C. Criado

Algorithm for normal random numbers

We propose a simple algorithm for generating normally distributed pseudorandom numbers. The algorithm simulates N molecules that exchange energy among themselves following a simple stochastic rule. We prove that the system is ergodic, and that a Maxwell-like distribution that may be used as a source of normally distributed random deviates follows in the N-->infinity limit. The algorithm passes various performance tests, including Monte Carlo simulation of a finite two-dimensional Ising model using Wolffs algorithm. It only requires four simple lines of computer code, and is approximately ten times faster than the Box-Muller algorithm.

Electrical conductivity of alumina-pillared α-tin phosphate

Abstract ac conductivity of Al 2 O 3 -pillared tin(IV) phosphate and the Li + exchanged sample have been measured by an impedance method. The material Li + exchanged pillared α-tin phosphate is dual, with two types of charge carriers, H + from zeolite water and Li + . Conductivity is related to zeolitic water at low temperature, whereas at T reversible in the interval 250–500°C.

Lithium insertion in vanadyl phosphate

Abstract The reaction between LiNO 3 and VOPO 4 ·2H 2 O in acetone medium takes place, besides a redox process, by an acid-basic reaction. The material obtained, Li 1.6 VOPO 4 ·H 2 O, is a non-homogeneous solid, which is converted to a crystalline solid if annealed at 450°C. The existence of lithium ion within the intracrystalline spaces of lithium intercalate as well as the reduction of partial V(v) to V(iv) leads to a mixed ionic-electronic conductor. This fact is confirmed by the impedance spectroscopy study.

Optical properties of conics: a method for obtaining reflecting and focusing profiles

An original method is proposed for determining suitable profiles for two different problems: to produce a given family of wave fronts from a single point source after reflecting on it, and to focus the given wave front on a fixed point. The method uses the optical properties of conics to obtain both reflecting and focusing profiles as the envelope of a specific family of conic sections. It also offers a procedure for determining the caustic of the wave front.

Generalized antiorthotomics and their singularities

In this paper we construct, for a given wavefront and a source point, an uniparametric family of mirrors with the characteristic property of producing the given wavefront, after reflecting on each mirror, from the source point. This family is made up of the envelopes of certain families of hyperquadrics of revolution, and includes the antiorthotomic of the wavefront with respect to the source point. We prove that the singularities of these generalized antiorthotomics sweep out the caustic of the wavefront. We also give a method to determine the generalized antiorthotomics starting from the associated caustic.

A link between the bounds on relativistic velocities and areas of hyperbolic triangles

In this paper we show the mathematical equivalence between two well-known facts: the existence of an upper bound for the area in Lobachevskian geometry and the existence of a limit for relativistic velocities. The key point is that the space of relativistic velocities can be interpreted as a Lobachevskian space.

Hopping conductivity in lithium-exchanged pillared layered tin phosphate materials

Abstract Hopping conductivity in lithium-exchanged alumina pillared layered tin phosphate materials is analysed on the basis of the coupling model. The electrical conductivity is correlated with the lithium content and the basal distance of the pillared materials. Characteristic parameters such as dc and ac activation energies, and the attempt and coupling frequencies show a marked dependence on the basal distance and the lithium content. The migration entropy of the hopping process is greater for samples with higher Li contents and lower basal distances. The conductivity time correlation function has a stretched exponential (or KWW) shape, in which the coupling parameter decreases to a minimum value for the sample with the highest basal distance.

A method to construct refracting profiles

We propose an original method for determining suitable refracting profiles between two media to solve two related problems: to produce a given wavefront from a single point source after refraction at the refracting profile, and to focus a given wavefront at a fixed point. These profiles are obtained as envelopes of specific families of Cartesian ovals. We study the singularities of these profiles and give a method to construct them from the data of the associated caustic.

Reflecting profiles and generalized holodiagrams

Summary The concepts of reflecting profiles and that of holodiagrams are examined and links between them are found so that the classical Abramsons Holodiagram idea can be generalized. The broader concept of Generalized Holodiagrams encompasses then the possibility of using different wave front shapes, not only spherical. Many of the nice properties of the classical holodiagram are shared by its generalized versions.

Ionic conduction in sepiolite

Abstract The solid state reaction between sepiolite and LiCl at 200°C gives intersalation compounds. The lithium composites obtained, x LiCl-SEP ( x =2, 4, 6 and 8), keep the sepiolite framework but the presence of the halide in its channels causes a gradual breakdown with the increase of temperature. At low temperatures, the polarizing character of Li + induces protonic conductivity in the zeolitic water system. The Cl − and Li + ions move through the channels above 170°C.