COLLOQUIUM 4:10 p.m., Room 1415 BPS Bldg. Department of Physics and Astronomy Predrag Cvitanovic Center for Nonlinear Science, School of Physics Georgia Institute of Technology, Atlanta Recurrent flows: The clockwork behind turbulence 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. 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? SATE October 10th, 2014 Friday at 11:30 a.m. with refreshments served at 11:15 a.m. Interdisciplinary Physics - 1400 BPS Noise is your friend, or: How well can we resolve state space? Predrag Cvitanović<http://www.cns.gatech.edu/%7Epredrag/> ABSTRACT All physical systems are affected by some noise that limits the resolution that can be attained in partitioning their state space. What is the best resolution possible for a given physical system? It turns out that for nonlinear dynamical systems the noise itself is highly nonlinear, with the effective noise different for different regions of system's state space. The best obtainable resolution thus depends on the observed state, the interplay of local stretching/contraction with the smearing due to noise, as well as the memory of its previous states. We show how that is computed, orbit by orbit. But noise also associates to each orbit a finite state space volume, thus helping us by both smoothing out what is deterministically a fractal strange attractor, and restricting the computation to a set of unstable periodic orbits of finite period. By computing the local eigenfunctions of the Fokker-Planck evolution operator, forward operator along stable linearized directions and the adjoint operator along the unstable directions, we determine the `finest attainable' partition for a given hyperbolic dynamical system and a given weak additive noise. The space of all chaotic spatiotemporal states is infinite, but noise kindly coarse-grains it into a finite set of resolvable states. Shawna Prater / Secretary Astrophysics Group Michigan State University 567 Wilson Road, Room 3261 Biomedical Physical Sciences Bldg East Lansing, MI 48824-2320 Ph: (517) 884-5601 Fax (517) 432-8802 [log in to unmask]<mailto:[log in to unmask]>, [log in to unmask]<mailto:[log in to unmask]> This e-mail may contain confidential information. If you are not the intended recipient of this e-mail, you are hereby notified that any dissemination, distribution or copying of this message is strictly prohibited. If you received this message in error, please delete it immediately.