NBIA Colloquium: Predrag Cvitanović
Friday, August 1st at 3:15 PM in Aud. A
Speaker: Predrag Cvitanovic (Georgia Institute of Technology, Atlanta)
Title: Turbulence, and what to do about it
Abstract: Ruelle dynamical zeta functions for chaotic dynamical systems and statistical mechanics partition sums are always presented in ways that make them appear as disjoint, unrelated theories. However, recent advances in describing fluid turbulence by its dynamical, deterministic Navier-Stokes underpinning, without any statistical assumptions, have led to a common field-theoretic description of both (low-dimension) chaotic dynamical systems, and (infinite-dimension) spatiotemporally turbulent flows.
We use a lattice discretized field theory in 1 and 1+1 dimensions to explain how temporal `chaos' and `spatiotemporal chaos' are profitably cast into the same field-theoretic framework.
Brief bio-sketch: Predrag Cvitanović's contributions to the foundations of nonlinear dynamics span a broad range of physical problems, from renormalization in transitions to chaos to periodic orbit theory of quantum systems to dynamical theory of hydrodynamical turbulence.
In 1976 he derived in collaboration with M.J. Feigenbaum the universal equation for period doubling. In order to describe the topological structure of "strange attractors" of Henon type, he introduced the notion of pruning front, still actively investigated by both physicists and mathematicians. Cvitanovic's highly cited contributions to nonlinear dynamics include introduction of "cycle expansions" and their applications to semiclassical quantization, "wave chaos" in acoustics, symmetry decomposition of dynamical zeta functions, and discovery of phase transitions on "strange sets". Recently he has worked towards a periodic orbit theory of spatiotemporal turbulence of infinite dimensional dynamical systems such as boundary shear flows.
Other frequently cited contributions include calculation of the sixth-order magnetic moment of the electron, his group theory for Feynman diagrams in non-Abelian gauge theories, his "Magic Triangle" for exceptional Lie algebras, and his planar field theory. Cvitanović is also known for his monographs/webbooks on Field Theory, Group Theory, and Chaos.