Fractal Location and Anomalous Diffusion Dynamics for Oil Wells from the KY Geological Survey

Utilizing data available from the Kentucky Geonet (KYGeonet.ky.gov) the fossil fuel mining locations created by the Kentucky Geological Survey geo-locating oil and gas wells are mapped using ESRI ArcGIS in Kentucky single plain 1602 ft projection. This data was then exported into a spreadsheet showing latitude and longitude for each point to be used for modeling at different scales to determine the fractal dimension of the set. Following the porosity and diffusivity studies of Tarafdar and Roy1 we extract fractal dimensions of the fossil fuel mining locations and search for evidence of scaling laws for the set of deposits. The Levy index is used to determine a match to a statistical mechanically motivated generalized probability function for the wells. This probability distribution corresponds to a solution of a dynamical anomalous diffusion equation of fractional order that describes the Levy paths which can be solved in the diffusion limit by the Fox H function ansatz.Comment: : 8 pages, 3 figures, AIPG Conference Meeting, Grand Junction CO, Oct. 200

Laser Based Mid-Infrared Spectroscopic Imaging – Exploring a Novel Method for Application in Cancer Diagnosis

A number of biomedical studies have shown that mid-infrared spectroscopic images can provide both morphological and biochemical information that can be used for the diagnosis of cancer. Whilst this technique has shown great potential it has yet to be employed by the medical profession. By replacing the conventional broadband thermal source employed in modern FTIR spectrometers with high-brightness, broadly tuneable laser based sources (QCLs and OPGs) we aim to solve one of the main obstacles to the transfer of this technology to the medical arena; namely poor signal to noise ratios at high spatial resolutions and short image acquisition times. In this thesis we take the first steps towards developing the optimum experimental configuration, the data processing algorithms and the spectroscopic image contrast and enhancement methods needed to utilise these high intensity laser based sources. We show that a QCL system is better suited to providing numerical absorbance values (biochemical information) than an OPG system primarily due to the QCL pulse stability. We also discuss practical protocols for the application of spectroscopic imaging to cancer diagnosis and present our spectroscopic imaging results from our laser based spectroscopic imaging experiments of oesophageal cancer tissue

Sharing and reusing rich media: lessons from The Open University

OpenCourseWare and Open Educational Resources comprise many types of assets including rich media. However dynamic rich media offer different opportunities and challenges for learners, teachers and higher education institutions alike than do more static items such as text. The Open University in the UK has been extensively developing and using rich media in its distance teaching programmes since it was established in 1969, often in partnership with the BBC. As new media technologies have arrived so has the capabilities of The Open University to create rich media. This paper describes these developments and then discusses the approaches required to guide them in a way that both serves the university and the wider higher education community. It concludes that rich media are an essential part of the developing OCW/OER landscape and that openly sharing them brings defined benefits to an HEI beyond their traditional student body

Toric Hypersymplectic Quotients

We study the hypersymplectic spaces obtained as quotients of flat hypersymplectic space R^{4d} by the action of a compact Abelian group. These 4n-dimensional quotients carry a multi-Hamilitonian action of an n-torus. The image of the hypersymplectic moment map for this torus action may be described by a configuration of solid cones in R^{3n}. We give precise conditions for smoothness and non-degeneracy of such quotients and show how some properties of the quotient geometry and topology are constrained by the combinatorics of the cone configurations. Examples are studied, including non-trivial structures on R^{4n} and metrics on complements of hypersurfaces in compact manifolds.Comment: 26 pages, 6 figures, small linguistic correction

Average liar count for degree-2 Frobenius pseudoprimes

In this paper we obtain lower and upper bounds on the average number of liars for the Quadratic Frobenius Pseudoprime Test of Grantham, generalizing arguments of Erd\H{o}s and Pomerance, and Monier. These bounds are provided for both Jacobi symbol plus and minus cases, providing evidence for the existence of several challenge pseudoprimes.Comment: 19 pages, published in Mathematics of Computation, revised version fixes typos and made a minor correction to the proof of Lemma 18 (result remains unchanged

Fractional Quantum Hall Physics in Jaynes-Cummings-Hubbard Lattices

Jaynes-Cummings-Hubbard arrays provide unique opportunities for quantum emulation as they exhibit convenient state preparation and measurement, and in-situ tuning of parameters. We show how to realise strongly correlated states of light in Jaynes-Cummings-Hubbard arrays under the introduction of an effective magnetic field. The effective field is realised by dynamic tuning of the cavity resonances. We demonstrate the existence of Fractional Quantum Hall states by com- puting topological invariants, phase transitions between topologically distinct states, and Laughlin wavefunction overlap.Comment: 5 pages, 3 figure