Experimental observation of resonance manifold shrinking under zonal flow shear.

In two-dimensional turbulent systems the redistribution of energy can be described by quadratic nonlinear three-wave interactions, which are limited by resonance conditions. The set of coupling modes can be understood as resonant manifold. It has been predicted by theory that, in the presence of a shear flow, the resonant manifold in wave-number space shrinks in time favoring large-scale structures. The phenomenon of manifold shrinking in the presence of shear flows is studied the first time experimentally in drift wave turbulence at the stellarator TJ-K by bicoherence analysis. By estimating effective mode numbers characterizing the width of the manifold, it is demonstrated that increasing shear leads to a shrinking of the resonance manifold.

Constructing criteria to diagnose the likelihood of extreme events in the case of the electric power grid.

A set of new criteria for the diagnosis of the possible occurrence of a large blackout are constructed, using the output from a model for the dynamics of the electric power grid (the OPA model). The approach used is to look for maximum values of the Transfer Entropy between time series of the system variables and the time series of large blackouts. The best criterion is found by looking at the number of overloaded lines at the beginning of the day.

Relevance of uncorrelated Lorentzian pulses for the interpretation of turbulence in the edge of magnetically confined toroidal plasmas.

Recently, it has been proposed that the turbulent fluctuations measured in a linear plasma device could be described as a superposition of uncorrelated Lorentzian pulses with a narrow distribution of durations, which would provide an explanation for the reported quasiexponential power spectra. Here, we study the applicability of this proposal to edge fluctuations in toroidal magnetic confinement fusion plasmas. For the purpose of this analysis, we introduce a novel wavelet-based pulse-detection technique that offers important advantages over existing techniques. This technique allows for extracting the properties of individual pulses from the experimental time series, and for quantifying the distribution of pulse duration and energy as well as temporal correlations. We apply the wavelet technique to edge turbulent fluctuation data from the W7-AS stellarator and the JET tokamak, and find that the pulses detected in the data do not have a narrow distribution of durations and are not uncorrelated. Instead, the distributions are of the power-law type, exhibiting temporal correlations over scales much longer than the typical pulse duration. These results suggest that turbulence in open and closed field line systems may be distinct, and cast doubts on the proposed ubiquity of exponential power spectra in this context.

Analytical model for tracer dispersion in porous media.

In this work, we present a novel analytical model for tracer dispersion in laminar flow through porous media. Based on a straightforward physical argument, it describes the generic behavior of dispersion over a wide range of Péclet numbers (exceeding eight orders of magnitude). In particular, the model accurately captures the intermediate scaling behavior of longitudinal dispersion, obviating the need to subdivide the dispersional behavior into a number of disjunct regimes or using empirical power-law expressions. The analysis also suggests the possible existence of a new material property, the critical Péclet number, reflecting the mesoscale geometric properties of the microscopic pore structure.

Dynamical coupling between gradients and transport in fusion plasmas.

The dynamical coupling between density gradients and particle transport has been investigated using similar experimental tools in the plasma boundary of different tokamak (JET, ISTTOK) and stellarator (TJ-II) devices, showing that the size of turbulent events is minimum in the proximity of the most probable density gradient. Experimental results were found to be consistent with results from two very different models of plasma turbulence and transport. The present findings, common to several plasma devices, suggest the importance of self-regulation mechanisms between plasma transport and gradients in fusion devices.

Integrated data analysis at TJ-II: the density profile.

An integrated data analysis system based on Bayesian inference has been developed for the TJ-II stellarator. It reconstructs the electron density profile at a single time point, using data from interferometry, reflectometry, Thomson scattering, and the Helium beam, while providing a detailed error analysis. In this work, we present a novel analysis of the ambiguity inherent in profile reconstruction from reflectometry and show how the integrated data analysis approach elegantly resolves it. Several examples of the application of the technique are provided, in both low-density discharges with and without electrode biasing, and in high-density discharges with an (L-H) confinement transition.

Fractional generalization of Fick's law: a microscopic approach.

In the study of transport in inhomogeneous systems it is common to construct transport equations invoking the inhomogeneous Fick law. The validity of this approach requires that at least two ingredients be present in the system. First, finite characteristic length and time scales associated with the dominant transport process must exist. Second, the transport mechanism must satisfy a microscopic symmetry: global reversibility. Global reversibility is often satisfied in nature. However, many complex systems exhibit a lack of finite characteristic scales. In this Letter we show how to construct a generalization of the inhomogeneous Fick law that does not require the existence of characteristic scales while still satisfying global reversibility.

Renormalization of tracer turbulence leading to fractional differential equations.

For many years quasilinear renormalization has been applied to numerous problems in turbulent transport. This scheme relies on the localization hypothesis to derive a linear transport equation from a simplified stochastic description of the underlying microscopic dynamics. However, use of the localization hypothesis narrows the range of transport behaviors that can be captured by the renormalized equations. In this paper, we construct a renormalization procedure that manages to avoid the localization hypothesis completely and produces renormalized transport equations, expressed in terms of fractional differential operators, that exhibit much more of the transport phenomenology observed in nature. This technique provides a first step toward establishing a rigorous link between the microscopic physics of turbulence and the fractional transport models proposed phenomenologically for a wide variety of turbulent systems such as neutral fluids or plasmas.

Fluid limit of nonintegrable continuous-time random walks in terms of fractional differential equations.

The fluid limit of a recently introduced family of nonintegrable (nonlinear) continuous-time random walks is derived in terms of fractional differential equations. In this limit, it is shown that the formalism allows for the modeling of the interaction between multiple transport mechanisms with not only disparate spatial scales but also different temporal scales. For this reason, the resulting fluid equations may find application in the study of a large number of nonlinear multiscale transport problems, ranging from the study of self-organized criticality to the modeling of turbulent transport in fluids and plasmas.

Quiet-time statistics of electrostatic turbulent fluxes from the JET tokamak and the W7-AS and TJ-II stellarators.

The statistics of the quiet times between successive turbulent flux bursts measured at the edge of the JET tokamak and the W7-AS and TJ-II stellarators are analyzed in search for evidence of self-organized critical behavior. The results obtained are consistent with what would be expected in the situation where the underlying plasma is indeed in a near critical state.

Quiet-time statistics: a tool to probe the dynamics of self-organized-criticality systems from within the strong overlapping regime.

A method is presented that allows one to obtain information about the underlying dynamics of a self-organized-criticality system even when the strong-overlapping or hydrodynamic regime (in which individual avalanches are no longer distinguishable) is the only one amenable of probing. The method is based on the analysis of the statistics of the lapses of time between activity bursts or quiet times. The case of a randomly driven running sandpile is used to illustrate the use and capabilities of this technique.

In search of the elusive zonal flow using cross-bicoherence analysis

We show that the modulational instability growth rate of zonal flows is determined directly from the quasilinear wave kinetic equation. We also demonstrate the relation between zonal-flow growth and the cross bispectrum of the high-frequency drift-wave-driven Reynolds stress and the low-frequency plasma potential by explicit calculation. Experimental measurements of the spatiotemporal evolution of the spectrum integrated bicoherence at the L-->H transition near the edge shear layer indicate a modification in the nonlinear phase coupling, which might be linked to the generation of sheared ExB flows.

Comments on "An accelerated learning algorithm for multilayer perceptrons: optimization layer by layer".

This letter analyzes the performance of the neural network training method known as optimization layer by layer. We show, from theoretical considerations, that the amount of work required with OLL-Learning scales as the third power of the network size, compared with the square of the network size for commonly used conjugate gradient training algorithms. This theoretical estimate is confirmed through a practical example. Thus, although OLL is shown to function very well for small neural networks (less than about 500 weights per layer), it is slower than CG for large neural networks. Second, we show that OLL does not always improve on the accuracy that can be obtained with CG. It seems that the final accuracy that can be obtained depends strongly on the initial network weights.