Frequency-domain algorithm for the Lorenz-gauge gravitational self-force

State-of-the-art computations of the gravitational self-force (GSF) on massive particles in black hole spacetimes involve numerical evolution of the metric perturbation equations in the time-domain, which is computationally very costly. We present here a new strategy, based on a frequency-domain treatment of the perturbation equations, which offers considerable computational saving. The essential ingredients of our method are (i) a Fourier-harmonic decomposition of the Lorenz-gauge metric perturbation equations and a numerical solution of the resulting coupled set of ordinary equations with suitable boundary conditions; (ii) a generalized version of the method of extended homogeneous solutions [Phys. Rev. D {\bf 78}, 084021 (2008)] used to circumvent the Gibbs phenomenon that would otherwise hamper the convergence of the Fourier mode-sum at the particle's location; and (iii) standard mode-sum regularization, which finally yields the physical GSF as a sum over regularized modal contributions. We present a working code that implements this strategy to calculate the Lorenz-gauge GSF along eccentric geodesic orbits around a Schwarzschild black hole. The code is far more efficient than existing time-domain methods; the gain in computation speed (at a given precision) is about an order of magnitude at an eccentricity of 0.2, and up to three orders of magnitude for circular or nearly circular orbits. This increased efficiency was crucial in enabling the recently reported calculation of the long-term orbital evolution of an extreme mass ratio inspiral [Phys. Rev. D {\bf 85}, 061501(R) (2012)]. Here we provide full technical details of our method to complement the above report.Comment: 27 pages, 4 figure

Numerical computation of the EOB potential q using self-force results

The effective-one-body theory (EOB) describes the conservative dynamics of compact binary systems in terms of an effective Hamiltonian approach. The Hamiltonian for moderately eccentric motion of two non-spinning compact objects in the extreme mass-ratio limit is given in terms of three potentials: $a(v), \bar{d}(v), q(v)$. By generalizing the first law of mechanics for (non-spinning) black hole binaries to eccentric orbits, [\prd{\bf92}, 084021 (2015)] recently obtained new expressions for $\bar{d}(v)$ and $q(v)$ in terms of quantities that can be readily computed using the gravitational self-force approach. Using these expressions we present a new computation of the EOB potential $q(v)$ by combining results from two independent numerical self-force codes. We determine $q(v)$ for inverse binary separations in the range $1/1200 \le v \lesssim 1/6$. Our computation thus provides the first-ever strong-field results for $q(v)$. We also obtain $\bar{d}(v)$ in our entire domain to a fractional accuracy of $\gtrsim 10^{-8}$. We find to our results are compatible with the known post-Newtonian expansions for $\bar{d}(v)$ and $q(v)$ in the weak field, and agree with previous (less accurate) numerical results for $\bar{d}(v)$ in the strong field.Comment: 4 figures, numerical data at the end. Fixed the typos, added the journal referenc

Efficient hardware implementations of low bit depth motion estimation algorithms

In this paper, we present efficient hardware implementation of multiplication free one-bit transform (MF1BT) based and constraint one-bit transform (C-1BT) based motion estimation (ME) algorithms, in order to provide low bit-depth representation based full search block ME hardware for real-time video encoding. We used a source pixel based linear array (SPBLA) hardware architecture for low bit depth ME for the first time in the literature. The proposed SPBLA based implementation results in a genuine data flow scheme which significantly reduces the number of data reads from the current block memory, which in turn reduces the power consumption by at least 50% compared to conventional 1BT based ME hardware architecture presented in the literature. Because of the binary nature of low bit-depth ME algorithms, their hardware architectures are more efficient than existing 8 bits/pixel representation based ME architectures

Critical phenomena at the threshold of immediate merger in binary black hole systems: the extreme mass ratio case

In numerical simulations of black hole binaries, Pretorius and Khurana [Class. Quant. Grav. {\bf 24}, S83 (2007)] have observed critical behaviour at the threshold between scattering and immediate merger. The number of orbits scales as $n\simeq -\gamma\ln|p-p_*|$ along any one-parameter family of initial data such that the threshold is at $p=p_*$. Hence they conjecture that in ultrarelavistic collisions almost all the kinetic energy can be converted into gravitational waves if the impact parameter is fine-tuned to the threshold. As a toy model for the binary, they consider the geodesic motion of a test particle in a Kerr black hole spacetime, where the unstable circular geodesics play the role of critical solutions, and calculate the critical exponent $\gamma$. Here, we incorporate radiation reaction into this model using the self-force approximation. The critical solution now evolves adiabatically along a sequence of unstable circular geodesic orbits under the effect of the self-force. We confirm that almost all the initial energy and angular momentum are radiated on the critical solution. Our calculation suggests that, even for infinite initial energy, this happens over a finite number of orbits given by $n_\infty\simeq 0.41/\eta$, where $\eta$ is the (small) mass ratio. We derive expressions for the time spent on the critical solution, number of orbits and radiated energy as functions of the initial energy and impact parameter.Comment: Version published in PR

To what extent are the mob languages responsible for the rise and success of ethnically based organized crime in the U.S. from late 19th century to early 20th century?

Mob language studies have seen various attempts at explaining the major effect of the use of this specific language and its contribution to the rise of Mafia in the USA. Different scholars, writers and researchers have variously emphasized the role of crime subcultures and their unique vernaculars in the U.S. In this paper, I would like to report on an even more ambitious claim that the rise organized crime in the U.S. would have not been possible were it not to the wielding of specific mob languages. The goal of the paper is to analyze the selection and use of special vocabulary to bind organized crime members together and avoid the governmental and judiciary control. This paper aims to show how mob languages developed as fusion languages resulting from the interaction of English with the experiences of different groups of people at different times. Crime usually results from socio-economic despair and dissatisfaction. We usually come across these two factors as an end product of immigrant stories and ostracism of different ethnic and socio-economic groups within a society. Out of this situation evolves many things: literature, songs, movies and arts related to this feeling of being the “outcasts”. However, lack of opportunities, feeling of alienation and despair also result in a tendency towards crime. When this situation of becoming the “outcast” occurs to any group, the group’s self-identification changes with its specific circumstances and gives rise to a specific language and culture that is self-evident in various cultural artifacts related to the group. When criminal tendencies permeate the group, this development of language and culture results in the development of a mob language that in return brings about many advantages for organized crime. As far as my research is concerned, my conclusion is that the creation of specific mob languages in the organized crime scene of U.S. has greatly shaped the successes of these criminal organizations