The response of laser interferometers to a gravitational wave

Laser interferometer detectors are now widely used in an attempt to detect gravitational waves (gw). The interaction of the gw with the light circulating in the interferometer is usually explained in terms of the motion of the "free" mirrors that form the interferometer arms. It is however instructive to show that the same result can be obtained by simply calculating the propagation of an electromagnetic plane wave between "free mirrors" in the curved space-time induced by the gw. One finds that the plane wave acquires frequency modulation sidebands at the gw frequency, as would be expected from the absorption and emission of gravitons from and to the gw. Such sidebands are completely equivalent to the time-dependent phase shift imposed on the plane wave, that follows from the conventional calculation

Effect of noise on coupled chaotic systems

Effect of noise in inducing order on various chaotically evolving systems is reviewed, with special emphasis on systems consisting of coupled chaotic elements. In many situations it is observed that the uncoupled elements when driven by identical noise, show synchronization phenomena where chaotic trajectories exponentially converge towards a single noisy trajectory, independent of the initial conditions. In a random neural network, with infinite range coupling, chaos is suppressed due to noise and the system evolves towards a fixed point. Spatiotemporal stochastic resonance phenomenon has been observed in a square array of coupled threshold devices where a temporal characteristic of the system resonates at a given noise strength. In a chaotically evolving coupled map lattice with logistic map as local dynamics and driven by identical noise at each site, we report that the number of structures (a structure is a group of neighbouring lattice sites for whom values of the variable follow certain predefined pattern) follow a power-law decay with the length of the structure. An interesting phenomenon, which we call stochastic coherence, is also reported in which the abundance and lifetimes of these structures show characteristic peaks at some intermediate noise strength.Comment: 21 page LaTeX file for text, 5 Postscript files for figure

High-frequency corrections to the detector response and their effect on searches for gravitational waves

Searches for gravitational waves with km-scale laser interferometers often involve the long-wavelength approximation to describe the detector response. The prevailing assumption is that the corrections to the detector response due to its finite size are small and the errors due to the long-wavelength approximation are negligible. Recently, however, Baskaran and Grishchuk (2004 Class. Quantum Grav. 21 4041) found that in a simple Michelson interferometer such errors can be as large as 10 percent. For more accurate analysis, these authors proposed to use a linear-frequency correction to the long wavelength approximation. In this paper we revisit these calculations. We show that the linear-frequency correction is inadequate for certain locations in the sky and therefore accurate analysis requires taking into account the exact formula, commonly derived from the photon round-trip propagation time. Also, we extend the calculations to include the effect of Fabry-Perot resonators in the interferometer arms. Here we show that a simple approximation which combines the long-wavelength Michelson response with the single-pole approximation to the Fabry-Perot transfer function produces rather accurate results. In particular, the difference between the exact and the approximate formulae is at most 2-3 percent for those locations in the sky where the detector response is greater than half of its maximum value. We analyse the impact of such errors on detection sensitivity and parameter estimation in searches for periodic gravitational waves emitted by a known pulsar, and in searches for an isotropic stochastic gravitational-wave background. At frequencies up to 1 kHz, the effect of such errors is at most 1-2 percent. For higher frequencies, or if more accuracy is required, one should use the exact formula for the response.Comment: 13 pages, 6 figures, accepted by Classical and Quantum Gravity for GWDAW12 proceeding

Family history of premature cardiovascular disease: blood pressure control and long-term mortality outcomes in hypertensive patients

<b>Aims</b> Current guidelines recommend early referral and initiation of intensive cardiovascular (CV) risk reduction in individuals with a positive family history of coronary heart disease (CHD). We hypothesized that a family history of premature CHD and stroke [CV disease (CVD)] would lead to earlier referral of hypertensive patients to secondary care clinic, leading to better control of risk factors, mitigating the excess risk seen in these individuals.<p></p> <b>Methods and results</b> We studied the association of a positive family history of CVD in 10 787 individuals with longitudinal changes in risk factors and long-term cause-specific mortality in the Glasgow Blood Pressure Clinic using generalized estimating equations and the Cox proportional hazard models, respectively. The total time at risk was 193 756 person-years with a median survival time of 29.2 years. A positive family history of CVD was associated with an earlier presentation to the clinic, a lower burden of traditional CV risk factors, and similar longitudinal blood pressure reduction and drug adherence compared with those without. But despite these positive features, all-cause [hazard ratio (HR) = 1.12, 95% confidence interval 1.01–1.25] and CV (HR = 1.20, 1.04–1.38) mortality independent of baseline risk factors were worse. Consistent results were observed in propensity score-matched analysis. Inclusion of family history of CVD did not improve mortality risk discrimination over and above traditional risk factors.<p></p> <b>Conclusion</b> Our study suggests that despite earlier referral and treatment of individuals with a positive family history of premature CVD, excess risk persists, indicating the need for continued and sustained efforts to reduce risk factors and drug adherence in these individuals.<p></p&gt

1997 price control review British Gas' transportation and storage; the Director General's initial proposals, volume 1: consultation document

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