An Integral Spectral Representation of the Propagator for the Wave Equation in the Kerr Geometry

We consider the scalar wave equation in the Kerr geometry for Cauchy data which is smooth and compactly supported outside the event horizon. We derive an integral representation which expresses the solution as a superposition of solutions of the radial and angular ODEs which arise in the separation of variables. In particular, we prove completeness of the solutions of the separated ODEs. This integral representation is a suitable starting point for a detailed analysis of the long-time dynamics of scalar waves in the Kerr geometry.Comment: 41 pages, 4 figures, minor correction

Investigation of the New Local Group Galaxy VV 124

We present the results of our stellar photometry and spectroscopy for the new Local Group galaxy VV 124 (UGC 4879) obtained with the 6-m BTA telescope. The presence of a few bright supergiants in the galaxy indicates that the current star formation process is weak. The apparent distribution of stars with different ages in VV 124 does not differ from the analogous distributions of stars in irregular galaxies, but the ratio of the numbers of young and old stars indicates that VV 124 belongs to the rare Irr/Sph type of galaxies. The old stars (red giants) form the most extended structure, a thick disk with an exponential decrease in the star number density to the edge. Definitely, the young population unresolvable in images makes a great contribution to the background emission from the central galactic regions. The presence of young stars is also confirmed by the [O III] emission line visible in the spectra that belongs to extensive diffuse galactic regions. The mean radial velocity of several components (two bright supergiants, the unresolvable stellar population, and the diffuse gas) is v_h = -70+/-15 km/s and the velocity with which VV 124 falls into the Local Group is v_LG = -12+/-15 km/s. We confirm the distance to the galaxy D = 1.1+/-0.1 Mpc and the metallicity of red giants ([Fe/H] = -1.37) found by Kopylov et al. (2008).VV 124 is located on the periphery of the Local Group approximately at the same distance from M 31 and our Galaxy and is isolated from other galaxies. The galaxy LeoA nearest to it is 0.5 Mpc away.Comment: 10 pages, 8 figures. Accepted for publication in Astronomy Letters (2010, Vol. 36, No. 5, pp. 309-318

Nanoelectromechanical Resonator Arrays for Ultrafast, Gas-Phase Chromatographic Chemical Analysis

Miniaturized gas chromatography (GC) systems can provide fast, quantitative analysis of chemical vapors in an ultrasmall package. We describe a chemical sensor technology based on resonant nanoelectromechanical systems (NEMS) mass detectors that provides the speed, sensitivity, specificity, and size required by the microscale GC paradigm. Such NEMS sensors have demonstrated detection of subparts per billion (ppb) concentrations of a phosphonate analyte. By combining two channels of NEMS detection with an ultrafast GC front-end, chromatographic analysis of 13 chemicals was performed within a 5 s time window

Short communication: Pelleting increases the metabolizable energy of de-hulled sunflower seed meal for broilers

The study examined the effects of two methods of processing de-hulled sunflower seed meal (SFM) from the same batch of sunflower seeds. Sunflower seed meal was fed to broilers as meal (MSFM) or after it had been pelleted (PSFM) at 75 °C and 360 kPa pressure to pass through a 3 mm mesh. Three diets were prepared, namely a balancer feed (BF) and two diets containing 200 g/kg MSFM or 200 g/kg PSFM. They were fed to 30 pens (two birds each) with male Ross 308 broilers, from 8 to 21 days old, following randomization. Data were analysed by ANOVA. Two pre-planned orthogonal contrast tests were performed to compare overall differences between the diets containing SFM and BF and between diets containing the MSFM and PSFM. The BF had a very different nutrient composition from the complete feeds containing SFM so, as expected, there were differences in growth performance and nutrient retention. The diet containing PSFM had greater apparent metabolizable energy corrected for N retention (AMEn) and dry matter retention (DMR) than that containing MSFM. The use of the substitution method showed the PSFM had AMEn that was 18% greater than the MSFM (8.79 vs 7.47 MJ/kg DM). Under the conditions of the current study, incorporating PSFM in a mash broiler feed increased dietary AMEn compared with the same feed containing MSFM. Further studies are needed to identify whether the benefits of pre-pelleting SFM remain after this product has been incorporated in complete pelleted broiler feeds

Thermodynamics of Reissner-Nordstrom-anti-de Sitter black holes in the grand canonical ensemble

The thermodynamical properties of the Reissner-Nordstr\"om-anti-de Sitter black hole in the grand canonical ensemble are investigated using York's formalism. The black hole is enclosed in a cavity with finite radius where the temperature and electrostatic potential are fixed. The boundary conditions allow us to compute the relevant thermodynamical quantities, e.g. thermal energy, entropy and charge. The stability conditions imply that there are thermodynamically stable black hole solutions, under certain conditions. Instantons with negative heat capacity are also found.Comment: 15 pages, 9 figures, Revtex. Published version. Changes: figures added to tex

Quantum Theory of Black Holes

A solvable 2-dimensional conformally invariant midi-superspace model for black holes is obtained by imposing spherical symmetry in 4-dimensional conformally invariant Einstein gravity. The Wheeler-DeWitt equation for the theory is solved exactly to obtain the unique quantum wave functional for an isolated black hole with fixed mass. By suitably relaxing the boundary conditions, a non-perturbative ansatz is obtained for the wave functional of a black hole interacting with its surroundings.Comment: Plain-TeX, 13 pages, no figures, WIN-92-9, UNB Tech. Rep. 92-0

Relationship between ecosystem productivity and photosynthetically-active radiation for northern peatlands

We analyzed the relationship between net ecosystem exchange of carbon dioxide (NEE) and irradiance (as photosynthetic photon flux density or PPFD), using published and unpublished data that have been collected during midgrowing season for carbon balance studies at seven peatlands in North America and Europe. NEE measurements included both eddy-correlation tower and clear, static chamber methods, which gave very similar results. Data were analyzed by site, as aggregated data sets by peatland type (bog, poor fen, rich fen, and all fens) and as a single aggregated data set for all peatlands. In all cases, a fit with a rectangular hyperbola (NEE = α PPFD Pmax/(α PPFD + Pmax) + R) better described the NEE-PPFD relationship than did a linear fit (NEE = β PPFD + R). Poor and rich fens generally had similar NEE-PPFD relationships, while bogs had lower respiration rates (R = −2.0μmol m−2s−1 for bogs and −2.7 μmol m−2s−1 for fens) and lower NEE at moderate and high light levels (Pmax = 5.2 μmol m−2s−1 for bogs and 10.8 μmol m−2s−1 for fens). As a single class, northern peatlands had much smaller ecosystem respiration (R = −2.4 μmol m−2s−1) and NEE rates (α = 0.020 and Pmax = 9.2μmol m−2s−1) than the upland ecosystems (closed canopy forest, grassland, and cropland) summarized by Ruimy et al. [1995]. Despite this low productivity, northern peatland soil carbon pools are generally 5–50 times larger than upland ecosystems because of slow rates of decomposition caused by litter quality and anaerobic, cold soils

Hamiltonian thermodynamics of two-dimensional vacuum dilatonic black holes

We consider the Hamiltonian dynamics and thermodynamics of the two-dimensional vacuum dilatonic black hole in the presence of a timelike boundary with a fixed value of the dilaton field. A~canonical transformation, previously developed by Varadarajan and Lau, allows a reduction of the classical dynamics into an unconstrained Hamiltonian system with one canonical pair of degrees of freedom. The reduced theory is quantized, and a partition function of a canonical ensemble is obtained as the trace of the analytically continued time evolution operator. The partition function exists for any values of the dilaton field and the temperature at the boundary, and the heat capacity is always positive. For temperatures higher than $\beta_c^{-1} = \hbar\lambda/(2\pi)$, the partition function is dominated by a classical black hole solution, and the dominant contribution to the entropy is the two-dimensional Bekenstein-Hawking entropy. For temperatures lower than~$\beta_c^{-1}$, the partition function remains well-behaved and the heat capacity is positive in the asymptotically flat space limit, in contrast to the corresponding limit in four-dimensional spherically symmetric Einstein gravity; however, in this limit, the partition function is not dominated by a classical black hole solution.Comment: 20 pages, REVTEX. Added a discussion on the boundary action and boundary terms in Sec. IIIA. Minor changes in Acknowledgements and Reference

Is the brick-wall model unstable for a rotating background?

The stability of the brick wall model is analyzed in a rotating background. It is shown that in the Kerr background without horizon but with an inner boundary a scalar field has complex-frequency modes and that, however, the imaginary part of the complex frequency can be small enough compared with the Hawking temperature if the inner boundary is sufficiently close to the horizon, say at a proper altitude of Planck scale. Hence, the time scale of the instability due to the complex frequencies is much longer than the relaxation time scale of the thermal state with the Hawking temperature. Since ambient fields should settle in the thermal state in the latter time scale, the instability is not so catastrophic. Thus, the brick wall model is well defined even in a rotating background if the inner boundary is sufficiently close to the horizon.Comment: Latex, 17 pages, 1 figure, accepted for publication in Phys. Rev.