The generation of a Gaussian random process in a position parameter

Analog computer method for approximating stationary Gaussian random process depending only on position paramete

The Cosmological Constant and Advanced Gravitational Wave Detectors

Interferometric gravitational wave detectors could measure the frequency sweep of a binary inspiral [characterized by its chirp mass] to high accuracy. The observed chirp mass is the intrinsic chirp mass of the binary source multiplied by $(1+z)$, where $z$ is the redshift of the source. Assuming a non-zero cosmological constant, we compute the expected redshift distribution of observed events for an advanced LIGO detector. We find that the redshift distribution has a robust and sizable dependence on the cosmological constant; the data from advanced LIGO detectors could provide an independent measurement of the cosmological constant.Comment: 13 pages plus 5 figure, LaTeX. Revised and final version, to appear in Phys. Rev.

Binary inspiral, gravitational radiation, and cosmology

Observations of binary inspiral in a single interferometric gravitational wave detector can be cataloged according to signal-to-noise ratio $\rho$ and chirp mass $\cal M$. The distribution of events in a catalog composed of observations with $\rho$ greater than a threshold $\rho_0$ depends on the Hubble expansion, deceleration parameter, and cosmological constant, as well as the distribution of component masses in binary systems and evolutionary effects. In this paper I find general expressions, valid in any homogeneous and isotropic cosmological model, for the distribution with $\rho$ and $\cal M$ of cataloged events; I also evaluate these distributions explicitly for relevant matter-dominated Friedmann-Robertson-Walker models and simple models of the neutron star mass distribution. In matter dominated Friedmann-Robertson-Walker cosmological models advanced LIGO detectors will observe binary neutron star inspiral events with $\rho>8$ from distances not exceeding approximately $2\,\text{Gpc}$, corresponding to redshifts of $0.48$ (0.26) for $h=0.8$ ($0.5$), at an estimated rate of 1 per week. As the binary system mass increases so does the distance it can be seen, up to a limit: in a matter dominated Einstein-deSitter cosmological model with $h=0.8$ ($0.5$) that limit is approximately $z=2.7$ (1.7) for binaries consisting of two $10\,\text{M}_\odot$ black holes. Cosmological tests based on catalogs of the kind discussed here depend on the distribution of cataloged events with $\rho$ and $\cal M$. The distributions found here will play a pivotal role in testing cosmological models against our own universe and in constructing templates for the detection of cosmological inspiraling binary neutron stars and black holes.Comment: REVTeX, 38 pages, 9 (encapsulated) postscript figures, uses epsf.st

Detecting an association between γ\gamma Ray and Gravitational Wave Bursts

If $\gamma$-ray bursts (GRBs) are accompanied by gravitational wave bursts (GWBs) the correlated output of two gravitational wave detectors evaluated in the moments just prior to a GRB will differ from that evaluated at times not associated with a GRB. We can test for this difference independently of any model of the GWB signal waveform. If we invoke a model for the GRB source population and GWB radiation spectral density we can find a confidence interval or upper limit on the root-mean-square GWB signal amplitude in the detector waveband. To illustrate we adopt a simple, physically motivated model and estimate that initial LIGO detector observations coincident with 1000 GRBs could lead us to exclude, with 95% confidence, associated GWBs with $h_{RMS} be Gaussian or that any inter-detector correlated noise be measured or measurable; it does not require advanced or a priori knowledge of the source waveform; and the limits obtained on the wave-strength improve with the number of observed GRBs

Crustal Oscillations of Slowly Rotating Relativistic Stars

We study low-amplitude crustal oscillations of slowly rotating relativistic stars consisting of a central fluid core and an outer thin solid crust. We estimate the effect of rotation on the torsional toroidal modes and on the interfacial and shear spheroidal modes. The results compared against the Newtonian ones for wide range of neutron star models and equations of state.Comment: 15 page

On the spin of gravitational bosons

We unearth spacetime structure of massive vector bosons, gravitinos, and gravitons. While the curvatures associated with these particles carry a definite spin, the underlying potentials cannot be, and should not be, interpreted as single spin objects. For instance, we predict that a spin measurement in the rest frame of a massive gravitino will yield the result 3/2 with probability one half, and 1/2 with probability one half. The simplest scenario leaves the Riemannian curvature unaltered; thus avoiding conflicts with classical tests of the theory of general relativity. However, the quantum structure acquires additional contributions to the propagators, and it gives rise to additional phases.Comment: Honorable mention, 2002 Gravity Research Foundation Essay

Unstable Nonradial Oscillations on Helium Burning Neutron Stars

Material accreted onto a neutron star can stably burn in steady state only when the accretion rate is high (typically super-Eddington) or if a large flux from the neutron star crust permeates the outer atmosphere. For such situations we have analyzed the stability of nonradial oscillations, finding one unstable mode for pure helium accretion. This is a shallow surface wave which resides in the helium atmosphere above the heavier ashes of the ocean. It is excited by the increase in the nuclear reaction rate during the oscillations, and it grows on the timescale of a second. For a slowly rotating star, this mode has a frequency of approximately 20-30 Hz (for l=1), and we calculate the full spectrum that a rapidly rotating (>>30 Hz) neutron star would support. The short period X-ray binary 4U 1820--30 is accreting helium rich material and is the system most likely to show this unstable mode,especially when it is not exhibiting X-ray bursts. Our discovery of an unstable mode in a thermally stable atmosphere shows that nonradial perturbations have a different stability criterion than the spherically symmetric thermal perturbations that generate type I X-ray bursts.Comment: Accepted for publication in Astrophysical Journal, 22 pages, 14 figure

The Organic Retail Market in Wales

This report on retail data provides an estimate of the value of the organic market in Wales and its borders, which shows the importance of this sector to the Welsh economy both directly and as a multiplier of the Welsh Government’s investment in organic farming under the Rural Development Plan (RDP) agri-environment schemes. The report combines data from three sources: Nielsen Scantrack which covers sales through ma-jor food and drink retailers (supermarkets) in Wales/West, surveys of Welsh organic businesses (independent retailers, processors, box schemes, farm shops and others) carried out by the Soil Association and data from the Welsh producer survey carried out by Organic Centre Wales. In addition, comments were invited from a number of industry experts

Alternative splicing of tropomyosin pre-mRNAs in vitro and in vivo

A single rat gene encodes both fibroblast TM-1 and skeletal muscle beta-tropomyosin by an alternative RNA-processing mechanism. The gene contains 11 exons: Exons 1-5 and exons 8 and 9 are constitutive exons common to all mRNAs expressed from this gene; exons 6 and 11 are used in fibroblasts as well as smooth muscle; exons 7 and 10 are used exclusively in skeletal muscle. We have studied the internal alternative RNA splice choice (exons 6 and 7) of the rat tropomyosin 1 gene in vitro, using nuclear extracts obtained from HeLa cells. Use of alternative splice sites in vitro is dependent on the ionic conditions of the assay, and correct splicing occurs only under well-defined salt conditions. Splicing of exon 5 to exon 6 (fibroblast-type splice) and exon 5 to exon 7 (skeletal muscle-type splice) was dependent on precursors in which exon 6 or 7 was first joined to exon 8. The same patterns of alternatively spliced RNAs were formed when similar templates were introduced in HeLa cells by transfection. Thus, there appears to be an ordered pathway of splicing in which the internal alternatively spliced exons must first be joined to the downstream constitutive exon before they can be spliced to the upstream constitutive exon. The data are consistent with a model in which the critical event in alternative splicing occurs during the joining of exon 6 to exon 8 (fibroblast-type splice) or exon 7 to exon 8 (skeletal muscle-type splice)