November 05, 2010, 1100 Webb

In the world of moderate Reynolds number, everyday turbulence of fluids flowing across planes and down pipes a velvet revolution is taking place. Experiments are almost as detailed as the numerical simulations, DNS is yielding exact numerical solutions that one dared not dream about a decade ago, and dynamical systems visualization of turbulent fluid\’s state space geometry is unexpectedly elegant. Suppose you have no interest in turbulence, but you do want to live long. Well, the same insights might enable us to nudge your heart away from a disagreeable cardiac arrhythmia and back to life by applying milliwatts instead frying you with kilowatt jolts. We shall take you on a tour of this newly breached, hitherto inaccessible territory. Mastery of fluid mechanics is no prerequisite, and perhaps a hindrance: the talk is aimed at anyone who had ever wondered why – if no cloud is ever seen twice – we know a cloud when we see one? And how do we turn that into mathematics?

Predrag Cvitanovic'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 T. Kinoshita and P.C. 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.

Cvitanovic is also known for his monographs/webbooks on Field Theory, Group Theory, and Chaos