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

Optimal detection of burst events in gravitational wave interferometric observatories

We consider the problem of detecting a burst signal of unknown shape. We introduce a statistic which generalizes the excess power statistic proposed by Flanagan and Hughes and extended by Anderson et al. The statistic we propose is shown to be optimal for arbitrary noise spectral characteristic, under the two hypotheses that the noise is Gaussian, and that the prior for the signal is uniform. The statistic derivation is based on the assumption that a signal affects only affects N samples in the data stream, but that no other information is a priori available, and that the value of the signal at each sample can be arbitrary. We show that the proposed statistic can be implemented combining standard time-series analysis tools which can be efficiently implemented, and the resulting computational cost is still compatible with an on-line analysis of interferometric data. We generalize this version of an excess power statistic to the multiple detector case, also including the effect of correlated noise. We give full details about the implementation of the algorithm, both for the single and the multiple detector case, and we discuss exact and approximate forms, depending on the specific characteristics of the noise and on the assumed length of the burst event. As a example, we show what would be the sensitivity of the network of interferometers to a delta-function burst.Comment: 21 pages, 5 figures in 3 groups. Submitted for publication to Phys.Rev.D. A Mathematica notebook is available at http://www.ligo.caltech.edu/~avicere/nda/burst/Burst.nb which allows to reproduce the numerical results of the pape

Cervical end of an occipitocervical fusion: a biomechanical evaluation of 3 constructs

Journal ArticleObject. Stabilization with rigid screw/rod fixation is the treatment of choice for craniocervical disorders requiring operative stabilization. The authors compare the relative immediate stiffness for occipital plate fixation in concordance with transarticular screw fixation (TASF), C-1 lateral mass and C-2 pars screw (C1L-C2P), and C-1 lateral mass and C-2 laminar screw (C1L-C2L) constructs, with and without a cross-link. Methods. Ten intact human cadaveric spines (Oc-C4) were prepared and mounted in a 7-axis spine simulator. Each specimen was precycled and then tested in the intact state for flexion/extension, lateral bending, and axial rotation. Motion was tracked using the OptoTRAK 3D tracking system. The specimens were then destabilized and instrumented with an occipital plate and TASF. The spine was tested with and without the addition of a cross-link. The C1L-C2P and C1L-C2L constructs were similarly tested. Results. All constructs demonstrated a significant increase in stiffness after instrumentation. The C1L-C2P construct was equivalent to the TASF in all moments. The C1L-C2L was significantly weaker than the C1L-C2P construct in all moments and significantly weaker than the TASF in lateral bending. The addition of a cross-link made no difference in the stiffness of any construct. Conclusions. All constructs provide significant immediate stability in the destabilized occipitocervical junction. Although the C1L-C2P construct performed best overall, the TASF was similar, and either one can be recommended. Decreased stiffness of the C1L-C2L construct might affect the success of clinical fusion. This construct should be reserved for cases in which anatomy precludes the use of the other two

Magnetic Flux Tube Reconnection: Tunneling Versus Slingshot

The discrete nature of the solar magnetic field as it emerges into the corona through the photosphere indicates that it exists as isolated flux tubes in the convection zone, and will remain as discrete flux tubes in the corona until it collides and reconnects with other coronal fields. Collisions of these flux tubes will in general be three dimensional, and will often lead to reconnection, both rearranging the magnetic field topology in fundamental ways, and releasing magnetic energy. With the goal of better understanding these dynamics, we carry out a set of numerical experiments exploring fundamental characteristics of three dimensional magnetic flux tube reconnection. We first show that reconnecting flux tubes at opposite extremes of twist behave very differently: in some configurations, low twist tubes slingshot while high twist tubes tunnel. We then discuss a theory explaining these differences: by assuming helicity conservation during the reconnection one can show that at high twist, tunneled tubes reach a lower magnetic energy state than slingshot tubes, whereas at low twist the opposite holds. We test three predictions made by this theory. 1) We find that the level of twist at which the transition from slingshot to tunnel occurs is about two to three times higher than predicted on the basis of energetics and helicity conservation alone, probably because the dynamics of the reconnection play a large role as well. 2) We find that the tunnel occurs at all flux tube collision angles predicted by the theory. 3) We find that the amount of magnetic energy a slingshot or a tunnel reconnection releases agrees reasonably well with the theory, though at the high resistivities we have to use for numerical stability, a significant amount of magnetic energy is lost to diffusion, independent of reconnection.Comment: 21 pages, 15 figures, submitted to Ap

Surgical treatment of occipitocervical instability

Journal ArticleOBJECTIVE: Instability of the occipitocervical junction can be a challenging surgical problem because of the unique anatomic and biomechanical characteristics of this region. We review the causes of instability and the development of surgical techniques to stabilize the occipitocervical junction. METHODS: Occipitocervical instrumentation has advanced significantly, and modern modular screw-based constructs allow for rigid short-segment fixation of unstable elements while providing the stability needed to achieve successful fusion in nearly 100% of patients. This article reviews the preoperative planning, the variety of instrumentation and surgical strategies, as well as the postoperative care of these patients. RESULTS: Current constructs use occipital plates that are rigidly fixed to the thick midline keel of the occipital bone, polyaxial screws that can be placed in many different trajectories, and rods that are bent to approximate the acute occipitocervical angle. These modular constructs provide a variety of methods to achieve fixation in the atlantoaxial complex, including transarticular screws or C1 lateral mass screws in combination with C2 pars, C2 pedicle, or C2 translaminar trajectories. CONCLUSION: Surgical techniques for occipitocervical instrumentation and fusion are technically challenging and require meticulous preoperative planning and a thorough understanding of the regional anatomy, instrumentation, and constructs. Modern screw-based techniques for occipitocervical fusion have established clinical success and demonstrated biomechanical stability, with fusion rates approaching 100%

Templates for stellar mass black holes falling into supermassive black holes

The spin modulated gravitational wave signals, which we shall call smirches, emitted by stellar mass black holes tumbling and inspiralling into massive black holes have extremely complicated shapes. Tracking these signals with the aid of pattern matching techniques, such as Wiener filtering, is likely to be computationally an impossible exercise. In this article we propose using a mixture of optimal and non-optimal methods to create a search hierarchy to ease the computational burden. Furthermore, by employing the method of principal components (also known as singular value decomposition) we explicitly demonstrate that the effective dimensionality of the search parameter space of smirches is likely to be just three or four, much smaller than what has hitherto been thought to be about nine or ten. This result, based on a limited study of the parameter space, should be confirmed by a more exhaustive study over the parameter space as well as Monte-Carlo simulations to test the predictions made in this paper.Comment: 12 pages, 4 Tables, 4th LISA symposium, submitted to CQ

Frequency of invasive plant occurrence is not a suitable proxy for abundance in the Northeast United States

Measuring and predicting invasive plant abundance is critical for understanding impacts on ecosystems and economies. Although spatial abundance datasets remain rare, occurrence datasets are increasingly available across broad regional scales. We asked whether the frequency of these point occurrences can be used as a proxy for abundance of invasive plants. We compiled both occurrence and abundance data for 13 regionally important invasive plants in the northeast United States from herbarium records and several contributed distribution datasets. We integrated all available abundance information based on infested area, stem count, percent cover, or qualitative descriptions into abundance rankings ranging from 0 (absent) to 4 (highly abundant). Within equal-area grid cells of 800 m, we counted numbers of occurrence points and used ordinal regression to test whether higher densities of occurrence points increased the odds of a higher abundance ranking. We compiled a total of 86,854 occurrence points in 34,596 grid cells, of which 26,114 points (30%) within 11,976 cells (35%) had some form of abundance information. Eleven of the 13 species had a slight but significantly positive odds ratio; that is, more occurrence points of a species increased the odds that the species was abundant within the grid cell. However, the predictive ability of the models was poor (κ \u3c 0.2) for the majority of species. Additionally, most grid cells contained only one or two occurrence points, making it impossible to infer abundance in all but a few locations. These results suggest that currently available occurrence datasets do not effectively represent abundance, which could explain why many distribution models based on occurrence data are poor predictors of abundance. Increased efforts to consistently collect and report invasive species abundance, ideally estimating both infested area and average cover, are strongly needed for regional-scale assessments of potential abundance and associated impact

Second Order Phase Transitions : From Infinite to Finite Systems

We investigate the Equation of State (EOS) of classical systems having 300 and 512 particles confined in a box with periodic boundary conditions. We show that such a system, independently on the number of particles investigated, has a critical density of about 1/3 the ground state density and a critical temperature of about $2.5~ MeV$. The mass distribution at the critical point exhibits a power law with $\tau = 2.23$. Making use of the grand partition function of Fisher's droplet model, we obtain an analytical EOS around the critical point in good agreement with the one extracted from the numerical simulations.Comment: RevTex file, 17 pages + 9 figures available upon request from [email protected]