Metric perturbations from eccentric orbits on a Schwarzschild black hole: I. Odd-parity Regge-Wheeler to Lorenz gauge transformation and two new methods to circumvent the Gibbs phenomenon

We calculate the odd-parity, radiative ($\ell \ge 2$) parts of the metric perturbation in Lorenz gauge caused by a small compact object in eccentric orbit about a Schwarzschild black hole. The Lorenz gauge solution is found via gauge transformation from a corresponding one in Regge-Wheeler gauge. Like the Regge-Wheeler gauge solution itself, the gauge generator is computed in the frequency domain and transferred to the time domain. The wave equation for the gauge generator has a source with a compact, moving delta-function term and a discontinuous non-compact term. The former term allows the method of extended homogeneous solutions to be applied (which circumvents the Gibbs phenomenon). The latter has required the development of new means to use frequency domain methods and yet be able to transfer to the time domain while avoiding Gibbs problems. Two new methods are developed to achieve this: a partial annihilator method and a method of extended particular solutions. We detail these methods and show their application in calculating the odd-parity gauge generator and Lorenz gauge metric perturbations. A subsequent paper will apply these methods to the harder task of computing the even-parity parts of the gauge generator.Comment: 17 pages, 9 figures, Updated with one modified figure and minor changes to the text. Added DOI and Journal referenc

Gravitational perturbations and metric reconstruction: Method of extended homogeneous solutions applied to eccentric orbits on a Schwarzschild black hole

We calculate the gravitational perturbations produced by a small mass in eccentric orbit about a much more massive Schwarzschild black hole and use the numerically computed perturbations to solve for the metric. The calculations are initially made in the frequency domain and provide Fourier-harmonic modes for the gauge-invariant master functions that satisfy inhomogeneous versions of the Regge-Wheeler and Zerilli equations. These gravitational master equations have specific singular sources containing both delta function and derivative-of-delta function terms. We demonstrate in this paper successful application of the method of extended homogeneous solutions, developed recently by Barack, Ori, and Sago, to handle source terms of this type. The method allows transformation back to the time domain, with exponential convergence of the partial mode sums that represent the field. This rapid convergence holds even in the region of $r$ traversed by the point mass and includes the time-dependent location of the point mass itself. We present numerical results of mode calculations for certain orbital parameters, including highly accurate energy and angular momentum fluxes at infinity and at the black hole event horizon. We then address the issue of reconstructing the metric perturbation amplitudes from the master functions, the latter being weak solutions of a particular form to the wave equations. The spherical harmonic amplitudes that represent the metric in Regge-Wheeler gauge can themselves be viewed as weak solutions. They are in general a combination of (1) two differentiable solutions that adjoin at the instantaneous location of the point mass (a result that has order of continuity $C^{-1}$ typically) and (2) (in some cases) a delta function distribution term with a computable time-dependent amplitude.Comment: 25 pages, 5 figures, Updated with minor change

Indian Gaming: Issues and Prospects

This article explains the evolution of Indian gaming from economic and social perspectives. Many of the political opportunities and threats to Indian gaming are examined, and current and future issues surrounding Indian gaming are further explored

Learning Articulated Motions From Visual Demonstration

Many functional elements of human homes and workplaces consist of rigid components which are connected through one or more sliding or rotating linkages. Examples include doors and drawers of cabinets and appliances; laptops; and swivel office chairs. A robotic mobile manipulator would benefit from the ability to acquire kinematic models of such objects from observation. This paper describes a method by which a robot can acquire an object model by capturing depth imagery of the object as a human moves it through its range of motion. We envision that in future, a machine newly introduced to an environment could be shown by its human user the articulated objects particular to that environment, inferring from these "visual demonstrations" enough information to actuate each object independently of the user. Our method employs sparse (markerless) feature tracking, motion segmentation, component pose estimation, and articulation learning; it does not require prior object models. Using the method, a robot can observe an object being exercised, infer a kinematic model incorporating rigid, prismatic and revolute joints, then use the model to predict the object's motion from a novel vantage point. We evaluate the method's performance, and compare it to that of a previously published technique, for a variety of household objects.Comment: Published in Robotics: Science and Systems X, Berkeley, CA. ISBN: 978-0-9923747-0-

Ion-Neutral Collisions in the Interstellar Medium: Wave Damping and Elimination of Collisionless Processes

Most phases of the interstellar medium contain neutral atoms in addition to ions and electrons. This introduces differences in plasma physics processes in those media relative to the solar corona and the solar wind at a heliocentric distance of 1 astronomical unit. In this paper, we consider two well-diagnosed, partially-ionized interstellar plasmas. The first is the Diffuse Ionized Gas (DIG) which is probably the extensive phase in terms of volume. The second is the gas that makes up the Local Clouds of the Very Local Interstellar Medium (VLISM). Ion-neutral interactions seem to be important in both media. In the DIG, ion-neutral collisions are relatively rare, but sufficiently frequent to damp magnetohydrodynamic (MHD) waves (as well as propagating MHD eddies) within less than a parsec of the site of generation. This result raises interesting questions about the sources of turbulence in the DIG. In the case of the VLISM, the ion-neutral collision frequency is higher than that in the DIG, because the hydrogen is partially neutral rather than fully ionized. We present results showing that prominent features of coronal and solar wind turbulence seem to be absent in VLISM turbulence. For example, ion temperature does not depend on ion mass. This difference may be attributable to ion-neutral collisions, which distribute power from more effectively heated massive ions such as iron to other ion species and neutral atoms.Comment: Submitted to American Institute of Physics Conference Proceedings for conference "Partially Ionized Plasmas Throughout the Cosmos", Dastgeer Shaikh, edito

Observational Tests of the Properties of Turbulence in the Very Local Interstellar Medium

The Very Local Interstellar Medium (VLISM) contains clouds which consist of partially-ionized plasma. These clouds can be effectively diagnosed via high resolution optical and ultraviolet spectroscopy of the absorption lines they form in the spectra of nearby stars. Among the information provided by these spectroscopic measurements are the root-mean-square velocity fluctuation due to turbulence in these clouds and the ion temperature, which may be partially determined by dissipation of turbulence. We consider whether this turbulence resembles the extensively studied and well-diagnosed turbulence in the solar wind and solar corona. Published observations are used to determine if the velocity fluctuations are primarily transverse to a large-scale magnetic field, whether the temperature perpendicular to the large scale field is larger than that parallel to the field, and whether ions with larger Larmor radii have higher temperatures than smaller gyroradius ions. Although a thorough investigation of the data is underway, a preliminary examination of the published data shows neither evidence for anisotropy of the velocity fluctuations or temperature, nor Larmor radius-dependent heating. These results indicate differences between solar wind and Local Cloud turbulence.Comment: Paper submitted to Nonlinear Processes in Geophysic

Mississippi River Research Conclusions Executive Summary

Briefing paper requested by Senator Bond detailing the conclusions from the Mississippi River research to date.Agricultural and Food Policy, Environmental Economics and Policy,