Highly eccentric inspirals into a black hole

We model the inspiral of a compact stellar-mass object into a massive nonrotating black hole including all dissipative and conservative first-order-in-the-mass-ratio effects on the orbital motion. The techniques we develop allow inspirals with initial eccentricities as high as $e\sim0.8$ and initial separations as large as $p\sim 50$ to be evolved through many thousands of orbits up to the onset of the plunge into the black hole. The inspiral is computed using an osculating elements scheme driven by a hybridized self-force model, which combines Lorenz-gauge self-force results with highly accurate flux data from a Regge-Wheeler-Zerilli code. The high accuracy of our hybrid self-force model allows the orbital phase of the inspirals to be tracked to within $\sim0.1$ radians or better. The difference between self-force models and inspirals computed in the radiative approximation is quantified.Comment: Updated to reflect published versio

Evolution of small-mass-ratio binaries with a spinning secondary

We calculate the evolution and gravitational-wave emission of a spinning compact object inspiraling into a substantially more massive (non-rotating) black hole. We extend our previous model for a non-spinning binary [Phys. Rev. D 93, 064024] to include the Mathisson-Papapetrou-Dixon spin-curvature force. For spin-aligned binaries we calculate the dephasing of the inspiral and associated waveforms relative to models that do not include spin-curvature effects. We find this dephasing can be either positive or negative depending on the initial separation of the binary. For binaries in which the spin and orbital angular momentum are not parallel, the orbital plane precesses and we use a more general osculating element prescription to compute inspirals.Comment: 17 pages, 6 figure

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

Managing Risk After Intracerebral Hemorrhage in Concomitant Atrial Fibrillation and Cerebral Amyloid Angiopathy.

The Dunhill Medical Trust (Grant ID: RTF44/0114)This is the author accepted manuscript. The final version is available from the American Heart Association via http://dx.doi.org/10.1161/STROKEAHA.116.01332

Direct conversion of rheological compliance measurements into storage and loss moduli

We remove the need for Laplace/inverse-Laplace transformations of experimental data, by presenting a direct and straightforward mathematical procedure for obtaining frequency-dependent storage and loss moduli ($G'(\omega)$ and $G"(\omega)$ respectively), from time-dependent experimental measurements. The procedure is applicable to ordinary rheological creep (stress-step) measurements, as well as all microrheological techniques, whether they access a Brownian mean-square displacement, or a forced compliance. Data can be substituted directly into our simple formula, thus eliminating traditional fitting and smoothing procedures that disguise relevant experimental noise.Comment: 4 page

Repeated faint quasinormal bursts in extreme-mass-ratio inspiral waveforms: Evidence from frequency-domain scalar self-force calculations on generic Kerr orbits

We report development of a code to calculate the scalar self-force on a scalar-charged particle moving on generic bound orbits in the Kerr spacetime. The scalar self-force model allows rapid development of computational techniques relevant to generic gravitational extreme-mass-ratio inspirals (EMRIs). Our frequency-domain calculations are made with arbitrary numerical precision code written in \textsc{Mathematica}. We extend spectral source integration techniques to the Kerr spacetime, increasing computational efficiency. We model orbits with nearly arbitrary inclinations $0\leq\iota<\pi/2$ and eccentricities up to $e \lesssim 0.8$. This effort extends earlier work by Warburton and Barack where motion was restricted to the equatorial plane or to inclined spherical orbits. Consistent with a recent discovery by Thornburg and Wardell \cite{ThorWard17} in time-domain calculations, we observe self-force oscillations during the radially-outbound portion of highly eccentric orbits around a rapidly rotating black hole. As noted previously, these oscillations reflect coupling into the self-force by quasinormal modes excited during pericenter passage. Our results confirm the effect with a frequency-domain code. \emph{More importantly, we find that quasinormal bursts (QNBs) appear directly in the waveform following each periastron passage.} These faint bursts are shown to be a superposition of the least-damped overtone (i.e., fundamental) of at least four ($l=m \le 4$) quasinormal modes. Our results suggest that QNBs should appear in gravitational waveforms, and thus provide a gauge-invariant signal. Potentially observable in high signal-to-noise ratio EMRIs, QNBs would provide high-frequency components to the parameter estimation problem that would complement low-frequency elements of the waveform.Comment: 28 pages, 11 figures, 5 tables; Updated to reflect published versio

Spontaneous Breaking of Translational Invariance in One-Dimensional Stationary States on a Ring

We consider a model in which positive and negative particles diffuse in an asymmetric, CP-invariant way on a ring. The positive particles hop clockwise, the negative counterclockwise and oppositely-charged adjacent particles may swap positions. Monte-Carlo simulations and analytic calculations suggest that the model has three phases; a "pure" phase in which one has three pinned blocks of only positive, negative particles and vacancies, and in which translational invariance is spontaneously broken, a "mixed" phase with a non-vanishing current in which the three blocks are positive, negative and neutral, and a disordered phase without blocks.Comment: 7 pages, LaTeX, needs epsf.st

Superconductivity from perturbative one-gluon exchange in high density quark matter

We study color superconductivity in QCD at asymptotically large chemical potential. In this limit, pairing is dominated by perturbative one-gluon exchange. We derive the Eliashberg equation for the pairing gap and solve this equation numerically. Taking into account both magnetic and electric gluon exchanges, we find $\Delta\sim g^{-5}\exp(-c/g)$ with $c=3\pi^2/\sqrt{2}$, verifying a recent result by Son. For chemical potentials that are of physical interest, $\mu< 1$ GeV, the calculation ceases to be reliable quantitatively, but our results suggest that the gap can be as large as 100 MeV.Comment: 19 pages, 6 figures. I accidentally replaced the paper with an outdated version. This version has typos corrected and will appear in PR

Non-equilibrium Lorentz gas on a curved space

The periodic Lorentz gas with external field and iso-kinetic thermostat is equivalent, by conformal transformation, to a billiard with expanding phase-space and slightly distorted scatterers, for which the trajectories are straight lines. A further time rescaling allows to keep the speed constant in that new geometry. In the hyperbolic regime, the stationary state of this billiard is characterized by a phase-space contraction rate, equal to that of the iso-kinetic Lorentz gas. In contrast to the iso-kinetic Lorentz gas where phase-space contraction occurs in the bulk, the phase-space contraction rate here takes place at the periodic boundaries

Steady-state conduction in self-similar billiards

The self-similar Lorentz billiard channel is a spatially extended deterministic dynamical system which consists of an infinite one-dimensional sequence of cells whose sizes increase monotonically according to their indices. This special geometry induces a nonequilibrium stationary state with particles flowing steadily from the small to the large scales. The corresponding invariant measure has fractal properties reflected by the phase-space contraction rate of the dynamics restricted to a single cell with appropriate boundary conditions. In the near-equilibrium limit, we find numerical agreement between this quantity and the entropy production rate as specified by thermodynamics