SUMMARY OF RESEARCH HIGHLIGHTS, WORK IN PROGRESS, AND FUTURE PLANS

My recent research work,both in Condensed Matter Theory and in Mathematical Epidemiology, are in two of the most active, important, and competitive fields in which theorists and applied mathematicians are working at the present time: namely HIV/AIDS and the physics of electron systems that have restricted dimensionality; in particular 2D electron systems in confining potentials and perpendicular magnetic fields. Publications in this field led to an invited paper at the 1994 March meeting of The American Physical Society in Pittsburg. My published work on AIDS was presented at the 1995 WORLD CONGRESS ON MEDICAL PHYSICS AND BIOMEDICAL ENGINEERING in Rio de Janeiro, which I had been invited to attend.

My work in progress is directly inspired by new experimental techniques that have led to the fabrication of semiconductor heterostructures containing nanometer scale two-dimensional electron systems, whose density can be varied with gate voltages. Such electron systems can be subject to confining potentials which are well represented by parabolic potentials that permit exact solutions to Schrodinger's equation for electronic energy levels, and also to static magnetic and electric fields that dramatically affect the electrons' density of states. New device possibilities have conseqently emerged, which require the analytical and numerical study of optical transition matrix elements that determine the photonic properties of a comfined 2D electron system, as well as its magnetic and thermodynamic characteristics in the presence of static electric and magnetic fields. When the two-dimentional electron system is located in a confining one-dimentional parabolic quantum well in its own plane, the potential energy thereby acquired will reintroduce dispersion into the electron system, when a perpendicular magnetic field is applied. The Landau levels broaden and lead to an oscillatory dependence of properties on magnetic and electric fields that suggests novel device applications. I have now calculated analytical expressions for all the necessary matrix elements that determine the optical properties of the system, as a function of magnetic and electric fields. My future plans consist of incorporating these matrix elements into expressions for observable quantities that measure the response of the system to incident electromagnetic radiation, as a function of applied magnetic and electric fields

Research has also been completed for a paper entitled "Orbital Magnetism of a Spin-Polarized 2DEG Confined by a Parabolic Potential Near Its Half-filled Landau Level".

In the extreme quantum limit the orbital magnetism of a confined two-dimensional electron system becomes strongle paramagnetic, rather than diamagnetic! If the magnetisation is sufficiently large, then the possibility of self-sustained orbital ferromagmetism may exist in layered heterostructures that contain suitable electron densities in 2DEG systems.

I am extending my calculation of the mean incubation time for the development of AIDS, beginning with initial HIV seropositivity, based on published AIDS incidence data and my own previously published mathematical theory that connects the incubation time distribution and HIV infection to reported clinical AIDS incidence.

The Cubic Growth of AIDS Cases: General Dependence on Early Infection Rates and Distribution of Times to Appearance of Clinical Symptoms. J. Math. Biol. 27, 523 (1989)

Modification of the Velocity of Sound in Water by Solute Ions. Chem. Phys. Lett. 161, (4,5), 420 (1989)

Exact Quantum Mechanical Propagator for an Electron in a Saddle-Point Potential and a Magnetic Field. Phys. Rev. B 39, 3780 (1989)

Diamagnetic Spike Modification of a Two-Dimensional Electric Gas Confined Within a Parabolic Quantum Well. Phys. Rev. B 45, 3815 (1992)

Paramagnetic and Heat Capacity Oscillations of Two-Dimensional Electron Systems Confined Within Parabolic Quantum Wells. Phys. Rev. B48, 5668 (1993)

Fields From Multipole Moment Distributions With Spherical Symmetry: The Fermi Contact Ineraction. Am. J. Phys. 62 (9), 828 (1994)

Computer-Assisted Assignments in a Large Physics Class; Computer Education, 27, 2;141 (1996)