E-mail: egolf [at] physics [dot] georgetown [dot] edu
David Egolf was an A.B. Duke Scholar at Duke University and earned his B.S. in 1990 as a Program II major, meeting the major requirements for Physics, Chemistry, and Math. He received a Ph.D. in Physics from Duke in 1994 for his work on spatiotemporal chaos. After completing his Ph.D., he became a National Science Foundation Postdoctoral Fellow in Computational Science and Engineering at Cornell University working with Prof. Eberhard Bodenschatz. After his time at Cornell, he became the Richard P. Feynman Fellow for Theory and Computing at Los Alamos National Laboratory, collaborating with Dr. Robert Ecke on pattern formation and spatiotemporal chaos at the Center for Nonlinear Studies. Professor Egolf has been a faculty member at Georgetown University since 2000.
Professor Egolf is a computational and theoretical physicist whose research focuses on trying to understand systems far-from-equilibrium (meaning that the energy input and the energy dissipated are not precisely balanced at all times). Unlike the situation for systems in equilibrium, researchers have so far been stymied in their efforts to develop a general, predictive theory of nonequilibrium systems. His research group uses the tools of nonlinear dynamics and statistical physics to try to establish the underpinnings for such a theory. Most of the work involves the used of large-scale computation, mostly of his computer clusters of about 100 CPUs. The types of systems he studies range from fluid and granular systems to electrochemical waves in heart tissue to idealized mathematical models. In addition to this work in statistical physics, Professor Egolf is part of a collaboration studying effective theories of quantum chromodynamics. His research has been supported by the National Science Foundation, Research Corporation, NASA, and the Alfred P. Sloan Foundation.
Professor Egolf is also a dedicated teacher and was awarded the Dean's Award for Excellence in Teaching in 2008. Most years, an undergraduate or two also work with him on their senior thesis research.
Dynamical Events in Fluids, Fibrillation, and Jamming
The behaviors of systems far-from-equilibrium can often appear hopelessly complicated --- a muddled situation with a wide variety of length scales and time scales and often a chaotic dynamics that defies prediction. We have been using the mathematical tools of nonlinear dynamics to identify within this wild behavior particular events which determine the future evolution of the system. Using massively-parallel simulations of Rayleigh-Benard convection, we found that the complex behavior of the Spiral Defect Chaos state of convection is actually largely determined by particular events (convection roll breaking) that are highly localized in space and time. It is only in the vicinity of these events that the system is particularly sensitive to small perturbations, so the rest of the system, although complex-looking, is to a large degree predictable.
We have been applying these same techniques to a model of fibrillating heart tissue, with the hope of inspiring the development of targeted defibrillation in which tiny electrical (or chemical) pulses can be introduced in specified portions of the heart to lead the heart out of fibrillation in a gentle way. Again, we found that particular events within the complicated chaotic dynamics of fibrillation largely determine the future behavior of the fibrillating tissue.
We have also been using the same dynamical analysis techniques to study the behavior of a two-dimensional granular layer subjected to shear. This system has been studied extensively since Bob Behringer and collaborators discovered that the system goes through a glass-like jamming transition as the density of grains is varied. We have found intriguing connections between the Lyapunov vectors describing the most important dynamical modes and the grains that are rearranging cooperatively near the jamming transition. In addition, we have measured mathematically well-defined dynamical length scales and time scales that diverge near the jamming transition density.
Building Blocks of Spatiotemporal Chaos
Such complicated behavior arising from isolated events provides hope that we may be able to develop an understanding of these systems by characterizing the events and the parts of the system involved in the events (much like the way we can understand a great deal about gases by understanding atoms and the ways they interact when they get close to each other). The idea that spatiotemporal chaotic systems could be considered as a collection of weakly-interacting subsystems was originally argued by Ruelle and later expanded upon by Cross and Hohenberg and others. In a series of papers, we have explored this idea in hopes of identifying these building blocks on which to base a statistical mechanics of spatiotemporal chaos.
Statistical Mechanics Far-from-equilibrium
One of the reasons researchers are hopeful that a statistical mechanics of spatiotemporal chaos might be developed is that the behavior of many of these systems resembles the phase transitions of equilibrium systems. In a paper in Science, I showed that, remarkably, a coarse-graining of a simple spatiotemporal chaotic system is indistinguishable from an equilibrium system of the Ising universality class.
QCD Calculations using Chiral Perturbation Theory
My scientific interests are quite broad, so I occasionally work on projects far afield from my usual research. I have been working with Professor Roxanne Springer at Duke to calculate various quantities using an effective theory of low energy quantum chromodynamics (QCD) --- heavy baryon chiral perturbation theory. In the more recent of our two joint papers, at the request of experimentalists at Fermilab, we calculated the decay rates of doubly-heavy baryons into a variety of channels.
- P. Melby, A. Prevost, D. A. Egolf, and J. S. Urbach, Depletion force in a bi-disperse granular layer, Phys. Rev. E 76, 051307 (2007).
- M. P. Fishman and D. A. Egolf, Revealing the building blocks of spatiotemporal chaos: Deviations from extensivity, Phys. Rev. Lett. 96, 054103 (2006).
- D. A. Egolf, R. P. Springer, and J. Urban, SU(3) predictions for weak decays of doubly heavy baryons, including SU(3) breaking terms, Phys. Rev. D 68, 013003 (2003).
- A. Prevost, D. A. Egolf, and J. S. Urbach, Forcing and velocity correlations in a vibrated granular layer, Phys. Rev. Lett. 89, 084301 (2002).
- D. A. Egolf, I. V. Melnikov, W. Pesch, and R. E. Ecke, Mechanisms of extensive spatiotemporal chaos in Rayleigh-Benard convection, Nature 404, 733 (2000).
- D. A. Egolf, Equilibrium regained: from nonequilibrium chaos to statistical mechanics, Science 287, 101 (2000).
- D. A. Egolf, I. V. Melnikov, and R. P. Springer, Weak nonleptonic Omega(-) decay in chiral perturbation theory. Phys. Lett. B 451, 267 (1999).
- D. A. Egolf, The dynamical dimension of defects in spatiotemporal chaos, Phys. Rev. Lett. 81, 4120 (1998).
- D. A. Egolf, I. V. Melnikov, and E. Bodenschatz, The importance of local pattern properties in spiral defect chaos, Phys. Rev. Lett. 80, 3228 (1998).
- D. A. Egolf and H. S. Greenside, Relation between fractal dimension and spatial correlation length for extensive chaos, Nature 369, 129 (1994).