Monochromatic geometric k-factors in red-blue sets with white and Steiner points

We study the existence of monochromatic planar geometric k-factors on sets of red and blue points. When it is not possible to find a k-factor we make use of auxiliary points: white points, whose position is given as a datum and which color is free; and Steiner points whose position and color is free. We present bounds on the number of white and/or Steiner points necessary and/or sufficient to draw a monochromatic planar geometric k-factor

Monochromatic geometric k-factors for bicolored point sets with auxiliary points

Given a bicolored point set S, it is not always possible to construct a monochromatic geometric planar k-factor of S. We consider the problem of finding such a k-factor of S by using auxiliary points. Two types are considered: white points whose position is fixed, and Steiner points which have no fixed position. Our approach provides algorithms for constructing those k-factors, and gives bounds on the number of auxiliary points needed to draw a monochromatic geometric planar k-factor of S

On Embeddability of Buses in Point Sets

Set membership of points in the plane can be visualized by connecting corresponding points via graphical features, like paths, trees, polygons, ellipses. In this paper we study the \emph{bus embeddability problem} (BEP): given a set of colored points we ask whether there exists a planar realization with one horizontal straight-line segment per color, called bus, such that all points with the same color are connected with vertical line segments to their bus. We present an ILP and an FPT algorithm for the general problem. For restricted versions of this problem, such as when the relative order of buses is predefined, or when a bus must be placed above all its points, we provide efficient algorithms. We show that another restricted version of the problem can be solved using 2-stack pushall sorting. On the negative side we prove the NP-completeness of a special case of BEP.Comment: 19 pages, 9 figures, conference version at GD 201

On some partitioning problems for two-colored point sets

Let S be a two-colored set of n points in general position in the plane. We show that S admits at least 2 n 17 pairwise disjoint monochromatic triangles with vertices in S and empty of points of S. We further show that S can be partitioned into 3 n 11 subsets with pairwise disjoint convex hull such that within each subset all but at most one point have the same color. A lower bound on the number of subsets needed in any such partition is also given.Postprint (published version

Near-Infrared interferometry of Eta Carinae with high spatial and spectral resolution using the VLTI and the AMBER instrument

We present the first NIR spectro-interferometry of the LBV Eta Carinae. The K band observations were performed with the AMBER instrument of the ESO Very Large Telescope Interferometer using three 8.2m Unit Telescopes with baselines from 42 to 89m. The aim of this work is to study the wavelength dependence of Eta Car's optically thick wind region with a high spatial resolution of 5 mas (11 AU) and high spectral resolution. The medium spectral resolution observations (R=1,500) were performed in the wavelength range around both the HeI 2.059 micron and the Br gamma 2.166 micron emission lines, the high spectral resolution observations (R=12,000) only in the Br gamma line region. In the K-band continuum, a diameter of 4.0 +/-0.2 mas (Gaussian FWHM, fit range 28-89m) was measured for Eta Car's optically thick wind region. If we fit Hillier et al. (2001) model visibilities to the observed AMBER visibilities, we obtain 50 % encircled-energy diameters of 4.2, 6.5 and 9.6mas in the 2.17 micron continuum, the HeI, and the Br gamma emission lines, respectively. In the continuum near the Br gamma line, an elongation along a position angle of 120+/-15 degrees was found, consistent with previous VLTI/VINCI measurements by van Boekel et al. (2003). We compare the measured visibilities with predictions of the radiative transfer model of Hillier et al. (2001), finding good agreement. Furthermore, we discuss the detectability of the hypothetical hot binary companion. For the interpretation of the non-zero differential and closure phases measured within the Br gamma line, we present a simple geometric model of an inclined, latitude-dependent wind zone. Our observations support theoretical models of anisotropic winds from fast-rotating, luminous hot stars with enhanced high-velocity mass loss near the polar regions.Comment: 22 pages, 14 figures, 2 tables; A&A in pres

Interfacial Relaxation and Two-Fluid Flow in Porous Media: A Fast X-Ray Microtomography Study

The flow of multiple immiscible fluids within a porous medium controls many natural and engineered systems in the environment including: geologic CO2 sequestration, enhanced oil recovery from underground reservoirs, and contaminant remediation of groundwater. The need to understand how fluids are transported and distributed in these processes is important for designing accurate models that can improve process efficiency. The research comprising this dissertation developed and utilized a fast X-ray microtomography technique that allows for three-dimensional, near real-time, investigations of multiphase flow. Constitutive relationships based on multiphase state variables (saturation, capillary pressure, interfacial area, fluid topology) are tested for accurate predictions of quasi- and non-equilibrium two-fluid flow experiments in an effort to better understand the role of fluid relaxation on these relationships and state variables. The effect of bubble generation and transport, relevant to multiphase processes such as air stripping, on these relationships is also studied. Collectively, results show the need for constitutive relationships which include all four measured state variables to uniquely predict two-fluid flow independent of flow condition or bubble generation. An empirical relationship is also developed to predict interfacial area, an important mass transfer parameter, depending on the degree of relaxation within the system. Overall, the presented findings may help design more efficient engineering practices and transport models

Optimising Light Source Spectrum to Reduce the Energy Absorbed by Objects

Light is used to illuminate objects in the built environment. Humans can only observe light reflected from an object. Light absorbed by an object turns into heat and does not contribute to visibility. Since the spectral output of the new lighting technologies can be tuned, it is possible to imagine a lighting system that detects the colours of objects and emits customised light to minimise the absorbed energy. Previous optimisation studies investigated the use of narrowband LEDs to maximise the efficiency and colour quality of a light source. While these studies aimed to tune a white light source for general use, the lighting system proposed here minimises the energy consumed by lighting by detecting colours of objects and emitting customised light onto each coloured part of the object. This thesis investigates the feasibility of absorption-minimising light source spectra and their impact on the colour appearance of objects and energy consumption. Two computational studies were undertaken to form the theoretical basis of the absorption-minimising light source spectra. Computational simulations show that the theoretical single-peak spectra can lower the energy consumption up to around 38 % to 62 %, and double-peak test spectra can result in energy savings up to 71 %, without causing colour shifts. In these studies, standard reference illuminants, theoretical test spectra and coloured test samples were used. These studies are followed by the empirical evidence collected from two psychophysical experiments. Data from the experiments show that observers find the colour appearance of objects equally natural and attractive under spectrally optimised spectra and reference white light sources. An increased colour difference, to a certain extent, is found acceptable, which allows even higher energy savings. However, the translucent nature of some objects may negatively affect the results

Wide field x-ray spectral imaging using bent Laue monochromators

X-ray Absorption Spectroscopy (XAS) is a widely used method for determining the local environment and/or speciation of elements. Conventionally, synchrotron based XAS requires mechanically scanning through the desired energy range using a flat double-crystal monochromator. Energy Dispersive XAS (EDXAS) is a variant of the XAS technique, which typically uses a bent crystal monochromator to provide a focused x-ray beam that contains all the energies required to make an XAS measurement. An obvious advantage of EDXAS over conventional XAS is the high efficiency and stability, because mechanical energy scanning is not needed. With a high brilliance x-ray source and high speed detection system, EDXAS enables XAS studies associated with extreme conditions, femtosecond time resolution and atomic level precision. The thesis describes the development of a Wide Field EDXAS imaging system, employing a specially designed bent Laue crystal monochromator that matches the so-called 'magic condition' which was previously described for spectral K-edge subtraction imaging. Compared to a classic EDXAS system, the Wide Field EDXAS system has the following advantages. (i) The diffracted beam from a bend magnet synchrotron source is focused in the vertical dimension and unaltered in the horizontal dimension. This focused line beam takes advantage of the width of a bend magnet x-ray beam and records spatial information across the beam. Combining the information from the energy dispersion dimension and the spatial dimension, the Wide Field EDXAS system can acquire several thousand spectra per exposure. (ii) A bent crystal that matches the 'magic condition' provides a good energy resolution in addition to the optimized focal size. The improved energy resolution enables the system to investigate the fine structure of x-ray absorption spectra with good spatial resolution using a single x-ray optic. To make the use of the Wide Field EDXAS system more accessible, user-friendly software has been developed to process and extract concentration information from images acquired in either projection (2D) or computed tomography (3D) mode of operation. This software is made available at the Canadian Light Source BMIT-BM beamline and is compatible with another contrast element imaging method - spectral K-edge subtraction imaging. The energy resolution of a bent crystal at the 'magic condition' is still not as good as that of a flat double-crystal monochromator. To pursue the ultimate energy resolution of a bent Laue crystal, a new approach has been developed for describing the general behavior of bent Laue crystals from a ray-tracing point of view. The so-called quasi-mono beam approach provides an intuitive view of bent crystal diffraction and leads to deeper insights. It explains the energy and spatial properties of common and special cases of bent Laue optics, predicts phenomena that can improve energy dispersion related x-ray imaging techniques and provides a theory framework that makes ray-tracing simulation easier to realize

Colour and Colorimetry Multidisciplinary Contributions Vol. XIb

It is well known that the subject of colour has an impact on a range of disciplines. Colour has been studied in depth for many centuries, and as well as contributing to theoretical and scientific knowledge, there have been significant developments in applied colour research, which has many implications for the wider socio-economic community. At the 7th Convention of Colorimetry in Parma, on the 1st October 2004, as an evolution of the previous SIOF Group of Colorimetry and Reflectoscopy founded in 1995, the "Gruppo del Colore" was established. The objective was to encourage multi and interdisciplinary collaboration and networking between people in Italy that addresses problems and issues on colour and illumination from a professional, cultural and scientific point of view. On the 16th of September 2011 in Rome, in occasion of the VII Color Conference, the members assembly decided to vote for the autonomy of the group. The autonomy of the Association has been achieved in early 2012. These are the proceedings of the English sessions of the XI Conferenza del Colore