Some Further Properties of the Accelerated Kerr-Schild Metrics

We extend the previously found accelerated Kerr-Schild metrics for Einstein-Maxwell-null dust and Einstein-Born-Infeld-null dust equations to the cases including the cosmological constant. This way we obtain the generalization of the charged de Sitter metrics in static space-times. We also give a generalization of the zero acceleration limit of our previous Einstein-Maxwell and Einstein-Born-Infeld solutions.     

Effective Values of Variable Components of the Refractive Index upon Nonlinear Recording of Phase Holograms

The diffraction of a plane wave incident on a thick hologram at the first and second Bragg angles in the process of nonlinear recording is analyzed using the coupled-wave equations. It is shown that, in this case, the two-wave approximation with the use of effective modulation amplitudes of the refractive index, n _1ef and n _2ef, can be applied. Analytical dependences of n _1ef and n _2ef on the modulation amplitudes of the refractive index n ₁ and n ₂ at the fundamental and doubled spatial frequencies are obtained and the criteria of their applicability are determined. The dependences found are used to calculate the parameters of gratings recorded in a photopolymeric material.     

An alternative approach for non-linear optimal control problems based on the method of moments

We propose an alternative method for computing effectively the solution of non-linear, fixed-terminal-time, optimal control problems when they are given in Lagrange, Bolza or Mayer forms. This method works well when the nonlinearities in the control variable can be expressed as polynomials. The essential of this proposal is the transformation of a non-linear, non-convex optimal control problem into an equivalent optimal control problem with linear and convex structure. The method is based on global optimization of polynomials by the method of moments. With this method we can determine either the existence or lacking of minimizers. In addition, we can calculate generalized solutions when the original problem lacks of minimizers. We also present the numerical schemes to solve several examples arising in science and technology.     

Scaling probability, key to the equilibrium statistical volume distribution in foams

The equilibrium statistical volume distribution in foams, which has been previously demonstrated to be the so-called log-normal, is accounted on probability grounds by a scaling law on the bubble's volume time-evolution. This law states that the conditional probability for a given bubble to have the volume v(t + Δt), he assumption that it was v(t), to depend solely on the relationship v(t + Δt)/v(t), and in particular, to be independent of the time t. The theoretical results, however, allow to go further. Indeed, since the time dependece of its parameters (expectation and variance) are given functions of time, only two parameters are necessary to describe completely the foam.     

Shape preservation regions for six-dimensional spaces

We analyze the critical length for design purposes of six-dimensional spaces invariant under translations and reflections containing the functions 1, cos t and sin t. These spaces also contain the first degree polynomials as well as trigonometric and/or hyperbolic functions. We identify the spaces whose critical length for design purposes is greater than 2π and find its maximum 4π. By a change of variables, two biparametric families of spaces arise. We call shape preservation region to the set of admissible parameters in order that the space has shape preserving representations for curves. We describe the shape preserving regions for both families. To our friend Mariano Gasca on occasion of his 60th birthday Research partially supported by the Spanish Research Grant MTM2006-03388, by Gobierno de Aragón and Fondo Social Europeo.     

Elastic instability of the nano-structured state as an intrinsic probe to study the early formation stages of sol–gel derived (Pb<Subscript>1-x</Subscript>Ca<Subscript>x</Subscript>)TiO<Subscript>3</Subscript> thin films

A novel method to investigate the early formation stages of polycrystalline (Pb_1-xCa_x)TiO₃ (PCT) perovskite films by means of traditional Brillouin and micro-Brillouin spectroscopy (BS, mBS) is described in the present work. The films were prepared by chemical solution deposition (CSD) onto oxidized (100)Si substrates and treated at temperatures between 350–650 °C by rapid thermal processing (RTP). The elastic instability observed by Brillouin spectroscopy at the nano-structured state of the PCT films was used here to determine their crystallization temperatures. Coexistence of different nanocrystalline phases (e.g., pyrochlore, perovskite) in the films could also be detected by this technique. The reliability of these results is demonstrated by complementary information obtained by X-ray diffraction (XRD) and scanning force microscopy (SFM). The effects of the annealing temperature and of the Ca²⁺ content on the crystallization process of these films are also discussed. PACS 78.35.+c; 77.84.-s; 61.82.Rx