The absence of efficient dual pairs of spanning trees in planar graphs

A spanning tree T in a finite planar connected graph G determines a dual spanning tree T* in the dual graph G such that T and T* do not intersect. We show that it is not always possible to find T in G, such that the diameters of T and T* are both within a uniform multiplicative constant (independent of G) of the diameters of their ambient graphs.Comment: 7 pages, 3 figure

Program to design, fabricate, test, and deliver a thermal control-mixing control device for the George C. Marshall Space Flight Center

The development and testing of a temperature sensor and pulse duration modulation (PDM) diverter valve for a thermal control-mixing control device are described. The temperature sensor selected for use uses a fluidic pin amplifier in conjunction with an expansion device. This device can sense changes of less than 0.25 F with greater than 15:1 signal to noise ratio when operating with a typical Freon pump supplied pressure. The pressure sensitivity of the sensor is approximately 0.0019 F/kPa. The valve which was selected was tested and performed with 100% flow diversion. In addition, the valve operates with a flow efficiency of at least 95%, with the possibility of attaining 100% if the vent flow of the PDM can be channeled through the last stage of the diverter valve. A temperature sensor which utilized an orifice bridge circuit and proportional-vortex combination mixing valve were also evaluated, but the concepts were rejected due to various problems

Nondestructive x-ray Scattering Characterization of High Temperature Superconducting Wires

The purpose of this CRADA was to characterize the structural properties of the superconductor material within the wires in order to determine which processing procedures produce the best superconductor texture and phase development, and hence the best ultimate current carrying capacity

Geometry and observables in (2+1)-gravity

We review the geometrical properties of vacuum spacetimes in (2+1)-gravity with vanishing cosmological constant. We explain how these spacetimes are characterised as quotients of their universal cover by holonomies. We explain how this description can be used to clarify the geometrical interpretation of the fundamental physical variables of the theory, holonomies and Wilson loops. In particular, we discuss the role of Wilson loop observables as the generators of the two fundamental transformations that change the geometry of (2+1)-spacetimes, grafting and earthquake. We explain how these variables can be determined from realistic measurements by an observer in the spacetime.Comment: Talk given at 2nd School and Workshop on Quantum Gravity and Quantum Geometry (Corfu, September 13-20 2009); 10 pages, 13 eps figure

Black Holes in Three Dimensional Topological Gravity

We investigate the black hole solution to (2+1)-dimensional gravity coupled to topological matter, with a vanishing cosmological constant. We calculate the total energy, angular momentum and entropy of the black hole in this model and compare with results obtained in Einstein gravity. We find that the theory with topological matter reverses the identification of energy and angular momentum with the parameters in the metric, compared with general relativity, and that the entropy is determined by the circumference of the inner rather than the outer horizon. We speculate that this results from the contribution of the topological matter fields to the conserved currents. We also briefly discuss two new possible (2+1)-dimensional black holes.Comment: 14 pages, LateX, UNB Tech. Rep. 94-03, UCD- 94-3

Photocatalysis Using Semiconductor Nanoclusters

We report on experiments using nanosize MoS{sub 2} to photo-oxidize organic pollutants in water using visible light as the energy source. We have demonstrated that we can vary the redox potentials and absorbance characteristics of these small semiconductors by adjusting their size, and our studies of the photooxidation of organic molecules have revealed that the rate of oxidation increases with increasing bandgap (i.e. more positive valence band and more negative conduction band potentials). Because these photocatalysis reactions can be performed with the nanoclusters fully dispersed and stable in solution, liquid chromatography can be used to determine both the intermediate reaction products and the state of the nanoclusters during the reaction. We have demonstrated that the MoS{sub 2} nanoclusters remain unchanged during the photooxidation process by this technique. We also report on studies of MoS{sub 2} nanoclusters deposited on TiO{sub 2} powder

On the Nature of Andromeda IV

Lying at a projected distance of 40' or 9 kpc from the centre of M31, Andromeda IV is an enigmatic object first discovered during van den Bergh's search for dwarf spheroidal companions to M31. Being bluer, more compact and higher surface brightness than other known dwarf spheroidals, it has been suggested that And IV is either a relatively old `star cloud' in the outer disk of M31 or a background dwarf galaxy. We present deep HST WFPC2 observations of And IV and the surrounding field which, along with ground-based long-slit spectroscopy and Halpha imagery, are used to decipher the true nature of this puzzling object. We find compelling evidence that And IV is a background galaxy seen through the disk of M31. The moderate surface brightness (SB(V)~24), very blue colour (V-I<~0.6), low current star formation rate (~0.001 solar mass/yr) and low metallicity (~10% solar) reported here are consistent with And IV being a small dwarf irregular galaxy, perhaps similar to Local Group dwarfs such as IC 1613 and Sextans A. Although the distance to And IV is not tightly constrained with the current dataset, various arguments suggest it lies in the range 5<~D<~8 Mpc, placing it well outside the confines of the Local Group. It may be associated with a loose group of galaxies, containing major members UGC 64, IC 1727 and NGC 784. We report an updated position and radial velocity for And IV.Comment: 26 pages, LaTex with 9 figures (including 6 jpg plates). Accepted for publication in A

Physical Conditions in the Narrow-Line Region of M51

We have investigated the physical conditions in the narrow-line region (NLR) of M51 using long-slit spectra obtained with the Space Telescope Imaging Spectrograph (STIS) aboard the Hubble Space Telescope (HST) and 3.6 cm radio continuum observations obtained with the Very Large Array (VLA). Emission-line diagnostics were employed for nine NLR clouds, which extend 2.5" (102 pc) from the nucleus, to examine the electron density, temperature, and ionization state of the NLR gas. The emission-line ratios are consistent with those typically found in Seyfert nuclei and indicate that within the inner near-nuclear region (r ~< 1") the ionization decreases with increasing radius. Upper-limits to the [O III] electron temperature (T ~< 11,000 K) for the inner NLR clouds indicate that photoionization is the dominant ionization mechanism close to the nucleus. The emission-line fluxes for most of the NLR clouds can be reproduced reasonably well by simple photoionization models using a central power-law continuum source and supersolar nitrogen abundances. Shock+precursor models, however, provide a better fit to the observed fluxes of an NLR cloud ~2.5" south of the nucleus that is identified with the extra-nuclear cloud (XNC). The large [O III] electron temperature of this cloud (T = 24,000 K) further suggests the presence of shocks. This cloud is straddled by two radio knots and lies near the location where a weak radio jet, ~2.5" (102pc) in extent, connects the near-nuclear radio emission with a diffuse lobe structure spanning \~4" (163 pc). It is plausible that this cloud represents the location where the radio jet impinges on the disk ISM.Comment: 25 pages, 26 figures (9 color), 7 tables. Accepted for publication in the Astrophysical Journa

Twin paradox and space topology

If space is compact, then a traveller twin can leave Earth, travel back home without changing direction and find her sedentary twin older than herself. We show that the asymmetry between their spacetime trajectories lies in a topological invariant of their spatial geodesics, namely the homotopy class. This illustrates how the spacetime symmetry invariance group, although valid {\it locally}, is broken down {\it globally} as soon as some points of space are identified. As a consequence, any non--trivial space topology defines preferred inertial frames along which the proper time is longer than along any other one.Comment: 6 pages, latex, 3 figure