Navigation in Curved Space-Time

A covariant and invariant theory of navigation in curved space-time with respect to electromagnetic beacons is written in terms of J. L. Synge's two-point invariant world function. Explicit equations are given for navigation in space-time in the vicinity of the Earth in Schwarzschild coordinates and in rotating coordinates. The restricted problem of determining an observer's coordinate time when their spatial position is known is also considered

Heat Kernel Asymptotics on Homogeneous Bundles

We consider Laplacians acting on sections of homogeneous vector bundles over symmetric spaces. By using an integral representation of the heat semi-group we find a formal solution for the heat kernel diagonal that gives a generating function for the whole sequence of heat invariants. We argue that the obtained formal solution correctly reproduces the exact heat kernel diagonal after a suitable regularization and analytical continuation.Comment: 29 pages, Proceedings of the 2007 Midwest Geometry Conference in Honor of Thomas P. Branso

Extinction Curves, Distances, and Clumpiness of Diffuse Interstellar Dust Clouds

We present CCD photometry in UBVRI of several thousand Galactic field stars in four large (>1 degree^2) regions centered on diffuse interstellar dust clouds, commonly referred to as ``cirrus'' clouds (with optical depth A_V less than unity). Our goal in studying these stars is to investigate the properties of the cirrus clouds. A comparison of the observed stellar surface density between on-cloud and off-cloud regions as a function of apparent magnitude in each of the five bands effectively yields a measure of the extinction through each cloud. For two of the cirrus clouds, this method is used to derive UBVRI star counts-based extinction curves, and U-band counts are used to place constraints on the cloud distance. The color distribution of stars and their location in (U-B, B-V) and (B-V, V-I) color-color space are analyzed in order to determine the amount of selective extinction (reddening) caused by the cirrus. The color excesses, A_lambda-A_V, derived from stellar color histogram offsets for the four clouds, are better fit by a reddening law that rises steeply towards short wavelengths [R_V==A_V/E(B-V)<=2] than by the standard law (R_V=3.1). This may be indicative of a higher-than-average abundance of small dust grains relative to larger grains in diffuse cirrus clouds. The shape of the counts-based effective extinction curve and a comparison of different estimates of the dust optical depth (extinction optical depth derived from background star counts/colors; emission optical depth derived from far infrared measurements), are used to measure the degree of clumpiness in clouds. The set of techniques explored in this paper can be readily adapted to the Sloan Digital Sky Survey data set in order to carry out a systematic, large-scale study of cirrus clouds.Comment: 22 pages, 13 figures (postscript, gif, jpg). Accepted for publication in the Astronomical Journal, scheduled for the May 1999 issue. Full resolution postscript versions of all figures are available at http://www.ucolick.org/~arpad

Step-wedge cluster-randomised community-based trials: An application to the study of the impact of community health insurance

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.BACKGROUND: We describe a step-wedge cluster-randomised community-based trial which has been conducted since 2003 to accompany the implementation of a community health insurance (CHI) scheme in West Africa. The trial aims at overcoming the paucity of evidence-based information on the impact of CHI. Impact is defined in terms of changes in health service utilisation and household protection against the cost of illness. Our exclusive focus on the description and discussion of the methods is justified by the fact that the study relies on a methodology previously applied in the field of disease control, but never in the field of health financing. METHODS: First, we clarify how clusters were defined both in respect of statistical considerations and of local geographical and socio-cultural concerns. Second, we illustrate how households within clusters were sampled. Third, we expound the data collection process and the survey instruments. Finally, we outline the statistical tools to be applied to estimate the impact of CHI. CONCLUSION: We discuss all design choices both in relation to methodological considerations and to specific ethical and organisational concerns faced in the field. On the basis of the appraisal of our experience, we postulate that conducting relatively sophisticated trials (such as our step-wedge cluster-randomised community-based trial) aimed at generating sound public health evidence, is both feasible and valuable also in low income settings. Our work shows that if accurately designed in conjunction with local health authorities, such trials have the potential to generate sound scientific evidence and do not hinder, but at times even facilitate, the implementation of complex health interventions such as CHI

A close look into the carbon disk at the core of the planetary nebula CPD-568032

We present high spatial resolution observations of the dusty core of the Planetary Nebula with Wolf-Rayet central star CPD-568032. These observations were taken with the mid-infrared interferometer VLTI/MIDI in imaging mode providing a typical 300 mas resolution and in interferometric mode using UT2-UT3 47m baseline providing a typical spatial resolution of 20 mas. The visible HST images exhibit a complex multilobal geometry dominated by faint lobes. The farthest structures are located at 7" from the star. The mid-IR environment of CPD-568032 is dominated by a compact source, barely resolved by a single UT telescope in a 8.7 micron filter. The infrared core is almost fully resolved with the three 40-45m projected baselines ranging from -5 to 51 degree but smooth oscillating fringes at low level have been detected in spectrally dispersed visibilities. This clear signal is interpreted in terms of a ring structure which would define the bright inner rim of the equatorial disk. Geometric models allowed us to derive the main geometrical parameters of the disk. For instance, a reasonably good fit is reached with an achromatic and elliptical truncated Gaussian with a radius of 97+/-11 AU, an inclination of 28+/-7 degree and a PA for the major axis at 345+/-7 degree. Furthermore, we performed some radiative transfer modeling aimed at further constraining the geometry and mass content of the disk, by taking into account the MIDI dispersed visibilities, spectra, and the large aperture SED of the source. These models show that the disk is mostly optically thin in the N band and highly flared.Comment: Paper accepted in A&

Medium Effects on Binary Collisions with the Delta Resonance

To facilitate the relativistic heavy-ion calculations based on transport equations, the binary collisions involving a $\Delta$ resonance in either the entrance channel or the exit channel are investigated within a Hamiltonian formulation of $\pi NN$ interactions. An averaging procedure is developed to define a quasi-particle $\Delta^*$ and to express the experimentally measured $NN\rightarrow \pi NN$ cross section in terms of an effective $NN\rightarrow N\Delta^\ast$ cross section. In contrast to previous works, the main feature of the present approach is that the mass and the momentum of the produced $\Delta^*$'s are calculated dynamically from the bare $\Delta \leftrightarrow \pi N$ vertex interaction of the model Hamiltonian and are constrained by the unitarity condition. The procedure is then extended to define the effective cross sections for the experimentally inaccessible $N\Delta^\ast \rightarrow NN$ and $N\Delta^\ast \rightarrow N\Delta^\ast$ reactions. The predicted cross sections are significantly different from what are commonly assumed in relativistic heavy-ion calculations. The $\Delta$ potential in nuclear matter has been calculated by using a Bruckner-Hartree-Fock approximation. By including the mean-field effects on the $\Delta$ propagation, the effective cross sections of the $NN\rightarrow N\Delta^\ast$, $N\Delta^\ast \rightarrow NN$ and $N\Delta^\ast \rightarrow N\Delta^\ast$ reactions in nuclear matter are predicted. It is demonstrated that the density dependence is most dramatic in the energy region close to the pion production threshold.Comment: 20 pages, RevTe

New method to study stochastic growth equations: a cellular automata perspective

We introduce a new method based on cellular automata dynamics to study stochastic growth equations. The method defines an interface growth process which depends on height differences between neighbors. The growth rule assigns a probability $p_{i}(t)=\rho$ exp$[\kappa \Gamma_{i}(t)]$ for a site $i$ to receive one particle at a time $t$ and all the sites are updated simultaneously. Here $\rho$ and $\kappa$ are two parameters and $\Gamma_{i}(t)$ is a function which depends on height of the site $i$ and its neighbors. Its functional form is specified through discretization of the deterministic part of the growth equation associated to a given deposition process. In particular, we apply this method to study two linear equations - the Edwards-Wilkinson (EW) equation and the Mullins-Herring (MH) equation - and a non-linear one - the Kardar-Parisi-Zhang (KPZ) equation. Through simulations and statistical analysis of the height distributions of the profiles, we recover the values for roughening exponents, which confirm that the processes generated by the method are indeed in the universality classes of the original growth equations. In addition, a crossover from Random Deposition to the associated correlated regime is observed when the parameter $\kappa$ is varied.Comment: 6 pages, 7 figure

Quark-Gluon String Model Description of Baryon Production in K^{\pm}N Interactions

The process of baryon production in K p collisions at high energies is considered in the framework of the Quark-Gluon String Model. The contribution of the string-junction mechanism to the strange baryon production is analysed. The results of numerical calculations are in reasonable agreement with the data on inclusive spectra of p, Lambda, bar{Lambda}, and on the bar{Lambda}/Lambda asymmetry. The predictions for Xi and Omega baryons are presented.Comment: 19 pages, 7 figure