Quasilocal Energy for a Kerr black hole

The quasilocal energy associated with a constant stationary time slice of the Kerr spacetime is presented. The calculations are based on a recent proposal \cite{by} in which quasilocal energy is derived from the Hamiltonian of spatially bounded gravitational systems. Three different classes of boundary surfaces for the Kerr slice are considered (constant radius surfaces, round spheres, and the ergosurface). Their embeddings in both the Kerr slice and flat three-dimensional space (required as a normalization of the energy) are analyzed. The energy contained within each surface is explicitly calculated in the slow rotation regime and its properties discussed in detail. The energy is a positive, monotonically decreasing function of the boundary surface radius. It approaches the Arnowitt-Deser-Misner (ADM) mass at spatial infinity and reduces to (twice) the irreducible mass at the horizon of the Kerr black hole. The expressions possess the correct static limit and include negative contributions due to gravitational binding. The energy at the ergosurface is compared with the energies at other surfaces. Finally, the difficulties involved in an estimation of the energy in the fast rotation regime are discussed.Comment: 22 pages, Revtex, Alberta-Thy-18-94. (the approximations in Section IV have been improved. To appear in Phys. Rev. D

Growth, Characterization, and Electrochemical Properties of Doped n-Type KTaO_3 Photoanodes

The effects of compositionally induced changes on the semiconducting properties, optical response, chemical stability, and overall performance of KTaO_3 photoanodes in photoelectrochemical (PEC) cells have been investigated. Single crystals of n-type Ca- and Ba-doped KTaO_3 with carrier concentrations ranging from 0.45 to 11.5×10^(19) cm^(−3) were grown and characterized as photoanodes in basic aqueous electrolyte PEC cells. The PEC properties of the crystals, including the photocurrent, photovoltage, and flatband potential in contact with 8.5 M NaOH(aq) were relatively independent of whether Ca or Ba was used to produce the semiconducting form of KTaO_3. All of the Ca- or Ba-doped KTaO_3 single-crystal photoanodes were chemically stable in the electrolyte and, based on the open-circuit potential and the band-edge positions, were capable of unassisted photochemical H_2 and O_2 evolution from H_2O. The minority-carrier diffusion lengths values were small and comparable to the depletion region width. Photoanodic currents were only observed for photoanode illumination with light above the bandgap (i.e., λ<340 nm). The maximum external quantum yield occurred at λ=255 nm (4.85 eV), and the depletion width plus the minority-carrier diffusion length ranged from 20 to 65 nm for the various KTaO_3-based photoanode materials

Thermodynamics of a black hole in a cavity

We present a unified thermodynamical description of the configurations consisting on self-gravitating radiation with or without a black hole. We compute the thermal fluctuations and evaluate where will they induce a transition from metastable configurations towards stable ones. We show that the probability of finding such a transition is exponentially small. This indicates that, in a sequence of quasi equilibrium configurations, the system will remain in the metastable states till it approaches very closely the critical point beyond which no metastable configuration exists. Near that point, we relate the divergence of the local temperature fluctuations to the approach of the instability of the whole system, thereby generalizing the usual fluctuations analysis in the cases where long range forces are present. When angular momentum is added to the cavity, the above picture is slightly modified. Nevertheless, at high angular momentum, the black hole loses most of its mass before it reaches the critical point at which it evaporates completely.Comment: 27 pages, latex file, contains 3 figures available on request at [email protected]

Influence of barium on rectification in rat neocortical neurons

The effect of low concentrations of barium on the membrane properties of rat neocortical neurons was studied in vitro. Potassium currents were examined using single-electrode current- and voltage-clamp techniques. Neurons responded to bath application of barium (10–100 μM) with a membrane depolarization associated with an increase in input resistance. Under voltage clamp conditions, an inward shift in holding current was observed. The effects of barium were rapidly reversible upon washing and persisted in the presence of TTX. The equilibrium potential for the barium-induced inward current was near −110 mV, suggesting that barium inhibited a tonically active potassium conductance. Measurements of current voltage relationships indicated an inward rectification of this conductance between −50 and −130 mV. These results provide strong evidence that barium blocks a persistent potassium ‘leak’ current in neocortical neurons that contributes to the resting potential of these cells

Conserved Charges in Einstein Gauss-Bonnet theory

Using Noether's identities, we define a superpotential with respect to a background for the Einstein Gauss-Bonnet theory of gravity. As an example, we show that its associated conserved charge yields the mass-energy of a D-dimensional Gauss-Bonnet black hole in an anti-de Sitter spacetime.Comment: 17 pages, LaTeX, references added, typos corrected, version to appear in Class. Quant. Gra

Towards Gradient-Based Design Optimization of Flexible Transport Aircraft with Flutter Constraints

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/140443/1/6.2014-2726.pd

Towards an 'average' version of the Birch and Swinnerton-Dyer Conjecture

The Birch and Swinnerton-Dyer conjecture states that the rank of the Mordell-Weil group of an elliptic curve E equals the order of vanishing at the central point of the associated L-function L(s,E). Previous investigations have focused on bounding how far we must go above the central point to be assured of finding a zero, bounding the rank of a fixed curve or on bounding the average rank in a family. Mestre showed the first zero occurs by O(1/loglog(N_E)), where N_E is the conductor of E, though we expect the correct scale to study the zeros near the central point is the significantly smaller 1/log(N_E). We significantly improve on Mestre's result by averaging over a one-parameter family of elliptic curves, obtaining non-trivial upper and lower bounds for the average number of normalized zeros in intervals on the order of 1/log(N_E) (which is the expected scale). Our results may be interpreted as providing further evidence in support of the Birch and Swinnerton-Dyer conjecture, as well as the Katz-Sarnak density conjecture from random matrix theory (as the number of zeros predicted by random matrix theory lies between our upper and lower bounds). These methods may be applied to additional families of L-functions.Comment: 20 pages, 2 figures, revised first draft (fixed some typos

Data mining of a remote behavioral tracking system for Type 2 Diabetes patients: A prospective, cohort study

Background: Complications from type 2 diabetes mellitus can be prevented when patients perform health behaviors such as vigorous exercise and glucose-regulated diet. The use of smartphones for tracking such behaviors has demonstrated success in type 2 diabetes management while generating repositories of analyzable digital data, which, when better understood, may help improve care. Data mining methods were used in this study to better understand self-monitoring patterns using smartphone tracking software. Objective: Associations were evaluated between the smartphone monitoring of health behaviors and HbA1c reductions in a patient subsample with type 2 diabetes who demonstrated clinically significant benefits after participation in a randomized controlled trial. Methods: A priori association-rule algorithms, implemented in the C language, were applied to app-discretized use data involving three primary health behavior trackers (exercise, diet, and glucose monitoring) from 29 participants who achieved clinically significant HbA1c reductions. Use was evaluated in relation to improved HbA1c outcomes. Results: Analyses indicated that nearly a third (9/29, 31%) of participants used a single tracker, half (14/29, 48%) used two primary trackers, and the remainder (6/29, 21%) of the participants used three primary trackers. Decreases in HbA1c were observed across all groups (0.97-1.95%), but clinically significant reductions were more likely with use of one or two trackers rather than use of three trackers (OR 0.18, P=.04). Conclusions: Data mining techniques can reveal relevant coherent behavior patterns useful in guiding future intervention structure. It appears that focusing on using one or two trackers, in a symbolic function, was more effective (in this sample) than regular use of all three trackers.The authors would like to thank NexJ Systems Inc. for their partnership in this trial and for the use of the Connected Wellness Platform as a clinical research tool. Funding was provided by the Public Health Agency of Canada and the Federal Development Agency of Southern Ontario. We offer special thanks to the staff of the Black Creek Community Health Centre and trial participants from the Jane-Finch community of Toronto, Ontario. Joel Katz is supported by a Canadian Institutes of Health Research Canada Research Chair in Health Psychology. The authors would like to acknowledge with sadness the untimely passing of study co-author, colleague, and friend, Dr. Nicholas Cercone. Dr. Cercone’s expertise and mentorship on data mining theory and technique was invaluable. His inspiring and supportive presence will be deeply missed