Convergence analysis of the scaled boundary finite element method for the Laplace equation

The scaled boundary finite element method (SBFEM) is a relatively recent boundary element method that allows the approximation of solutions to PDEs without the need of a fundamental solution. A theoretical framework for the convergence analysis of SBFEM is proposed here. This is achieved by defining a space of semi-discrete functions and constructing an interpolation operator onto this space. We prove error estimates for this interpolation operator and show that optimal convergence to the solution can be obtained in SBFEM. These theoretical results are backed by a numerical example.Comment: 15 pages, 3 figure

Clustering and light profiles of galaxies in the environment of 20 Ultra Steep Spectrum Radio sources

We have analyzed galaxy properties in the neighborhood of 20 Ultra-Steep Spectrum Radio sources (USS) taken from the WISH catalog of De Breuck et al. (2002). Galaxies in these USS fields were identified in deep observations that were carried out in the K'-band using the OSIRIS imager at the CTIO 4m telescope. We find a statistically significant signal of clustering around our sample of USS. The angular extension of the detected USS-galaxy clustering is theta_c~20" corresponding to a spatial scale ~120 h^{-1}kpc, assuming the sources are at z~1 in a Omega_m=0.3, Omega_{\Lambda}=0.7 model universe. These results are in agreement with those obtained by Best (2000) for radio galaxy-galaxy correlation, and Best et al. (2003) for radio-loud AGN-galaxy correlation. We have also analyzed the light distribution of the galaxies by fitting Sersic's law profiles. Our results show no significant dependence of the galaxy shape parameters on the projected distance to the USS.Comment: Accepted for its publication in Astronomical Journal, 9 figure

Phase lags of quasi-periodic oscillations across source states in the low-mass X-ray binary 4U 1636-53

While there are many dynamical mechanisms and models that try to explain the origin and phenomenology of the quasi-periodic oscillations (QPOs) seen in the X-ray light curves of low-mass X-ray binaries, few of them address how the radiative processes occurring in these extreme environments give rise to the rich set of variability features actually observed in these light curves. A step towards this end comes from the study of the energy and frequency dependence of the phase lags of these QPOs. Here we used a methodology that allowed us to study, for the first time, the dependence of the phase lags of all QPOs in the range of 1 Hz to 1300 Hz detected in the low-mass X-ray binary 4U 1636-53 upon energy and frequency as the source changes its states as it moves through the colour-colour diagram. Our results suggest that within the context of models of up-scattering Comptonization, the phase lags dependencies upon frequency and energy can be used to extract size scales and physical conditions of the medium that produces the lags

Quantum work for sudden quenches in Gaussian random Hamiltonians

In the context of nonequilibrium quantum thermodynamics, variables like work behave stochastically. A particular definition of the work probability density function (pdf) for coherent quantum processes allows the verification of the quantum version of the celebrated fluctuation theorems, due to Jarzynski and Crooks, that apply when the system is driven away from an initial equilibrium thermal state. Such a particular pdf depends basically on the details of the initial and final Hamiltonians, on the temperature of the initial thermal state, and on how some external parameter is changed during the coherent process. Using random matrix theory we derive a simple analytic expression that describes the general behavior of the work characteristic function G(u), associated with this particular work pdf for sudden quenches, valid for all the traditional Gaussian ensembles of Hamiltonians matrices. This formula well describes the general behavior of G(u) calculated from single draws of the initial and final Hamiltonians in all ranges of temperatures.Fil: Arrais, Eric G.. Universidade Federal do Rio de Janeiro; BrasilFil: Wisniacki, Diego Ariel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Céleri, Lucas C.. Universidade Federal de Goiás; BrasilFil: De Almeida, Norton G.. Universidade Federal de Goiás; BrasilFil: Roncaglia, Augusto Jose. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Toscano, Fabricio. Universidade Federal do Rio de Janeiro; Brasi

Photometric observations of Southern Abell Cluster Redshifts Survey Clusters: Structure of galaxies in the inner region of clusters of galaxies

We analyze photometric properties of 1384 cluster galaxies as a function of the normalized distance to cluster center. These galaxies were selected in the central region ($r/r_{200} \leq$ 0.8) of 14 southern Abell clusters chosen from the Southern Abell Cluster Redshifts Survey (SARS). For 507 of these galaxies we also obtained their luminosity profiles. We have studied the morphology-clustercentric distance relation on the basis of the shape parameter $n$ of the S\'ersic's law. We also have analyzed the presence of a possible segregation in magnitude for both, the galaxy total luminosity and that of their components (i.e. the bulge and the disk). Results show a marginal ($2\sigma$ level) decrease of the total luminosity as a function of normalized radius. However, when bulges are analyzed separately, a significant luminosity segregation is found ($3\sigma$ and $2\sigma$ for galaxies in projection and member galaxies respectively). The fraction of bulges brighter than $M_B \leq -22$ is three times larger in the core of clusters than in the outer region. Our analysis of the disk component suggests that disks are, on average, less luminous in the cluster core than at $r/r_{200} \sim 0.8$. In addition, we found that the magnitude-size relation as a function of $r/r_{200}$ indicates (at $2\sigma$ level) that disks are smaller and centrally brighter in the core of clusters. However, the Kormendy relation (the bulge magnitude-size relation) appears to be independent of environment.Comment: To appear in the A

Third-order nonlinear optical properties of bismuth-borate glasses measured by conventional and thermally managed eclipse Z scan

Third-order nonlinearity one order of magnitude larger than silica is measured in bismuth-borate glasses presenting a fast response (<200 fs). The results for the sign and magnitude of the nonlinearity were obtained using a combination of the eclipse Z scan with thermal nonlinearity managed Z scan, whereas the Kerr shutter technique was employed to obtain the electronic time response of the nonlinearity, all performed with 76 MHz repetition rate 150 fs pulses at 800 nm. Conventional Z scans in the picosecond regime at 532 and 1064 nm were also independently performed, yielding the values of the third-order nonlinear susceptibilities at those wavelengths. The results obtained for the femtosecond response, enhanced third-order nonlinearity of this glass (with respect to silica), place this glass system as an important tool in the development of photonics devices. Electro-optical modulators, optical switches, and frequency converters are some of the applications using second-order nonlinear properties of the Bi-glass based on the rectification model