Highly-Resolved Numerical Simulation of the Turbulent Combustion Process in Experimental Burners

This paper presents investigations of experimentally well-characterised turbulent flames with highly-resolved Large Eddy Simulations (LES) and Direct Numerical Simulations (DNS). The combustion process is modelled with a flamelet-based approach, which assumes that the local turbulent flame structure can be described by an ensemble of wrinkled laminar flames. Good agreements between the simulation results and experimental measurement data is achieved. The governing equations are discretised with the Finite Volume Method (FVM). The numerical implementation is tailored for massively parallel simulations on a large number of grid cells. The computational efficiency benefits from the applied simple grid structure and the use of non-blocking Message Passing Interface (MPI) parallelisation

Circular orbits and spin in black-hole initial data

The construction of initial data for black-hole binaries usually involves the choice of free parameters that define the spins of the black holes and essentially the eccentricity of the orbit. Such parameters must be chosen carefully to yield initial data with the desired physical properties. In this paper, we examine these choices in detail for the quasiequilibrium method coupled to apparent-horizon/quasiequilibrium boundary conditions. First, we compare two independent criteria for choosing the orbital frequency, the "Komar-mass condition" and the "effective-potential method," and find excellent agreement. Second, we implement quasi-local measures of the spin of the individual holes, calibrate these with corotating binaries, and revisit the construction of non-spinning black hole binaries. Higher-order effects, beyond those considered in earlier work, turn out to be important. Without those, supposedly non-spinning black holes have appreciable quasi-local spin; furthermore, the Komar-mass condition and effective potential method agree only when these higher-order effects are taken into account. We compute a new sequence of quasi-circular orbits for non-spinning black-hole binaries, and determine the innermost stable circular orbit of this sequence.Comment: 24 pages, 17 figures, accepted for publication in Physical Review D, revtex4; Fixed error in computing proper separation and updated figures and tables accordingly, added reference to Sec. IV.A, fixed minor error in Sec. IV.B, added new data to Tables IV and V, fixed 1 reference, fixed error in Eq. (A7b), included minor changes from PRD editin

Post-Newtonian Freely Specifiable Initial Data for Binary Black Holes in Numerical Relativity

Construction of astrophysically realistic initial data remains a central problem when modelling the merger and eventual coalescence of binary black holes in numerical relativity. The objective of this paper is to provide astrophysically realistic freely specifiable initial data for binary black hole systems in numerical relativity, which are in agreement with post-Newtonian results. Following the approach taken by Blanchet, we propose a particular solution to the time-asymmetric constraint equations, which represent a system of two moving black holes, in the form of the standard conformal decomposition of the spatial metric and the extrinsic curvature. The solution for the spatial metric is given in symmetric tracefree form, as well as in Dirac coordinates. We show that the solution differs from the usual post-Newtonian metric up to the 2PN order by a coordinate transformation. In addition, the solutions, defined at every point of space, differ at second post-Newtonian order from the exact, conformally flat, Bowen-York solution of the constraints.Comment: 41 pages, no figures, accepted for publication in Phys. Rev. D, significant revision in presentation (including added references and corrected typos

The Loschmidt Echo as a robust decoherence quantifier for many-body systems

We employ the Loschmidt Echo, i.e. the signal recovered after the reversal of an evolution, to identify and quantify the processes contributing to decoherence. This procedure, which has been extensively used in single particle physics, is here employed in a spin ladder. The isolated chains have 1/2 spins with XY interaction and their excitations would sustain a one-body like propagation. One of them constitutes the controlled system S whose reversible dynamics is degraded by the weak coupling with the uncontrolled second chain, i.e. the environment E. The perturbative SE coupling is swept through arbitrary combinations of XY and Ising like interactions, that contain the standard Heisenberg and dipolar ones. Different time regimes are identified for the Loschmidt Echo dynamics in this perturbative configuration. In particular, the exponential decay scales as a Fermi golden rule, where the contributions of the different SE terms are individually evaluated and analyzed. Comparisons with previous analytical and numerical evaluations of decoherence based on the attenuation of specific interferences, show that the Loschmidt Echo is an advantageous decoherence quantifier at any time, regardless of the S internal dynamics.Comment: 12 pages, 6 figure

Aligned Spins: Orbital Elements, Decaying Orbits, and Last Stable Circular Orbit to high post-Newtonian Orders

In this article the quasi-Keplerian parameterisation for the case that spins and orbital angular momentum in a compact binary system are aligned or anti-aligned with the orbital angular momentum vector is extended to 3PN point-mass, next-to-next-to-leading order spin-orbit, next-to-next-to-leading order spin(1)-spin(2), and next-to-leading order spin-squared dynamics in the conservative regime. In a further step, we use the expressions for the radiative multipole moments with spin to leading order linear and quadratic in both spins to compute radiation losses of the orbital binding energy and angular momentum. Orbital averaged expressions for the decay of energy and eccentricity are provided. An expression for the last stable circular orbit is given in terms of the angular velocity type variable $x$.Comment: 30 pages, 2 figures, v2: update to match published versio

Gravitational radiation reaction in compact binary systems: Contribution of the quadrupole-monopole interaction

The radiation reaction in compact spinning binaries on eccentric orbits due to the quadrupole-monopole interaction is studied. This contribution is of second post-Newtonian order. As result of the precession of spins the magnitude $L$ of the orbital angular momentum is not conserved. Therefore a proper characterization of the perturbed radial motion is provided by the energy $E$ and angular average $\bar{L}$. As powerful computing tools, the generalized true and eccentric anomaly parametrizations are introduced. Then the secular losses in energy and magnitude of orbital angular momentum together with the secular evolution of the relative orientations of the orbital angular momentum and spins are found for eccentric orbits by use of the residue theorem. The circular orbit limit of the energy loss agrees with Poisson's earlier result.Comment: accepted for publication in Phys. Rev.

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

Gravitational radiation reaction in compact binary systems: Contribution of the magnetic dipole-magnetic dipole interaction

We study the gravitational radiation reaction in compact binary systems composed of neutron stars with spin and huge magnetic dipole moments (magnetars). The magnetic dipole moments undergo a precessional motion about the respective spins. At sufficiently high values of the magnetic dipole moments, their interaction generates second post-Newtonian order contributions both to the equations of motion and to the gravitational radiation escaping the system. We parametrize the radial motion and average over a radial period in order to find the secular contributions to the energy and magnitude of the orbital angular momentum losses, in the generic case of \textit{eccentric} orbits. Similarly as for the spin-orbit, spin-spin, quadrupole-monopole interactions, here too we deduce the secular evolution of the relative orientations of the orbital angular momentum and spins. These equations, supplemented by the evolution equations for the angles characterizing the orientation of the dipole moments form a first order differential system, which is closed. The circular orbit limit of the energy loss agrees with Ioka and Taniguchi's earlier result

Spin-spin effects in radiating compact binaries

The dynamics of a binary system with two spinning components on an eccentric orbit is studied, with the inclusion of the spin-spin interaction terms appearing at the second post-Newtonian order. A generalized true anomaly parametrization properly describes the radial component of the motion. The average over one radial period of the magnitude of the orbital angular momentum $\bar{L}$ is found to have no nonradiative secular change. All spin-spin terms in the secular radiative loss of the energy and magnitude of orbital angular momentum are given in terms of $\bar{L}$ and other constants of the motion. Among them, self-interaction spin effects are found, representing the second post-Newtonian correction to the 3/2 post-Newtonian order Lense-Thirring approximation.Comment: 12 pages, to appear in Phys. Rev.

Spin effects in gravitational radiation backreaction II. Finite mass effects

A convenient formalism for averaging the losses produced by gravitational radiation backreaction over one orbital period was developed in an earlier paper. In the present paper we generalize this formalism to include the case of a closed system composed from two bodies of comparable masses, one of them having the spin S. We employ the equations of motion given by Barker and O'Connell, where terms up to linear order in the spin (the spin-orbit interaction terms) are kept. To obtain the radiative losses up to terms linear in the spin, the equations of motion are taken to the same order. Then the magnitude L of the angular momentum L, the angle kappa subtended by S and L and the energy E are conserved. The analysis of the radial motion leads to a new parametrization of the orbit. From the instantaneous gravitational radiation losses computed by Kidder the leading terms and the spin-orbit terms are taken. Following Apostolatos, Cutler, Sussman and Thorne, the evolution of the vectors S and L in the momentary plane spanned by these vectors is separated from the evolution of the plane in space. The radiation-induced change in the spin is smaller than the leading-order spin terms in the momentary angular momentum loss. This enables us to compute the averaged losses in the constants of motion E, L and L_S=L cos kappa. In the latter, the radiative spin loss terms average to zero. An alternative description using the orbital elements a,e and kappa is given. The finite mass effects contribute terms, comparable in magnitude, to the basic, test-particle spin terms in the averaged losses.Comment: 12 pages, 1 figure, Phys.Rev.D15, March, 199