Implications of the r-mode instability of rotating relativistic stars

Several recent surprises appear dramatically to have improved the likelihood that the spin of rapidly rotating, newly formed neutron stars (and, possibly, of old stars spun up by accretion) is limited by a nonaxisymmetric instability driven by gravitational waves. Except for the earliest part of the spin-down, the axial l=m=2 mode (an r-mode) dominates the instability, and the emitted waves may be observable by detectors with the sensitivity of LIGO II. A review of these hopeful results is followed by a discussion of constraints on the instability set by dissipative mechanisms, including viscosity, nonlinear saturation, and energy loss to a magnetic field driven by differential rotation.Comment: 20 pages LaTeX2e (stylefile included), 6 eps figures. Review to appear in the proceedings of the 9th Marcel Grossman Meeting, World Scientific, ed. V. Gurzadyan, R. Jantzen, R. Ruffin

Gravitational-wave driven instability of rotating relativistic stars

A brief review of the stability of rotating relativistic stars is followed by a more detailed discussion of recent work on an instability of r-modes, modes of rotating stars that have axial parity in the slow-rotation limit. These modes may dominate the spin-down of neutron stars that are rapidly rotating at birth, and the gravitational waves they emit may be detectable.Comment: 14 pages PTPTeX v.1.0. Contribution to proceedings of the 1999 Yukawa International Semina

Revising the multipole moments of numerical spacetimes, and its consequences

Identifying the relativistic multipole moments of a spacetime of an astrophysical object that has been constructed numerically is of major interest, both because the multipole moments are intimately related to the internal structure of the object, and because the construction of a suitable analytic metric that mimics a numerical metric should be based on the multipole moments of the latter one, in order to yield a reliable representation. In this note we show that there has been a widespread delusion in the way the multipole moments of a numerical metric are read from the asymptotic expansion of the metric functions. We show how one should read correctly the first few multipole moments (starting from the quadrupole mass-moment), and how these corrected moments improve the efficiency of describing the metric functions with analytic metrics that have already been used in the literature, as well as other consequences of using the correct moments.Comment: article + supplemental materia

Quasi-Chemical and Structural Analysis of Polarizable Anion Hydration

Quasi-chemical theory is utilized to analyze the roles of solute polarization and size in determining the structure and thermodynamics of bulk anion hydration for the Hofmeister series Cl$^-$, Br$^-$, and I$^-$. Excellent agreement with experiment is obtained for whole salt hydration free energies using the polarizable AMOEBA force field. The quasi-chemical approach exactly partitions the solvation free energy into inner-shell, outer-shell packing, and outer-shell long-ranged contributions by means of a hard-sphere condition. Small conditioning radii, even well inside the first maximum of the ion-water(oxygen) radial distribution function, result in Gaussian behavior for the long-ranged contribution that dominates the ion hydration free energy. The spatial partitioning allows for a mean-field treatment of the long-ranged contribution, leading to a natural division into first-order electrostatic, induction, and van der Waals terms. The induction piece exhibits the strongest ion polarizability dependence, while the larger-magnitude first-order electrostatic piece yields an opposing but weaker polarizability dependence. In addition, a structural analysis is performed to examine the solvation anisotropy around the anions. As opposed to the hydration free energies, the solvation anisotropy depends more on ion polarizability than on ion size: increased polarizability leads to increased anisotropy. The water dipole moments near the ion are similar in magnitude to bulk water, while the ion dipole moments are found to be significantly larger than those observed in quantum mechanical studies. Possible impacts of the observed over-polarization of the ions on simulated anion surface segregation are discussed.Comment: slight revision, in press at J. Chem. Phy

Covariant Uniform Acceleration

We show that standard Relativistic Dynamics Equation F=dp/d\tau is only partially covariant. To achieve full Lorentz covariance, we replace the four-force F by a rank 2 antisymmetric tensor acting on the four-velocity. By taking this tensor to be constant, we obtain a covariant definition of uniformly accelerated motion. We compute explicit solutions for uniformly accelerated motion which are divided into four types: null, linear, rotational, and general. For null acceleration, the worldline is cubic in the time. Linear acceleration covariantly extends 1D hyperbolic motion, while rotational acceleration covariantly extends pure rotational motion. We use Generalized Fermi-Walker transport to construct a uniformly accelerated family of inertial frames which are instantaneously comoving to a uniformly accelerated observer. We explain the connection between our approach and that of Mashhoon. We show that our solutions of uniformly accelerated motion have constant acceleration in the comoving frame. Assuming the Weak Hypothesis of Locality, we obtain local spacetime transformations from a uniformly accelerated frame K' to an inertial frame K. The spacetime transformations between two uniformly accelerated frames with the same acceleration are Lorentz. We compute the metric at an arbitrary point of a uniformly accelerated frame. We obtain velocity and acceleration transformations from a uniformly accelerated system K' to an inertial frame K. We derive the general formula for the time dilation between accelerated clocks. We obtain a formula for the angular velocity of a uniformly accelerated object. Every rest point of K' is uniformly accelerated, and its acceleration is a function of the observer's acceleration and its position. We obtain an interpretation of the Lorentz-Abraham-Dirac equation as an acceleration transformation from K' to K.Comment: 36 page

Nonaxisymmetric Neutral Modes in Rotating Relativistic Stars

We study nonaxisymmetric perturbations of rotating relativistic stars. modeled as perfect-fluid equilibria. Instability to a mode with angular dependence $\exp(im\phi)$ sets in when the frequency of the mode vanishes. The locations of these zero-frequency modes along sequences of rotating stars are computed in the framework of general relativity. We consider models of uniformly rotating stars with polytropic equations of state, finding that the relativistic models are unstable to nonaxisymmetric modes at significantly smaller values of rotation than in the Newtonian limit. Most strikingly, the m=2 bar mode can become unstable even for soft polytropes of index $N \leq 1.3$, while in Newtonian theory it becomes unstable only for stiff polytropes of index $N \leq 0.808$. If rapidly rotating neutron stars are formed by the accretion-induced collapse of white dwarfs, instability associated with these nonaxisymmetric, gravitational-wave driven modes may set an upper limit on neutron-star rotation. Consideration is restricted to perturbations that correspond to polar perturbations of a spherical star. A study of axial perturbations is in progress.Comment: 57 pages, 9 figure

Bagging ensemble selection for regression

Bagging ensemble selection (BES) is a relatively new ensemble learning strategy. The strategy can be seen as an ensemble of the ensemble selection from libraries of models (ES) strategy. Previous experimental results on binary classification problems have shown that using random trees as base classifiers, BES-OOB (the most successful variant of BES) is competitive with (and in many cases, superior to) other ensemble learning strategies, for instance, the original ES algorithm, stacking with linear regression, random forests or boosting. Motivated by the promising results in classification, this paper examines the predictive performance of the BES-OOB strategy for regression problems. Our results show that the BES-OOB strategy outperforms Stochastic Gradient Boosting and Bagging when using regression trees as the base learners. Our results also suggest that the advantage of using a diverse model library becomes clear when the model library size is relatively large. We also present encouraging results indicating that the non negative least squares algorithm is a viable approach for pruning an ensemble of ensembles

Collisionless shocks in plasmas

Collisionless shocks in plasmas, dissipation and dispersion in determining shock structur

Ferromagnetism of 3^3He Films in the Low Field Limit

We provide evidence for a finite temperature ferromagnetic transition in 2-dimensions as $H \to 0$ in thin films of $^3$He on graphite, a model system for the study of two-dimensional magnetism. We perform pulsed and CW NMR experiments at fields of 0.03 - 0.48 mT on $^3$He at areal densities of 20.5 - 24.2 atoms/nm$^2$. At these densities, the second layer of $^3$He has a strongly ferromagnetic tendency. With decreasing temperature, we find a rapid onset of magnetization that becomes independent of the applied field at temperatures in the vicinity of 1 mK. Both the dipolar field and the NMR linewidth grow rapidly as well, which is consistent with a large (order unity) polarization of the $^3$He spins.Comment: 4 figure