Cosmological energy in a thermo-horizon and the first law

We consider a cosmological horizon, named thermo-horizon, to which are associated a temperature and an entropy of Bekenstein-Hawking and which obeys the first law for an energy flow calculated through the corresponding limit surface. We point out a contradiction between the first law and the definition of the total energy contained inside the horizon. This contradiction is removed when the first law is replaced by a Gibbs' equation for a vacuum-like component associated to the event horizon

Kerr Geodesics Following the Axis of Symmetry

We present here the general expressions for the acceleration of massive test particles along the symmetry axis of the Kerr metric, and then study the main properties of this acceleration in different regions of the spacetime. In particular, we show that there exists a region near the black hole in which the gravitational field is repulsive. We provide possible physical interpretations about the role of this effect in terms of the different conserved parameters. The studies of these geodesics are important not only to understand better the structure of the Kerr spacetime but also to its use as a possible mechanism for the production of extragalactic jets. Our results are obtained with the help of expressing the geodesics of the Kerr spacetime in terms of the Weyl coordinates.Comment: revtex4, no figures and tables. Gen. Relativ. Grav. 48 (2016) 6

Trajectory Clustering and an Application to Airspace Monitoring

This paper presents a framework aimed at monitoring the behavior of aircraft in a given airspace. Nominal trajectories are determined and learned using data driven methods. Standard procedures are used by air traffic controllers (ATC) to guide aircraft, ensure the safety of the airspace, and to maximize the runway occupancy. Even though standard procedures are used by ATC, the control of the aircraft remains with the pilots, leading to a large variability in the flight patterns observed. Two methods to identify typical operations and their variability from recorded radar tracks are presented. This knowledge base is then used to monitor the conformance of current operations against operations previously identified as standard. A tool called AirTrajectoryMiner is presented, aiming at monitoring the instantaneous health of the airspace, in real time. The airspace is "healthy" when all aircraft are flying according to the nominal procedures. A measure of complexity is introduced, measuring the conformance of current flight to nominal flight patterns. When an aircraft does not conform, the complexity increases as more attention from ATC is required to ensure a safe separation between aircraft.Comment: 15 pages, 20 figure

Composition and the thermoelectric performance of β-Zn_4Sb_3

β-Zn_4Sb_3 is a promising thermoelectric material due to the abundance of zinc and antimony and reports of high efficiency in bulk samples. This work establishes the high temperature properties of β-Zn_4Sb_3 across the phase stability window. By controlling the stoichiometry, the Hall carrier concentration can be tuned from 6–9 × 10^(19) cm^(−3) without requiring extrinsic dopants. The trend in Seebeck coefficient on carrier concentration is rationalized with a single, parabolic band model. Extremely low lattice thermal conductivity (0.4–0.6 W m^(−1) K^(−1)) coupled with a moderate effective mass (1.2 m_e) and mobility leads to a large figure of merit (zT of 0.8 by 550 K). The single parabolic band model is used to obtain the carrier concentration dependence of the figure of merit and an optimum carrier concentration near 5 × 10^(19) cm^(−3) is predicted

Kerr Geodesics, the Penrose Process and Jet Collimation by a Black Hole

We re-examine the possibility that astrophysical jet collimation may arise from the geometry of rotating black holes and the presence of high-energy particles resulting from a Penrose process, without the help of magnetic fields. Our analysis uses the Weyl coordinates, which are revealed better adapted to the desired shape of the jets. We numerically integrate the 2D-geodesics equations. We give a detailed study of these geodesics and give several numerical examples. Among them are a set of perfectly collimated geodesics with asymptotes $\rho =\rho_{1}$ parallel to the $z-$ axis, with $\rho_{1}$ only depending on the ratios $\frac{\mathcal{Q}}{E^{2}-1}$ and $\frac{a}{M}$, where $a$ and $M$ are the parameters of the Kerr black hole, $E$ the particle energy and $\mathcal{Q}$ the Carter's constant.Comment: Accepted by Astronomy and Astrophysics. AA style with 3 EPS figures. Content amended after AA's refereeing. Discussion of geodesics also corrected and expanded earlier. Conclusions amended accordingl