Detecting a stochastic background of gravitational waves by correlating n detectors

We discuss the optimal detection strategy for a stochastic background of gravitational waves in the case n detectors are available. In literature so far, only two cases have been considered: 2- and n-point correlators. We generalize these analysises to m-point correlators (with m<n) built out of the n detector signals, obtaining the result that the optimal choice is to combine 2-point correlators. Correlating n detectors in this optimal way will improve the (suitably defined) signal-to-noise ratio with respect to the n=2 case by a factor equal to the fourth root of n(n-1)/2. Finally we give an estimation of how this could improve the sensitivity for a network of multi-mode spherical antennas.Comment: 12 pages, version accepted by Class. & Quant. Gra

Hermite regularization of the Lattice Boltzmann Method for open source computational aeroacoustics

The lattice Boltzmann method (LBM) is emerging as a powerful engineering tool for aeroacoustic computations. However, the LBM has been shown to present accuracy and stability issues in the medium-low Mach number range, that is of interest for aeroacoustic applications. Several solutions have been proposed but often are too computationally expensive, do not retain the simplicity and the advantages typical of the LBM, or are not described well enough to be usable by the community due to proprietary software policies. We propose to use an original regularized collision operator, based on the expansion in Hermite polynomials, that greatly improves the accuracy and stability of the LBM without altering significantly its algorithm. The regularized LBM can be easily coupled with both non-reflective boundary conditions and a multi-level grid strategy, essential ingredients for aeroacoustic simulations. Excellent agreement was found between our approach and both experimental and numerical data on two different benchmarks: the laminar, unsteady flow past a 2D cylinder and the 3D turbulent jet. Finally, most of the aeroacoustic computations with LBM have been done with commercial softwares, while here the entire theoretical framework is implemented on top of an open source library (Palabos).Comment: 34 pages, 12 figures, The Journal of the Acoustical Society of America (in press

Regularized characteristic boundary condition for the Lattice Boltzmann methods at high Reynolds number flows

This paper reports the investigations done to adapt the Characteristic Boundary Conditions (CBC) to the Lattice-Boltzmann formalism for high Reynolds number applications. Three CBC formalisms are implemented and tested in an open source LBM code: the baseline one-dimension inviscid (BL-LODI) approach, its extension including the effects of the transverse terms (CBC-2D) and a local streamline approach in which the problem is reformulated in the incident wave framework (LS-LODI). Then all implementations of the CBC methods are tested for a variety of test cases, ranging from canonical problems (such as 2D plane and spherical waves and 2D vortices) to a 2D NACA profile at high Reynolds number (Re = 100,000), representative of aeronautic applications. The LS-LODI approach provides the best results for pure acoustics waves (plane and spherical waves). However, it is not well suited to the outflow of a convected vortex for which the CBC-2D associated with a relaxation on density and transverse waves provides the best results. As regards numerical stability, a regularized adaptation is necessary to increase the Reynolds number. The so-called regularized FD adaptation, a modified regularized approach where the off-equilibrium part of the stress tensor is computed thanks to a finite difference scheme, is the only tested adaptation that can handle the high Reynolds computation

Sensitivity analysis and determination of free relaxation parameters for the weakly-compressible MRT-LBM schemes

It is well-known that there exist several free relaxation parameters in the MRT-LBM. Although these parameters have been tuned via linear analysis, the sensitivity analysis of these parameters and other related parameters are still not sufficient for detecting the behaviors of the dispersion and dissipation relations of the MRT-LBM. Previous researches have shown that the bulk dissipation in the MRT-LBM induces a significant over-damping of acoustic disturbances. This indicates that MRT-LBM cannot be used to obtain the correct behavior of pressure fluctuations because of the fixed bulk relaxation parameter. In order to cure this problem, an effective algorithm has been proposed for recovering the linearized Navier-Stokes equations from the linearized MRT-LBM. The recovered L-NSE appear as in matrix form with arbitrary order of the truncation errors with respect to ${\delta}t$. Then, in wave-number space, the first/second-order sensitivity analyses of matrix eigenvalues are used to address the sensitivity of the wavenumber magnitudes to the dispersion-dissipation relations. By the first-order sensitivity analysis, the numerical behaviors of the group velocity of the MRT-LBM are first obtained. Afterwards, the distribution sensitivities of the matrix eigenvalues corresponding to the linearized form of the MRT-LBM are investigated in the complex plane. Based on the sensitivity analysis and the recovered L-NSE, we propose some simplified optimization strategies to determine the free relaxation parameters in the MRT-LBM. Meanwhile, the dispersion and dissipation relations of the optimal MRT-LBM are quantitatively compared with the exact dispersion and dissipation relations. At last, some numerical validations on classical acoustic benchmark problems are shown to assess the new optimal MRT-LBM

Mitochondrial Genomes Reveal an Explosive Radiation of Extinct and Extant Bears near the Miocene-Pliocene Boundary

Background: Despite being one of the most studied families within the Carnivora, the phylogenetic relationships among the members of the bear family (Ursidae) have long remained unclear. Widely divergent topologies have been suggested based on various data sets and methods. Results: We present a fully resolved phylogeny for ursids based on ten complete mitochondrial genome sequences from all eight living and two recently extinct bear species, the European cave bear (Ursus spelaeus) and the American giant short-faced bear (Arctodus simus). The mitogenomic data yield a well-resolved topology for ursids, with the sloth bear at the basal position within the genus Ursus. The sun bear is the sister taxon to both the American and Asian black bears, and this clade is the sister clade of cave bear, brown bear and polar bear confirming a recent study on bear mitochondrial genomes. Conclusion: Sequences from extinct bears represent the third and fourth Pleistocene species for which complete mitochondrial genomes have been sequenced. Moreover, the cave bear specimen demonstrates that mitogenomic studies can be applied to Pleistocene fossils that have not been preserved in permafrost, and therefore have a broad application within ancient DNA research. Molecular dating of the mtDNA divergence times suggests a rapid radiation of bears in both the Old and New Worlds around 5 million years ago, at the Miocene-Pliocene boundary. This coincides with major global changes, such as the Messinian crisis and the first opening of the Bering Strait, and suggests a global influence of such events on species radiations

Mitochondrial genomes reveal an explosive radiation of extinct and extant bears near the Miocene-Pliocene boundary

Background. Despite being one of the most studied families within the Carnivora, the phylogenetic relationships among the members of the bear family (Ursidae) have long remained unclear. Widely divergent topologies have been suggested based on various data sets and methods. Results. We present a fully resolved phylogeny for ursids based on ten complete mitochondrial genome sequences from all eight living and two recently extinct bear species, the European cave bear (Ursus spelaeus) and the American giant short-faced bear (Arctodus simus). The mitogenomic data yield a well-resolved topology for ursids, with the sloth bear at the basal position within the genus Ursus. The sun bear is the sister taxon to both the American and Asian black bears, and this clade is the sister clade of cave bear, brown bear and polar bear confirming a recent study on bear mitochondrial genomes. Conclusion. Sequences from extinct bears represent the third and fourth Pleistocene species for which complete mitochondrial genomes have been sequenced. Moreover, the cave bear specimen demonstrates that mitogenomic studies can be applied to Pleistocene fossils that have not been preserved in permafrost, and therefore have a broad application within ancient DNA research. Molecular dating of the mtDNA divergence times suggests a rapid radiation of bears in both the Old and New Worlds around 5 million years ago, at the Miocene-Pliocene boundary. This coincides with major global changes, such as the Messinian crisis and the first opening of the Bering Strait, and suggests a global influence of such events on species radiations.Facultad de Ciencias Naturales y Muse

Consistent subgrid scale modelling for lattice Boltzmann methods

International audienceThe lattice Boltzmann method has become a widely used tool for the numerical simulation of fluid flows and in particular of turbulent flows. In this frame the inclusion of subgrid scale closures is of crucial importance and is not completely understood from the theoretical point of view. Here, we propose a consistent way of introducing subgrid closures in the BGK Boltzmann equation for large eddy simulations of turbulent flows. Based on the Hermite expansion of the velocity distribution function, we construct a hierarchy of subgrid scale terms, which are similar to those obtained for the Navier–Stokes equations, and discuss their inclusion in the lattice Boltzmann method scheme. A link between our approach and the standard way on including eddy viscosity models in the lattice Boltzmann method is established. It is shown that the use of a single modified scalar relaxation time to account for subgrid viscosity effects is not consistent in the compressible case. Finally, we validate the approach in the weakly compressible case by simulating the time developing mixing layer and comparing with experimental results and direct numerical simulations

Advanced large-eddy simulation for lattice Boltzmann methods: The approximate deconvolution model

International audienceThe aim of this paper is to extend the approximate deconvolutionmodel for large-eddy simulations to the lattice Boltzmann method. This approach allows to directly act on the velocity distribution function and is based on the intrinsic nonlinearities of the lattice Boltzmann methods. It is not a straightforward extrapolation of classical eddy-viscosity models developed within the Navier–Stokes framework, which exhibits a convective quadratic nonlinearity in the incompressible flow case. A simple implementation is presented, which relies on the implementation of an ad hoc linear filter in any basic lattice Boltzmann solver. The new model is validated on the turbulent, time developing mixing layer, and a very satisfactory agreement is found with existing direct numerical simulations results. The equivalent Navier-Stokes-type macroscopic model is also discussed