Associate Professor of Physics and Director of Undergraduate Studies
420 Regents Hall
Telephone: (202) 687-1238
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 use of large-scale computation on computer clusters with hundreds or thousands 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. Granular materials are collections of discrete, macroscopic particles characterized by relatively straightforward interactions. Despite their apparent simplicity, these systems exhibit a number of intriguing phenomena, including the jamming transition, in which a disordered collection of grains becomes rigid when its density exceeds a critical value. We have been using dynamical analysis techniques to study the behavior of a two-dimensional granular layer subjected to shear. We have found that the transition from free-flowing states to jammed states is a dynamical transition from chaotic behavior to non-chaotic behavior. We also find that the dominant cooperative dynamical modes are strongly correlated with particle rearrangements and become increasingly unstable before stress jumps, providing a way to predict the times and locations of these striking stress-release events.
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 Effective Field Theories
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 effective theories of low energy quantum chromodynamics (QCD). In our most recent work, we found that a new 3-body force is required to describe the interactions of 3 nucleons when 2 of them are charged (but that force is not needed when only one is charged). In earlier work, at the request of experimentalists at Fermilab, we calculated the decay rates of doubly-heavy baryons into a variety of channels.
- J. Vanasse, D.A. Egolf, J. Kerin, S. Konig, and R.P. Springer, He-3 and pd scattering to next-to-leading order in pionless effective field theory, Phys. Rev. C 89, 064002 (2014).
- E.J. Banigan, M.K. Illich, D.J. Stace-Naughton, and D.A. Egolf, The chaotic dynamics of jamming, Nat. Phys. 9, 288-292 (2013).
- 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).