Department of Physics

Faculty Description


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Research Statement
  • Our research is primarily in applications of contemporary developments in dynamical systems and nonlinear dynamics to problems of physical interest in fluid and plasma physics. The particular problems we are working on include:

    Nonlinear stability of fluid flows in geophysical settings. We have developed a method for separating modes of an inviscid flow with significantly different time scales while retaining the Hamiltonian structure of the dynamics. This has been applied to the description of quasi-geostrophic flows in the ocean and atmosphere. This method also promises the ability to analyze the time scales in which nonlinear instabilities develop in physical systems. We are now applying this to the description of other flows with separated time scales such as waves on interfaces and wave motions internal to stratified fluids.

    Using notions of nonlinear dynamics, we are investigating the manner in which friction is exhibited by parts of a Hamiltonian system which develop on separated time scales. Characterizing the flow of information from one subsystem to another by the Liapunov exponents natural to chaotic motions and by correlation functions in phase space, we are able to determine on what time scales a system may look dissipative and possess strange attractors even though it is part of an overall Hamiltonian system.

    We are also beginning to investigate the spatial and temporal scales associated with nonlinear instabilities in a continuum system such as a fluid or plasma. This is an entirely new direction in the study on nonlinear instability and promises to have direct implications on experiments done here at UCSD and elsewhere which seek characteristics of these instabilities.
Awards & News
  • UC San Diego Receives $7 Million from DOD for Innovative Neural Research
  • An interdisciplinary team of scientists at UC San Diego composed of physicists, biologists, chemists, bioengineers and psychologists has received a five-year, $7 million grant from the U.S. Department of Defense to investigate the dynamic principles of collective brain activity.

    The innovative research effort, which is being funded by the Office of Naval Research under the Defense Department's MultiUniversity Research Initiative, or MURI, will also involve scientists at UC Berkeley and the University of Chicago.

    The team plans to conduct basic research on how collective action in the brain learns, modulates and produces coherent functional neural activity for coordinated behavior of complex systems.

    "This research will tie together theoretical ideas, hardware implementation of structural models and experimental investigations of human and animal behavior to develop a quantitative understanding and a predictive language for discussing complex physical and biological systems," said Henry Abarbanel, a physics professor at UC San Diego who is heading the collaboration.

    The grant will pay for the costs of new laboratory facilities at UC San Diego and the University Chicago, create powerful parallel computing capabilities for the three universities involved and employ 10 or more postdoctoral research fellows. Key UC San Diego researchers participating in the effort are Katja Lindenberg, professor of chemistry and biochemistry; Tim Gentner, associate professor of psychology; Gert Cauwenberghs, professor of bioengineering; Misha Rabinovich, research physicist in the BioCircuits Institute; and Terry Sejnowski, professor of biology.

    This is the fourth MURI award led by Abarbanel. The first focused on theory and experiment in complex fluid flows and was funded by the Defense Advanced Research and Projects Agency from 1988 to 1993. The second investigated chaotic communications strategies from 1998 to 2003 under sponsorship by the Army Research Office. The third developed advanced chemical sensing methodologies using animal olfactory dynamics and was funded by the Office of Naval Research from 2007 to 2012.

Selected Publications
  • - Analysis of High Reynolds Number Flows over a Buoyant Axisymmetric Body. With J. Cembrela, T. Frison, T. Galib and R. Katz. Phys. Rev. E 49, 4003 (1994).

  • - Nonlinear Systems. Encyclopedia of Applied Physics, Ed. G.L. Trigg, published by VCH Publishers in collaboration with the American Institute of Physics, the German Physical Society, the Japan Society of Applied Physics, and the Physical Society of Japan. To appear in 1994.

  • - The Analysis of Observed Chaotic Data in Physical Systems. With R. Brown, J. Sidorowich and L. Tsimring. Rev. of Mod. Phys. 65, 1331 (1993).