Showing papers by "Vickie E. Lynch published in 2005"

Nondiffusive Transport in Plasma Turbulence: A Fractional Diffusion Approach

Abstract: Numerical evidence of nondiffusive transport in three-dimensional, resistive pressure-gradient-driven plasma turbulence is presented. It is shown that the probability density function (pdf) of tracer particles' radial displacements is strongly non-Gaussian and exhibits algebraic decaying tails. To model these results we propose a macroscopic transport model for the pdf based on the use of fractional derivatives in space and time that incorporate in a unified way space-time nonlocality (non-Fickian transport), non-Gaussianity, and nondiffusive scaling. The fractional diffusion model reproduces the shape and space-time scaling of the non-Gaussian pdf of turbulent transport calculations. The model also reproduces the observed superdiffusive scaling.

Risk Assessment in Complex Interacting Infrastructure Systems

Abstract: Critical infrastructures have some of the characteristic properties of complex systems. They exhibit infrequent large failures events. These events, though infrequent, often obey a power law distribution in their probability versus size. This power law behavior suggests that ordinary risk analysis might not apply to these systems. It is thought that some of this behavior comes from different parts of the systems interacting with each other both in space and time. While these complex infrastructure systems can exhibit these characteristics on their own, in reality these individual infrastructure systems interact with each other in even more complex ways. This interaction can lead to increased or decreased risk of failure in the individual systems. To investigate this and to formulate appropriate risk assessment tools for such systems, a set of models are used to study to impact of coupling complex systems. A probabilistic model and a dynamical model that have been used to study blackout dynamics in the power transmission grid are used as paradigms. In this paper, we investigate changes in the risk models based on the power law event probability distributions, when complex systems are coupled.

Estimating Failure Propagation In Models Of Cascading Blackouts

Abstract: We compare and test statistical estimates of failure propagation in data from versions of a probabilistic model of loading-dependent cascading failure and a power system blackout model of cascading transmission line overloads. The comparisons suggest mechanisms affecting failure propagation and are an initial step toward monitoring failure propagation from practical system data. Approximations to the probabilistic model describe the forms of probability distribution of cascade sizes.

Topological instability along invariant surfaces and pseudochaotic transport.

Abstract: The paper describes the complex topological structure of invariant surfaces that appears in a quasistationary regime of the tokamak plasma, and it considers in detail anomalous transport of particles along the invariant surfaces (isosurfaces) that have topological genus greater than 1. Such dynamics is pseudochaotic; i.e. it has a zero Lyapunov exponent. Simulations discover such surfaces in confined plasmas under a fairly low ratio of pressure to the magnetic field energy ({beta}). The isosurfaces correspond to quasicoherent structures called ''streamers,'' and the streamers are connected by filaments. We study distribution of time of particle separation, Poincare recurrences of trajectories, and first time arrival to the system's edge. A model of a multibar-in-square billiard, introduced by Carreras et al. [Chaos 13, 1175 (2003)] is studied with renormalization group method to obtain a distribution of the first time of particles arrival to the edge as a function of the number of bars, which appears to be power-like. The characteristic exponent of this distribution is discussed with respect to its dependence on the number of filaments that connect adjacent streamers.

Determination of long-range correlations by quiet-time statistics

Abstract: Quiet-time statistics is an approach to the analysis of fluctuation time series that, by measuring the duration of successive transport events and the quiet times between them, allows the extraction of information on the long-range correlations in the system. It provides information similar to that obtained from rescaled adjusted range (R∕S) statistics. However, when the data are contaminated by extraneous oscillations, it is difficult to effectively use R∕S statistics or standard quiet-time analysis. In this paper, quiet-time analysis is generalized so that time series contaminated by oscillations can be treated. This new technique is effective over a wide range of time scales.