Physics Commons^™

Fractal Location And Anomalous Diffusion Dynamics For Oil Wells From The Ky Geological Survey, Keith Andrew, Karla M. Andrew, Kevin A. Andrew

Physics & Astronomy Faculty Publications

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 Roy[1] we extract fractal dimensions of the fossil fuel mining locations and search for evidence of scaling laws for the set of deposits. The …

Midwave Infrared Imaging Fourier Transform Spectrometry Of Combustion Plumes, Kenneth C. Bradley

Theses and Dissertations

A midwave infrared (MWIR) imaging Fourier transform spectrometer (IFTS) was used to successfully capture and analyze hyperspectral imagery of combustion plumes. Jet engine exhaust data from a small turbojet engine burning diesel fuel at a flow rate of 300 cm³/min was collected at 1 cm⁻¹ resolution from a side-plume vantage point on a 200x64 pixel window at a range of 11.2 meters. Spectral features of water, CO, and CO² were present, and showed spatial variability within the plume structure. An array of thermocouple probes was positioned within the plume to aid in temperature analysis. A single-temperature …

Section Abstracts: Astronomy, Mathematics, And Physics & Materials Science

Virginia Journal of Science

Abstracts of the Astronomy, Mathematics and Physics & Materials Science Section for the 87th Annual Meeting of the Virginia Academy of Science, May 27-29, 2009, Virginia Commonwealth University, Richmond VA.

Research On Fractal Mathematics And Some Application In Mechanics, Yang Xiaojun

Xiao-Jun Yang

Since Mandelbrot proposed the concept of fractal in 1970s’, fractal has been applied in various areas such as science, economics, cultures and arts because of the universality of fractal phenomena. It provides a new analytical tool to reveal the complexity of the real world. Nowadays the calculus in a fractal space becomes a hot topic in the world. Based on the established definitions of fractal derivative and fractal integral, the fundamental theorems of fractal derivatives and fractal integrals are investigated in detail. The fractal double integral and fractal triple integral are discussed and the variational principle in fractal space has …

Volume 02, Joseph A. Mann, Kathryn J. Greenly, Scott E. Jenkins, Andrew E. Puckette, Daniel M. Honey, Jeffery P. Ravenhorst, Jamie Elizabeth Mesrobian, Thomas Scott, Jay Crowell, Sarah Spangenberg, Amy S. Eason, Kenny Wolfe, Liz Hale, Rachel Bouchard, Will Semonco, Carley York, Ryan Higgenbothom, Adrienne Heinbaugh, Melissa Dorton, Madeline Hunter, June Ashmore, Clark Barkley, Jay Haley

Incite: The Journal of Undergraduate Scholarship

Introduction from Dean Dr. Charles Ross

Mike's Nite: New Jazz for an Old Instrument by Joseph A. Mann

Investigation of the use of Cucumis Sativus for Remediation Of Chromium from Contaminated Environmental Matrices: An Interdisciplinary Instrumental Analysis Project by Kathryn J. Greenly, Scott E. Jenkins, and Andrew E. Puckette

Development of GC-MS and Chemometric Methods for the Analysis of Accelerants in Arson Cases by Scott Jenkins

Building and Measuring Scalable Computing Systems by Daniel M. Honey and Jeffery P. Ravenhorst

Nomini Hall: A Case Study in the Use of Archival Resources as Guides for Excavation at An Archaeological Site by …

Transitional Probabilities For The Four-State Random Walk On A Lattice In The Presence Of Partially Reflecting Boundaries, Ramakrishna Janaswamy

Ramakrishna Janaswamy

The four-state random walk (4RW) model, wherein the particle is endowed with two states of spin and two states of directional motion in each space coordinate, permits a stochastic solution of the Schrödinger equation (or the equivalent parabolic equation) without resorting to the usual analytical continuation in complex space of the particle trajectories. Analytical expressions are derived here for the various transitional probabilities in a 4RW by employing generating functions and eigenfunction expansions when the particle moves on a 1+1 space-time lattice with two-point boundary conditions. The most general case of dissimilar boundaries with partially reflecting boundary conditions is treated …

Generalized Helmholtz-Kirchhoff Model For Two-Dimensional Distributed Vortex Motion, Raymond J. Nagem, Guido Sandri, David Uminsky, C. Eugene Wayne

Mathematics

The two-dimensional Navier-Stokes equations are rewritten as a system of coupled nonlinear ordinary differential equations. These equations describe the evolution of the moments of an expansion of the vorticity with respect to Hermite functions and of the centers of vorticity concentrations. We prove the convergence of this expansion and show that in the zero viscosity and zero core size limit we formally recover the Helmholtz-Kirchhoff model for the evolution of point vortices. The present expansion systematically incorporates the effects of both viscosity and finite vortex core size. We also show that a low-order truncation of our expansion leads to the …

The Fundamentals Of Local Fractional Derivative Of The One-Variable Non-Differentiable Functions, Yang Xiaojun

Xiao-Jun Yang

Based on the theory of Jumarie’s fractional calculus, local fractional derivative is modified in detail and its fundamentals of local fractional derivative are proposed in this paper. The uniqueness of local fractional derivative is obtained and the Rolle’s theorem, the mean value theorem, the Cauchy’s generalized mean value theorem and the L’Hospital’s rules are proved.

Local Fractional Newton’S Method Derived From Modified Local Fractional Calculus, Yang Xiao-Jun

Xiao-Jun Yang

A local fractional Newton’s method, which is derived from the modified local fractional calculus , is proposed in the present paper. Its iterative function is obtained and the convergence of the iterative function is discussed. The comparison between the classical Newton iteration and the local fractional Newton iteration has been carried out. It is shown that the iterative value of the local fractional Newton method better approximates the real-value than that of the classical one.

Converging Flow Between Coaxial Cones, O. Hall, A. D. Gilbert, C. P. Hills

Articles

Fluid flow governed by the Navier-Stokes equation is considered in a domain bounded by two cones with the same axis. In the first, 'non-parallel' case, the two cones have the same apex and different angles θ = α and β in spherical polar coordinates (r, θ, φ). In the second, 'parallel' case, the two cones have the same opening angle α, parallel walls separated by a gap h and apices separated by a distance h/sinα. Flows are driven by a source Q at the origin, the apex of the lower cone in the parallel case. The Stokes solution for the …

Nonaxisymmetric Stokes Flow Between Concentric Cones, O. Hall, C. P. Hills, A. D. Gilbert

Articles

We study the fully three-dimensional Stokes flow within a geometry consisting of two infinite cones with coincident apices. The Stokes approximation is valid near the apex and we consider the dominant flow features as it is approached. The cones are assumed to be stationary and the flow to be driven by an arbitrary far-field disturbance. We express the flow quantities in terms of eigenfunction expansions and allow for the first time for nonaxisymmetric flow regimes through an azimuthal wave number. The eigenvalue problem is solved numerically for successive wave numbers. Both real and complex sequences of eigenvalues are found, their …

Gas-Kinetic Schemes For Direct Numerical Simulations Of Compressible Homogeneous Turbulence, Wei Liao, Yan Peng, Li-Shi Luo

Mathematics & Statistics Faculty Publications

We apply the gas-kinetic scheme (GKS) for the direct numerical simulations (DNSs) of compressible decaying homogeneous isotropic turbulence (DHIT). We intend to study the accuracy, stability, and efficiency of the gas-kinetic scheme for DNS of compressible homogeneous turbulence depending on both flow conditions and numerics. In particular, we study the GKS with multidimensional, quasi-one-dimensional, dimensional-splitting, and smooth-flow approximations. We simulate the compressible DHIT with the Taylor microscale Reynolds number Reλ =72.0 and the turbulence Mach number Ma_t between 0.1 and 0.6. We compute the low-order statistical quantities including the total kinetic energy K (t), the dissipation rate ε (t), …

Problems Of Local Fractional Definite Integral Of The One-Variable Non-Differentiable Function, Yang Xiao-Jun

Xiao-Jun Yang

It is proposed that local fractional calculas introduced by Kolwankar and Gangal is extended by the concept of Jumarie’s fractional calculus and local fractional definite integral is redefined. The properties and the theorems of local fractional calculus are discussed in this paper.