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| Thursday, January 4 — Session 5: Chaos and Noise |
| 1:50-2:30 pm |
Bernard Derrida
ENS & Universite Paris VI
Noisy traveling waves in models of evolution
Authors: B. Derrida, E. Brunet, A. Mueller and S. Munier
Some models of evolution in presence of selection can be formulated as noisy traveling waves such as the Fisher-KPP equation. This talk will review some recent results obtained on the effect of noise on the velocity and on the diffusion constant of these noisy traveling waves. The exact solution of a special case reveals statistical properties of genealogical trees which are quantitatively identical to those of spin glasses, as predicted by the Parisi theory.
E. Brunet, B. Derrida, A. H. Mueller, S. Munier,
Noisy traveling waves: effect of selection on genealogies
Europhys. Lett. 76, 1-7 (2006) cond-mat/0603160
E. Brunet, B. Derrida, A. H. Mueller, S. Munier,
A phenomenological theory giving the full statistics of the position of
fluctuating pulled fronts
Phys. Rev. E 73 (2006) 056126
E. Brunet, B. Derrida,
Effect of Microscopic Noise on Front Propagation
J. Stat. Phys. 103, 269-282 (2001)
E. Brunet, B. Derrida,
Shift in the velocity of a front due to a cutoff
Phys. Rev. E 56, 2597-2604 (1997)
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| 2:30-2:50 pm |
Thomas Carroll
Naval Research Lab
Email: Thomas.L.Carroll@nrl.navy.mil
Using a Phase Space Statistic to Identify Resonant Objects
Conducting objects have natural resonances when driven by electromagnetic waves. The resonances occur when some dimension of the object is equal to a half integral number of wavelengths of the electromagnetic wave. Since the resonance frequencies depend on the size and shape of the object, they may be used to identify the object.
The standard technique for finding these resonance frequencies is to emit a large electromagnetic impulse, which causes a transient ringing response from the object. There are problems with this method, which limit its practical application. I have developed a method based on the Kaplan-Glass phase space statistic that is sensitive to the phase shifts imposed by resonance, and has some practical advantages over the impulse technique. The phase space statistic works with a variety of different signals, which may be chaotic or non-chaotic.
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| 2:50-3:30 pm |
Edward Ott
University of Maryland, College Park
Estimating the state of large spatio-temporally chaotic systems:
weather forecasting, etc.
For the purposes of scientific investigation, forecasting and control,
it is often neccessary to determine good real-time approximations to the state of a dynamically evolving system from measured data. Typically, such data are noisy and incomplete. Given an approximate model for the evolution of the system, there are effective classical methods for treating the state estimation problem. Unfortunately, however, these classical methods become infeasible for dynamical systems that are large, in the sense that it is neccessary to give the values of a very great number of variables in order to specify the system state. In this talk, we discuss a technique[1] for accurately treating large, spatio-temporally chaotic systems. Recently obtained results testing this technique will be presented. So far, the main application and motivation for the technique has been in weather
forecasting, but it is more general, and we will also report on an application to laboratory experiments on Rayleigh-Benard convection in a large aspect ratio cell.
[1] E.Ott, B.R.Hunt, I.Szunyogh, et al., Tellus A, vol.56, p.415 (2004);
Phys. Lett. A, vol.330, p.365 (2004).
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| 3:30-3:50 pm |
Elana Fertig
University of Maryland
Email: ejfertig@math.umd.edu
authors: Elana Fertig, University of Maryland, College Park, MD; Hong Li, University of Maryland, College Park, MD; Junjie Liu, University of Maryland, College Park, MD; Jose Aravequia, University of Maryland, College Park, MD; Brian Hunt, University of Maryland, College Park, MD
Eugenia Kalnay, University of Maryland, College Park, MD; Eric Kostelich, Arizona State University, Tempe, AZ; Istvan Szunyogh, University of Maryland, College Park, MD
Using satellite data to improve forecasts for chaotic physical processes
Accurate forecasts of chaotic physical systems, like the atmosphere, require accurate estimates of the initial state. In practice, estimates of this state are obtained by combining information from past forecasts and observations relative to their uncertainties. One such algorithm for estimating the current state of the atmosphere is the ensemble Kalman filter, which evolves an ensemble of forecasts to obtain a flow dependent estimate of the forecast uncertainty. While this method has been shown to be effective in incorporating many convential observations (e.g., from weather balloons), few experiments have been conducted using satellite observations. We therefore use the ensemble Kalman filter to incorporate satellite observations from the Atmosphereic Infrared Sounder (AIRS) on an operational weather model, the NCEP GFS. We find that this algorithm is able to extract information from these observations to successfully improve the estimate for the current state of the atmosphere and the corresponding forecasts. |
| 4:20-5 pm |
Irving Epstein
Brandeis University
Email: epstein@brandeis.edu
authors: Irving R. Epstein* and Vladimir K. Vanag, Brandeis University,
Waltham, MA 02454
Spatiotemporal Pattern Formation in Reactive Microemulsions
I will present a survey of recent results obtained in experiments on the Belousov-Zhabotinsky oscillating chemical reaction in an oil-water-surfactant (AOT) microemulsion. This system consists essentially of a very large number(~10^(17)) of water droplets 5-10 nm in diameter, each surrounded by a monolayer of AOT and floating in a sea of oil, in which the oscillating chemical reaction can take place. By varying the proportions of oil, water and surfactant, one can tune the droplet size and distance between droplets. Changing the reactant concentrations allows for control over the chemistry. Searching this parameter space reveals a rich variety of patterns, including Turing patterns, inwardly and outwardly moving spirals, standing waves, segmented waves, etc. I will also touch briefly on efforts to model and simulate this behavior. |
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