Closed-Form Expressions for Irradiance from Non-Uniform Lambertian Luminaires Part I: Linearly-Varying Radiant Exitance

We present a closed-form expression for the irradiance at a point on a surface due to an arbitrary polygonal Lambertian lurninaire with linearly-varying radiant exitance. The solution consists of elementary functions and a single well-behaved special function that can be either approximated directly or computed exactly in terms of classical special functions such as Clausen's integral or the closely related dilogarithm. We first provide a general boundary integral that applies to all planar luminaires and then derive the closed-form expression that applies to arbitrary polygons, which is the result most relevant for global illumination. Our approach is to express the problem as an integral of a simple class of rational functions over regions of the sphere, and to convert the surface integral to a boundary integral using a generalization of irradiance tensors. The result extends the class of available closed-form expressions for computing direct radiative transfer from finite areas to differential areas. We provide an outline of the derivation, a detailed proof of the resulting formula, and complete pseudo-code of the resulting algorithm. Finally, we demonstrate the validity of our algorithm by comparison with Monte Carlo. While there are direct applications of this work, it is primarily of theoretical interest as it introduces much of the machinery needed to derive closed-form solutions for the general case of luminaires with radiance distributions that vary polynomially in both position and direction

Boundary layer analysis of the Navier-Stokes equations with Generalized Navier boundary conditions

We study the weak boundary layer phenomenon of the Navier-Stokes equations in a 3D bounded domain with viscosity, $\epsilon > 0$, under generalized Navier friction boundary conditions, in which we allow the friction coefficient to be a (1, 1) tensor on the boundary. When the tensor is a multiple of the identity we obtain Navier boundary conditions, and when the tensor is the shape operator we obtain conditions in which the vorticity vanishes on the boundary. By constructing an explicit corrector, we prove the convergence of the Navier-Stokes solutions to the Euler solution as the viscosity vanishes. We do this both in the natural energy norm with a rate of order $\epsilon^{3/4}$ as well as uniformly in time and space with a rate of order $\epsilon^{3/8 - \delta}$ near the boundary and $\epsilon^{3/4 - \delta'}$ in the interior, where $\delta, \delta'$ decrease to 0 as the regularity of the initial velocity increases. This work simplifies an earlier work of Iftimie and Sueur, as we use a simple and explicit corrector (which is more easily implemented in numerical applications). It also improves a result of Masmoudi and Rousset, who obtain convergence uniformly in time and space via a method that does not yield a convergence rate.Comment: Additional references and several typos fixe

Color Magnitude Relation and Morphology of Low-Redshift ULIRGs in SDSS

We present color-magnitude and morphological analysis of 54 low-redshift ULIRGs, a subset of the IRAS 1Jy sample (Kim & Sanders, 1998), in the SDSS. The ULIRGs are on average 1 magnitude brighter in M0.1r than the SDSS galaxies within the same redshift range. The majority of the ULIRGs (~87%) have the colors typical of the blue cloud, and only 4 sources (~7%) are located in the red sequence. While ULIRGs are popularly thought to be precursors to a QSO phase, we find few (~6%) in the "green valley" where the majority of the X-ray and IR selected AGNs are found, and none of which harbors an AGN. For the 14 previously spectroscopic identified AGNs (~28%), we perform PSF subtractions and find that on average the central point sources contribute less than one third to the total luminosity, and that their high optical luminosities and overall blue colors are apparently the result of star formation activity of the host galaxies. Visual inspection of the SDSS images reveals a wide range of disturbed morphologies. A detailed morphology analysis using Gini and M20 coefficients shows that slightly less than one half (~42% in g band) of the ULIRGs are located in the region where most local mergers are found. The heterogeneous distribution of ULIRGs in the G-M20 space is qualitatively consistent with the results found by numerical simulations of disk-disk mergers. Our study also shows that the measured morphological parameters are systematically affected by the SNR and thus the merging galaxies can appear at various regions in the G-M20 space. In general, our results reinforce the view that ULIRGs contain young stellar populations and are mergers in progress. Our study provides a uniform comparison sample for studying ULIRGs at higher redshifts such as Spitzer mid-IR selected ULIRGs at z=1~2 and submm galaxies.Comment: 42 pages, 11 figures, ApJ accepte

Atmospheric Chemistry for Astrophysicists: A Self-consistent Formalism and Analytical Solutions for Arbitrary C/O

We present a self-consistent formalism for computing and understanding the atmospheric chemistry of exoplanets from the viewpoint of an astrophysicist. Starting from the first law of thermodynamics, we demonstrate that the van't Hoff equation (which describes the equilibrium constant), Arrhenius equation (which describes the rate coefficients) and procedures associated with the Gibbs free energy (minimisation, rescaling) have a common physical and mathematical origin. We address an ambiguity associated with the equilibrium constant, which is used to relate the forward and reverse rate coefficients, and restate its two definitions. By necessity, one of the equilibrium constants must be dimensionless and equate to an exponential function involving the Gibbs free energy, while the other is a ratio of rate coefficients and must therefore possess physical units. We demonstrate that the Arrhenius equation takes on a functional form that is more general than previously stated without recourse to tagging on ad hoc functional forms. Finally, we derive analytical models of chemical systems, in equilibrium, with carbon, hydrogen and oxygen. We include acetylene and are able to reproduce several key trends, versus temperature and carbon-to-oxygen ratio, published in the literature. The rich variety of behavior that mixing ratios exhibit as a function of the carbon-to-oxygen ratio is merely the outcome of stoichiometric book-keeping and not the direct consequence of temperature or pressure variations.Comment: Accepted by ApJ. 9 pages, 4 figure

The Timing of Broadband Provision: The Role of Competition and Demographics

We examine the supply of DSL broadband by the incumbent local exchange company (LEC) in five U.S. states in the earlier years of deployment. Our empirical analysis shows that income, other demographics, and cost factors are important determinants of entry and availability, and thus, the supply side of the digital divide. After controlling for other factors, the racial characteristics of the area do not affect DSL provision. Demand-side factors explain possible redlining in the region studied, and there is no need for policies aimed at overcoming discrimination on the part of the provider. Our objective in gauging the importance of the various factors is to highlight the important drivers of broadband provision for policy makers. We conclude that policies to accelerate the narrowing of the broadband digital divide must either focus on the demand side of the market or increase the firms' profitability of entering less desirable areas.

Efficient geographic information systems: Data structures, Boolean operations and concurrency control

Geographic Information Systems (GIS) are crucial to the ability of govern mental agencies and business to record, manage and analyze geographic data efficiently. They provide methods of analysis and simulation on geographic data that were previously infeasible using traditional hardcopy maps. Creation of realistic 3-D sceneries by overlaying satellite imagery over digital elevation models (DEM) was not possible using paper maps. Determination of suitable areas for construction that would have the fewest environmental impacts once required manual tracing of different map sets on mylar sheets; now it can be done in real time by GIS. Geographic information processing has significant space and time require ments. This thesis concentrates on techniques which can make existing GIS more efficient by considering these issues: Data Structure, Boolean Operations on Geographic Data, Concurrency Control. Geographic data span multiple dimensions and consist of geometric shapes such as points, lines, and areas, which cannot be efficiently handled using a traditional one-dimensional data structure. We therefore first survey spatial data structures for geographic data and then show how a spatial data structure called an R-tree can be used to augment the performance of many existing GIS. Boolean operations on geographic data are fundamental to the spatial anal ysis common in geographic data processing. They allow the user to analyze geographic data by using operators such as AND, OR, NOT on geographic ob jects. An example of a boolean operation query would be, Find all regions that have low elevation AND soil type clay. Boolean operations require signif icant time to process. We present a generalized solution that could significantly improve the time performance of evaluating complex boolean operation queries. Concurrency control on spatial data structures for geographic data processing is becoming more critical as the size and resolution of geographic databases increase. We present algorithms to enable concurrent access to R-tree spatial data structures so that efficient sharing of geographic data can occur in a multi user GIS environment

A Wireless Implantable System for Facilitating Gastrointestinal Motility.

Gastrointestinal (GI) electrical stimulation has been shown in several studies to be a potential treatment option for GI motility disorders. Despite the promising preliminary research progress, however, its clinical applicability and usability are still unknown and limited due to the lack of a miniaturized versatile implantable stimulator supporting the investigation of effective stimulation patterns for facilitating GI dysmotility. In this paper, we present a wireless implantable GI modulation system to fill this technology gap. The system consists of a wireless extraluminal gastrointestinal modulation device (EGMD) performing GI electrical stimulation, and a rendezvous device (RD) and a custom-made graphical user interface (GUI) outside the body to wirelessly power and configure the EGMD to provide the desired stimuli for modulating GI smooth muscle activities. The system prototype was validated in bench-top and in vivo tests. The GI modulation system demonstrated its potential for facilitating intestinal transit in the preliminary in vivo chronic study using porcine models