SATE - SCIENCE at the Edge
Interdisciplinary Physics
Room - 1400 BPS
October 10th, 2014 Friday at 11:30 a.m.
with refreshments served at 11:15 a.m.
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
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