Test particle propagation in magnetostatic turbulence. 3: The approach to equilibrium

The asymptotic behavior, for large time, of the quasi-linear diabatic solutions and their local approximations is considered. A time averaging procedure is introduced which yields the averages of these solutions over time intervals which contain only large time values. A discussion of the quasi-linear diabatic solutions which is limited to those solutions that are bounded from below as functions of time is given. It is shown that as the upper limit of the time averaging interval is allowed to approach infinity the time averaged quasi-linear diabatic solutions must approach isotropy (mu-independence). The first derivative with respect to mu of these solutions is also considered. This discussion is limited to first derivatives which are bounded functions of time. It is shown that as the upper limit of the time averaging interval is allowed to approach infinity, the time averaged first derivative must approach zero everywhere in mu except at mu = 0 where it must approach a large value which is calculated. The impact of this large derivative on the quasi-linear expansion scheme is discussed. An H-theorem for the first local approximation to the quasi-linear diabatic solutions is constructed. Without time averaging, the H-theorem is used to determine sufficient conditions for the first local approximate solutions to asymptote, with increasing time, to exactly the same final state which the time averaged quasi-linear diabatic solutions must approach as discussed above

Test particle propagation in magnetostatic turbulence. 2: The local approximation method

An approximation method for statistical mechanics is presented and applied to a class of problems which contains a test particle propagation problem. All of the available basic equations used in statistical mechanics are cast in the form of a single equation which is integrodifferential in time and which is then used as the starting point for the construction of the local approximation method. Simplification of the integrodifferential equation is achieved through approximation to the Laplace transform of its kernel. The approximation is valid near the origin in the Laplace space and is based on the assumption of small Laplace variable. No other small parameter is necessary for the construction of this approximation method. The n'th level of approximation is constructed formally, and the first five levels of approximation are calculated explicitly. It is shown that each level of approximation is governed by an inhomogeneous partial differential equation in time with time independent operator coefficients. The order in time of these partial differential equations is found to increase as n does. At n = 0 the most local first order partial differential equation which governs the Markovian limit is regained

Test particle propagation in magnetostatic turbulence. 1. Failure of the diffusion approximation

The equation which governs the quasi-linear approximation to the ensemble and gyro-phase averaged one-body probability distribution function is constructed from first principles. This derived equation is subjected to a thorough investigation in order to calculate the possible limitations of the quasi-linear approximation. It is shown that the reduction of this equation to a standard diffusion equation in the Markovian limit can be accomplished through the application of the adiabatic approximation. A numerical solution of the standard diffusion equation in the Markovian limit is obtained for the narrow parallel beam injection. Comparison of the diabatic and adiabatic results explicitly demonstrates the failure of the Markovian description of the probability distribution function. Through the use of a linear time-scale extension the failure of the adiabatic approximation, which leads to the Markovian limit, is shown to be due to mixing of the relaxation and interaction time scales in the presence of the strong mean field

Early Identification of Violent Criminal Gang Members

Gang violence is a major problem in the United States accounting for a large fraction of homicides and other violent crime. In this paper, we study the problem of early identification of violent gang members. Our approach relies on modified centrality measures that take into account additional data of the individuals in the social network of co-arrestees which together with other arrest metadata provide a rich set of features for a classification algorithm. We show our approach obtains high precision and recall (0.89 and 0.78 respectively) in the case where the entire network is known and out-performs current approaches used by law-enforcement to the problem in the case where the network is discovered overtime by virtue of new arrests - mimicking real-world law-enforcement operations. Operational issues are also discussed as we are preparing to leverage this method in an operational environment.Comment: SIGKDD 201

Zero temperature optical conductivity of ultra-clean Fermi liquids and superconductors

We calculate the low-frequency optical conductivity sigma(w) of clean metals and superconductors at zero temperature neglecting the effects of impurities and phonons. In general, the frequency and temperature dependences of sigma have very little in common. For small Fermi surfaces in three dimensions (but not in 2D) we find for example that Re sigma(w>0)=const. for low w which corresponds to a scattering rate Gamma proportional to w^2 even in the absence of Umklapp scattering when there is no T^2 contribution to Gamma. In the main part of the paper we discuss in detail the optical conductivity of d-wave superconductors in 2D where Re sigma(w>0) \propto w^4 for the smallest frequencies and the Umklapp processes typically set in smoothly above a finite threshold w_0 smaller than twice the maximal gap Delta. In cases where the nodes are located at (pi/2, pi/2), such that direct Umklapp scattering among them is possible, one obtains Re sigma(w) \propto w^2.Comment: 7 pages, 3 figure

Adaptive Optics Images of Kepler Objects of Interest

All transiting planets are at risk of contamination by blends with nearby, unresolved stars. Blends dilute the transit signal, causing the planet to appear smaller than it really is, or produce a false positive detection when the target star is blended with eclipsing binary stars. This paper reports on high spatial-resolution adaptive optics images of 90 Kepler planetary candidates. Companion stars are detected as close as 0.1 arcsec from the target star. Images were taken in the near-infrared (J and Ks bands) with ARIES on the MMT and PHARO on the Palomar Hale 200-inch. Most objects (60%) have at least one star within 6 arcsec separation and a magnitude difference of 9. Eighteen objects (20%) have at least one companion within 2 arcsec of the target star; 6 companions (7%) are closer than 0.5 arcsec. Most of these companions were previously unknown, and the associated planetary candidates should receive additional scrutiny. Limits are placed on the presence of additional companions for every system observed, which can be used to validate planets statistically using the BLENDER method. Validation is particularly critical for low-mass, potentially Earth-like worlds, which are not detectable with current-generation radial velocity techniques. High-resolution images are thus a crucial component of any transit follow-up program.Comment: 9 pages, 4 figures, accepted to A

The Mid-Infrared Spectrum of the Short Orbital Period Polar EF Eridani from the Spitzer Space Telescope

We present the first mid-infrared (5.5-14.5 micron) spectrum of a highly magnetic cataclysmic variable, EF Eridani, obtained with the Infrared Spectrograph on the Spitzer Space Telescope. The spectrum displays a relatively flat, featureless continuum. A spectral energy distribution model consisting of a 9500 K white dwarf, L5 secondary star, cyclotron emission corresponding to a B~13 MG white dwarf magnetic field, and an optically thin circumbinary dust disk is in reasonable agreement with the extant 2MASS, IRAC, and IRS observations of EF Eri. Cyclotron emission is ruled out as a dominant contributor to the infrared flux density at wavelengths >3 microns. The spectral energy distribution longward of ~5 microns is dominated by dust emission. Even longer wavelength observations would test the model's prediction of a continuing gradual decline in the circumbinary disk-dominated region of the spectral energy distribution.Comment: To be published in The Astrophysical Journa