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In order to study the complex global dynamics of a series of blackouts in power transmission systems a dynamical model of such a system has been developed. This model includes a simple representation of the dynamical evolution by incorporating the growth of power demand, the engineering response to system failures, and the upgrade of generator capacity. Two types of blackouts have been identified, each having different dynamical properties. One type of blackout involves the loss of load due to transmission lines reaching their load limits but no line outages. The second type of blackout is associated with multiple line outages. The dominance of one type of blackout over the other depends on operational conditions and the proximity of the system to one of its two critical points. The model displays characteristics such as a probability distribution of blackout sizes with power tails similar to that observed in real blackout data from North America., (Copyright 2004 American Institute of Physics)

In dynamical systems with a zero Lyapunov exponent, weak mixing can be governed by a specific topological structure of some surfaces that are invariant with respect to particle dynamics. In particular, when the genus of the invariant surfaces is more than one, they may have weak mixing and the corresponding fractional kinetics. This possibility is demonstrated by using a typical example from plasma physics, a three-dimensional resistive pressure-gradient-driven turbulence model. In a toroidal geometry and with a low-pressure gradient, this model shows the emergence of quasicoherent structures. In this situation, the isosurfaces of the velocity stream function have a web structure with filamentary surfaces emerging from the outer region of the torus and covering the inner region. The filamentary surfaces can result in stochastic jets of particles that cause a "topological instability." In such a situation, particle transport along the surfaces is of the anomalous superdiffusion type., (Copyright 2003 American Institute of Physics.)

The use of reaction-diffusion models rests on the key assumption that the diffusive process is Gaussian. However, a growing number of studies have pointed out the presence of anomalous diffusion, and there is a need to understand reactive systems in the presence of this type of non-Gaussian diffusion. Here we study front dynamics in reaction-diffusion systems where anomalous diffusion is due to asymmetric Levy flights. Our approach consists of replacing the Laplacian diffusion operator by a fractional diffusion operator of order alpha, whose fundamental solutions are Levy alpha-stable distributions that exhibit power law decay, x(-(1+alpha)). Numerical simulations of the fractional Fisher-Kolmogorov equation and analytical arguments show that anomalous diffusion leads to the exponential acceleration of the front and a universal power law decay, x(-alpha), of the front's tail.

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.

Cascading failures in large-scale electric power transmission systems are an important cause of blackouts. Analysis of North American blackout data has revealed power law (algebraic) tails in the blackout size probability distribution which suggests a dynamical origin. With this observation as motivation, we examine cascading failure in a simplified transmission system model as load power demand is increased. The model represents generators, loads, the transmission line network, and the operating limits on these components. Two types of critical points are identified and are characterized by transmission line flow limits and generator capability limits, respectively. Results are obtained for tree networks of a regular form and a more realistic 118-node network. It is found that operation near critical points can produce power law tails in the blackout size probability distribution similar to those observed. The complex nature of the solution space due to the interaction of the two critical points is examined.(c) 2002 American Institute of Physics.

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.

The probability distribution function of the avalanche size in the sandpile model does not verify strict self-similarity under changes of the sandpile size. Here we show the existence of avalanches with different space-time structure, and each type of avalanche has a different scaling with the sandpile size. This is the main cause of the lack of self-similarity of the probability distribution function of the avalanche sizes, although the boundary effects can also play a role.

The transition from the low to the high mode of plasma confinement ( L-H transition) is studied in the DIII-D by an experimental technique which allows an arbitrarily slow transition. During an initial transition, periodic turbulent instability bursts are observed near the separatrix which inhibit the full transition. These bursts are damped by self-generated shear flows, and a predator-prey-type relationship is shown to give a good description of the data. As the neutral-beam power is raised, the oscillations change to type III edge localized modes. Another transition then leads to a quiet H mode.

A running sandpile is shown to undergo a dynamical transition as diffusion is increased from zero. The transition takes place after the local diffusion has become so large as to erase the local inhomogeneities, caused by the intermittent rain of sand, before they can trigger avalanche activity. The system then undergoes an abrupt change with the self-similar structure of the dynamics being replaced with quasiperiodic, near system-size transport events. These results may have significant implications for many of the driven physical systems for which self-organized criticality based dynamical models have been proposed.

It is argued that a system governed by self-organized-criticality (SOC) dynamics can lack Poisson waiting-time statistics not only when the experimental resolution lies within the self-similar scale range but also if the system is slowly driven in a correlated way. This result thus suggests that waiting time statistics cannot be used as a necessary test for SOC behavior in real physical systems.

To explore the character of underlying transport in a sandpile, we have followed the motion of tracer particles. Moments of the distribution function of the particle positions, =D(0)t(nnu(n)), are determined as a function of the elapsed time. The numerical results show that the transport mechanism for distances less than the sandpile length is superdiffusive with an exponent nu(n) close to 0.75, for n<1.