Regularity Theory and Superalgebraic Solvers for Wire Antenna Problems

We consider the problem of evaluating the current distribution $J(z)$ that is induced on a straight wire antenna by a time-harmonic incident electromagnetic field. The scope of this paper is twofold. One of its main contributions is a regularity proof for a straight wire occupying the interval $[-1,1]$. In particular, for a smooth time-harmonic incident field this theorem implies that $J(z) = I(z)/\sqrt{1-z^2}$, where $I(z)$ is an infinitely differentiable function—the previous state of the art in this regard placed $I$ in the Sobolev space $W^{1,p}$, $p>1$. The second focus of this work is on numerics: we present three superalgebraically convergent algorithms for the solution of wire problems, two based on Hallén's integral equation and one based on the Pocklington integrodifferential equation. Both our proof and our algorithms are based on two main elements: (1) a new decomposition of the kernel of the form $G(z) = F_1(z) \ln\! |z| + F_2(z)$, where $F_1(z)$ and $F_2(z)$ are analytic functions on the real line; and (2) removal of the end-point square root singularities by means of a coordinate transformation. The Hallén- and Pocklington-based algorithms we propose converge superalgebraically: faster than $\mathcal{O}(N^{-m})$ and $\mathcal{O}(M^{-m})$ for any positive integer $m$, where $N$ and $M$ are the numbers of unknowns and the number of integration points required for construction of the discretized operator, respectively. In previous studies, at most the leading-order contribution to the logarithmic singular term was extracted from the kernel and treated analytically, the higher-order singular derivatives were left untreated, and the resulting integration methods for the kernel exhibit $\mathcal{O}(M^{-3})$ convergence at best. A rather comprehensive set of tests we consider shows that, in many cases, to achieve a given accuracy, the numbers $N$ of unknowns required by our codes are up to a factor of five times smaller than those required by the best solvers previously available; the required number $M$ of integration points, in turn, can be several orders of magnitude smaller than those required in previous methods. In particular, four-digit solutions were found in computational times of the order of four seconds and, in most cases, of the order of a fraction of a second on a contemporary personal computer; much higher accuracies result in very small additional computing times

Microwave ISM Emission Observed by WMAP

We investigate the nature of the diffuse Galactic emission in the Wilkinson Microwave Anisotropy Probe (WMAP) temperature anisotropy data. Substantial dust-correlated emission is observed at all WMAP frequencies, far exceeding the expected thermal dust emission in the lowest frequency channels (23, 33, 41 GHz). The WMAP team (Bennett et al.) interpret this emission as dust-correlated synchrotron radiation, attributing the correlation to the natural association of relativistic electrons produced by SNae with massive star formation in dusty clouds, and deriving an upper limit of 5% on the contribution of Draine & Lazarian spinning dust at K-band (23 GHz). We pursue an alternative interpretation that much, perhaps most, of the dust-correlated emission at these frequencies is indeed spinning dust, and explore the spectral dependence on environment by considering a few specific objects as well as the full sky average. Models similar to Draine & Lazarian spinning dust provide a good fit to the full-sky data. The full-sky fit also requires a significant component with free-free spectrum uncorrelated with \Halpha, possibly hot (~million K) gas within 30 degrees of the Galactic center.Comment: ApJ in press (accepted 5 Dec 2003), version 2: corrected typos and added references. 23 pages, 5 figures, 2 tables. Free-free haze map is available at http://skymaps.inf

Microwave ISM Emission in the Green Bank Galactic Plane Survey: Evidence for Spinning Dust

We observe significant dust-correlated emission outside of H II regions in the Green Bank Galactic Plane Survey (-4 < b < 4 degrees) at 8.35 and 14.35 GHz. The rising spectral slope rules out synchrotron and free-free emission as majority constituents at 14 GHz, and the amplitude is at least 500 times higher than expected thermal dust emission. When combined with the Rhodes (2.326 GHz), and WMAP (23-94 GHz) data it is possible to fit dust-correlated emission at 2.3-94 GHz with only soft synchrotron, free-free, thermal dust, and an additional dust-correlated component similar to Draine & Lazarian spinning dust. The rising component generally dominates free-free and synchrotron for \nu >~ 14 GHz and is overwhelmed by thermal dust at \nu > 60 GHz. The current data fulfill most of the criteria laid out by Finkbeiner et al. (2002) for detection of spinning dust.Comment: ApJ in press. 26 pages, 11 figures, figures jpeg compressed to save spac

Accounting for decarbonisation and reducing capital at risk in the S&P500

This document is the Accepted Manuscript version of the following article: Colin Haslam, Nick Tsitsianis, Glen Lehman, Tord Andersson, and John Malamatenios, ‘Accounting for decarbonisation and reducing capital at risk in the S&P500’, Accounting Forum, Vol. 42 91): 119-129, March 2018. Under embargo until 7 August 2019. The final, definitive version is available online at doi: https://doi.org/10.1016/j.accfor.2018.01.004.This article accounts for carbon emissions in the S&P 500 and explores the extent to which capital is at risk from decarbonising value chains. At a global level it is proving difficult to decouple carbon emissions from GDP growth. Top-down legal and regulatory arrangements envisaged by the Kyoto Protocol are practically redundant given inconsistent political commitment to mitigating global climate change and promoting sustainability. The United Nations Environment Programme (UNEP) and European Commission (EC) are promoting the role of financial markets and financial institutions as drivers of behavioural change mobilising capital allocations to decarbonise corporate activity.Peer reviewe

Galactic emission at 19 GHz

We cross-correlate a 19 GHz full sky Cosmic Microwave Background (CMB) survey with other maps to quantify the foreground contribution. Correlations are detected with the Diffuse Infrared Background Experiment (DIRBE) 240, 140 and 100 micron maps at high latitudes (|b|>30degrees), and marginal correlations are detected with the Haslam 408 MHz and the Reich & Reich 1420 MHz synchrotron maps. The former agree well with extrapolations from higher frequencies probed by the COBE DMR and Saskatoon experiments and are consistent with both free-free and rotating dust grain emission.Comment: 4 pages, with 4 figures included. Accepted for publication in ApJL. Color figure and links at http://www.sns.ias.edu/~angelica/foreground.html#19 or from [email protected]

A radio continuum survey of the southern sky at 1420 MHz. Observations and data reduction

We describe the equipment, observational method and reduction procedure of an absolutely calibrated radio continuum survey of the South Celestial Hemisphere at a frequency of 1420 MHz. These observations cover the area 0h < R.A. < 24h for declinations less than -10 degree. The sensitivity is about 50 mK T_B (full beam brightness) and the angular resolution (HPBW) is 35.4', which matches the existing northern sky survey at the same frequency.Comment: 9 pages with 9 figures, A&A, in pres

Global 21cm signal experiments: a designer's guide

[Abridged] The spatially averaged global spectrum of the redshifted 21cm line has generated much experimental interest, for it is potentially a direct probe of the Epoch of Reionization and the Dark Ages. Since the cosmological signal here has a purely spectral signature, most proposed experiments have little angular sensitivity. This is worrisome because with only spectra, the global 21cm signal can be difficult to distinguish from foregrounds such as Galactic synchrotron radiation, as both are spectrally smooth and the latter is orders of magnitude brighter. We establish a mathematical framework for global signal data analysis in a way that removes foregrounds optimally, complementing spectra with angular information. We explore various experimental design trade-offs, and find that 1) with spectral-only methods, it is impossible to mitigate errors that arise from uncertainties in foreground modeling; 2) foreground contamination can be significantly reduced for experiments with fine angular resolution; 3) most of the statistical significance in a positive detection during the Dark Ages comes from a characteristic high-redshift trough in the 21cm brightness temperature; and 4) Measurement errors decrease more rapidly with integration time for instruments with fine angular resolution. We show that if observations and algorithms are optimized based on these findings, an instrument with a 5 degree beam can achieve highly significant detections (greater than 5-sigma) of even extended (high Delta-z) reionization scenarios after integrating for 500 hrs. This is in contrast to instruments without angular resolution, which cannot detect gradual reionization. Abrupt ionization histories can be detected at the level of 10-100's of sigma. The expected errors are also low during the Dark Ages, with a 25-sigma detection of the expected cosmological signal after only 100 hrs of integration.Comment: 34 pages, 30 figures. Replaced (v2) to match accepted PRD version (minor pedagogical additions to text; methods, results, and conclusions unchanged). Fixed two typos (v3); text, results, conclusions etc. completely unchange

Separation of foregrounds from cosmic microwave background observations with the MAP satellite

Simulated observations of a 10\dg \times 10\dg field by the Microwave Anisotropy Probe (MAP) are analysed in order to separate cosmic microwave background (CMB) emission from foreground contaminants and instrumental noise and thereby determine how accurately the CMB emission can be recovered. The simulations include emission from the CMB, the kinetic and thermal Sunyaev-Zel'dovich (SZ) effects from galaxy clusters, as well as Galactic dust, free-free and synchrotron. We find that, even in the presence of these contaminating foregrounds, the CMB map is reconstructed with an rms accuracy of about 20 $\mu$K per 12.6 arcmin pixel, which represents a substantial improvement as compared to the individual temperature sensitivities of the raw data channels. We also find, for the single 10\dg \times 10\dg field, that the CMB power spectrum is accurately recovered for \ell \la 600.Comment: 7 pages, 7 figures, MNRAS submitte

MHD Turbulence as a Foreground for CMB Studies

Measurements of intensity and polarization of diffuse Galactic synchrotron emission as well as starlight polarization reveal power law spectra of fluctuations. We show that these fluctuations can arise from magnetohydrodynamic (MHD) turbulence in the Galactic disk and halo. To do so we take into account the converging geometry of lines of sight for the observations when the observer is within the turbulent volume. Assuming that the intensity of turbulence changes along the line of sight, we get a reasonable fit to the observed synchrotron data. As for the spectra of polarized starlight we get a good fit to the observations taking into account the fact that the observational sample is biased toward nearby stars.Comment: 10 pages, 6 figures, Astrophyscal J., submitte