Dr. Keith Andrew
Chairman: Department of Physics
Phone O: 217-581-3220, P1:217-581-6424
Office 2131
FAX (217) 581-6613
- Professor, Dept. of Physics
- Theoretical and High Energy Physics
B.S.: Worcester Polytechnic Institute
M.A.: The Basis of Twistor Theory, University of Arkansas
Ph.D.: The Glueball Mass Spectrum, University of Arkansas Thesis supervisor: Dr. M. Lieber
SCI/PHY
5090 – Special Topics: Computer Visualization of Weather
(Offered 4-week session I: Time to be Arranged) 1 semester hour Call #1852
A basic introduction to the physical principles of weather dynamics and near real time computer visualization of weather phenomena. Topics include buoyancy and Archimedes principle, fluid flow, cloud formation and types, severe weather, global climate, and access to the atmospheric radiation measurement project data (run by Argonne National Labs). Link to Web Page:
Research Interests
1. Superstring Phenomenology: We are examining corrections to Einstein's Field Equations in a Low Temperature Effective Superstring Theory, this work includes supercomputer simulations of the geodesic structure of these spacetimes in the neighborhood of massive objects, including superstring generated black holes, or in the early universe, looking at the cosmological implications of Dilaton terms and Gauss-Bonnet terms in the effective Lagrangian, and an examination of simple Dirac Equation generation dependent models in 10 and 26 dimensions. Models with novel equations of state, including a d-dimensional polytropic state and models of small masses orbiting d-dimensional superstring generated compact objects with an internal SU(n) symmetry that give rise to chaotic orbits are being studied. A simple general d-brane transformation method is used to generate interesting field equations.
2. Laser-Matter Interactions: We are currently developing a matrix Optical-Bloch method for investigating the effects of a pulsed laser on a two-state system, emphasis is on the Cayley-Hamilton method to find the final state of the Bloch vector, including applications to FM spectroscopy, general modes of scattering and the generalized quantum area theorem, topics of particluar interest have close ties to ongoing pulsed laser experiments.
3. Chaos and Lyapunov Exponents: we are examining the nature of autocatalytic chemical reactions within the context of oscillating reactions, such as the well known Belousov-Zhabotinski reaction, an examination of period doubling and exponential deviation of orbits in a classical nonlinear coupled ODE model, with the associated data to determine the Lyapunov exponents, is being pursued for a host of novel reactions. Mapping of the empircal attractors from simultaneous multiwavelength spectroscopy, identifying the corresponding iterative map, FFT of time series data for period doubling, and developing a set of ODEs to model the reaction dynamics are ongoing areas of investigation.
Graduate Student Research Projects
1. Systems far from Equilibrium: We have been analyzing model systems that are far from equilibrium in order to elucidate the underlying dynamics in terms of fundamental principles. A wide class of such systems are known and share in a universality for parameter ranges that give rise to the onset of chaos. A simple chemical system is the Belousov-Zhabotinski reaction. This system gives rise to thin film nonlinear chemical wavefronts and bulk matter sensitivity to concentration, at the 0.01 and 0.001 molarity levels. The system displays Hopf bifurcations, global entropy production, has a phase space attractor, a positive Lyaponuv exponent and a measurable Feigenbaum number. A general system of ODEs can be used to describe this system for nonintegrer reaction orders, in the sense of Prigogine. Models developed in a Mathematica format for numerical integration and Phasor iterative maps can be classified topologically. Features of this system can be used to model early cosmological epochs where nonlinear instablilities can describe particle production. Students: David Steir, Elizabeth Prince, Chuck Dietz, Vernice Veranga.
2. Superstring Cosmology and Compact Objects: We have been looking at a variety of applications of superstring correction terms to the Einstein field equations. In the low energy effective superstring theory an infinite number of corrections to the Einstein field equations can be found from the vanishing of the beta function. These corrections may be expressed as a power series in superstring tension parameter, the lowest order corrections being quadratic in the curvature. Such corrections should give rise to exact d-dimensional equations that can be applied to regions of high curvature or in the early universe, closer to the Planck time, than classical theory allows. For a compact object this will alter the Hawking radiation spectrum and timescale, change the intrinsic entropy and give different orbital equations of motion. In the early universe the new equations call for a subtle matching of boundary conditions from the compactification era to possible inflationary epochs and a modified Wheeler-DeWitt equation even in the absence of a dilaton. Student: Chris Klaus
Undergraduate Student Research Projects
1. Orbits and the Three Body Problem in a Superstring Geometry: We investigate an effective potential method for analyzing orbits in a two body problem. The effective potential differs from the general relativistic effective potential, and gives rise to a chaotic three body problem. Student: Scott Ness
2. A Compactification Model in Early Cosmology: We
look at a 10-d semiclassical superstring Gauss-Bonnet
early universe for which six dimensions compactify on
a sphere. Consistency conditions are derived for the Gauss-Bonnet equations for
de-Sitter like solutions to the field equations. Students:
3. Wave Function of the Universe in String Theory: Boundary conditions and solutions are examined for a simple minisuperspace version of the Wheeler-deWitt equation for superstring motivated geometries. Partitioning of the solution space into equivalance classes and interpretation of the wave function are studied. Students: Andrew Distelburger, Dakota Prentice, Joe Ancheta, Alvie Hitesman
4. Stellar Spectroscopy: Raw Spectrum of Vega with 16” Drew University Observatory, SBIG Spectrometer and SBIG 8E CCD, undergraduate student project:
Using Visual Basic interface to run Synspec to generate a synthetic spectrum- solving Saha and Boltzmann equations- to model the stellar atmosphere from the spectrum,
Program code developed and available through R.O.Gray, Department of Physics and Astronomy, Appalachian State University: http://www1.appstate.edu/dept/physics/spectrum/spectrum.html
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