Bulletin of the American Physical Society
APS March Meeting 2018
Monday–Friday, March 5–9, 2018; Los Angeles, California
Session C58: Large Deviations and the Butterfly EffectInvited

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Sponsoring Units: GSNP Chair: Michael Wilkinson, Open Univ Room: LACC Petree Hall C 
Monday, March 5, 2018 2:30PM  3:06PM 
C58.00001: Is space time? A spatiotemporal theory of transitional turbulence Invited Speaker: Predrag Cvitanovic Recent advances in fluid dynamics reveal that the recurrent flows observed in moderate Reynolds number turbulence result from close passes to unstable invariant solutions of NavierStokes equations. By now hundreds of such solutions been computed for a variety of flow geometries, but always confined to small computational domains (minimal cells). 
Monday, March 5, 2018 3:06PM  3:42PM 
C58.00002: Large Deviation Theory of Planetary Jets Invited Speaker: John Marston The Reynolds stress, or equivalently the momentum flux, is key to understanding the statistical properties of turbulent flows. Both typical and rare fluctuations of the time averaged momentum flux are needed to fully characterize the slow flow evolution. The fluctuations are described by a large deviation rate function that may be calculated either from numerical simulation, or from theory. We show that, for parameter regimes in which a quasilinear approximation is accurate, the rate function can be found by solving a matrix Riccati equation. Using this tool we compute for the first time the large deviation rate function for the Reynolds stress of a turbulent barotropic flow on a rotating sphere, and show that the fluctuations are highly nonGaussian. This work opens up new perspectives for the study of rare transitions between attractors in turbulent flows. 
Monday, March 5, 2018 3:42PM  4:18PM 
C58.00003: Modelfree Machine Learning Analysis of Chaotic Dynamics Including that of Large Spatiotemporally Chaotic Systems Invited Speaker: Edward Ott We consider the common situation in which a finite length timeseries data produced by a chaotic dynamical system is available, and it is desired to infer dynamical information solely from this data (i.e., in the absence of knowledge of the datagenerating system itself). Examples of the types of infered information that it might be desired to are the future evolution of the system (i.e., the task of prediction), the Lyapunov exponents of the system generating the data, and the inference of unmeasured state variables from future partial measurements. Using the machine learning technique known as Reservoir Computing we show how these tasks can be accomplished. In particular, use as illustrative examples low dimensional chaotic systems, as well as high dimensional extensively chaotic spatiotemporal systems. Our general conclusion is that machine learning is exceptionally good performing tasks of this type, and, in some cases can accomplish these tasks in situations for which successful previous methods are not available. [Collaborators: Jaideep Pathak, Zhixin Lu, Brian Hunt, Michelle Girvan.] 
Monday, March 5, 2018 4:18PM  4:54PM 
C58.00004: Convergent Chaos Invited Speaker: Marc Pradas Chaos is widely understood as being a consequence of sensitive dependence upon initial conditions. This is the result of an instability in phase space, which separates trajectories exponentially. Here, we investigate the dynamics of a chaotic onedimensional model for inertial particles in a random velocity field and demonstrate that despite their overall intrinsic instability, trajectories may be very strongly convergent in phase space over extremely long periods. We establish that this strong convergence is a multifacetted phenomenon, in which the clustering is intense, widespread and balanced by lacunarity of other regions [1]. Power laws, indicative of scalefree features, characterize the distribution of particles in the system. We use largedeviation theory and extremevalue statistics to explain this effect, and in particular, we develop the largedeviation theory for fluctuations of the finitetime Lyapunov exponent of this system. We show that the determination of the entropy function for the distribution reduces to the analysis of a Schrödinger equation, which is tackled by semiclassical methods [2]. The system has ‘generic’ instability properties, and we consider the broader implications of our observation of longterm stability in chaotic systems. Our results show that the interpretation of the ‘butterfly effect’ needs to be carefully qualified. [1] M. Pradas, A. Pumir, G. Huber, M. Wilkinson, J. Phys A 50, 275101 (2017); [2] G. Huber, M. Pradas, A. Pumir, M. Wilkinson, Physica A (in press, 2017). 
Monday, March 5, 2018 4:54PM  5:30PM 
C58.00005: Diffusion, Deviation and Divergence: Limits to Predictability in Nonlinear Systems Invited Speaker: Leonard Smith What limits the predictability of physical systems? And what rational expectations can we hold for simulationbased forecasting? Chaos reflects only the growth of infinitesimal uncertainties  and infinitesimal uncertainties never pose a limit to predictability. Many forecasting models simply model the dynamics of the system poorly; this is easily established when they fail to φ shadow under any reasonable observational noise model. But what could be achieved by a very good simulation model? 
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