Nonlinear Couplings of R-modes: Energy Transfer and Saturation Amplitudes at Realistic Timescales

Non-linear interactions among the inertial modes of a rotating fluid can be described by a network of coupled oscillators. We use such a description for an incompressible fluid to study the development of the r-mode instability of rotating neutron stars. A previous hydrodynamical simulation of the r-mode reported the catastrophic decay of large amplitude r-modes. We explain the dynamics and timescale of this decay analytically by means of a single three mode coupling. We argue that at realistic driving and damping rates such large amplitudes will never actually be reached. By numerically integrating a network of nearly 5000 coupled modes, we find that the linear growth of the r-mode ceases before it reaches an amplitude of around 10^(-4). The lowest parametric instability thresholds for the r-mode are calculated and it is found that the r-mode becomes unstable to modes with 13<n<15 if modes up to n=30 are included. Using the network of coupled oscillators, integration times of 10^6 rotational periods are attainable for realistic values of driving and damping rates. Complicated dynamics of the modal amplitudes are observed. The initial development is governed by the three mode coupling with the lowest parametric instability. Subsequently a large number of modes are excited, which greatly decreases the linear growth rate of the r-mode.Comment: 3 figures 4 pages Submitted to PR

Post-mission Viking data anaysis

Three Mars data analysis projects from the Viking Mars program were identified initially, and three more came into being as the work proceeded. All together, these six pertained to: (1) the veritical distribution of scattering particles in the Martian atmosphere at various locations in various seasons, (2) the physical parameters that define photometric properties of the Martian surface and atmosphere, (3) patterns of dust-cloud and global dust-storm development, (4) a direct comparison of near-simultaneous Viking and ground-based observations, (5) the annual formation and dissipation of polar frost caps, and (6) evidence concerning possible present-day volcanism or venting. A list of publications pertaining to the appropriate projects is included

Semiannual Status Report, 1 July 1975 Through 31 December 1975

No abstract availabl

Self-similar solutions of semilinear wave equations with a focusing nonlinearity

We prove that in three space dimensions a nonlinear wave equation $u_{tt}-\Delta u = u^p$ with $p\geq 7$ being an odd integer has a countable family of regular spherically symmetric self-similar solutions.Comment: 12 pages, 3 figures, minor corrections to match the published versio

A new source detection algorithm using FDR

The False Discovery Rate (FDR) method has recently been described by Miller et al (2001), along with several examples of astrophysical applications. FDR is a new statistical procedure due to Benjamini and Hochberg (1995) for controlling the fraction of false positives when performing multiple hypothesis testing. The importance of this method to source detection algorithms is immediately clear. To explore the possibilities offered we have developed a new task for performing source detection in radio-telescope images, Sfind 2.0, which implements FDR. We compare Sfind 2.0 with two other source detection and measurement tasks, Imsad and SExtractor, and comment on several issues arising from the nature of the correlation between nearby pixels and the necessary assumption of the null hypothesis. The strong suggestion is made that implementing FDR as a threshold defining method in other existing source-detection tasks is easy and worthwhile. We show that the constraint on the fraction of false detections as specified by FDR holds true even for highly correlated and realistic images. For the detection of true sources, which are complex combinations of source-pixels, this constraint appears to be somewhat less strict. It is still reliable enough, however, for a priori estimates of the fraction of false source detections to be robust and realistic.Comment: 17 pages, 7 figures, accepted for publication by A

De-biased Populations of Kuiper Belt Objects from the Deep Ecliptic Survey

The Deep Ecliptic Survey (DES) discovered hundreds of Kuiper Belt objects from 1998-2005. Follow-up observations yielded 304 objects with good dynamical classifications (Classical, Scattered, Centaur, or 16 mean-motion resonances with Neptune). The DES search fields are well documented, enabling us to calculate the probability of detecting objects with particular orbital parameters and absolute magnitudes at a randomized point in each orbit. Grouping objects together by dynamical class leads, we estimate the orbital element distributions (a, e, i) for the largest three classes (Classical, 3:2, and Scattered) using maximum likelihood. Using H-magnitude as a proxy for the object size, we fit a power law to the number of objects for 8 classes with at least 5 detected members (246 objects). The best Classical slope is alpha=1.02+/-0.01 (observed from 5<=H<=7.2). Six dynamical classes (Scattered plus 5 resonances) are consistent in slope with the Classicals, though the absolute number of objects is scaled. The exception to the power law relation are the Centaurs (non-resonant with perihelia closer than Neptune, and thus detectable at smaller sizes), with alpha=0.42+/-0.02 (7.5<H<11). This is consistent with a knee in the H-distribution around H=7.2 as reported elsewhere (Bernstein et al. 2004, Fraser et al. 2014). Based on the Classical-derived magnitude distribution, the total number of objects (H<=7) in each class are: Classical (2100+/-300 objects), Scattered (2800+/-400), 3:2 (570+/-80), 2:1 (400+/-50), 5:2 (270+/-40), 7:4 (69+/-9), 5:3 (60+/-8). The independent estimate for the number of Centaurs in the same H range is 13+/-5. If instead all objects are divided by inclination into "Hot" and "Cold" populations, following Fraser et al. (2014), we find that alphaHot=0.90+/-0.02, while alphaCold=1.32+/-0.02, in good agreement with that work.Comment: 26 pages emulateapj, 6 figures, 5 tables, accepted by A

The 13 November 1984 occultation of BD +08 deg 0471 by (1) Ceres

The 13 November 1984 occultation of BD +08 deg 0471 was discovered during a photographic search carried out with the 0.5 meter Carnegie Double Astrograph at Lick Observatory and the Lowell Observatory PDS microdensitometer. Such a search was stimulated by the curious fact that few favorably located occultations of AGK3 or SAO catalog starts by Ceres will occur during the 1980s. The occultation on 13 November, however, is a particularly good event. The star is 1000 cubic M in V, yielding a predicted drop at occultation of about 10%. Such a drop can be detected by small telescopes equipped with photoelectric photometers, but is too small to be seen visually. The track was predicted to cross the Caribbean, Florida, southern Texas, and Mexico. Based on this prediction, preparations were made to observe the event in Mexico using four portable occultation data systems

Regularization independent of the noise level: an analysis of quasi-optimality

The quasi-optimality criterion chooses the regularization parameter in inverse problems without taking into account the noise level. This rule works remarkably well in practice, although Bakushinskii has shown that there are always counterexamples with very poor performance. We propose an average case analysis of quasi-optimality for spectral cut-off estimators and we prove that the quasi-optimality criterion determines estimators which are rate-optimal {\em on average}. Its practical performance is illustrated with a calibration problem from mathematical finance.Comment: 18 pages, 3 figure

Solution space heterogeneity of the random K-satisfiability problem: Theory and simulations

The random K-satisfiability (K-SAT) problem is an important problem for studying typical-case complexity of NP-complete combinatorial satisfaction; it is also a representative model of finite-connectivity spin-glasses. In this paper we review our recent efforts on the solution space fine structures of the random K-SAT problem. A heterogeneity transition is predicted to occur in the solution space as the constraint density alpha reaches a critical value alpha_cm. This transition marks the emergency of exponentially many solution communities in the solution space. After the heterogeneity transition the solution space is still ergodic until alpha reaches a larger threshold value alpha_d, at which the solution communities disconnect from each other to become different solution clusters (ergodicity-breaking). The existence of solution communities in the solution space is confirmed by numerical simulations of solution space random walking, and the effect of solution space heterogeneity on a stochastic local search algorithm SEQSAT, which performs a random walk of single-spin flips, is investigated. The relevance of this work to glassy dynamics studies is briefly mentioned.Comment: 11 pages, 4 figures. Final version as will appear in Journal of Physics: Conference Series (Proceedings of the International Workshop on Statistical-Mechanical Informatics, March 7-10, 2010, Kyoto, Japan