Fast spectral source integration in black hole perturbation calculations

This paper presents a new technique for achieving spectral accuracy and fast computational performance in a class of black hole perturbation and gravitational self-force calculations involving extreme mass ratios and generic orbits. Called \emph{spectral source integration} (SSI), this method should see widespread future use in problems that entail (i) point-particle description of the small compact object, (ii) frequency domain decomposition, and (iii) use of the background eccentric geodesic motion. Frequency domain approaches are widely used in both perturbation theory flux-balance calculations and in local gravitational self-force calculations. Recent self-force calculations in Lorenz gauge, using the frequency domain and method of extended homogeneous solutions, have been able to accurately reach eccentricities as high as $e \simeq 0.7$. We show here SSI successfully applied to Lorenz gauge. In a double precision Lorenz gauge code, SSI enhances the accuracy of results and makes a factor of three improvement in the overall speed. The primary initial application of SSI--for us its \emph{raison d'\^{e}tre}--is in an arbitrary precision \emph{Mathematica} code that computes perturbations of eccentric orbits in the Regge-Wheeler gauge to extraordinarily high accuracy (e.g., 200 decimal places). These high accuracy eccentric orbit calculations would not be possible without the exponential convergence of SSI. We believe the method will extend to work for inspirals on Kerr, and will be the subject of a later publication. SSI borrows concepts from discrete-time signal processing and is used to calculate the mode normalization coefficients in perturbation theory via sums over modest numbers of points around an orbit. A variant of the idea is used to obtain spectral accuracy in solution of the geodesic orbital motion.Comment: 15 pages, 7 figure

Experiencing Joy Through Confession

The step of trust (confession) is what led to joy for David in Psalm 32, and it can lead to joy for each of us. Posting about repentance from In All Things - an online hub committed to the claim that the life, death, and resurrection of Jesus Christ has implications for the entire world. http://inallthings.org/experiencing-joy-through-confession

The Pursuit of Personal Development Preparing for a Holistic Mentoring Relationship

This research explores how self reflection can be used in the development of personal development goals to aid in guiding the mentoring process. The following research methods used for this study: a literature review investigation of self-reflection practices/models to identify strategies for the development of personal development goals; a survey to evaluate how identified goals may aid in mentor selection; and interviews with self-development professionals to analyze their insights on what role personal development goals play in guiding the mentoring process. Findings were based on parallels found between the data gathered from the various sources

Determination of new coefficients in the angular momentum and energy fluxes at infinity to 9PN for eccentric Schwarzschild extreme-mass-ratio inspirals using mode-by-mode fitting

We present an extension of work in an earlier paper showing high precision comparisons between black hole perturbation theory and post-Newtonian (PN) theory in their region of overlapping validity for bound, eccentric-orbit, Schwarzschild extreme-mass-ratio inspirals. As before we apply a numerical fitting scheme to extract eccentricity coefficients in the PN expansion of the gravitational wave fluxes, which are then converted to exact analytic form using an integer-relation algorithm. In this work, however, we fit to individual $lmn$ modes to exploit simplifying factorizations that lie therein. Since the previous paper focused solely on the energy flux, here we concentrate initially on analyzing the angular momentum flux to infinity. A first step involves finding convenient forms for hereditary contributions to the flux at low-PN order, analogous to similar terms worked out previously for the energy flux. We then apply the upgraded techniques to find new PN terms through 9PN order and (at many PN orders) to $e^{30}$ in the power series in eccentricity. With the new approach applied to angular momentum fluxes, we return to the energy fluxes at infinity to extend those previous results. Like before, the underlying method uses a \textsc{Mathematica} code based on use of the Mano-Suzuki-Takasugi (MST) function expansion formalism to represent gravitational perturbations and spectral source integration (SSI) to find numerical results at arbitrarily high precision.Comment: 36 pages, 1 figur

The Pursuit of Acquisition Intrapreneurs

This report represents research conducted at the Massachusetts Institute of Technology under the Lean Aerospace Initiative (LAI) program. The research focused on identifying Acquisition Intrapreneurs, viewed and defined for the purpose of this research as, individuals within the acquisition profession who take direct responsibility for turning ideas into products through assertive risk taking. The basis for this research stems from the agile acquisition push for “breeding innovators” to achieve a leaner and more responsive approach to the design, build, test and fielding of warfighting systems

Extro-spection, Empowering Expectations, and Convenient Healing?

Faith and healing can be experienced in prayer, touch, medical expertise, words, intercession, and so much more. Posting about ­­­­­­­­the Centurion\u27s faith from In All Things - an online hub committed to the claim that the life, death, and resurrection of Jesus Christ has implications for the entire world. http://inallthings.org/extro-spection-empowering-expectations-and-convenient-healing

Three Steps of I Am

Jesus lived out the antithesis ‘I am’ by deflecting attention, avoiding defensiveness, and slipping away from unnecessary confrontations. Posting about giving God the glory during the Lenten season from In All Things - an online hub committed to the claim that the life, death, and resurrection of Jesus Christ has implications for the entire world. http://inallthings.org/three-steps-of-i-am