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
   
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

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