed calculation procedure is very consistent with critically selected experimental data.

Temperature and concentration dependence of heat capacity of model aqueous solutions

Heat capacities of binary aqueous solutions of different concentrations of sucrose, glucose, fructose, citric acid, malic acid, and inorganic salts were measured with a differential scanning calorimeter in the temperature range from 5degreesC to 65degreesC. Heat capacity increased with increasing water content and increasing temperature. At low concentrations, heat capacity approached that of pure water, with a less pronounced effect of temperature, and similar abnormal behavior of pure water with a minimum around 30degreesC-40degreesC. Literature data, when available agreed relatively well with experimental values. A correction factor, based on the assumption of chemical equilibrium between liquid and gas phase in the Differential Scanning Calorimeter, was proposed to correct for the water evaporation due to temperature rise. Experimental data were fitted to predictive models. Excess molar heat capacity was calculated using the Redlich-Kister equation to represent the deviation from the additive ideal model.

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.

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.

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.

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.

On stability of differential equations with piecewise constant argument using dichotomic maps

This paper deals with the study of the basic theory of existence, uniqueness and continuation of solutions of di®erential equations with piecewise constant argument. Results about asymptotic stability of the equation x(t) =-bx(t) + f(x([t])) with argu- ment [t], where [t] designates the greatest integer function, are established by means of dichotomic maps. Other example is given to illustrate the application of the method. Copyright © 2011 Watam Press.

Pluronics F-127/L-81 Binary Hydrogels as Drug-Delivery Systems: Influence of Physicochemical Aspects on Release Kinetics and Cytotoxicity

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