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

Proceedings of the 24th annual Central Plains irrigation conference

Presented at Proceedings of the 24th annual Central Plains irrigation conference held on February 21-22 in Colby, Kansas.Includes bibliographical references

Post-1995 French cinema: return of the social, return of the political?

A key trend in post-1995 French cinema has been the return of the social. Analysing this trend, this article seeks to evaluate its politic impact. Using Hervé Le Roux’s Reprise (1997) and Agnès Varda’s Les Glaneurs et la glaneuse (2000) as key meta-texts, it suggests that the current wave of politically engaged cinema needs to be approached in new ways that recognise how films trace the impact of a politically unmediated, ‘raw’ real on groups or individuals. It further suggests that the withdrawal of political mediation gives the films an essential ambiguity and a melodramatic quality that, rather than mere cliché, may be a privileged way to engage with the violence of the real. Film is now not so much in the van but dans le bain of a diverse socio-political stirring

The Slowly Formed Guiselin Brush

We study polymer layers formed by irreversible adsorption from a polymer melt. Our theory describes an experiment which is a ``slow'' version of that proposed by Guiselin [Europhys. Lett., v. 17 (1992) p. 225] who considered instantaneously irreversibly adsorbing chains and predicted a universal density profile of the layer after swelling with solvent to produce the ``Guiselin brush.'' Here we ask what happens when adsorption is not instantaneous. The classic example is chemisorption. In this case the brush is formed slowly and the final structure depends on the experiment's duration, $t_{final}$. We find the swollen layer consists of an inner region of thickness $z^* \sim t_{final}^{-5/3}$ with approximately constant density and an outer region extending up to height $h \sim N^{5/6}$ which has the same density decay $\sim z^{-2/5}$ as for the Guiselin case.Comment: 7 pages, submitted to Europhysics Letter

Novel model for end-neuroma formation in the amputated rabbit forelimb

<p>Abstract</p> <p>Background</p> <p>The forelimb amputee poses many reconstructive challenges in the clinical setting, and there is a paucity of established surgical models for study. To further elucidate the pathogenic process in amputation neuroma formation, we created a reproducible, well-tolerated rabbit forelimb amputation model.</p> <p>Methods</p> <p>Upon approval from the Institutional Animal Care and Use Committee, 5 New Zealand White rabbits underwent left forelimb amputation. During this initial surgery, the median, radial and ulnar nerves were transected 1.6-2.5 (mean 2.0) cm distal to the brachial plexus, transposed onto the anterior chest wall and preserved at length. Six weeks subsequent to the amputation, the distal 5 mm of each neuroma was excised, and the remaining stump underwent histomorphometric analysis.</p> <p>Results</p> <p>The nerve cross sectional areas increased by factors of 1.99, 3.17, and 2.59 in the median (p = 0.077), radial (p < 0.0001) and the ulnar (p = 0.0026) nerves, respectively. At the axonal level, the number and cross-sectional area of myelinated fibers demonstrated an inverse relationship whereby the number of myelinated fibers in the median, radial and ulnar nerves increased by factors of 5.13 (p = 0.0043), 5.25 (p = 0.0056) and 5.59 (p = 0.0027), and the cross-sectional areas of these myelinated fibers decreased by factors of 4.62 (p < 0.001), 3.51 (p < 0.01), and 4.29 (p = 0.0259), respectively.</p> <p>Conclusion</p> <p>Given that the surgical model appears well-tolerated by the rabbits and that patterns of morphologic change are consistent and reproducible, we are encouraged to further investigate the utility of this model in the pathogenesis of neuroma formation.</p

Evaporating hydrophilic and superhydrophobic droplets in electric fields

Evaporating water droplets on a heated substrate are investigated in this work. Specifically, the influences of electric fields are studied in the context of the heat flux distribution beneath the droplets as well as the droplet mechanics and resulting shapes and forces. To facilitate a deeper understanding of the problem, both hydrophilic and superhydrophobic droplets are considered for an entire evaporation period with and without electric field effects. Both wetting scenarios show that the net radial directed electric force is directed inward, resulting in a compressive force which influences the droplet shape in such a way that it appears elongated. Conversely, the net vertically directed electric force is determined to be downwardly directed for hydrophilic droplets, pressing the droplet to the surface, whereas it is upwardly directed for the superhydrophobic droplets, representing a lifting force. With regard to the heat transfer to the droplets, only a pronounced electric field effect was observed for the superhydrophobic droplet. For all droplets, the contact line density, representing the ratio of the contact line perimeter to the total base area of the droplet, is determined to be a parameter that unifies the average heat flux from the heater to the droplets. This suggests that the heat transfer to the base of the droplet in the presence of an electric field is dominated by the electric fields influence, or lack thereof, on the contact line density

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