This is a CAREER award for a program of large-scale computation to study the properties of far-from-equilibrium dynamical systems that exhibit temporally-chaotic, spatially-disordered behavior. This persistent, complex dynamical behavior found in a wide variety of systems such as fibrillating heart tissue, large aperture lasers, planetary atmospheres and oceans, fluid turbulence, and environmental ecosystems is currently not well understood due to the strong nonlinearities and the lack of an extremal principle in these systems. The grant goals are to develop new tools for analyzing these complicated dynamical systems and to use these tools to achieve an understanding of the important internal dynamical processes. Such an understanding could ultimately lead to a unified statistical theory for describing the macroscopic properties of these systems without detailed knowledge of the microscopic behavior. Through computational studies of experimentally relevant equations and simpler model equations, three questions will be answered: (i) What are the sources of chaotic behavior in these systems and how do these deterministic sources lead to loss of predictability and the effective stochastic nature of the systems? (ii) What are the appropriate mesoscopic degrees of freedom in a reduced description of the dynamics? (iii) Which properties of equilibrium statistical mechanics can we salvage for a description of the long-wavelength properties of far-from-equilibrium systems with differing microscopic physical processes? The results of this work will lead not only to a better understanding of the behavior of far-from-equilibrium systems, but will provide new tools for analyzing and simulating other highly complex scientifically and commercially important phenomena.
Also, as part of this project, new interdisciplinary courses will be developed in computational science for upper-level undergraduates and graduate students in the industrial physics program at Georgetown. Through performance of the research described above, undergraduates and postdoctoral fellows will develop skills in large-scale computing and modeling and in analyzing complex phenomena, which will serve the students and postdoctoral fellows well in careers in a wide variety of scientific fields. Also, an outreach program will be developed to bring the fast-evolving field of computational science to high school students and teachers. The PI and others at Georgetown will provide guidance and mentoring for students preparing computational science projects for science fairs and the Intel Science Talent Search. %%% This is a CAREER award for a program of large-scale computation to study the properties of far-from-equilibrium dynamical systems that exhibit temporally-chaotic, spatially-disordered behavior. This persistent, complex dynamical behavior found in a wide variety of systems such as fibrillating heart tissue, large aperture lasers, planetary atmospheres and oceans, fluid turbulence, and environmental ecosystems is currently not well understood due to the strong nonlinearities and the lack of an extremal principle in these systems. The grant goals are to develop new tools for analyzing these complicated dynamical systems and to use these tools to achieve an understanding of the important internal dynamical processes.
Also, as part of this project, new interdisciplinary courses will be developed in computational science for upper-level undergraduates and graduate students in the industrial physics program at Georgetown. Through performance of the research described above, undergraduates and postdoctoral fellows will develop skills in large-scale computing and modeling and in analyzing complex phenomena, which will serve the students and postdoctoral fellows well in careers in a wide variety of scientific fields. Also, an outreach program will be developed to bring the fast-evolving field of computational science to high school students and teachers. The PI and others at Georgetown will provide guidance and mentoring for students preparing computational science projects for science fairs and the Intel Science Talent Search. ***
