The exact evaluation of the corner-to-corner resistance of an M x N resistor network: Asymptotic expansion

We study the corner-to-corner resistance of an M x N resistor network with resistors r and s in the two spatial directions, and obtain an asymptotic expansion of its exact expression for large M and N. For M = N, r = s =1, our result is R_{NxN} = (4/pi) log N + 0.077318 + 0.266070/N^2 - 0.534779/N^4 + O(1/N^6).Comment: 12 pages, re-arranged section

Indications for grain growth and mass decrease in cold dust disks around Classical T Tauri stars in the MBM 12 young association

We report detection of continuum emission at 850 and 450 micron from disks around four Classical T Tauri stars in the MBM 12 (L1457) young association. Using a simple model we infer masses of 0.0014-0.012 M_sun for the disk of LkHa 263 ABC, 0.005-0.021 M_sun for S18 ABab, 0.03-0.18 M_sun for LkHa 264 A, and 0.023-0.23 M_sun for LkHa 262. The disk mass found for LkHa 263 ABC is consistent with the 0.0018 M_sun inferred from the scattered light image of the edge-on disk around component C. Comparison to earlier 13CO line observations indicates CO depletion by up to a factor 300 with respect to dark-cloud values. The spectral energy distributions (SED) suggest grain growth, possibly to sizes of a few hundred micron, but our spatially unresolved data cannot rule out opacity as an explanation for the SED shape. Our observations show that these T Tauri stars are still surrounded by significant reservoirs of cold material at an age of 1-5 Myr. We conclude that the observed differences in disk mass are likely explained by binary separation affecting the initial value. With available accretion rate estimates we find that our data are consistent with theoretical expectations for viscously evolving disks having decreased their masses by ~30%.Comment: 15 pages, 3 figures, uses aastex. ApJ Letters, in pres

On the degrees of freedom of a semi-Riemannian metric

A semi-Riemannian metric in a n-manifold has n(n-1)/2 degrees of freedom, i.e. as many as the number of components of a differential 2-form. We prove that any semi-Riemannian metric can be obtained as a deformation of a constant curvature metric, this deformation being parametrized by a 2-for

A Millimeter-Wave Galactic Plane Survey With The BICEP Polarimeter

In addition to its potential to probe the Inflationary cosmological paradigm, millimeter-wave polarimetry is a powerful tool for studying the Milky Way galaxy's composition and magnetic field structure. Towards this end, presented here are Stokes I, Q, and U maps of the Galactic plane from the millimeter-wave polarimeter BICEP covering the Galactic longitude range 260 - 340 degrees in three atmospheric transmission windows centered on 100, 150, and 220 GHz. The maps sample an optical depth 1 < AV < 30, and are consistent with previous characterizations of the Galactic millimeter-wave frequency spectrum and the large-scale magnetic field structure permeating the interstellar medium. Polarized emission is detected over the entire region within two degrees of the Galactic plane and indicates that the large-scale magnetic field is oriented parallel to the plane of the Galaxy. An observed trend of decreasing polarization fraction with increasing total intensity rules out the simplest model of a constant Galactic magnetic field throughout the Galaxy. Including WMAP data in the analysis, the degree-scale frequency spectrum of Galactic polarization fraction is plotted between 23 and 220 GHz for the first time. A generally increasing trend of polarization fraction with electromagnetic frequency is found, which varies from 0.5%-1.5%at frequencies below 50 GHz to 2.5%-3.5%above 90 GHz. The BICEP and WMAP data are fit to a two-component (synchrotron and dust) model showing that the higher frequency BICEP data are necessary to tightly constrain the amplitude and spectral index of Galactic dust. Furthermore, the dust amplitude predicted by this two-component fit is consistent with model predictions of dust emission in the BICEP bands

On the Antenna Beam Shape Reconstruction Using Planet Transit

The calibration of the in-flight antenna beam shape and possible beamdegradation is one of the most crucial tasks for the upcoming Planck mission. We examine several effects which could significantly influence the in-flight main beam calibration using planet transit: the problems of the variability of the Jupiter's flux, the antenna temperature and passing of the planets through the main beam. We estimate these effects on the antenna beam shape calibration and calculate the limits on the main beam and far sidelobe measurements, using observations of Jupiter and Saturn. We also discuss possible effects of degradation of the mirror surfaces and specify corresponding parameters which can help us to determine these effects.Comment: 10 pages, 8 figure

The Vega Debris Disk -- A Surprise from Spitzer

We present high spatial resolution mid- and far-infrared images of the Vega debris disk obtained with the Multiband Imaging Photometer for Spitzer (MIPS). The disk is well resolved and its angular size is much larger than found previously. The radius of the disk is at least 43" (330 AU), 70"(543 AU), and 105" (815 AU) in extent at 24, 70 and 160 um, respectively. The disk images are circular, smooth and without clumpiness at all three wavelengths. The radial surface brightness profiles imply an inner boundary at a radius of 11"+/-2" (86 AU). Assuming an amalgam of amorphous silicate and carbonaceous grains, the disk can be modeled as an axially symmetric and geometrically thin disk, viewed face-on, with the surface particle number density following an r^-1 power law. The disk radiometric properties are consistent with a range of models using grains of sizes ~1 to ~50 um. We find that a ring, containing grains larger than 180 um and at radii of 86-200 AU from the star, can reproduce the observed 850 um flux, while its emission does not violate the observed MIPS profiles. This ring could be associated with a population of larger asteroidal bodies analogous to our own Kuiper Belt. Cascades of collisions starting with encounters amongthese large bodies in the ring produce the small debris that is blown outward by radiation pressure to much larger distances where we detect its thermal emission. The dust production rate is >~10^15 g/s based on the MIPS results. This rate would require a very massive asteroidal reservoir for the dust to be produced in a steady state throughout Vega's life. Instead, we suggest that the disk we imaged is ephemeral and that we are witnessing the aftermath of a large and relatively recent collisional event, and subsequent collisional cascade.Comment: 13 pages, 17 figures, accepted for publication in ApJ. (Figures 2, 3a, 3b and 4 have been degraded to lower resolutions.

Whirling Hexagons and Defect Chaos in Hexagonal Non-Boussinesq Convection

We study hexagon patterns in non-Boussinesq convection of a thin rotating layer of water. For realistic parameters and boundary conditions we identify various linear instabilities of the pattern. We focus on the dynamics arising from an oscillatory side-band instability that leads to a spatially disordered chaotic state characterized by oscillating (whirling) hexagons. Using triangulation we obtain the distribution functions for the number of pentagonal and heptagonal convection cells. In contrast to the results found for defect chaos in the complex Ginzburg-Landau equation and in inclined-layer convection, the distribution functions can show deviations from a squared Poisson distribution that suggest non-trivial correlations between the defects.Comment: 4 mpg-movies are available at http://www.esam.northwestern.edu/~riecke/lit/lit.html submitted to New J. Physic

Inelastic neutron scattering study of magnetic excitations in Sr2_2RuO4_4

Magnetic excitations in \srruo ~ have been studied by inelastic neutron scattering. The magnetic fluctuations are dominated by incommensurate peaks related to the Fermi surface nesting of the quasi-one-dimensional $d_{xz}$- and $d_{yz}$-bands. The shape of the incommensurate signal agrees well with RPA calculations. At the incommensurate {\bf Q}-positions the energy spectrum considerably softens upon cooling pointing to a close magnetic instability : \srruo ~does not exhibit quantum criticality but is very close to it. $\omega / T$-scaling may be fitted to the data for temperatures above 30 K. Below the superconducting transition, the magnetic response at the nesting signal is not found to change in the energy range down to 0.4meV.Comment: 11 pages 9 figure

Indications of coherence-incoherence crossover in layered transport

For many layered metals the temperature dependence of the interlayer resistance has a different behavior than the intralayer resistance. In order to better understand interlayer transport we consider a concrete model which exhibits this behavior. A small polaron model is used to illustrate how the interlayer transport is related to the coherence of quasi-particles within the layers. Explicit results are given for the electron spectral function, interlayer optical conductivity and the interlayer magnetoresistance. All these quantities have two contributions: one coherent (dominant at low temperatures) and one incoherent (dominant at high temperatures).Comment: 6 pages, 4 figures, REVTEX

Interplane magnetic coupling effects in the multilattice compound Y_2Ba_4Cu_7O_{15}

We investigate the interplane magnetic coupling of the multilattice compound Y_2Ba_4Cu_7O_{15} by means of a bilayer Hubbard model with inequivalent planes. We evaluate the spin response, effective interaction and the intra- and interplane spin-spin relaxation times within the fluctuation exchange approximation. We show that strong in-plane antiferromagnetic fluctuations are responsible for a magnetic coupling between the planes, which in turns leads to a tendency of the fluctuation in the two planes to equalize. This equalization effect grows whit increasing in-plane antiferromagnetic fluctuations, i. e., with decreasing temperature and decreasing doping, while it is completely absent when the in-layer correlation length becomes of the order of one lattice spacing. Our results provide a good qualitative description of NMR and NQR experiments in Y_2Ba_4Cu_7O_{15}.Comment: Final version, to appear. in Phys. Rev. B (Rapid Communications), sched. Jan. 9