Noise is your friend, or: How well can we resolve state space?

Cvitanović, Predrag

Title:

Noise is your friend, or: How well can we resolve state space?

dc.contributor.author	Cvitanović, Predrag
dc.contributor.corporatename	Georgia Institute of Technology. School of Civil and Environmental Engineering	en_US
dc.contributor.corporatename	Georgia Institute of Technology. School of Physics	en_US
dc.date.accessioned	2014-09-15T13:35:00Z
dc.date.available	2014-09-15T13:35:00Z
dc.date.issued	2014-09-05
dc.description	Presented on September 5, 2014 at 1:00 p.m. in the Jesse W. Mason Building, room 3133.	en_US
dc.description	Predrag Cvitanović is an endowed Professor of Physics at the Georgia Institute of Technology. He is highly regarded for his work in nonlinear dynamics, particularly his contributions to periodic orbit theory. Perhaps his best-known work is his introduction of cycle expansions—that is, expansions based on using periodic orbit theory—to approximate chaotic dynamics in a controlled perturbative way. This technique has proven to be widely useful for diagnosing and quantifying chaotic dynamics in problems ranging from atomic physics to neurophysiology.	en_US
dc.description	Runtime: 54:47 minutes
dc.description.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.	en_US
dc.embargo.terms	null	en_US
dc.format.extent	54:47 minutes
dc.identifier.uri	http://hdl.handle.net/1853/52360
dc.relation.ispartofseries	EFMWR Seminar Series
dc.subject	Chaos	en_US
dc.subject	Noise	en_US
dc.subject	Nonlinear dynamics	en_US
dc.subject	Stochastic processes	en_US
dc.title	Noise is your friend, or: How well can we resolve state space?	en_US
dc.type	Moving Image
dc.type.genre	Lecture
dspace.entity.type	Publication
local.contributor.author	Cvitanović, Predrag
local.contributor.corporatename	School of Civil and Environmental Engineering
local.contributor.corporatename	College of Engineering
local.relation.ispartofseries	EFMWR Seminar Series
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