Reducing orbital eccentricity in binary black hole simulations

Binary black hole simulations starting from quasi-circular (i.e., zero radial velocity) initial data have orbits with small but non-zero orbital eccentricities. In this paper the quasi-equilibrium initial-data method is extended to allow non-zero radial velocities to be specified in binary black hole initial data. New low-eccentricity initial data are obtained by adjusting the orbital frequency and radial velocities to minimize the orbital eccentricity, and the resulting ($\sim 5$ orbit) evolutions are compared with those of quasi-circular initial data. Evolutions of the quasi-circular data clearly show eccentric orbits, with eccentricity that decays over time. The precise decay rate depends on the definition of eccentricity; if defined in terms of variations in the orbital frequency, the decay rate agrees well with the prediction of Peters (1964). The gravitational waveforms, which contain $\sim 8$ cycles in the dominant l=m=2 mode, are largely unaffected by the eccentricity of the quasi-circular initial data. The overlap between the dominant mode in the quasi-circular evolution and the same mode in the low-eccentricity evolution is about 0.99.Comment: 27 pages, 9 figures; various minor clarifications; accepted to the "New Frontiers" special issue of CQ

Growth rates of nucleation mode particles in Hyytiälä during 2003−2009: variation with particle size, season, data analysis method and ambient conditions

The condensational growth rate of aerosol particles formed in atmospheric new particle formation events is one of the most important factors influencing the lifetime of these particles and their ability to become climatically relevant. Diameter growth rates (GR) of nucleation mode particles were studied based on almost 7 yr of data measured during the years 2003–2009 at a boreal forest measurement station SMEAR II in Hyytiälä, Finland. The particle growth rates were estimated using particle size distributions measured with a Differential Mobility Particle Sizer (DMPS), a Balanced Scanning Mobility Analyzer (BSMA) and an Air Ion Spectrometer (AIS). Two GR analysis methods were tested. The particle growth rates were also compared to an extensive set of ambient meteorological parameters and trace gas concentrations to investigate the processes/constituents limiting the aerosol growth. The median growth rates of particles in the nucleation mode size ranges with diameters of 1.5–3 nm, 3–7 nm and 7–20 nm were 1.9 nm h⁻¹, 3.8 nm h⁻¹, and 4.3 nm h⁻¹, respectively. The median relative uncertainties in the growth rates due to the size distribution instrumentation in these size ranges were 25%, 19%, and 8%, respectively. For the smallest particles (1.5–3 nm) the AIS data yielded on average higher growth rate values than the BSMA data, and higher growth rates were obtained from positively charged size distributions as compared with negatively charged particles. For particles larger than 3 nm in diameter no such systematic differences were found. For these particles the uncertainty in the growth rate related to the analysis method, with relative uncertainty of 16%, was similar to that related to the instruments. The growth rates of 7–20 nm particles showed positive correlation with monoterpene concentrations and their oxidation rate by ozone. The oxidation rate by OH did not show a connection with GR. Our results indicate that the growth of nucleation mode particles in Hyytiälä is mainly limited by the concentrations of organic precursors

Towards absorbing outer boundaries in General Relativity

We construct exact solutions to the Bianchi equations on a flat spacetime background. When the constraints are satisfied, these solutions represent in- and outgoing linearized gravitational radiation. We then consider the Bianchi equations on a subset of flat spacetime of the form [0,T] x B_R, where B_R is a ball of radius R, and analyze different kinds of boundary conditions on \partial B_R. Our main results are: i) We give an explicit analytic example showing that boundary conditions obtained from freezing the incoming characteristic fields to their initial values are not compatible with the constraints. ii) With the help of the exact solutions constructed, we determine the amount of artificial reflection of gravitational radiation from constraint-preserving boundary conditions which freeze the Weyl scalar Psi_0 to its initial value. For monochromatic radiation with wave number k and arbitrary angular momentum number l >= 2, the amount of reflection decays as 1/(kR)^4 for large kR. iii) For each L >= 2, we construct new local constraint-preserving boundary conditions which perfectly absorb linearized radiation with l <= L. (iv) We generalize our analysis to a weakly curved background of mass M, and compute first order corrections in M/R to the reflection coefficients for quadrupolar odd-parity radiation. For our new boundary condition with L=2, the reflection coefficient is smaller than the one for the freezing Psi_0 boundary condition by a factor of M/R for kR > 1.04. Implications of these results for numerical simulations of binary black holes on finite domains are discussed.Comment: minor revisions, 30 pages, 6 figure

From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity

This article reviews some aspects in the current relationship between mathematical and numerical General Relativity. Focus is placed on the description of isolated systems, with a particular emphasis on recent developments in the study of black holes. Ideas concerning asymptotic flatness, the initial value problem, the constraint equations, evolution formalisms, geometric inequalities and quasi-local black hole horizons are discussed on the light of the interaction between numerical and mathematical relativists.Comment: Topical review commissioned by Classical and Quantum Gravity. Discussion inspired by the workshop "From Geometry to Numerics" (Paris, 20-24 November, 2006), part of the "General Relativity Trimester" at the Institut Henri Poincare (Fall 2006). Comments and references added. Typos corrected. Submitted to Classical and Quantum Gravit

Status of NINJA: the Numerical INJection Analysis project

The 2008 NRDA conference introduced the Numerical INJection Analysis project (NINJA), a new collaborative effort between the numerical relativity community and the data analysis community. NINJA focuses on modeling and searching for gravitational wave signatures from the coalescence of binary system of compact objects. We review the scope of this collaboration and the components of the first NINJA project, where numerical relativity groups shared waveforms and data analysis teams applied various techniques to detect them when embedded in colored Gaussian noise

Apraxia and motor dysfunction in corticobasal syndrome

Background: Corticobasal syndrome (CBS) is characterized by multifaceted motor system dysfunction and cognitive disturbance; distinctive clinical features include limb apraxia and visuospatial dysfunction. Transcranial magnetic stimulation (TMS) has been used to study motor system dysfunction in CBS, but the relationship of TMS parameters to clinical features has not been studied. The present study explored several hypotheses; firstly, that limb apraxia may be partly due to visuospatial impairment in CBS. Secondly, that motor system dysfunction can be demonstrated in CBS, using threshold-tracking TMS, and is linked to limb apraxia. Finally, that atrophy of the primary motor cortex, studied using voxel-based morphometry analysis (VBM), is associated with motor system dysfunction and limb apraxia in CBS.   Methods: Imitation of meaningful and meaningless hand gestures was graded to assess limb apraxia, while cognitive performance was assessed using the Addenbrooke's Cognitive Examination - Revised (ACE-R), with particular emphasis placed on the visuospatial subtask. Patients underwent TMS, to assess cortical function, and VBM.   Results: In total, 17 patients with CBS (7 male, 10 female; mean age 64.4+/2 6.6 years) were studied and compared to 17 matched control subjects. Of the CBS patients, 23.5% had a relatively inexcitable motor cortex, with evidence of cortical dysfunction in the remaining 76.5% patients. Reduced resting motor threshold, and visuospatial performance, correlated with limb apraxia. Patients with a resting motor threshold <50% performed significantly worse on the visuospatial sub-task of the ACE-R than other CBS patients. Cortical function correlated with atrophy of the primary and pre-motor cortices, and the thalamus, while apraxia correlated with atrophy of the pre-motor and parietal cortices.   Conclusions: Cortical dysfunction appears to underlie the core clinical features of CBS, and is associated with atrophy of the primary motor and pre-motor cortices, as well as the thalamus, while apraxia correlates with pre-motor and parietal atrophy

Testing gravitational-wave searches with numerical relativity waveforms: Results from the first Numerical INJection Analysis (NINJA) project

The Numerical INJection Analysis (NINJA) project is a collaborative effort between members of the numerical relativity and gravitational-wave data analysis communities. The purpose of NINJA is to study the sensitivity of existing gravitational-wave search algorithms using numerically generated waveforms and to foster closer collaboration between the numerical relativity and data analysis communities. We describe the results of the first NINJA analysis which focused on gravitational waveforms from binary black hole coalescence. Ten numerical relativity groups contributed numerical data which were used to generate a set of gravitational-wave signals. These signals were injected into a simulated data set, designed to mimic the response of the Initial LIGO and Virgo gravitational-wave detectors. Nine groups analysed this data using search and parameter-estimation pipelines. Matched filter algorithms, un-modelled-burst searches and Bayesian parameter-estimation and model-selection algorithms were applied to the data. We report the efficiency of these search methods in detecting the numerical waveforms and measuring their parameters. We describe preliminary comparisons between the different search methods and suggest improvements for future NINJA analyses.Comment: 56 pages, 25 figures; various clarifications; accepted to CQ

Eastern partnership migrants in Germany: outcomes, potentials and challenges

Despite the ongoing dialogue on facilitating mobility between the European Union and the Eastern Partnership (EaP) countries, very little is known about the magnitude and characteristics of migration from these countries. We find that EaP migrants experience worse labor market outcomes than other migrant groups, but current and potential migrants hold qualifications in those areas were skill shortages are expected. Therefore, the monitoring and supervision of EaP integration will be consequential in order to understand how much of the current brain waste is driven by poor assessment of foreign qualifications, and to unleash the potential of migration for the German economy