J. A. del Río

Tailoring the photonic band gap of a porous silicon dielectric mirror

A systematic method to fabricate porous-silicon one-dimensional photonic crystals has been engineered to have a photonic bandwidth up to 2000 nm. The observation of the tailorability of the photonic band gap (PBG) underscores the requirement of the large refractive index contrast for making broad PBG structures. In this letter, we present the fabrication and characteristics of such structures that may be promising structures for a large variety of applications.

Maxwell's equations in two-phase systems I : Local electrodynamic equilibrium

The method of volume averaging is used to examine the form of Maxwells equations in two-phase systems. The volume averaged equations for the individual phases are developed and used to identify the condition of local electrodynamic equilibrium. When this condition is satisfied, the electric and magnetic fields in the two phases are close enough so that single equations can be used to describe these fields. The one-equation model for the electric and magnetic fields is obtained without the need for closure problems; however, the constraints associated with the principle of local electrodynamic equilibrium are very severe and are not satisfied for many processes.

Influence of surface coverage on the effective optical properties of porous silicon modeled as a Si-wire array

The effective dielectric function, effective absorption coefficient and effective refractive index for a model of porous silicon (PS) are calculated using the volume and surface averaging method. The model consists of periodic Si wires with different surface coverages. This approach allows to obtain analytical results within certain approximations. The method uses experimental parameters to characterize the bulk and the surface. We choose the bulk c-Si, and cover it with three different possible surface skins: siloxanes, a-Si:H and SiO2. The results are compared with PS experimental data and other theoretical approaches for silicon wires. We obtain good agreement for certain coatings. Our results emphasize the important role of surface coatings in the effective response of porous silicon.

Flow of Maxwell fluids in porous media

In this paper we analyze the flow of a Maxwell fluid in a rigid porous medium using the method of volume averaging. We first present the local volume averaged momentum equation which contains Darcy-scale elastic effects and undetermined integrals of the spatial deviations of the pressure and velocity. A closure problem is developed in order to determine the spatial deviations and thus obtain a closed form of the momentum equation that contains a time-dependent permeability tensor. To gain some insight into the effects of elasticity on the dynamics of flow in porous media, the entire problem is transformed to the frequency domain through a temporal Fourier transform. This leads to a dynamic generalization of Darcys law. Analytical results are provided for the case in which the porous medium is modeled as a bundle of capillary tubes, and a scheme is presented to solve the transformed closure problem for a general microstructure.

Formula for the conductivity of a two-component material based on the reciprocity theorem

In this communication we obtain an approximate formula for the effective electrical conductivity for a two-component two-dimensional material. The basis of the formula is Kellers reciprocity theorem. The derived formula satisfies the reciprocity condition at all values of the concentration, and the predictions of the formula agree well with data on the electrical conductivity of several two-component materials.

NEW KIND OF PHASE SEPARATION IN A CA TRAFFIC MODEL WITH ANTICIPATION

A cellular automaton model of traffic flow taking into account velocity anticipation is introduced. The strength of anticipation can be varied to describe different driving schemes. We find a new phase separation into a free-flow regime and a so-called v-platoon in an intermediate density regime. In a v-platoon all cars move with velocity v and have vanishing headway. The velocity v of a platoon only depends on the strength of anticipation. At high densities, a congested state characterized by the coexistence of a 0-platoon with several v-platoons is reached. The results are not only relevant for automated highway systems, but also help to elucidate the effects of anticipation that play an essential role in realistic traffic models. From a physics point of view the model is interesting because it exhibits phase separation with a condensed phase in which particles move coherently with finite velocity coexisting with either a non-condensed (free-flow) phase or another condensed phase that is non-moving.

Perfect light transmission in Fibonacci arrays of dielectric multilayers

In this paper we study the propagation of light through an asymmetric array of dielectric multilayers built by joining two porous silicon substructures in a Fibonacci sequence. Each Fibonacci substructure follows the well-known recursive rule but in the second substructure dielectric layers A and B are exchanged. Even without mirror symmetry, this array gives rise to multiple transparent states, which follow the scaling properties and self-similar spectra of a single Fibonacci multilayer. We apply the transfer matrix formalism to calculate the transmittance. By setting the transfer matrix of the array equal to ± I, the identity matrix, frequencies of perfect light transmission are reproduced in our theoretical calculations. Although the light absorption of porous silicon in the optical range limits our experimental study to low Fibonacci generations, the positions of the transparent states are well predicted by the above-mentioned condition. We conclude that mirror symmetry in arrays of Fibonacci multilayers is sufficient but not necessary to generate multiple transparent states, opening broader applications of quasiperiodic systems as filters and microcavities of multiple frequencies.

Electrohydrodynamics in Porous Media

In this work we develop the volume averaged form of the frequency-dependent governing equations for electrohydrodynamics in a saturated porous medium. The concept of local electrical equilibrium is identified, and when this condition is valid we obtain a one-equation model describing the coupled transport of momentum and electric charge. When local electrical equilibrium is not valid, separate forms of Maxwells equations must be developed for both the fluid and solid phases.

Maxwell's Equations in Two-Phase Systems II: Two-Equation Model *

The method of volume averaging is used to derive the two-equation model for Maxwells equations in a two-phase system. The analysis provides a set of macroscopic transport equations for the electric and magnetic fields that are completely coupled in terms of the closure problem. When the closure problem is quasi-steady, a formal solution is obtained and estimates are developed for the differences between the averaged fields in the individual phases. These estimates lead to constraints for the condition of local electrodynamic equilibrium.

Experimental observation of dramatic differences in the dynamic response of Newtonian and Maxwellian fluids.

An experimental study of the dynamic response of a Newtonian fluid and a Maxwellian fluid under an oscillating pressure gradient is presented. Laser Doppler anemometry is used in order to determine the velocity of the fluid inside a cylindrical tube. In the case of the Newtonian fluid, the dissipative nature is observed. In the dynamic response of the Maxwellian fluid an enhancement at the frequencies predicted by theory is observed.