The Frenet Serret Description of Gyroscopic Precession

The phenomenon of gyroscopic precession is studied within the framework of Frenet-Serret formalism adapted to quasi-Killing trajectories. Its relation to the congruence vorticity is highlighted with particular reference to the irrotational congruence admitted by the stationary, axisymmetric spacetime. General precession formulae are obtained for circular orbits with arbitrary constant angular speeds. By successive reduction, different types of precessions are derived for the Kerr - Schwarzschild - Minkowski spacetime family. The phenomenon is studied in the case of other interesting spacetimes, such as the De Sitter and G\"{o}del universes as well as the general stationary, cylindrical, vacuum spacetimes.Comment: 37 pages, Paper in Late

Bubbles pinned on electrodes: Friends or foes of aqueous electrochemistry?

Electrochemists and engineers regard adherent gas bubbles as redox-inactive and therefore blocking entities. Adhesion of bubbles at electrodes generally carries an energy penalty. But this is not always the case: bubbles pinned on an electrode surface initiate the oxidation of water-soluble species under conditions where such reactions would normally be considered impossible. Here we critically review the recent literature that is beginning to unveil the novel concept of on-water electrochemistry. Harnessing electrochemical reactivity of the water–gas–electrode interface has the potential to become a game-changer in organic electrosynthesis, accelerating the transition toward a sustainable chemical industry by simplifying the direct integration of renewable electricity into the production of commodity chemicals

Studies on morphometry and hydrology of Gandhisagar Reservoir with special reference to its fisheries

Gandhisagar, the second largest reservoir of India is located in Mandsaur district of Madhya Pradesh at latitude 24°44'N and longitude 75°33'E at an altitude of 403.56m MSL in orientation from NE to SE. It has an extensive water spread area of 66000 ha at full reservoir level with a maximum and mean depth of 49.52 and 11.73 m respectively. The maximum length and width of the reservoir are 112 and 16km having a total shore line of 442km. Details of catchment area, bathymetry, standard hydrological data giving water level relation of the basin to water spread area, volume and fish production and the bottom topographical details of 11 experimental fishing stations and 6 fish landing centres are discussed

Performability Modeling Based on Real Data: A Case Study

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryNASA / NAG-1-613IBM CorporationJoint Services Electronics Program / N00014-84-C-0149Air Force Office of Scientific Research / AFOSR-84-013

Experiences of pride, not guilt, predict pro-environmental behavior when pro-environmental descriptive norms are more positive

Emotions can greatly influence behavior, yet research on links between incidental emotions and pro-environmental behavior is limited. The present study uses an experience sampling design to examine how pride and guilt relate to daily pro-environmental behavior. Ninety-six university students recorded their engagement in specific pro-environmental behaviors, and their feelings of pride and guilt about these behaviors, at four time points each day for three consecutive days. Results showed that pro-environmental behavior during a 2.5-hour time period was positively related to pride, and negatively related to guilt, during that same time period. Pride about environmental behavior was positively related to subsequent engagement in pro-environmental behavior (i.e., during the following 2.5-hour time period), but only for people who perceived more positive pro-environmental descriptive norms. Guilt was not related to subsequent pro-environmental behavior. We discuss implications for further research on the complex associations between daily experiences of moral emotions and pro-environmental behavior

Light's Bending Angle due to Black Holes: From the Photon Sphere to Infinity

The bending angle of light is a central quantity in the theory of gravitational lensing. We develop an analytical perturbation framework for calculating the bending angle of light rays lensed by a Schwarzschild black hole. Using a perturbation parameter given in terms of the gravitational radius of the black hole and the light ray's impact parameter, we determine an invariant series for the strong-deflection bending angle that extends beyond the standard logarithmic deflection term used in the literature. In the process, we discovered an improvement to the standard logarithmic deflection term. Our perturbation framework is also used to derive as a consistency check, the recently found weak deflection bending angle series. We also reformulate the latter series in terms of a more natural invariant perturbation parameter, one that smoothly transitions between the weak and strong deflection series. We then compare our invariant strong deflection bending-angle series with the numerically integrated exact formal bending angle expression, and find less than 1% discrepancy for light rays as far out as twice the critical impact parameter. The paper concludes by showing that the strong and weak deflection bending angle series together provide an approximation that is within 1% of the exact bending angle value for light rays traversing anywhere between the photon sphere and infinity.Comment: 22 pages, 5 figure

Gravitational waves from inspiralling compact binaries: Energy loss and waveform to second--post-Newtonian order

Gravitational waves generated by inspiralling compact binaries are investigated to the second--post-Newtonian (2PN) approximation of general relativity. Using a recently developed 2PN-accurate wave generation formalism, we compute the gravitational waveform and associated energy loss rate from a binary system of point-masses moving on a quasi-circular orbit. The crucial new input is our computation of the 2PN-accurate ``source'' quadrupole moment of the binary. Tails in both the waveform and energy loss rate at infinity are explicitly computed. Gravitational radiation reaction effects on the orbital frequency and phase of the binary are deduced from the energy loss. In the limiting case of a very small mass ratio between the two bodies we recover the results obtained by black hole perturbation methods. We find that finite mass ratio effects are very significant as they increase the 2PN contribution to the phase by up to 52\%. The results of this paper should be of use when deciphering the signals observed by the future LIGO/VIRGO network of gravitational-wave detectors.Comment: 43 pages, LaTeX-ReVTeX, no figures

Post-Newtonian Gravitational Radiation

1 Introduction 2 Multipole Decomposition 3 Source Multipole Moments 4 Post-Minkowskian Approximation 5 Radiative Multipole Moments 6 Post-Newtonian Approximation 7 Point-Particles 8 ConclusionComment: 46 pages, in Einstein's Field Equations and Their Physical Implications, B. Schmidt (Ed.), Lecture Notes in Physics, Springe

Black Hole Entropy without Brick Walls

We present evidence which confirms a suggestion by Susskind and Uglum regarding black hole entropy. Using a Pauli-Villars regulator, we find that 't Hooft's approach to evaluating black hole entropy through a statistical-mechanical counting of states for a scalar field propagating outside the event horizon yields precisely the one-loop renormalization of the standard Bekenstein-Hawking formula, S=\A/(4G). Our calculation also yields a constant contribution to the black hole entropy, a contribution associated with the one-loop renormalization of higher curvature terms in the gravitational action.Comment: 15 pages, plain LaTex minor additions including some references; version accepted for publicatio

Logarithmic Corrections to Rotating Extremal Black Hole Entropy in Four and Five Dimensions

We compute logarithmic corrections to the entropy of rotating extremal black holes using quantum entropy function i.e. Euclidean quantum gravity approach. Our analysis includes five dimensional supersymmetric BMPV black holes in type IIB string theory on T^5 and K3 x S^1 as well as in the five dimensional CHL models, and also non-supersymmetric extremal Kerr black hole and slowly rotating extremal Kerr-Newmann black holes in four dimensions. For BMPV black holes our results are in perfect agreement with the microscopic results derived from string theory. In particular we reproduce correctly the dependence of the logarithmic corrections on the number of U(1) gauge fields in the theory, and on the angular momentum carried by the black hole in different scaling limits. We also explain the shortcomings of the Cardy limit in explaining the logarithmic corrections in the limit in which the (super)gravity description of these black holes becomes a valid approximation. For non-supersymmetric extremal black holes, e.g. for the extremal Kerr black hole in four dimensions, our result provides a stringent testing ground for any microscopic explanation of the black hole entropy, e.g. Kerr/CFT correspondence.Comment: LaTeX file, 50 pages; v2: added extensive discussion on the relation between boundary condition and choice of ensemble, modified analysis for slowly rotating black holes, all results remain unchanged, typos corrected; v3: minor additions and correction