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

Using entanglement to discern phases in the disordered one-dimensional Bose-Hubbard model

We perform a matrix product state based density matrix renormalisation group analysis of the phases for the disordered one-dimensional Bose-Hubbard model. For particle densities N/L = 1, 1/2 and 2 we show that it is possible to obtain a full phase diagram using only the entanglement properties, which come "for free" when performing an update. We confirm the presence of Mott insulating, superfluid and Bose glass phases when N/L = 1 and 1/2 (without the Mott insulator) as found in previous studies. For the N/L = 2 system we find a double lobed superfluid phase with possible reentrance.Comment: 6 pages, 4 figure

Sensing and decision-making in random search

While microscopic organisms can use gradient-based search to locate resources, this strategy can be poorly suited to the sensory signals available to macroscopic organisms. We propose a framework that models search-decision making in cases where sensory signals are infrequent, subject to large fluctuations, and contain little directional information. Our approach simultaneously models an organism's intrinsic movement behavior (e.g. Levy walk) while allowing this behavior to be adjusted based on sensory data. We find that including even a simple model for signal response can dominate other features of random search and greatly improve search performance. In particular, we show that a lack of signal is not a lack of information. Searchers that receive no signal can quickly abandon target-poor regions. Such phenomena naturally give rise to the area-restricted search behavior exhibited by many searching organisms

Numerical study of the derivative of the Riemann zeta function at zeros

The derivative of the Riemann zeta function was computed numerically on several large sets of zeros at large heights. Comparisons to known and conjectured asymptotics are presented.Comment: 13 pages, 5 figures; minor typos fixe

Exhumation history of eastern Ladakh revealed by Ar-40/Ar-39 and fission-track ages: the Indus River-Tso Morari transect, NW Himalaya

Fission-track and Ar-40/Ar-39 ages place time constraints on the exhumation of the North Himalayan nappe stack, the Indus Suture Zone and Molasse, and the Transhimalayan Batholith in eastern Ladakh (NW India). Results from this and previous studies on a north-south transect passing near Tso Morari Lake suggest that the SW-directed North Himalayan nappe stack (comprising the Mata, Tetraogal and Tso Morari nappes) was emplaced and metamorphosed by c. 50-45 Ma, and exhumed to moderately shallow depths (c. 10 km) by c. 45-40 Ma. From the mid-Eocene to the present, exhumation continued at a steady and slow rate except for the root zone of the Tso Morari nappe, which cooled faster than the rest of the nappe stack. Rapid cooling occurred at c. 20 Ma and is linked to brittle deformation along the normal Ribil-Zildat Fault concomitant with extrusion of the Crystalline nappe in the south. Data from the Indus Molasse suggest that sediments were still being deposited during the Miocene

The zeta function on the critical line: Numerical evidence for moments and random matrix theory models

Results of extensive computations of moments of the Riemann zeta function on the critical line are presented. Calculated values are compared with predictions motivated by random matrix theory. The results can help in deciding between those and competing predictions. It is shown that for high moments and at large heights, the variability of moment values over adjacent intervals is substantial, even when those intervals are long, as long as a block containing 10^9 zeros near zero number 10^23. More than anything else, the variability illustrates the limits of what one can learn about the zeta function from numerical evidence. It is shown the rate of decline of extreme values of the moments is modelled relatively well by power laws. Also, some long range correlations in the values of the second moment, as well as asymptotic oscillations in the values of the shifted fourth moment, are found. The computations described here relied on several representations of the zeta function. The numerical comparison of their effectiveness that is presented is of independent interest, for future large scale computations.Comment: 31 pages, 10 figures, 19 table

Generating the Baryon Asymmetry of the Universe in Split Fermion Models

The origin of the matter-antimatter asymmetry of the universe is one of the major unsolved problems in cosmology and particle physics. In this paper, we investigate the recently proposed possibility that split fermion models -- extra dimensional models where the standard model fermions are localized to different points around the extra dimension -- could provide a means to generate this asymmetry during the phase transition of the localizing scalars. After setting up the scenario that we consider, we use a single fermion toy model to estimate the reflection coefficients for scattering off the phase boundary using a more realistic scalar profile than previous work resulting in a different Kaluza Klein spectrum. The value we calculate for $n_B/s$ is consistent with the mechanism being the source of the baryon asymmetry of our universe provided the $B-L$ violating processes have an efficiency of order $10^{-5}$.Comment: 17 pages, 3 figures; References added; Minor changes, Accepted for publication in Phys. Rev.