Strong gravitational lensing by a rotating non-Kerr compact object

We study the strong gravitational lensing in the background of a rotating non-Kerr compact object with a deformed parameter $\epsilon$ and an unbound rotation parameter $a$. We find that the photon sphere radius and the deflection angle depend sharply on the parameters $\epsilon$ and $a$. For the case in which the black hole is more prolate than a Kerr black hole, the photon sphere exists only in the regime $\epsilon\leq\epsilon_{max}$ for prograde photon. The upper limit $\epsilon_{max}$ is a function of the rotation parameter $a$. As $\epsilon>\epsilon_{max}$, the deflection angle of the light ray closing very to the naked singularity is a positive finite value, which is different from those in both the usual Kerr black hole spacetime and in the rotating naked singularity described by Janis-Newman-Winicour metric. For the oblate black hole and the retrograde photon, there does not exist such a threshold value. Modelling the supermassive central object of the Galaxy as a rotating non-Kerr compact object, we estimated the numerical values of the coefficients and observables for gravitational lensing in the strong field limit.Comment: 16 pages, 10 figures. The corrected version to be appeared in Phys. Rev.

Quadrature LC VCO with passive coupling and phase combining network

A circuit and method for generating a signal is disclosed. The circuit includes a set of wide tuning LC tanks, a set of core transistors cross coupled to the set of wide tuning LC tanks, and a combining network coupled to the set of wide tuning LC tanks and the set of core transistors. The combining network further includes a set of inputs connected to the set of wide tuning LC tanks and the set of core transistors, a set of coupling transistors connected to the set of inputs, a set of source inductors connected to the set of coupling transistors, a coupling capacitor connected to the set of source inductors, a load resistor connected to the coupling capacitor. The combining network combines the set of inputs and the signal is delivered to the load resistor as a fourth order harmonic.Board of Regents, University of Texas Syste

A core eating network and its modulations underlie diverse eating phenomena

We propose that a core eating network and its modulations account for much of what is currently known about the neural activity underlying a wide range of eating phenomena in humans (excluding homeostasis and related phenomena). The core eating network is closely adapted from a network that Kaye, Fudge, and Paulus (2009) proposed to explain the neurocircuitry of eating, including a ventral reward pathway and a dorsal control pathway. In a review across multiple literatures that focuses on experiments using functional Magnetic Resonance Imaging (fMRI), we first show that neural responses to food cues, such as food pictures, utilize the same core eating network as eating. Consistent with the theoretical perspective of grounded cognition, food cues activate eating simulations that produce reward predictions about a perceived food and potentially motivate its consumption. Reviewing additional literatures, we then illustrate how various factors modulate the core eating network, increasing and/or decreasing activity in subsets of its neural areas. These modulating factors include food significance (palatability, hunger), body mass index (BMI, overweight/obesity), eating disorders (anorexia nervosa, bulimia nervosa, binge eating), and various eating goals (losing weight, hedonic pleasure, healthy living). By viewing all these phenomena as modulating a core eating network, it becomes possible to understand how they are related to one another within this common theoretical framework. Finally, we discuss future directions for better establishing the core eating network, its modulations, and their implications for behavior

Aeromechanical stability analysis of COPTER

A plan was formed for developing a comprehensive, second-generation system with analytical capabilities for predicting performance, loads and vibration, handling qualities, aeromechanical stability, and acoustics. This second-generation system named COPTER (COmprehensive Program for Theoretical Evaluation of Rotorcraft) is designed for operational efficiency, user friendliness, coding readability, maintainability, transportability, modularity, and expandability for future growth. The system is divided into an executive, a data deck validator, and a technology complex. At present a simple executive, the data deck validator, and the aeromechanical stability module of the technology complex were implemented. The system is described briefly, the implementation of the technology module is discussed, and correlation data presented. The correlation includes hingeless-rotor isolated stability, hingeless-rotor ground-resonance stability, and air-resonance stability of an advanced bearingless-rotor in forward flight

Nonlinear force-free field modeling of a solar active region using SDO/HMI and SOLIS/VSM data

We use SDO/HMI and SOLIS/VSM photospheric magnetic field measurements to model the force-free coronal field above a solar active region, assuming magnetic forces to dominate. We take measurement uncertainties caused by, e.g., noise and the particular inversion technique into account. After searching for the optimum modeling parameters for the particular data sets, we compare the resulting nonlinear force-free model fields. We show the degree of agreement of the coronal field reconstructions from the different data sources by comparing the relative free energy content, the vertical distribution of the magnetic pressure and the vertically integrated current density. Though the longitudinal and transverse magnetic flux measured by the VSM and HMI is clearly different, we find considerable similarities in the modeled fields. This indicates the robustness of the algorithm we use to calculate the nonlinear force-free fields against differences and deficiencies of the photospheric vector maps used as an input. We also depict how much the absolute values of the total force-free, virial and the free magnetic energy differ and how the orientation of the longitudinal and transverse components of the HMI- and VSM-based model volumes compares to each other.Comment: 9 pages, 5 figure

Strong gravitational lensing in a squashed Kaluza-Klein black hole spacetime

We investigate the strong gravitational lensing in a Kaluza-Klein black hole with squashed horizons. We find the size of the extra dimension imprints in the radius of the photon sphere, the deflection angle, the angular position and magnification of the relativistic images. Supposing that the gravitational field of the supermassive central object of the Galaxy can be described by this metric, we estimated the numerical values of the coefficients and observables for gravitational lensing in the strong field limit.Comment: 13pages, 5 figures, Final version appeared in PR

Diffeomorphism on Horizon as an Asymptotic Isometry of Schwarzschild Black Hole

It is argued that the diffeomorphism on the horizontal sphere can be regarded as a nontrivial asymptotic isometry of the Schwarzschild black hole. We propose a new boundary condition of asymptotic metrics near the horizon and show that the condition admits the local time-shift and diffeomorphism on the horizon as the asymptotic symmetry.Comment: 18 pages, no figures, corrected some typo

Eigenstates of Paraparticle Creation Operators

Eigenstates of the parabose and parafermi creation operators are constructed. In the Dirac contour representation, the parabose eigenstates correspond to the dual vectors of the parabose coherent states. In order $p=2$, conserved-charge parabose creation operator eigenstates are also constructed. The contour forms of the associated resolutions of unity are obtained.Comment: 14 pages, LaTex file, no macros, no figure