Mixed principal eigenvalues in dimension one

This is one of a series of papers exploring the stability speed of one-dimensional stochastic processes. The present paper emphasizes on the principal eigenvalues of elliptic operators. The eigenvalue is just the best constant in the $L^{2}$-Poincar\'e inequality and describes the decay rate of the corresponding diffusion process. We present some variational formulas for the mixed principal eigenvalues of the operators. As applications of these formulas, we obtain case by case explicit estimates, a criterion for positivity, and an approximating procedure for the eigenvalue.Comment: 45 pages; Front. Math. China, 201

An overview of out-of-step protection in power systems

Power system is subjected to an extensive variety of little or bigger disturbance to the system during the operation. The power system that designed as one of the main requirement is to survive from the larger type of disturbances like faults. The power swing in certain system is the variation in three phase power flow in the power system. This paper mainly discussed the power swing and distance relay and the effect of the power swing on the distance relay and demonstrate about the basic power system stability and power swing phenomena. Moreover, out of step protection and detection applications are revised as well. At the end, the paper also demonstrated the past study of out of step application of TNB 275 KV network

Geometry and optics calibration of WFCTA prototype telescopes using star light

The Large High Altitude Air Shower Observatory project is proposed to study high energy gamma ray astronomy ( 40 GeV-1 PeV ) and cosmic ray physics ( 20 TeV-1 EeV ). The wide field of view Cherenkov telescope array, as a component of the LHAASO project, will be used to study energy spectrum and compositions of cosmic ray by measuring the total Cherenkov light generated by air showers and shower maximum depth. Two prototype telescopes have been in operation since 2008. The pointing accuracy of each telescope is crucial to the direction reconstruction of the primary particles. On the other hand the primary energy reconstruction relies on the shape of the Cherenkov image on the camera and the unrecorded photons due to the imperfect connections between photomultiplier tubes. UV bright stars are used as point-like objects to calibrate the pointing and to study the optical properties of the camera, the spot size and the fractions of unrecorded photons in the insensitive areas of the camera.Comment: 5 pages, 6 figures, submitted to Chinese Physics

Comparison of the Geometrical Characters Inside Quark- and Gluon-jet Produced by Different Flavor Quarks

The characters of the angular distributions of quark jets and gluon jets with different flavors are carefully studied after introducing the cone angle of jets. The quark jets and gluon jets are identified from the 3-jet events which are produced by Monte Carlo simulation Jetset7.4 in e+e- collisions at $\sqrt s$=91.2GeV. It turns out that the ranges of angular distributions of gluon jets are obviously wider than that of quark jets at the same energies. The average cone angles of gluon jets are much larger than that of quark jets. As the multiplicity or the transverse momentum increases, the cone-angle distribution without momentum weight of both the quark jet and gluon jet all increases, i.e the positive linear correlation are present, but the cone-angle distribution with momentum weight decreases at first, then increases when n > 4 or p_t > 2 GeV. The characters of cone angular distributions of gluon jets produced by quarks with different flavors are the same, while there are obvious differences for that of the quark jets with different flavors.Comment: 13 pages, 6 figures, to be published on the International Journal of Modern Physics

Ceiling-fan-integrated air conditioning: Airflow and temperature characteristics of a sidewall-supply jet interacting with a ceiling fan

Ceiling-Fan-Integrated Air Conditioning (CFIAC) is a proposed system that can greatly increase buildings’ cooling efficiency. In it, terminal supply ducts and diffusers are replaced by vents/nozzles, jetting supply air toward ceiling fans that serve to mix and distribute it within the room. Because of the fans’ air movement, the system provides comfort at higher room temperatures than in conventional commercial/ institutional/retail HVAC. We have experimentally evaluated CFIAC in a test room. This paper covers the distributions of air-speed, temperature, and calculated comfort level throughout the room. Two subsequent papers report tests of human subject comfort and ventilation effectiveness in the same experimental conditions. The room’s supply air emerged from a high-sidewall vent directed toward a ceiling fan on the jet centerline; we also tested this same jet on a fan located off to the side of the jet. Primary variables are: ceiling fan flow volumes in downward and upward directions, supply air volume, and room-vs-supply temperature difference. Velocity, turbulence, and temperature distributions are presented for vertical and horizontal transects of the room. The occupied zone is then evaluated for velocity and temperature non-uniformity, and for comfort as predicted by the ASHRAE Standard 55 elevated air speed method. We show that temperatures are well-mixed and uniform across the room for all of the fan-on configurations, for fans both within or out of the supply jet centerline. The ceiling fan flow dominates the CFIAC airflow, and even though non-uniform is capable of providing comfortable conditions throughout the occupied area of the room