Contact complete integrability

Complete integrability in a symplectic setting means the existence of a Lagrangian foliation leaf-wise preserved by the dynamics. In the paper we describe complete integrability in a contact set-up as a more subtle structure: a flag of two foliations, Legendrian and co-Legendrian, and a holonomy-invariant transverse measure of the former in the latter. This turns out to be equivalent to the existence of a canonical $\R\ltimes \R^{n-1}$ structure on the leaves of the co-Legendrian foliation. Further, the above structure implies the existence of $n$ contact fields preserving a special contact 1-form, thus providing the geometric framework and establishing equivalence with previously known definitions of contact integrability. We also show that contact completely integrable systems are solvable in quadratures. We present an example of contact complete integrability: the billiard system inside an ellipsoid in pseudo-Euclidean space, restricted to the space of oriented null geodesics. We describe a surprising acceleration mechanism for closed light-like billiard trajectories

High-vacuum-compatible high-power Faraday isolators for gravitational-wave interferometers

Faraday isolators play a key role in the operation of large-scale gravitational-wave detectors. Second-generation gravitational-wave interferometers such as the Advanced Laser Interferometer Gravitational-Wave Observatory (LIGO) and Advanced Virgo will use high-average-power cw lasers (up to 200 W) requiring specially designed Faraday isolators that are immune to the effects resulting from the laser beam absorption–degraded isolation ratio, thermal lensing, and thermally induced beam steering. In this paper, we present a comprehensive study of Faraday isolators designed specifically for high-performance operation in high-power gravitational-wave interferometers

Influence of carbon and nitrogen on electronic structure and hyperfine interactions in fcc iron-based alloys

Carbon and nitrogen austenites, modeled by Fe8N and Fe8C superstructures are studied by full-potential LAPW method. Structure parameters, electronic and magnetic properties as well as hyperfine interaction parameters are obtained. Calculations prove that Fe-C austenite can be successfully modeled by ordered Fe8C superstructure. The results show that chemical Fe-C bond in Fe8C has higher covalent part than in Fe8N. Detailed analysis of electric field gradient formation for both systems is performed. The calculation of electric field gradient allow us to carry out a good interpretation of Moessbauer spectra for Fe-C and Fe-N systems.Comment: 8 pages, 3 figures, IOP-style LaTeX, submitted to J. Phys. Condens. Matte

Transient Shear Wave Propagation in a Viscoelastic Gel Cylinder: Comparison of Theory to MRI-Based Measurements

ABSTRACT Shear strain patterns in a cylindrical gelatin sample under transient angular acceleration were measured by tagged magnetic resonance imaging (MRI). Measured strain fields were compared to theoretical strain fields obtained by finite element (FE) simulation. Agreement between theory and experiment is very good. The current results support the utility of the experimental approach for tasks such as measurement of shear waves in brain tissue during angular acceleration of the skull. The results also show that a simple viscoelastic model is suitable to describe rapid shear deformation of a gel biomaterial

Confidence Intervals for Concentration and Brightness from Fluorescence Fluctuation Measurements

AbstractThe theory of photon count histogram (PCH) analysis describes the distribution of fluorescence fluctuation amplitudes due to populations of fluorophores diffusing through a focused laser beam and provides a rigorous framework through which the brightnesses and concentrations of the fluorophores can be determined. In practice, however, the brightnesses and concentrations of only a few components can be identified. Brightnesses and concentrations are determined by a nonlinear least-squares fit of a theoretical model to the experimental PCH derived from a record of fluorescence intensity fluctuations. The χ2 hypersurface in the neighborhood of the optimum parameter set can have varying degrees of curvature, due to the intrinsic curvature of the model, the specific parameter values of the system under study, and the relative noise in the data. Because of this varying curvature, parameters estimated from the least-squares analysis have varying degrees of uncertainty associated with them. There are several methods for assigning confidence intervals to the parameters, but these methods have different efficacies for PCH data. Here, we evaluate several approaches to confidence interval estimation for PCH data, including asymptotic standard error, likelihood joint-confidence region, likelihood confidence intervals, skew-corrected and accelerated bootstrap (BCa), and Monte Carlo residual resampling methods. We study these with a model two-dimensional membrane system for simplicity, but the principles are applicable as well to fluorophores diffusing in three-dimensional solution. Using simulated fluorescence fluctuation data, we find the BCa method to be particularly well-suited for estimating confidence intervals in PCH analysis, and several other methods to be less so. Using the BCa method and additional simulated fluctuation data, we find that confidence intervals can be reduced dramatically for a specific non-Gaussian beam profile

Reconstruction of the gravitational wave signal h(t)h(t) during the Virgo science runs and independent validation with a photon calibrator

The Virgo detector is a kilometer-scale interferometer for gravitational wave detection located near Pisa (Italy). About 13 months of data were accumulated during four science runs (VSR1, VSR2, VSR3 and VSR4) between May 2007 and September 2011, with increasing sensitivity. In this paper, the method used to reconstruct, in the range 10 Hz-10 kHz, the gravitational wave strain time series $h(t)$ from the detector signals is described. The standard consistency checks of the reconstruction are discussed and used to estimate the systematic uncertainties of the $h(t)$ signal as a function of frequency. Finally, an independent setup, the photon calibrator, is described and used to validate the reconstructed $h(t)$ signal and the associated uncertainties. The uncertainties of the $h(t)$ time series are estimated to be 8% in amplitude. The uncertainty of the phase of $h(t)$ is 50 mrad at 10 Hz with a frequency dependence following a delay of 8 $\mu$s at high frequency. A bias lower than $4\,\mathrm{\mu s}$ and depending on the sky direction of the GW is also present.Comment: 35 pages, 16 figures. Accepted by CQ

Calibration and sensitivity of the Virgo detector during its second science run

The Virgo detector is a kilometer-length interferometer for gravitational wave detection located near Pisa (Italy). During its second science run (VSR2) in 2009, six months of data were accumulated with a sensitivity close to its design. In this paper, the methods used to determine the parameters for sensitivity estimation and gravitational wave reconstruction are described. The main quantities to be calibrated are the frequency response of the mirror actuation and the sensing of the output power. Focus is also put on their absolute timing. The monitoring of the calibration data as well as the parameter estimation with independent techniques are discussed to provide an estimation of the calibration uncertainties. Finally, the estimation of the Virgo sensitivity in the frequency-domain is described and typical sensitivities measured during VSR2 are shown.Comment: 30 pages, 23 figures, 1 table. Published in Classical and Quantum Gravity (CQG), Corrigendum include

Virgo calibration and reconstruction of the gravitational wave strain during VSR1

Virgo is a kilometer-length interferometer for gravitational waves detection located near Pisa. Its first science run, VSR1, occured from May to October 2007. The aims of the calibration are to measure the detector sensitivity and to reconstruct the time series of the gravitational wave strain h(t). The absolute length calibration is based on an original non-linear reconstruction of the differential arm length variations in free swinging Michelson configurations. It uses the laser wavelength as length standard. This method is used to calibrate the frequency dependent response of the Virgo mirror actuators and derive the detector in-loop response and sensitivity within ~5%. The principle of the strain reconstruction is highlighted and the h(t) systematic errors are estimated. A photon calibrator is used to check the sign of h(t). The reconstructed h(t) during VSR1 is valid from 10 Hz up to 10 kHz with systematic errors estimated to 6% in amplitude. The phase error is estimated to be 70 mrad below 1.9 kHz and 6 micro-seconds above.Comment: 8 pages, 8 figures, proceedings of Amaldi 8 conference, to be published in Journal of Physics Conference Series (JPCS). Second release: correct typo

Locomotor adaptability in persons with unilateral transtibial amputation

Background Locomotor adaptation enables walkers to modify strategies when faced with challenging walking conditions. While a variety of neurological injuries can impair locomotor adaptability, the effect of a lower extremity amputation on adaptability is poorly understood. Objective Determine if locomotor adaptability is impaired in persons with unilateral transtibial amputation (TTA). Methods The locomotor adaptability of 10 persons with a TTA and 8 persons without an amputation was tested while walking on a split-belt treadmill with the parallel belts running at the same (tied) or different (split) speeds. In the split condition, participants walked for 15 minutes with the respective belts moving at 0.5 m/s and 1.5 m/s. Temporal spatial symmetry measures were used to evaluate reactive accommodations to the perturbation, and the adaptive/de-adaptive response. Results Persons with TTA and the reference group of persons without amputation both demonstrated highly symmetric walking at baseline. During the split adaptation and tied post-adaptation walking both groups responded with the expected reactive accommodations. Likewise, adaptive and de-adaptive responses were observed. The magnitude and rate of change in the adaptive and de-adaptive responses were similar for persons with TTA and those without an amputation. Furthermore, adaptability was no different based on belt assignment for the prosthetic limb during split adaptation walking. Conclusions Reactive changes and locomotor adaptation in response to a challenging and novel walking condition were similar in persons with TTA to those without an amputation. Results suggest persons with TTA have the capacity to modify locomotor strategies to meet the demands of most walking conditions despite challenges imposed by an amputation and use of a prosthetic limb

The variable finesse locking technique

Virgo is a power recycled Michelson interferometer, with 3 km long Fabry-Perot cavities in the arms. The locking of the interferometer has been obtained with an original lock acquisition technique. The main idea is to lock the instrument away from its working point. Lock is obtained by misaligning the power recycling mirror and detuning the Michelson from the dark fringe. In this way, a good fraction of light escapes through the antisymmetric port and the power build-up inside the recycling cavity is extremely low. The benefit is that all the degrees of freedom are controlled when they are almost decoupled, and the linewidth of the recycling cavity is large. The interferometer is then adiabatically brought on to the dark fringe. This technique is referred to as variable finesse, since the recycling cavity is considered as a variable finesse Fabry-Perot. This technique has been widely tested and allows us to reach the dark fringe in few minutes, in an essentially deterministic way