Proper generalized decomposition for parameterized Helmholtz problems in heterogeneous and unbounded domains: Application to harbor agitation

Solving the Helmholtz equation for a large number of input data in an heterogeneous media and unbounded domain still represents a challenge. This is due to the particular nature of the Helmholtz operator and the sensibility of the solution to small variations of the data. Here a reduced order model is used to determine the scattered solution everywhere in the domain for any incoming wave direction and frequency. Moreover, this is applied to a real engineering problem: water agitation inside real harbors for low to mid-high frequencies. The Proper Generalized Decomposition (PGD) model reduction approach is used to obtain a separable representation of the solution at any point and for any incoming wave direction and frequency. Here, its applicability to such a problem is discussed and demonstrated. More precisely, the separability of the operator is addressed taking into account both the non-constant co

Intermediate-mass-ratio-inspirals in the Einstein Telescope: I. Signal-to-noise ratio calculations

The Einstein Telescope (ET) is a proposed third generation ground-based interferometer, for which the target is a sensitivity that is a factor of ten better than Advanced LIGO and a frequency range that extends down to about 1Hz. ET will provide opportunities to test Einstein's theory of relativity in the strong field and will realize precision gravitational wave astronomy with a thousandfold increase in the expected number of events over the advanced ground-based detectors. A design study for ET is currently underway, so it is timely to assess the science that could be done with such an instrument. This paper is the first in a series that will carry out a detailed study of intermediate-mass-ratio inspirals (IMRIs) for ET. In the context of ET, an IMRI is the inspiral of a neutron star or stellar-mass black hole into an intermediate mass black hole (IMBH). In this paper we focus on the development of IMRI waveform models for circular and equatorial inspirals. We consider two approximations for the waveforms, which both incorporate the inspiral, merger and ringdown phases in a consistent way. One approximation, valid for IMBHs of arbitrary spin, uses the transition model of Ori and Thorne [1] to describe the merger, and this is then matched smoothly onto a ringdown waveform. The second approximation uses the Effective One Body (EOB) approach to model the merger phase of the waveform and is valid for non-spinning IMBHs. In this paper, we use both waveform models to compute signal-to-noise ratios (SNRs) for IMRI sources detectable by ET. At a redshift of z=1, we find typical SNRs for IMRI systems with masses 1.4+100 solar masses, 10+100 solar masses, 1.4+500 solar masses and 10+500 solar masses of about 10-25, 40-80, 3-15 and 10-60, respectively. We also find that the two models make predictions for non-spinning inspirals that are consistent to about ten percent.Comment: 27 pages, 9 figures, v3 has an updated reference for consistency with accepted versio

Symmetry limit properties of a priori mixing amplitudes for non-leptonic and weak radiative decays of hyperons

We show that the so-called parity-conserving amplitudes predicted in the a priori mixing scheme for non-leptonic and weak radiative decays of hyperons vanish in the strong-flavor symmetry limit

Proper generalised decomposition for the solution of geometrically parametrised Stokes flow problems

The ability to predict, and ultimately optimise, aerodynamic forces when the design variable is the geometric definition of the domain is of great importance in many areas of computational fluid dynamics. This problem is known to be extremely computationally intensive due to the vast number of configurations that must be tested and the high computational cost of each one of the simulations involved in the optimisation process. In this talk a novel approach for computing an off-line solution for a set of geometric parameters that define the computational domain will be presented. The proposed approach is based on the proper generalised decomposition and, contrary to similar approaches, the geometric parameters are the position of the control points that define the NURBS boundary representation. Examples involving the solution of Stokes flow problems in two and three dimensions will be used to demonstrate the potential of the proposed approach

X-ray photoelectron spectroscopy studies of non-stoichiometric superconducting NbB2+x

Polycrystalline samples of NbB2+x with nominal composition (B/Nb) = 2.0, 2.1, 2.2, 2.3, 2.4 and 2.5 were studied by X-ray photoelectron spectroscopy (XPS). The spectra revealed Nb and B oxides on the surface of the samples, mainly B2O3 and Nb2O5. After Ar ion etching the intensity of Nb and B oxides decreased. The Nb 3d5/2 and B 1s core levels associated with the chemical states (B/Nb) were identified and they do not change with etching time. The Binding Energy of the Nb 3d5/2 and B 1s core levels increase as boron content increases, suggesting a positive chemical shift in the core levels. On the other hand, analysis of Valence Band spectra showed that the contribution of the Nb 4d states slightly decreased while the contribution of the B 2p(pi) states increased as the boron content increased. As a consequence, the electronic and superconducting properties were substantially modified, in good agreement with band-structure calculations.Comment: 10 pages, 7 figures, 1 tabl

Initial Data and Eccentricity Reduction Toolkit for Binary Black Hole Numerical Relativity Waveforms

The production of numerical relativity waveforms that describe quasicircular binary black hole mergers requires high-quality initial data, and an algorithm to iteratively reduce residual eccentricity. To date, these tools remain closed source, or in commercial software that prevents their use in high performance computing platforms. To address these limitations, and to ensure that the broader numerical relativity community has access to these tools, herein we provide all the required elements to produce high-quality numerical relativity simulations in supercomputer platforms, namely: open source parameter files to numerical simulate spinning black hole binaries with asymmetric mass-ratios; open source $\texttt{Python}$ tools to produce high-quality initial data for numerical relativity simulations of spinning black hole binaries on quasi-circular orbits; open source $\texttt{Python}$ tools for eccentricity reduction, both as stand-alone software and deployed in the $\texttt{Einstein Toolkit}$'s software infrastructure. This open source toolkit fills in a critical void in the literature at a time when numerical relativity has an ever increasing role in the study and interpretation of gravitational wave sources. As part of our community building efforts, and to streamline and accelerate the use of these resources, we provide tutorials that describe, step by step, how to obtain and use these open source numerical relativity tools

Numerical stability of a fixed point iterative method to determine patterns of turbulent flow in a rectangular cavity with different aspect ratios

2D isothermal viscous incompressible flows are presented from the Navier- Stokes equations in the Stream function-vorticity formulation and in the velocity-vorticity formulation. The simulation is made using a numerical method based on a fixed point it- erative process to solve the nonlinear elliptic system that results after time discretization. The iterative process leads us to the solution of uncoupled, well-conditioned, symmetric linear elliptic problems from which efficient solvers exist regardless of the space discretiza- tion. The experiments take place on the lid driven cavity problem for Reynolds numbers up to Re = 10000 and different aspect ratios A (A=ratio of the height to the width) A = 1 and A /= 1 such aAs = 1/2, till A = 3. It appears that with velocity and vorticity variables is more difficult to solve this kind of flows, at least with a numerical procedure similar to the one applied in stream function and vorticity variables to solve an analogous nonlinear elliptic system. To obtain such flows is not an easy task, especially with the velocity-vorticity formulation. We report here results for moderate Reynolds numbers (Re 10000), although with them enough effectiveness is achieved to be able to vary the aspect ratio of the cavity A, which causes the flow to be more unstable. Con- tribution in this work is to consider rectangular cavities of drag, which can impact on isothermal turbulent flow patterns. Another contribution is to include a wide region of the Reynolds number as well as different aspect ratios where we tested stability of the numerical scheme

Hyperspherical entanglement entropy

The coefficient of the log term in the entanglement entropy associated with hyperspherical surfaces in flat space-time is shown to equal the conformal anomaly by conformally transforming Euclideanised space--time to a sphere and using already existing formulae for the relevant heat--kernel coefficients after cyclic factoring. The analytical reason for the result is that the conformal anomaly on the lune has an extremum at the ordinary sphere limit. A proof is given. Agreement with a recent evaluation of the coefficient is found.Comment: 7 pages. Final revision. Historical comments amended. Minor remarks adde