Improved filters for gravitational waves from inspiraling compact binaries

The order of the post-Newtonian expansion needed to extract in a reliable and accurate manner the fully general relativistic gravitational wave signal from inspiraling compact binaries is explored. A class of approximate wave forms, called P-approximants, is constructed based on the following two inputs: (a) the introduction of two new energy-type and flux-type functions e(v) and f(v), respectively, (b) the systematic use of the Padé approximation for constructing successive approximants of e(v) and f(v). The new P-approximants are not only more effectual (larger overlaps) and more faithful (smaller biases) than the standard Taylor approximants, but also converge faster and monotonically. The presently available (v/c)^5-accurate post-Newtonian results can be used to construct P-approximate wave forms that provide overlaps with the exact wave form larger than 96.5%, implying that more than 90% of potential events can be detected with the aid of P-approximants as opposed to a mere 10–15 % that would be detectable using standard post-Newtonian approximants

Fast acoustic tweezers for the two-dimensional manipulation of individual particles in microfluidic channels

This paper presents a microfluidic device that implements standing surface acoustic waves in order to handle single cells, droplets, and generally particles. The particles are moved in a very controlled manner by the two-dimensional drifting of a standing wave array, using a slight frequency modulation of two ultrasound emitters around their resonance. These acoustic tweezers allow any type of motion at velocities up to few 10mm/s, while the device transparency is adapted for optical studies. The possibility of automation provides a critical step in the development of lab-on-a-chip cell sorters and it should find applications in biology, chemistry, and engineering domains

Effective hydrodynamic boundary conditions for microtextured surfaces

We report measurements of the hydrodynamic drag force acting on a smooth sphere falling down under gravity to a plane decorated with microscopic periodic grooves. Both surfaces are lyophilic, so that a liquid (silicone oil) invades the surface texture being in the Wenzel state. A significant decrease in the hydrodynamic resistance force as compared with that predicted for two smooth surfaces is observed. To quantify the effect of roughness we use the effective no-slip boundary condition, which is applied at the imaginary smooth homogeneous isotropic surface located at an intermediate position between top and bottom of grooves. Such an effective condition fully characterizes the force reduction measured with the real surface, and the location of this effective plane is related to geometric parameters of the texture by a simple analytical formula.Comment: 4 pages, submitted to Phys. Rev.

Local and global avalanches in a 2D sheared granular medium

We present the experimental and numerical studies of a 2D sheared amorphous material constituted of bidisperse photo-elastic disks. We analyze the statistics of avalanches during shear including the local and global fluctuations in energy and changes in particle positions and orientations. We find scale free distributions for these global and local avalanches denoted by power-laws whose cut-offs vary with inter-particle friction and packing fraction. Different exponents are found for these power-laws depending on the quantity from which variations are extracted. An asymmetry in time of the avalanche shapes is evidenced along with the fact that avalanches are mainly triggered from the shear bands. A simple relation independent from the intensity, is found between the number of local avalanches and the global avalanches they form. We also compare these experimental and numerical results for both local and global fluctuations to predictions from meanfield and depinning theories

Gravitational self-force and the effective-one-body formalism between the innermost stable circular orbit and the light ring

We compute the conservative piece of the gravitational self-force (GSF) acting on a particle of mass m_1 as it moves along an (unstable) circular geodesic orbit between the innermost stable circular orbit (ISCO) and the light ring of a Schwarzschild black hole of mass m_2>> m_1. More precisely, we construct the function h_{uu}(x) = h_{\mu\nu} u^{\mu} u^{\nu} (related to Detweiler's gauge-invariant "redshift" variable), where h_{\mu\nu} is the regularized metric perturbation in the Lorenz gauge, u^{\mu} is the four-velocity of m_1, and x= [Gc^{-3}(m_1+m_2)\Omega]^{2/3} is an invariant coordinate constructed from the orbital frequency \Omega. In particular, we explore the behavior of h_{uu} just outside the "light ring" at x=1/3, where the circular orbit becomes null. Using the recently discovered link between h_{uu} and the piece a(u), linear in the symmetric mass ratio \nu, of the main radial potential A(u,\nu) of the Effective One Body (EOB) formalism, we compute a(u) over the entire domain 0<u<1/3. We find that a(u) diverges at the light-ring as ~0.25 (1-3u)^{-1/2}, explain the physical origin of this divergence, and discuss its consequences for the EOB formalism. We construct accurate global analytic fits for a(u), valid on the entire domain 0<u<1/3 (and possibly beyond), and give accurate numerical estimates of the values of a(u) and its first 3 derivatives at the ISCO, as well as the O(\nu) shift in the ISCO frequency. In previous work we used GSF data on slightly eccentric orbits to compute a certain linear combination of a(u) and its first two derivatives, involving also the O(\nu) piece \bar d(u) of a second EOB radial potential {\bar D}(u,\nu). Combining these results with our present global analytic representation of a(u), we numerically compute {\bar d}(u)$ on the interval 0<u\leq 1/6.Comment: 44 pages, 8 figures. Extended discussion in Section V and minor typographical corrections throughout. Version to be published in PR

Accuracy and effectualness of closed-form, frequency-domain waveforms for non-spinning black hole binaries

The coalescences of binary black hole (BBH) systems, here taken to be non-spinning, are among the most promising sources for gravitational wave (GW) ground-based detectors, such as LIGO and Virgo. To detect the GW signals emitted by BBHs, and measure the parameters of the source, one needs to have in hand a bank of GW templates that are both effectual (for detection), and accurate (for measurement). We study the effectualness and the accuracy of the two types of parametrized banks of templates that are directly defined in the frequency-domain by means of closed-form expressions, namely 'post-Newtonian' (PN) and 'phenomenological' models. In absence of knowledge of the exact waveforms, our study assumes as fiducial, target waveforms the ones generated by the most accurate version of the effective one body (EOB) formalism. We find that, for initial GW detectors the use, at each point of parameter space, of the best closed-form template (among PN and phenomenological models) leads to an effectualness >97% over the entire mass range and >99% in an important fraction of parameter space; however, when considering advanced detectors, both of the closed-form frequency-domain models fail to be effectual enough in significant domains of the two-dimensional [total mass and mass ratio] parameter space. Moreover, we find that, both for initial and advanced detectors, the two closed-form frequency-domain models fail to satisfy the minimal required accuracy standard in a very large domain of the two-dimensional parameter space. In addition, a side result of our study is the determination, as a function of the mass ratio, of the maximum frequency at which a frequency-domain PN waveform can be 'joined' onto a NR-calibrated EOB waveform without undue loss of accuracy.Comment: 29 pages, 8 figures, 1 table. Accepted for publication in Phys. Rev.