Tight triangulations of closed 3-manifolds

A triangulation of a closed 2-manifold is tight with respect to a field of characteristic two if and only if it is neighbourly; and it is tight with respect to a field of odd characteristic if and only if it is neighbourly and orientable. No such characterization of tightness was previously known for higher dimensional manifolds. In this paper, we prove that a triangulation of a closed 3-manifold is tight with respect to a field of odd characteristic if and only if it is neighbourly, orientable and stacked. In consequence, the Kuhnel-Lutz conjecture is valid in dimension three for fields of odd characteristic. Next let F be a field of characteristic two. It is known that, in this case, any neighbourly and stacked triangulation of a closed 3-manifold is F-tight. For closed, triangulated 3-manifolds with at most 71 vertices or with first Betti number at most 188, we show that the converse is true. But the possibility of the existence of an F-tight, non-stacked triangulation on a larger number of vertices remains open. We prove the following upper bound theorem on such triangulations. If an F-tight triangulation of a closed 3-manifold has n vertices and first Betti number beta(1), then (n - 4) (617n - 3861) <= 15444 beta(1). Equality holds here if and only if all the vertex links of the triangulation are connected sums of boundary complexes of icosahedra. (C) 2015 Elsevier Ltd. All rights reserved.

Counting zero kernel pairs over a finite field

Helmke et al. have recently given a formula for the number of reachable pairs of matrices over a finite field. We give a new and elementary proof of the same formula by solving the equivalent problem of determining the number of so called zero kernel pairs over a finite field. We show that the problem is, equivalent to certain other enumeration problems and outline a connection with some recent results of Guo and Yang on the natural density of rectangular unimodular matrices over F-qx]. We also propose a new conjecture on the density of unimodular matrix polynomials. (C) 2016 Elsevier Inc. All rights reserved.

Investigation of Vaporized Kerosene Injection and Combustion in a Supersonic Model Combustor

Injection and combustion of vaporized kerosene was experimentally investigated in a Mach 2.5 model combustor at various fuel temperatures and injection pressures. A unique kerosene heating and delivery system, which can prepare heated kerosene up to 820 K at a pressure of 5.5 MPa with negligible fuel coking, was developed. A three-species surrogate was employed to simulate the thermophysical properties of kerosene. The calculated thermophysical properties of surrogate provided insight into the fuel flow control in experiments. Kerosene jet structures at various preheat temperatures injecting into both quiescent environment and a Mach 2.5 crossflow were characterized. It was shown that the use ofvaporized kerosene injection holds the potential of enhancing fuel-air mixing and promoting overall burning. Supersonic combustion tests further confirmed the preceding conjecture by comparing the combustor performances of supercritical kerosene with those of liquid kerosene and effervescent atomization with hydrogen barbotage. Under the similar flow conditions and overall kerosene equivalence ratios, experimental results illustrated that the combustion efficiency of supercritical kerosene increased approximately 10-15% over that of liquid kerosene, which was comparable to that of effervescent atomization.

The A Posteriori Aspects of Estuarine Modeling

This exercise is the application of an analytical method for systematically modeling ecosystems data to observations made on a naturally eutrophic, mesohaline planktonic microcosm. The theory and experimental design are briefly outlined and the particular steps in the acutal modeling process follow. Then there is a discussion as to how the whole endeavor can be refined to culminate in models with predictive capabilities. (PDF has 16 pages.)

Investigation of Vaporized Kerosene Injection and Combustion in a Supersonic Model Combustor

Injection and combustion of vaporized kerosene was experimentally investigated in a Mach 2.5 model combustor at various fuel temperatures and injection pressures. A unique kerosene heating and delivery system, which can prepare heated kerosene up to 820 K at a pressure of 5.5 MPa with negligible fuel coking, was developed. A three-species surrogate was employed to simulate the thermophysical properties of kerosene. The calculated thermophysical properties of surrogate provided insight into the fuel flow control in experiments. Kerosene jet structures at various preheat temperatures injecting into both quiescent environment and a Mach 2.5 crossflow were characterized. It was shown that the use ofvaporized kerosene injection holds the potential of enhancing fuel-air mixing and promoting overall burning. Supersonic combustion tests further confirmed the preceding conjecture by comparing the combustor performances of supercritical kerosene with those of liquid kerosene and effervescent atomization with hydrogen barbotage. Under the similar flow conditions and overall kerosene equivalence ratios, experimental results illustrated that the combustion efficiency of supercritical kerosene increased approximately 10-15% over that of liquid kerosene, which was comparable to that of effervescent atomization.

Cloud computing for research - final report

Curtis+Cartwright Consulting Ltd, working with the University of Surrey and Professor Charles Oppenheim, has been commissioned by Jisc to investigate Cloud Computing for Research. This document is the final report, and is accompanied by a briefing paper which provides advice targeted at researchers.

Techniques for spatial analysis and visualization of benthic mapping data: final report

The mapping and geospatial analysis of benthic environments are multidisciplinary tasks that have become more accessible in recent years because of advances in technology and cost reductions in survey systems. The complex relationships that exist among physical, biological, and chemical seafloor components require advanced, integrated analysis techniques to enable scientists and others to visualize patterns and, in so doing, allow inferences to be made about benthic processes. Effective mapping, analysis, and visualization of marine habitats are particularly important because the subtidal seafloor environment is not readily viewed directly by eye. Research in benthic environments relies heavily, therefore, on remote sensing techniques to collect effective data. Because many benthic scientists are not mapping professionals, they may not adequately consider the links between data collection, data analysis, and data visualization. Projects often start with clear goals, but may be hampered by the technical details and skills required for maintaining data quality through the entire process from collection through analysis and presentation. The lack of technical understanding of the entire data handling process can represent a significant impediment to success. While many benthic mapping efforts have detailed their methodology as it relates to the overall scientific goals of a project, only a few published papers and reports focus on the analysis and visualization components (Paton et al. 1997, Weihe et al. 1999, Basu and Saxena 1999, Bruce et al. 1997). In particular, the benthic mapping literature often briefly describes data collection and analysis methods, but fails to provide sufficiently detailed explanation of particular analysis techniques or display methodologies so that others can employ them. In general, such techniques are in large part guided by the data acquisition methods, which can include both aerial and water-based remote sensing methods to map the seafloor without physical disturbance, as well as physical sampling methodologies (e.g., grab or core sampling). The terms benthic mapping and benthic habitat mapping are often used synonymously to describe seafloor mapping conducted for the purpose of benthic habitat identification. There is a subtle yet important difference, however, between general benthic mapping and benthic habitat mapping. The distinction is important because it dictates the sequential analysis and visualization techniques that are employed following data collection. In this paper general seafloor mapping for identification of regional geologic features and morphology is defined as benthic mapping. Benthic habitat mapping incorporates the regional scale geologic information but also includes higher resolution surveys and analysis of biological communities to identify the biological habitats. In addition, this paper adopts the definition of habitats established by Kostylev et al. (2001) as a “spatially defined area where the physical, chemical, and biological environment is distinctly different from the surrounding environment.” (PDF contains 31 pages)

Taxonomic and ecological survey of the flora of Calvert County, Maryland

Resulted from a occasional field trips on the Patuxent River, 1964-1968. Taxonomy and ecology survey following the quarter method (Cottam and Curtis, 1956) Includes: Literature review: Forests, soils, ecology; Materials and Methods: location, criteria, map of Calvert county; Results: descriptive, species of trees sampled; soils, ecology; discussion: vegetational, soils, ecology; Summary; Climate; Physical features of Calvert County; Botanical descriptions; Tables, Current checklist of vascular plants; selective bibliography

Black holes in the early universe, in compact binaries, and as energy sources inside solar-type stars

This thesis consists of three separate studies of roles that black holes might play in our universe.

In the first part we formulate a statistical method for inferring the cosmological parameters of our universe from LIGO/VIRGO measurements of the gravitational waves produced by coalescing black-hole/neutron-star binaries. This method is based on the cosmological distance-redshift relation, with "luminosity distances" determined directly, and redshifts indirectly, from the gravitational waveforms. Using the current estimates of binary coalescence rates and projected "advanced" LIGO noise spectra, we conclude that by our method the Hubble constant should be measurable to within an error of a few percent. The errors for the mean density of the universe and the cosmological constant will depend strongly on the size of the universe, varying from about 10% for a "small" universe up to and beyond 100% for a "large" universe. We further study the effects of random gravitational lensing and find that it may strongly impair the determination of the cosmological constant.

In the second part of this thesis we disprove a conjecture that black holes cannot form in an early, inflationary era of our universe, because of a quantum-field-theory induced instability of the black-hole horizon. This instability was supposed to arise from the difference in temperatures of any black-hole horizon and the inflationary cosmological horizon; it was thought that this temperature difference would make every quantum state that is regular at the cosmological horizon be singular at the black-hole horizon. We disprove this conjecture by explicitly constructing a quantum vacuum state that is everywhere regular for a massless scalar field. We further show that this quantum state has all the nice thermal properties that one has come to expect of "good" vacuum states, both at the black-hole horizon and at the cosmological horizon.

In the third part of the thesis we study the evolution and implications of a hypothetical primordial black hole that might have found its way into the center of the Sun or any other solar-type star. As a foundation for our analysis, we generalize the mixing-length theory of convection to an optically thick, spherically symmetric accretion flow (and find in passing that the radial stretching of the inflowing fluid elements leads to a modification of the standard Schwarzschild criterion for convection). When the accretion is that of solar matter onto the primordial hole, the rotation of the Sun causes centrifugal hangup of the inflow near the hole, resulting in an "accretion torus" which produces an enhanced outflow of heat. We find, however, that the turbulent viscosity, which accompanies the convective transport of this heat, extracts angular momentum from the inflowing gas, thereby buffering the torus into a lower luminosity than one might have expected. As a result, the solar surface will not be influenced noticeably by the torus's luminosity until at most three days before the Sun is finally devoured by the black hole. As a simple consequence, accretion onto a black hole inside the Sun cannot be an answer to the solar neutrino puzzle.