Numerical solution of a coupled pair of elliptic equations from solid state electronics

Iterative methods are considered for the solution of a coupled pair of second order elliptic partial differential equations which arise in the field of solid state electronics. A finite difference scheme is used which retains the conservative form of the differential equations. Numerical solutions are obtained in two ways, by multigrid and dynamic alternating direction implicit methods. Numerical results are presented which show the multigrid method to be an efficient way of solving this problem

Reform and Representation: A New Method Applied to Recent Electoral Changes

Can electoral reforms such as an independent redistricting commission and the top-two primary create conditions that lead to better legislative representation? We explore this question by presenting a new method for measuring a key indicator of representation - the congruence between a legislator's ideological position and the average position of her district's voters. Our novel approach combines two methods: the joint classification of voters and political candidates on the same ideological scale, along with multilevel regression and post-stratification to estimate the position of the average voter across many districts in multiple elections. After validating our approach, we use it to study the recent impact of reforms in California, showing that they did not bring their hoped-for effects

After the games are over: life-history trade-offs drive dispersal attenuation following range expansion.

Increased dispersal propensity often evolves on expanding range edges due to the Olympic Village effect, which involves the fastest and fittest finding themselves together in the same place at the same time, mating, and giving rise to like individuals. But what happens after the ranges leading edge has passed and the games are over? Although empirical studies indicate that dispersal propensity attenuates following range expansion, hypotheses about the mechanisms driving this attenuation have not been clearly articulated or tested. Here, we used a simple model of the spatiotemporal dynamics of two phenotypes, one fast and the other slow, to propose that dispersal attenuation beyond preexpansion levels is only possible in the presence of trade-offs between dispersal and life-history traits. The Olympic Village effect ensures that fast dispersers preempt locations far from the ranges previous limits. When trade-offs are absent, this preemptive spatial advantage has a lasting impact, with highly dispersive individuals attaining equilibrium frequencies that are strictly higher than their introduction frequencies. When trade-offs are present, dispersal propensity decays rapidly at all locations. Our models results about the postcolonization trajectory of dispersal evolution are clear and, in principle, should be observable in field studies. We conclude that empirical observations of postcolonization dispersal attenuation offer a novel way to detect the existence of otherwise elusive trade-offs between dispersal and life-history traits

InSb Heterodyne Receivers For Submillimeter Astronomy

InSb hot electron bolometer mixer receivers have been used for submillimeter line studies of the interstellar medium up to frequencies of about 500 GHz (600u). Detections of new interstellar lines have been made, such as the ground state fine structure transition of atomic carbon at 492 GHz, and various transitions of molecules such as carbon monoxide and water. The bulk of this work has been performed with the NASA Kuiper Airborne Observatory telescope which is transported to an altitude of aboutl2,000 km by a C141 aircraft, so avoiding most of the effects of the Earth's atmosphere. Some observations have also been made at ground observatories with the 5 m Hale telescope at Mount Palomar and the NASA In-frared Telescope Facility at Mauna Kea, Hawaii. The heterodyne bolometer receivers have achieved noise temperatures of less than 400 K at all frequencies up to 500 GHz. Develop-ment work continues to extend the frequency range further into the submillimeter band

Strong CH^+ J = 1–0 emission and absorption in DR21

We report the first detection of the ground-state rotational transition of the methylidyne cation CH^+ towards the massive star-forming region DR 21 with the HIFI instrument onboard the Herschel satellite. The line profile exhibits a broad emission line, in addition to two deep and broad absorption features associated with the DR 21 molecular ridge and foreground gas. These observations allow us to determine a ^(12)CH^(+)J = 1–0 line frequency of ν = 835 137 ± 3 MHz, in good agreement with a recent experimental determination. We estimate the CH^+ column density to be a few 10^(13) cm^(-2) in the gas seen in emission, and >10^(14) cm^(-2) in the components responsible for the absorption, which is indicative of a high line of sight average abundance [CH^+] /[H] > 1.2 × 10^(-8). We show that the CH^+ column densities agree well with the predictions of state-of-the-art C-shock models in dense UV-illuminated gas for the emission line, and with those of turbulent dissipation models in diffuse gas for the absorption lines

Development of the Submillimeter Band

This short article attempts to summarize my contribution to the field of submillimeter spectroscopy in the dense interstellar medium. It is taken mainly from my recollections and as a result some of the dates may be inaccurate. It covers most of the enabling receiver technology from frequencies of about 100 GHz to 2 THz and discusses the development of hot electron bolometers (HEB) and superconducting tunnel junction detectors (SIS). Many new molecular lines and some atomic lines have been revealed. These detectors are in use in the modern major projects such as ALMA and Herschel and will play their part in the many exciting projects of the next decade. Certainly one of the major contributions to the field has been the generation of many students who obtained Ph.D.s (14) and postdocs (25) in my group. The total number of national and international students who have obtained Ph.D.s (75) with use of the Caltech Submillimeter Observatory (CSO) and those who are currently studying using the CSO (44) is even more impressive

Random matrix theory of unquenched two-colour QCD with nonzero chemical potential

We solve a random two-matrix model with two real asymmetric matrices whose primary purpose is to describe certain aspects of quantum chromodynamics with two colours and dynamical fermions at nonzero quark chemical potential mu. In this symmetry class the determinant of the Dirac operator is real but not necessarily positive. Despite this sign problem the unquenched matrix model remains completely solvable and provides detailed predictions for the Dirac operator spectrum in two different physical scenarios/limits: (i) the epsilon-regime of chiral perturbation theory at small mu, where mu^2 multiplied by the volume remains fixed in the infinite-volume limit and (ii) the high-density regime where a BCS gap is formed and mu is unscaled. We give explicit examples for the complex, real, and imaginary eigenvalue densities including Nf=2 non-degenerate flavours. Whilst the limit of two degenerate masses has no sign problem and can be tested with standard lattice techniques, we analyse the severity of the sign problem for non-degenerate masses as a function of the mass split and of mu. On the mathematical side our new results include an analytical formula for the spectral density of real Wishart eigenvalues in the limit (i) of weak non-Hermiticity, thus completing the previous solution of the corresponding quenched model of two real asymmetric Wishart matrices.Comment: 45 pages, 31 figures; references added, as published in JHE

A Line Survey of Orion KL from 325 to 360 GHz

We present a high-sensitivity spectral line survey of the high-mass star-forming region Orion KL in the 325-360 GHz frequency band. The survey was conducted at the Caltech Submillimeter Observatory on Mauna Kea, Hawaii. The sensitivity achieved is typically 0.1-0.5 K and is limited mostly by the sideband separation method utilized. We find 717 resolvable features consisting of 1004 lines, among which 60 are unidentified. The identified lines are due to 34 species and various isotopomers. Most of the unidentified lines are weak, and many of them most likely due to isotopomers or vibrationally or torsionally excited states of known species with unknown line frequencies, but a few reach the 2-5 K level. No new species have been identified, but we were able to strengthen evidence for the identification of ethanol in Orion and found the first nitrogen sulfide line in this source. The molecule dominating the integrated line emission is SO_2, which emits twice the intensity of CO, followed by SO, which is only slightly stronger than CO. In contrast, the largest number of lines is emitted from heavy organic rotors like HCOOCH_3, CH_3CH_2CN, and CH_3OCH_3, but their contribution to the total flux is unimportant. CH_3OH is also very prominent, both in the number of lines and in integrated flux. An interesting detail of this survey is the first detection of vibrationally excited HCN in the v_2 = 2 state, 2000 K above ground. Clearly this is a glimpse into the very inner part of the Orion hot core

Surface figure measurements of radio telescopes with a shearing interferometer

A new technique for determining the surface figure of large submillimeter wavelength telescopes is presented, which is based on measuring the telescope’s focal plane diffraction pattern with a shearing interferometer. In addition to the instrumental theory, results obtained using such an interferometer on the 10.4-m diam telescope of the Caltech Submillimeter Observatory are discussed. Using wavelengths near 1 mm, a measurement accuracy of 9 µm, or λ/115, has been achieved, and the rms surface accuracy has been determined to be just under 30 µm. The distortions of the primary reflector with changing elevation angle have also been measured and agree well with theoretical predictions of the dish deformation