The dependence of test-mass thermal noises on beam shape in gravitational-wave interferometers

In second-generation, ground-based interferometric gravitational-wave detectors such as Advanced LIGO, the dominant noise at frequencies $f \sim 40$ Hz to $\sim 200$ Hz is expected to be due to thermal fluctuations in the mirrors' substrates and coatings which induce random fluctuations in the shape of the mirror face. The laser-light beam averages over these fluctuations; the larger the beam and the flatter its light-power distribution, the better the averaging and the lower the resulting thermal noise. In semi-infinite mirrors, scaling laws for the influence of beam shape on the four dominant types of thermal noise (coating Brownian, coating thermoelastic, substrate Brownian, and substrate thermoelastic) have been suggested by various researchers and derived with varying degrees of rigour. Because these scaling laws are important tools for current research on optimizing the beam shape, it is important to firm up our understanding of them. This paper (1) gives a summary of the prior work and of gaps in the prior analyses, (2) gives a unified and rigorous derivation of all four scaling laws, and (3) explores, relying on work by J. Agresti, deviations from the scaling laws due to finite mirror size.Comment: 25 pages, 10 figures, submitted to Class. Quantum Gra

Coating thermal noise for arbitrary shaped beams

Advanced LIGO's sensitivity will be limited by coating noise. Though this noise depends on beam shape, and though nongaussian beams are being seriously considered for advanced LIGO, no published analysis exists to compare the quantitative thermal noise improvement alternate beams offer. In this paper, we derive and discuss a simple integral which completely characterizes the dependence of coating thermal noise on shape. The derivation used applies equally well, with minor modifications, to all other forms of thermal noise in the low-frequency limit.Comment: 3 pages. Originally performed in August 2004. Submitted to CQG. (v2) : Corrections from referee and other

LH RECEPTORS AND STEROIDOGENESIS IN DISTINCT POPULATIONS OF LEYDIG CELLS *

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/74634/1/j.1749-6632.1982.tb23168.x.pd

Compact Binary Coalescences in the Band of Ground-based Gravitational-Wave Detectors

As the ground-based gravitational-wave telescopes LIGO, Virgo, and GEO 600 approach the era of first detections, we review the current knowledge of the coalescence rates and the mass and spin distributions of merging neutron-star and black-hole binaries. We emphasize the bi-directional connection between gravitational-wave astronomy and conventional astrophysics. Astrophysical input will make possible informed decisions about optimal detector configurations and search techniques. Meanwhile, rate upper limits, detected merger rates, and the distribution of masses and spins measured by gravitational-wave searches will constrain astrophysical parameters through comparisons with astrophysical models. Future developments necessary to the success of gravitational-wave astronomy are discussed.Comment: Replaced with version accepted by CQG

Critical dimensions for random walks on random-walk chains

The probability distribution of random walks on linear structures generated by random walks in $d$-dimensional space, $P_d(r,t)$, is analytically studied for the case $\xi\equiv r/t^{1/4}\ll1$. It is shown to obey the scaling form $P_d(r,t)=\rho(r) t^{-1/2} \xi^{-2} f_d(\xi)$, where $\rho(r)\sim r^{2-d}$ is the density of the chain. Expanding $f_d(\xi)$ in powers of $\xi$, we find that there exists an infinite hierarchy of critical dimensions, $d_c=2,6,10,\ldots$, each one characterized by a logarithmic correction in $f_d(\xi)$. Namely, for $d=2$, $f_2(\xi)\simeq a_2\xi^2\ln\xi+b_2\xi^2$; for $3\le d\le 5$, $f_d(\xi)\simeq a_d\xi^2+b_d\xi^d$; for $d=6$, $f_6(\xi)\simeq a_6\xi^2+b_6\xi^6\ln\xi$; for $7\le d\le 9$, $f_d(\xi)\simeq a_d\xi^2+b_d\xi^6+c_d\xi^d$; for $d=10$, $f_{10}(\xi)\simeq a_{10}\xi^2+b_{10}\xi^6+c_{10}\xi^{10}\ln\xi$, {\it etc.\/} In particular, for $d=2$, this implies that the temporal dependence of the probability density of being close to the origin $Q_2(r,t)\equiv P_2(r,t)/\rho(r)\simeq t^{-1/2}\ln t$.Comment: LATeX, 10 pages, no figures submitted for publication in PR

Combinations of Maternal KIR and Fetal HLA-C Genes Influence the Risk of Preeclampsia and Reproductive Success

Preeclampsia is a serious complication of pregnancy in which the fetus receives an inadequate supply of blood due to failure of trophoblast invasion. There is evidence that the condition has an immunological basis. The only known polymorphic histocompatibility antigens on the fetal trophoblast are HLA-C molecules. We tested the idea that recognition of these molecules by killer immunoglobulin receptors (KIRs) on maternal decidual NK cells is a key factor in the development of preeclampsia. Striking differences were observed when these polymorphic ligand: receptor pairs were considered in combination. Mothers lacking most or all activating KIR (AA genotype) when the fetus possessed HLA-C belonging to the HLA-C2 group were at a greatly increased risk of preeclampsia. This was true even if the mother herself also had HLA-C2, indicating that neither nonself nor missing-self discrimination was operative. Thus, this interaction between maternal KIR and trophoblast appears not to have an immune function, but instead plays a physiological role related to placental development. Different human populations have a reciprocal relationship between AA frequency and HLA-C2 frequency, suggesting selection against this combination. In light of our findings, reproductive success may have been a factor in the evolution and maintenance of human HLA-C and KIR polymorphisms

Interpolating Detailed Simulations of Kilonovae: Adaptive Learning and Parameter Inference Applications

Detailed radiative transfer simulations of kilonovae are difficult to apply directly to observations; they only sparsely cover simulation parameters, such as the mass, velocity, morphology, and composition of the ejecta. On the other hand, semianalytic models for kilonovae can be evaluated continuously over model parameters, but neglect important physical details which are not incorporated in the simulations, thus introducing systematic bias. Starting with a grid of 2D anisotropic simulations of kilonova light curves covering a wide range of ejecta properties, we apply adaptive-learning techniques to iteratively choose new simulations and produce high-fidelity surrogate models for those simulations. These surrogate models allow for continuous evaluation across model parameters while retaining the microphysical details about the ejecta. Using a new code for multimessenger inference, we demonstrate how to use our interpolated models to infer kilonova parameters. Comparing to inferences using simplified analytic models, we recover different ejecta properties. We discuss the implications of this analysis which is qualitatively consistent with similar previous work using detailed ejecta opacity calculations and which illustrates systematic challenges for kilonova modeling. An associated data and code release provides our interpolated light-curve models, interpolation implementation which can be applied to reproduce our work or extend to new models, and our multimessenger parameter inference engine.Comment: 19 pages, 15 figure

Dimension in a Radiative Stellar Atmosphere

Dimensional scales are examined in an extended 3+1 Vaidya atmosphere surrounding a Schwarzschild source. At one scale, the Vaidya null fluid vanishes and the spacetime contains only a single spherical 2-surface. Both of these behaviors can be addressed by including higher dimensions in the spacetime metric.Comment: to appear in Gen. Rel. Gra