Geodesic motion in the neighbourhood of submanifolds embedded in warped product spaces

We study the classical geodesic motions of nonzero rest mass test particles and photons in (3 + 1 + n)- dimensional warped product spaces. An important feature of these spaces is that they allow a natural decoupling between the motions in the (3 + 1)-dimensional spacetime and those in the extra n dimensions. Using this decoupling and employing phase space analysis we investigate the conditions for confinement of particles and photons to the (3 + 1)- spacetime submanifold. In addition to providing information regarding the motion of photons, we also show that these motions are not constrained by the value of the extrinsic curvature. We obtain the general conditions for the confinement of geodesics in the case of pseudo-Riemannian manifolds as well as establishing the conditions for the stability of such confinement. These results also generalise a recent result of the authors concerning the embeddings of hypersurfaces with codimension one.     

Scattering Below Critical Energy for the Radial 4D Yang-Mills Equation and for the 2D Corotational Wave Map System

Given g and f  =  gg′, we consider solutions to the following non linear wave equation :

In‐situ synthesis of transparent and conductive carbon nanotube networks

A method for the production of transparent carbon nanotube networks (CNTNs) over transparent substrates was developed. In this method, CNTNs were grown directly in the target surface by applying the catalyst in specific zones of the substrate through lithographic techniques. The networks can be also transferred from the original substrate to other surfaces. The newly grown carbon nanotubes have a very high aspect ratio (>50000). Thus far, networks with an optical transmittance of 94% at 550 nm and a surface resistivity of 3.6 kΩ/sq have been produced. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Electrochemical impedance spectroscopy and linear polarization applied to evaluation of porosity of phosphate conversion coatings on electrogalvanized steels

In this work, electrochemical impedance spectroscopy and linear polarization are used in determining porosity of zinc phosphates, and of nickel and manganese modified zinc phosphates on electrogalvanized steel. The porosity of the phosphate layers ranges from 0.1% for the manganese-modified hopeite to 8% for hopeite, using the linear polarization and the electrochemical impedance spectroscopy techniques. The porosity values measured using the two techniques were in agreement. All impedance spectra of coated samples showed two steps, with two capacitive arcs and an inductive looping.     

Optical Absorption in Periodic Graphene Superlattices: Perpendicular Applied Magnetic Field and Temperature Effects

A detailed study of the magneto‐optical absorption is presented for graphene superlattices (SLs) subjected to a perpendicular magnetic field. For a given temperature, this quantity exhibits a resonant peak structure whose characteristics depend on the magnetic field regime, circular polarization of light and SL barrier height. For the intermediate field regime, we demonstrated that the resonant peak structure of is directly correlated to the partial joint density of states. Specifically, the latter exhibits van Hove‐like singularities and peaks at energies where takes its maximum values. We also investigated the magnetoabsorption in the weak field regime for SLs exhibiting one and extra Dirac points in the absence of the field. It was found that for SLs with only one Dirac point, the absorption spectra consist of resonant peaks satisfying the same circular polarization dependent selection rule as that for pristine graphene, except for one of them. For SLs with extra Dirac points, the resonant peaks arise from transitions between singlet subbands or between doublet subbands and satisfy a circular polarization and peak intensity dependent selection rule. It was also found that the resonant structure of can be observed experimentally at room temperature in clean SLs.     

Electromagnetic Propagation in a Relativistic Electron Gas at Finite Temperatures

The electromagnetic propagation in a relativistic electron gas at finite temperatures and carrier densities is described. Using quantum electrodynamics at finite temperatures, electric and magnetic responses and general constitutive relations are obtained. Rewriting the propagator for the electromagnetic field in terms of the electric and magnetic responses, the modes that propagate in the gas are identified. As expected, the usual collective excitations are obtained, i.e., a longitudinal electric and two transverse magnetic plasmonic modes. In addition, a purely photonic mode is found, which satisfies the wave equation in vacuum, for which the electron gas is transparent. Dispersion relations for the plasmon modes at zero and finite temperatures are presented and the intervals of frequency and wavelength where both electric and magnetic responses are simultaneously negative are identified, a behavior previously thought not to occur in natural systems. The investigation of the electromagnetic responses of a relativistic electron gas shows that, apart from the usual longitudinal electric plasmon mode and the two transverse magnetic plasmon modes, there is also a pure photonic mode that propagates with the speed of light, as if the medium were transparent. Furthermore, there is a region of frequencies and wavenumbers of the external fields where both the longitudinal electric permittivity and magnetic permeability are simultaneously negative, a property found in artificially constructed metamaterials.     

Analytical characterization of spectral anomalies in polychromatic apertured beams

The power spectrum of polychromatic apertured spherical waves changes strongly in the vicinity of phase singularities. A spectral shift effect is observed and, in some cases, a spectral switch occurs together with a broadening of the power spectrum. Low-order moments of the power spectrum are evaluated in points of the focal volume with spectral anomalies. First-order analytical expressions are proposed for the evaluation of the relative spectral shift and the relative spectral broadening in the transverse focal plane and along the optical axis. The influence of the fractional bandwidth and the selected singularity order is considered.     

On the Massive Antenna Suspension System in the Brazilian Gravitational Wave Detector SCHENBERG

SCHENBERG is a resonant-mass gravitational wave detector built in Brazil. Its spherical antenna, weighting 1.15 t, is connected to the outside world by a suspension system whose main function is to attenuate the external seismic noise. In this work, we report how the system was modeled using finite elements method. The model was validated on experimental data. The simulation showed that the attenuation obtained is of the order of 260 dB, which is sufficient for decreasing the seismic noise below the level of the thermal noise of the detector operating at 50 mK.