Detection template families for gravitational waves from the final stages of binary--black-hole inspirals: Nonspinning case

We investigate the problem of detecting gravitational waves from binaries of nonspinning black holes with masses m = 5--20 Msun, moving on quasicircular orbits, which are arguably the most promising sources for first-generation ground-based detectors. We analyze and compare all the currently available post--Newtonian approximations for the relativistic two-body dynamics; for these binaries, different approximations predict different waveforms. We then construct examples of detection template families that embed all the approximate models, and that could be used to detect the true gravitational-wave signal (but not to characterize accurately its physical parameters). We estimate that the fitting factor for our detection families is >~0.95 (corresponding to an event-rate loss <~15%) and we estimate that the discretization of the template family, for ~10^4 templates, increases the loss to <~20%.Comment: 58 pages, 38 EPS figures, final PRD version; small corrections to GW flux terms as per Blanchet et al., PRD 71, 129902(E)-129904(E) (2005

Non normal logics: semantic analysis and proof theory

We introduce proper display calculi for basic monotonic modal logic,the conditional logic CK and a number of their axiomatic extensions. These calculi are sound, complete, conservative and enjoy cut elimination and subformula property. Our proposal applies the multi-type methodology in the design of display calculi, starting from a semantic analysis based on the translation from monotonic modal logic to normal bi-modal logic

A quasi-physical family of gravity-wave templates for precessing binaries of spinning compact objects: Application to double-spin precessing binaries

The gravitational waveforms emitted during the adiabatic inspiral of precessing binaries with two spinning compact bodies of comparable masses, evaluated within the post-Newtonian approximation, can be reproduced rather accurately by the waveforms obtained by setting one of the two spins to zero, at least for the purpose of detection by ground-based gravitational-wave interferometers. Here we propose to use this quasi-physical family of single-spin templates to search for the signals emitted by double-spin precessing binaries, and we find that its signal-matching performance is satisfactory for source masses (m1,m2) in [3,15]Msun x [3,15]Msun. For this mass range, using the LIGO-I design sensitivity, we estimate that the number of templates required to yield a minimum match of 0.97 is ~320,000. We discuss also the accuracy to which the single-spin template family can be used to estimate the parameters of the original double-spin precessing binaries.Comment: REVTeX4, 11 EPS figures; a sequel to gr-qc/0310034; final PRD version; small corrections to GW flux terms as per Blanchet et al., PRD 71, 129902(E)-129904(E) (2005

Transition from inspiral to plunge in precessing binaries of spinning black holes

We investigate the non-adiabatic dynamics of spinning black hole binaries by using an analytical Hamiltonian completed with a radiation-reaction force, containing spin couplings, which matches the known rates of energy and angular momentum losses on quasi-circular orbits. We consider both a straightforward post-Newtonian-expanded Hamiltonian (including spin-dependent terms), and a version of the resummed post-Newtonian Hamiltonian defined by the Effective One-Body approach. We focus on the influence of spin terms onto the dynamics and waveforms. We evaluate the energy and angular momentum released during the final stage of inspiral and plunge. For an equal-mass binary the energy released between 40Hz and the frequency beyond which our analytical treatment becomes unreliable is found to be, when using the more reliable Effective One-Body dynamics: 0.6% M for anti-aligned maximally spinning black holes, 5% M for aligned maximally spinning black hole, and 1.8% M for non-spinning configurations. In confirmation of previous results, we find that, for all binaries considered, the dimensionless rotation parameter J/E^2 is always smaller than unity at the end of the inspiral, so that a Kerr black hole can form right after the inspiral phase. By matching a quasi-normal mode ringdown to the last reliable stages of the plunge, we construct complete waveforms approximately describing the gravitational wave signal emitted by the entire process of coalescence of precessing binaries of spinning black holes.Comment: 31 pages, 7 tables, and 13 figure

Fully anharmonic infrared cascade spectra of polycyclic aromatic hydrocarbons

The infrared (IR) emission of polycyclic aromatic hydrocarbons (PAHs) permeates our universe; astronomers have detected the IR signatures of PAHs around many interstellar objects. The IR emission of interstellar PAHs differs from their emission as seen under conditions on Earth, as they emit through a collisionless cascade down through their excited vibrational states from high internal energies. The difficulty in reproducing interstellar conditions in the laboratory results in a reliance on theoretical techniques. However, the size and complexity of PAHs requires careful consideration when producing the theoretical spectra. In this work we outline the theoretical methods necessary to lead to a fully theoretical IR cascade spectra of PAHs including: an anharmonic second order vibrational perturbation theory (VPT2) treatment; the inclusion of Fermi resonances through polyads; and the calculation of anharmonic temperature band shifts and broadenings (including resonances) through a Wang--Landau approach. We also suggest a simplified scheme to calculate vibrational emission spectra that retains the essential characteristics of the full IR cascade treatment and can directly transform low temperature absorption spectra in IR cascade spectra. Additionally we show that past astronomical models were in error in assuming a 15 cm$^{-1}$ correction was needed to account for anharmonic emission effects

Detecting gravitational waves from precessing binaries of spinning compact objects. II. Search implementation for low-mass binaries

Detection template families (DTFs) are built to capture the essential features of true gravitational waveforms using a small set of phenomenological waveform parameters. Buonanno, Chen, and Vallisneri [Phys. Rev. D 67, 104025 (2003)] proposed the ``BCV2'' DTF to perform computationally efficient searches for signals from precessing binaries of compact stellar objects. Here we test the signal-matching performance of the BCV2 DTF for asymmetric--mass-ratio binaries, and specifically for double--black-hole binaries with component masses (m1,m2): (6~12Msun, 1~3Msun), and for black-hole--neutron-star binaries with component masses (m1,m2) = (10Msun, 1.4Msun); we take all black holes to be maximally spinning. We find a satisfactory signal-matching performance, with fitting factors averaging between 0.94 and 0.98. We also scope out the region of BCV2 parameters needed for a template-based search, we evaluate the template match metric, we discuss a template-placement strategy, and we estimate the number of templates needed for searches at the LIGO design sensitivity. In addition, after gaining more insight in the dynamics of spin--orbit precession, we propose a modification of the BCV2 DTF that is parametrized by physical (rather than phenomenological) parameters. We test this modified ``BCV2P'' DTF for the (10Msun, 1.4Msun) black-hole--neutron-star system, finding a signal-matching performance comparable to the BCV2 DTF, and a reliable parameter-estimation capability for target-binary quantities such as the chirp mass and the opening angle (the angle between the black-hole spin and the orbital angular momentum).Comment: 18 pages, 15 figure

Comfort-Centered Design of a Lightweight and Backdrivable Knee Exoskeleton

This paper presents design principles for comfort-centered wearable robots and their application in a lightweight and backdrivable knee exoskeleton. The mitigation of discomfort is treated as mechanical design and control issues and three solutions are proposed in this paper: 1) a new wearable structure optimizes the strap attachment configuration and suit layout to ameliorate excessive shear forces of conventional wearable structure design; 2) rolling knee joint and double-hinge mechanisms reduce the misalignment in the sagittal and frontal plane, without increasing the mechanical complexity and inertia, respectively; 3) a low impedance mechanical transmission reduces the reflected inertia and damping of the actuator to human, thus the exoskeleton is highly-backdrivable. Kinematic simulations demonstrate that misalignment between the robot joint and knee joint can be reduced by 74% at maximum knee flexion. In experiments, the exoskeleton in the unpowered mode exhibits 1.03 Nm root mean square (RMS) low resistive torque. The torque control experiments demonstrate 0.31 Nm RMS torque tracking error in three human subjects.Comment: 8 pages, 16figures, Journa

Syntactic completeness of proper display calculi

A recent strand of research in structural proof theory aims at exploring the notion of analytic calculi (i.e. those calculi that support general and modular proof-strategies for cut elimination), and at identifying classes of logics that can be captured in terms of these calculi. In this context, Wansing introduced the notion of proper display calculi as one possible design framework for proof calculi in which the analiticity desiderata are realized in a particularly transparent way. Recently, the theory of properly displayable logics (i.e. those logics that can be equivalently presented with some proper display calculus) has been developed in connection with generalized Sahlqvist theory (aka unified correspondence). Specifically, properly displayable logics have been syntactically characterized as those axiomatized by analytic inductive axioms, which can be equivalently and algorithmically transformed into analytic structural rules so that the resulting proper display calculi enjoy a set of basic properties: soundness, completeness, conservativity, cut elimination and subformula property. In this context, the proof that the given calculus is complete w.r.t. the original logic is usually carried out syntactically, i.e. by showing that a (cut free) derivation exists of each given axiom of the logic in the basic system to which the analytic structural rules algorithmically generated from the given axiom have been added. However, so far this proof strategy for syntactic completeness has been implemented on a case-by-case base, and not in general. In this paper, we address this gap by proving syntactic completeness for properly displayable logics in any normal (distributive) lattice expansion signature. Specifically, we show that for every analytic inductive axiom a cut free derivation can be effectively generated which has a specific shape, referred to as pre-normal form.Comment: arXiv admin note: text overlap with arXiv:1604.08822 by other author