Coboson formalism for Cooper pairs used to derive Richardson's equations

We propose a many-body formalism for Cooper pairs which has similarities to the one we recently developed for composite boson excitons (coboson in short). Its Shiva diagram representation evidences that $N$ Cooper pairs differ from $N$ single pairs through electron exchange only: no direct coupling exists due to the very peculiar form of the BCS potential. As a first application, we here use this formalism to derive Richardson's equations for the exact eigenstates of $N$ Cooper pairs. This gives hints on why the $N(N-1)$ dependence of the $N$-pair ground state energy we recently obtained by solving Richardson's equations analytically in the low density limit, stays valid up to the dense regime, no higher order dependence exists even under large overlap, a surprising result hard to accept at first. We also briefly question the BCS wave function ansatz compared to Richardson's exact form, in the light of our understanding of coboson many-body effects

A fast and robust numerical scheme for solving models of charge carrier transport and ion vacancy motion in perovskite solar cells

Drift-diffusion models that account for the motion of both electronic and ionic charges are important tools for explaining the hysteretic behaviour and guiding the development of metal halide perovskite solar cells. Furnishing numerical solutions to such models for realistic operating conditions is challenging owing to the extreme values of some of the parameters. In particular, those characterising (i) the short Debye lengths (giving rise to rapid changes in the solutions across narrow layers), (ii) the relatively large potential differences across devices and (iii) the disparity in timescales between the motion of the electronic and ionic species give rise to significant stiffness. We present a finite difference scheme with an adaptive time step that is posed on a non-uniform staggered grid that provides second order accuracy in the mesh spacing. The method is able to cope with the stiffness of the system for realistic parameters values whilst providing high accuracy and maintaining modest computational costs. For example, a transient sweep of a current-voltage curve can be computed in only a few minutes on a standard desktop computer.Comment: 22 pages, 8 figure

Arc Phenomena in low-voltage current limiting circuit breakers

Circuit breakers are an important safety feature in most electrical circuits, and they act to prevent excessive currents caused by short circuits, for example. Low-voltage current limiting circuit breakers are activated by a trip solenoid when a critical current is exceeded. The solenoid moves two contacts apart to break the circuit. However, as soon as the contacts are separated an electric arc forms between them, ionising the air in the gap, increasing the electrical conductivity of air to that of the hot plasma that forms, and current continues to flow. The currents involved may be as large as 80,000 amperes. Critical to the success of the circuit breaker is that it is designed to cause the arc to move away from the contacts, into a widening wedge-shaped region. This lengthens the arc, and then moves it onto a series of separator plates called an arc divider or splitter. The arc divider raises the voltage required to sustain the arcs across it, above the voltage that is provided across the breaker, so that the circuit is broken and the arcing dies away. This entire process occurs in milliseconds, and is usually associated with a sound like an explosion and a bright ash from the arc. Parts of the contacts and the arc divider may melt and/or vapourise. The question to be addressed by the Study Group was to mathematically model the arc motion and extinction, with the overall aim of an improved understanding that would help the design of a better circuit breaker. Further discussion indicated that two key mechanisms are believed to contribute to the movement of the arc away from the contacts, one being self-magnetism (where the magnetic field associated with the arc and surrounding circuitry acts to push it towards the arc divider), and the other being air flow (where expansion of air combined with the design of the chamber enclosing the arc causes gas flow towards the arc divider). Further discussion also indicated that a key aspect of circuit breaker design was that it is desirable to have as fast a quenching of the arc as possible, that is, the faster the circuit breaker can act to stop current flow, the better. The relative importance of magnetic and air pressure effects on quenching speed is of central interest to circuit design

X-ray emission from PSR B1800-21, its wind nebula, and similar systems

We detected X-ray emission from PSR B1800-21 and its synchrotron nebula with the Chandra X-ray Observatory. The pulsar's observed flux is (1.4+/-0.2) 10^{-14} ergs cm^{-2} s^{-1} in the 1-6 keV band. The spectrum can be described by a two-component PL+BB model, suggesting a mixture of thermal and magnetospheric emission. For a plausible hydrogen column density n_{H}=1.4 10^{22} cm^{-2}, the PL component has a slope Gamma=1.4+/-0.6 and a luminosity L_{psr}^{nonth}=4 10^{31}(d/4 kpc)^2 ergs s^{-1}. The properties of the thermal component (kT=0.1-0.3 keV, L^{bol}=10^{31}-10^{33} ergs s^{-1}) are very poorly constrained because of the strong interstellar absorption. The compact, 7''\times4'', inner pulsar-wind nebula (PWN), elongated perpendicular to the pulsar's proper motion, is immersed in a fainter asymmetric emission. The observed flux of the PWN is (5.5+/-0.6) 10^{-14} ergs cm^{-2} s^{-1} in the 1-8 keV band. The PWN spectrum fits by a PL model with Gamma=1.6+/-0.3, L=1.6 10^{32} (d/4 kpc})^2 ergs s^{-1}. The shape of the inner PWN suggests that the pulsar moves subsonically and X-ray emission emerges from a torus associated with the termination shock in the equatorial pulsar wind. The inferred PWN-pulsar properties (e.g., the PWN X-ray efficiency, L_{pwn}/\dot{E}~10^{-4}; the luminosity ratio, L_{pwn}/L_{psr}^{nonth}=4; the pulsar wind pressure at the termination shock, p_s=10^{-9} ergs cm^{-3}) are very similar to those of other subsonically moving Vela-like objects detected with Chandra (L_{pwn}/\dot{E}=10^{-4.5}-10^{-3.5}, L_{pwn}/L_{psr}^{nonth}~5, p_s=10^{-10}-10^{-8} ergs cm^{-1}).Comment: 11 pages, 10 figures, 2 tables; submitted to ApJ. Version with the high-resolution figures is available at http://www.astro.psu.edu/users/green/B1800/B1800_ApJ.pd

Near infrared spectroscopy of W51 IRS-2

Near-infrared spectra at 2.95-3.5 μm and 3.99-10 μm have been obtained towards W51 IRS-2 and its surroundings, in order to investigate the spatial variations in intensity of the 3.28 μm unidentified feature and the 4.05 μm Brackett-α line. The Br-α and 3.28 μm features occupy a broadly similar spatial zone, which is characterised by an unresolved core responsible for most of the emission, and an extended and considerably weaker halo. Grain properties required to excite the 4.28 microns line, the nature of the 3.28 μm emission, and its relation to the source structure are discussed

Semileptonic and rare B meson decays into a light pseudoscalar meson

In the framework of a QCD relativistic potential model we evaluate the form factors describing the exclusive decays B => \pi l nu and B => K l+ l-. The present calculation extends a previous analysis of B meson decays into light vector mesons. We find results in agreement with the data, when available, and with the theoretical constraints imposed by the Callan-Treiman relation and the infinite heavy quark mass limit.Comment: 11 pages LaTeX + 2 figure

On spherical twisted conjugacy classes

Let G be a simple algebraic group over an algebraically closed field of good odd characteristic, and let theta be an automorphism of G arising from an involution of its Dynkin diagram. We show that the spherical theta-twisted conjugacy classes are precisely those intersecting only Bruhat cells corresponding to twisted involutions in the Weyl group. We show how the analogue of this statement fails in the triality case. We generalize to good odd characteristic J-H. Lu's dimension formula for spherical twisted conjugacy classes.Comment: proof of Lemma 6.4 polished. The journal version is available at http://www.springerlink.com/content/k573l88256753640

Method for Calculation of Counter Cyclical Payments Using State and National Trigger Levels (Major Crops)

Agricultural and Food Policy,

Alternative AMTA and Loan Rate Options for Program Crops With Counter Cyclical Payments Triggered at the National and State Level

This analysis focuses on four policy options, based on national formulas where implications are examined for varying levels of loan rates and base AMTA payment rates.Agricultural and Food Policy,