2,126 research outputs found

    A more effective coordinate system for parameter estimation of precessing compact binaries from gravitational waves

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    Ground-based gravitational wave detectors are sensitive to a narrow range of frequencies, effectively taking a snapshot of merging compact-object binary dynamics just before merger. We demonstrate that by adopting analysis parameters that naturally characterize this 'picture', the physical parameters of the system can be extracted more efficiently from the gravitational wave data, and interpreted more easily. We assess the performance of MCMC parameter estimation in this physically intuitive coordinate system, defined by (a) a frame anchored on the binary's spins and orbital angular momentum and (b) a time at which the detectors are most sensitive to the binary's gravitational wave emission. Using anticipated noise curves for the advanced-generation LIGO and Virgo gravitational wave detectors, we find that this careful choice of reference frame and reference time significantly improves parameter estimation efficiency for BNS, NS-BH, and BBH signals.Comment: 11 pages, 5 figures, submitted to Phys. Rev.

    Reactions at Polymer Interfaces: Transitions from Chemical to Diffusion-Control and Mixed Order Kinetics

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    We study reactions between end-functionalized chains at a polymer-polymer interface. For small chemical reactivities (the typical case) the number of diblocks formed, RtR_t, obeys 2nd order chemically controlled kinetics, Rt∌tR_t \sim t, until interfacial saturation. For high reactivities (e.g. radicals) a transition occurs at short times to 2nd order diffusion-controlled kinetics, with Rt∌t/ln⁥tR_t \sim t/\ln t for unentangled chains while t/ln⁥tt/\ln t and t1/2t^{1/2} regimes occur for entangled chains. Long time kinetics are 1st order and controlled by diffusion of the more dilute species to the interface: Rt∌t1/4R_t \sim t^{1/4} for unentangled cases, while Rt∌t1/4R_t \sim t^{1/4} and t1/8t^{1/8} regimes arise for entangled systems. The final 1st order regime is governed by center of gravity diffusion, Rt∌t1/2R_t \sim t^{1/2}.Comment: 11 pages, 3 figures, uses poliface.sty, minor changes, to appear in Europhysics Letter

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

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    In second-generation, ground-based interferometric gravitational-wave detectors such as Advanced LIGO, the dominant noise at frequencies f∌40f \sim 40 Hz to ∌200\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
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