For many years, my research was in the fields of low and intermediate-energy nuclear physics, particularly: (i) Studies of the static properties of finite nuclei with special emphasis on Hartree-Fock and Brueckner-Hartree-Fock calculations; (ii) Dynamical studies of fission and heavy-ion reactions including both (macroscopic) liquid-drop and (microscopic) time-dependent Hartree-Fock calculations, and (iii) In intermediate energy physics, solution of the Dyson equations that include nucleon, delta-particle, and pi-meson interactions.
As a spin-off from time-dependent Hartee-Fock theory, I became involved in the field of nonlinear dynamics, or chaos. I have performed many studies on the periodic trajectories occurring in nonlinear two-dimensional, dynamical systems. Such orbits repeat themselves and are important since they give great information about the basic structure of the dynamical systems. (This point was realized in the late 19th century by the great French mathematician and physicist, Henri Poincaré.) More recently, I have worked on synchronization in nature, which is modeled by a large number of non-linear, coupled equations. These studies have applicability to such phenomena as the flashing of fireflies and the sugar metabolism of suspensions of yeast cells.
Moreover, I have developed a calculus-based course in chaos that is being taught to undergraduate and graduate students from a number of departments: physics, mathematics and computer science, chemistry, biology, and education. The emphasis in this course is on understanding the fundamental nature of chaos, particularly "sensitivity to initial conditions" and with emphasis on special problems; e.g., calculating the dimensions of simple fractal objects and the construction of the famous Mandelbrot Set.
I also continue to work on various problems in mathematical physics; particularly on the mathematics and applications of dispersion relations and "principal-value integrals". Principal-value integrals go back to the time of Poincaré and are widely used in such diverse fields as nuclear and particle physics, transport theory, and condensed matter physics. In my work, various methods have been devised for analyzing and numerically evaluating such integrals.
Finally, I maintain interests in elementary-particle physics, general relativity, and cosmology. I have developed an undergraduate course in elementary-particle physics, in which we study the four fundamental forces in nature, the quark structure of matter, the Standard Model of Particle Physics, Grand Unification and other theories beyond the Standard Model, and the relationship between particle-physics and cosmology.
Phone: 412.396.5973
E-mail: davies@duq.edu |
