Black Hole Radiation and Volume Statistical Entropy

The simplest possible equation for Hawking radiation, and other black hole radiated power is derived in terms of black hole density. Black hole density also leads to the simplest possible model of a gas of elementary constituents confined inside a gravitational bottle of Schwarzchild radius at tremendous pressure, which yields identically the same functional dependence as the traditional black hole entropy. Variations of Sbh can be obtained which depend on the occupancy of phase space cells. A relation is derived between the constituent momenta and the black hole radius which is similar to the Compton wavelength relation.Comment: 11 pages, no figures. Key Words: Black Hole Entropy, Hawking Radiation, Black Hole density. This is a better pdf versio

Integration of Carbon, Nitrogen, and Oxygen Metabolism in Escherichia coli--Final Report

A key challenge for living systems is balancing utilization of multiple elemental nutrients, such as carbon, nitrogen, and oxygen, whose availability is subject to environmental fluctuations. As growth can be limited by the scarcity of any one nutrient, the rate at which each nutrient is assimilated must be sensitive not only to its own availability, but also to that of other nutrients. Remarkably, across diverse nutrient conditions, E. coli grows nearly optimally, balancing effectively the conversion of carbon into energy versus biomass. To investigate the link between the metabolism of different nutrients, we quantified metabolic responses to nutrient perturbations using LC-MS based metabolomics and built differential equation models that bridge multiple nutrient systems. We discovered that the carbonaceous substrate of nitrogen assimilation, ñ-ketoglutarate, directly inhibits glucose uptake and that the upstream glycolytic metabolite, fructose-1,6-bisphosphate, ultrasensitively regulates anaplerosis to allow rapid adaptation to changing carbon availability. We also showed that NADH controls the metabolic response to changing oxygen levels. Our findings support a general mechanism for nutrient integration: limitation for a nutrient other than carbon leads to build-up of the most closely related product of carbon metabolism, which in turn feedback inhibits further carbon uptake

Time Domain Explorations With Digital Sky Surveys

One of the new frontiers of astronomical research is the exploration of time variability on the sky at different wavelengths and flux levels. We have carried out a pilot project using DPOSS data to study strong variables and transients, and are now extending it to the new Palomar-QUEST synoptic sky survey. We report on our early findings and outline the methodology to be implemented in preparation for a real-time transient detection pipeline. In addition to large numbers of known types of highly variable sources (e.g., SNe, CVs, OVV QSOs, etc.), we expect to find numerous transients whose nature may be established by a rapid follow-up. Whereas we will make all detected variables publicly available through the web, we anticipate that email alerts would be issued in the real time for a subset of events deemed to be the most interesting. This real-time process entails many challenges, in an effort to maintain a high completeness while keeping the contamination low. We will utilize distributed Grid services developed by the GRIST project, and implement a variety of advanced statistical and machine learning techniques.Comment: 5 pages, 2 postscript figures, uses adassconf.sty. To be published in: "ADASS XIV (2004)", Eds. Patrick Shopbell, Matthew Britton and Rick Ebert, ASP Conference Serie

Positive solutions to indefinite Neumann problems when the weight has positive average

We deal with positive solutions for the Neumann boundary value problem associated with the scalar second order ODE $$u" + q(t)g(u) = 0, \quad t \in [0, T],$$ where $g: [0, +\infty[\, \to \mathbb{R}$ is positive on $\,]0, +\infty[\,$ and $q(t)$ is an indefinite weight. Complementary to previous investigations in the case $\int_0^T q(t) < 0$, we provide existence results for a suitable class of weights having (small) positive mean, when $g'(x) < 0$ at infinity. Our proof relies on a shooting argument for a suitable equivalent planar system of the type $$x' = y, \qquad y' = h(x)y^2 + q(t),$$ with $h(x)$ a continuous function defined on the whole real line.Comment: 17 pages, 3 figure

The Rising Light Curves of Type Ia Supernovae

We present an analysis of the early, rising light curves of 18 Type Ia supernovae (SNe Ia) discovered by the Palomar Transient Factory (PTF) and the La Silla-QUEST variability survey (LSQ). We fit these early data flux using a simple power-law $(f(t) = {\alpha\times t^n})$ to determine the time of first light $({t_0})$, and hence the rise-time $({t_{rise}})$ from first light to peak luminosity, and the exponent of the power-law rise ($n$). We find a mean uncorrected rise time of $18.98 {\pm} 0.54$ days, with individual SN rise-times ranging from $15.98$ to $24.7$ days. The exponent n shows significant departures from the simple 'fireball model' of $n = 2$ (or ${f(t) \propto t^2}$) usually assumed in the literature. With a mean value of $n = 2.44 {\pm} 0.13$, our data also show significant diversity from event to event. This deviation has implications for the distribution of 56Ni throughout the SN ejecta, with a higher index suggesting a lesser degree of 56Ni mixing. The range of n found also confirms that the 56Ni distribution is not standard throughout the population of SNe Ia, in agreement with earlier work measuring such abundances through spectral modelling. We also show that the duration of the very early light curve, before the luminosity has reached half of its maximal value, does not correlate with the light curve shape or stretch used to standardise SNe Ia in cosmological applications. This has implications for the cosmological fitting of SN Ia light curves.Comment: 19 pages, 19 figures, accepted for publication in MNRA

Tropical surface singularities

In this paper, we study tropicalisations of singular surfaces in toric threefolds. We completely classify singular tropical surfaces of maximal-dimensional type, show that they can generically have only finitely many singular points, and describe all possible locations of singular points. More precisely, we show that singular points must be either vertices, or generalized midpoints and baricenters of certain faces of singular tropical surfaces, and, in some cases, there may be additional metric restrictions to faces of singular tropical surfaces.Comment: A gap in the classification was closed. 37 pages, 29 figure

On the structure of the set of bifurcation points of periodic solutions for multiparameter Hamiltonian systems

This paper deals with periodic solutions of the Hamilton equation with many parameters. Theorems on global bifurcation of solutions with periods $2\pi/j,$ $j\in\mathbb{N},$ from a stationary point are proved. The Hessian matrix of the Hamiltonian at the stationary point can be singular. However, it is assumed that the local topological degree of the gradient of the Hamiltonian at the stationary point is nonzero. It is shown that (global) bifurcation points of solutions with given periods can be identified with zeros of appropriate continuous functions on the space of parameters. Explicit formulae for such functions are given in the case when the Hessian matrix of the Hamiltonian at the stationary point is block-diagonal. Symmetry breaking results concerning bifurcation of solutions with different minimal periods are obtained. A geometric description of the set of bifurcation points is given. Examples of constructive application of the theorems proved to analytical and numerical investigation and visualization of the set of all bifurcation points in given domain are provided. This paper is based on a part of the author's thesis [W. Radzki, ``Branching points of periodic solutions of autonomous Hamiltonian systems'' (Polish), PhD thesis, Nicolaus Copernicus University, Faculty of Mathematics and Computer Science, Toru\'{n}, 2005].Comment: 35 pages, 4 figures, PDFLaTe

Basic Connection between Superconductivity and Superfluidity

A basic and inherently simple connection is shown to exist between superconductivity and superfluidity. It is shown here that the author's previously derived general equation which agrees well with the superconducting transition temperatures for the heavy-electron superconductors, metallic superconductors, oxide supercon- ductors, metallic hydrogen, and neutron stars, also works well for the superfluid transition temperature of 2.6 mK for liquid 3He. Reasonable estimates are made from 10^-3 K to 10^9K -- a range of 12 orders of magnitude. The same paradigm applies to the superfluid transition temperature of liquid 4He, but results in a slightly different equation. The superfluid transition temperature for dilute solutions of 3He in superfluid 4He is estimated to be ~ 1 to 10mK. This paradigm works well in detail for metallic, cuprate, and organic superconductors.Comment: 16 pages, 2 figure

Determination of the Rate Coefficients of the SO2 plus O plus M yields SO3 plus M Reaction

Rate coefficients of the title reaction R(sub 31) (SO2 +O+M yields SO3 +M) and R(sub 56) (SO2 + HO2 yields SO3 +OH), important in the conversion of S(IV) to S(VI),were obtained at T =970-1150 K and rho (sub ave) = 16.2 micro mol/cubic cm behind reflected shock waves by a perturbation method. Shock-heated H2/ O2/Ar mixtures were perturbed by adding small amounts of SO2 (1%, 2%, and 3%) and the OH temporal profiles were then measured using laser absorption spectroscopy. Reaction rate coefficients were elucidated by matching the characteristic reaction times acquired from the individual experimental absorption profiles via simultaneous optimization of k(sub 31) and k(sub 56) values in the reaction modeling (for satisfactory matches to the observed characteristic times, it was necessary to take into account R(sub 56)). In the experimental conditions of this study, R(sub 31) is in the low-pressure limit. The rate coefficient expressions fitted using the combined data of this study and the previous experimental results are k(sub 31,0)/[Ar] = 2.9 10(exp 35) T(exp ?6.0) exp(?4780 K/T ) + 6.1 10(exp 24) T(exp ?3.0) exp(?1980 K/T ) cm(sup 6) mol(exp ?2)/ s at T = 300-2500 K; k(sub 56) = 1.36 10(exp 11) exp(?3420 K/T ) cm(exp 3)/mol/s at T = 970-1150 K. Computer simulations of typical aircraft engine environments, using the reaction mechanism with the above k(sub 31,0) and k(sub 56) expressions, gave the maximum S(IV) to S(VI) conversion yield of ca. 3.5% and 2.5% for the constant density and constant pressure flow condition, respectively. Moreover, maximum conversions occur at rather higher temperatures (?1200 K) than that where the maximum k(sub 31,0) value is located (approximately 800 K). This is because the conversion yield is dependent upon not only the k(sup 31,0) and k(sup 56) values (production flux) but also the availability of H, O, and HO2 in the system (consumption flux)