Hyperextended Scalar-Tensor Gravity

We study a general Scalar-Tensor Theory with an arbitrary coupling funtion $\omega (\phi )$ but also an arbitrary dependence of the ``gravitational constant'' $G(\phi )$ in the cases in which either one of them, or both, do not admit an analytical inverse, as in the hyperextended inflationary scenario. We present the full set of field equations and study their cosmological behavior. We show that different scalar-tensor theories can be grouped in classes with the same solution for the scalar field.Comment: latex file, To appear in Physical Review

The effect of problem perturbations on nonlinear dynamical systems and their reduced order models

Reduced order models are used extensively in many areas of science and engineering for simulation, design, and control. Reduction techniques for nonlinear dynamical systems produce models that depend strongly on the nominal set of parameters for which the reduction is carried out. In this paper we address the following two questions: 'What is the effect of perturbations in the problem parameters on the output functional of a nonlinear dynamical system?' and 'To what extent does the reduced order model capture this effect?

Isotropization of Bianchi type models and a new FRW solution in Brans-Dicke theory

Using scaled variables we are able to integrate an equation valid for isotropic and anisotropic Bianchi type I, V, IX models in Brans-Dicke (BD) theory. We analyze known and new solutions for these models in relation with the possibility that anisotropic models asymptotically isotropize, and/or possess inflationary properties. In particular, a new solution of curve ($k\neq0$) Friedmann-Robertson-Walker (FRW) cosmologies in Brans-Dicke theory is analyzed.Comment: 15 pages, 4 postscript figures, to appear in Gen. Rel. Grav., special issue dedicated in honour of Prof. H. Dehne

Isotropization of Bianchi-Type Cosmological Solutions in Brans-Dicke Theory

The cosmic, general analitic solutions of the Brans--Dicke Theory for the flat space of homogeneous and isotropic models containing perfect, barotropic, fluids are seen to belong to a wider class of solutions --which includes cosmological models with the open and the closed spaces of the Friedmann--Robertson--Walker metric, as well as solutions for models with homogeneous but anisotropic spaces corresponding to the Bianchi--Type metric clasification-- when all these solutions are expressed in terms of reduced variables. The existence of such a class lies in the fact that the scalar field, $\phi$, times a function of the mean scale factor or ``volume element'', $a^3 = a_1 a_2 a_3$, which depends on time and on the barotropic index of the equation of state used, can be written as a function of a ``cosmic time'' reduced in terms of another function of the mean scale factor depending itself again on the barotropic index but independent of the metrics here employed. This reduction procedure permites one to analyze if explicitly given anisotropic cosmological solutions ``isotropize'' in the course of their time evolution. For if so can happen, it could be claimed that there exists a subclass of solutions that is stable under anisotropic perturbations.Comment: 15 pages, Late

Integration of D-dimensional 2-factor spaces cosmological models by reducing to the generalized Emden-Fowler equation

The D-dimensional cosmological model on the manifold $M = R \times M_{1} \times M_{2}$ describing the evolution of 2 Einsteinian factor spaces, $M_1$ and $M_2$, in the presence of multicomponent perfect fluid source is considered. The barotropic equation of state for mass-energy densities and the pressures of the components is assumed in each space. When the number of the non Ricci-flat factor spaces and the number of the perfect fluid components are both equal to 2, the Einstein equations for the model are reduced to the generalized Emden-Fowler (second-order ordinary differential) equation, which has been recently investigated by Zaitsev and Polyanin within discrete-group analysis. Using the integrable classes of this equation one generates the integrable cosmological models. The corresponding metrics are presented. The method is demonstrated for the special model with Ricci-flat spaces $M_1,M_2$ and the 2-component perfect fluid source.Comment: LaTeX file, no figure

Chaotic Inflationary Universe on Brane

The chaotic inflationary model of the early universe, proposed by Linde is explored in the brane world considering matter described by a minimally coupled self interacting scalar field. We obtain cosmological solutions which admit evolution of a universe either from a singularity or without a singularity. It is found that a very weakly coupled self-interacting scalar field is necessary for a quartic type potential in the brane world model compared to that necessary in general relativity. In the brane world sufficient inflation may be obtained even with an initial scalar field having value less than the Planck scale. It is found that if the universe is kinetic energy dominated to begin with, it transits to an inflationary stage subsequently.Comment: 13 pages, no fig., accepted in Physical Review

Simulations of slip flow on nanobubble-laden surfaces

On microstructured hydrophobic surfaces, geometrical patterns may lead to the appearance of a superhydrophobic state, where gas bubbles at the surface can have a strong impact on the fluid flow along such surfaces. In particular, they can strongly influence a detected slip at the surface. We present two-phase lattice Boltzmann simulations of a flow over structured surfaces with attached gas bubbles and demonstrate how the detected slip depends on the pattern geometry, the bulk pressure, or the shear rate. Since a large slip leads to reduced friction, our results allow to assist in the optimization of microchannel flows for large throughput.Comment: 22 pages, 12 figure

QCD corrections to the forward-backward asymmetries of cc and bb quarks at the Z pole

Measurements of the forward-backward production asymmetry of heavy quarks in Z decays provide a precise determination of \swsqeffl . The asymmetries are sensitive to QCD effects, in particular hard gluon radiation. In this paper QCD corrections for \AFBbb~ and \AFBcc~ are discussed. The interplay between the experimental techniques used to measure the asymmetries and the QCD effects is investigated using simulated events. A procedure to estimate the correction needed for experimental measurements is proposed, and some specific examples are given