A stochastic theory for temporal fluctuations in self-organized critical systems

A stochastic theory for the toppling activity in sandpile models is developed, based on a simple mean-field assumption about the toppling process. The theory describes the process as an anti-persistent Gaussian walk, where the diffusion coefficient is proportional to the activity. It is formulated as a generalization of the It\^{o} stochastic differential equation with an anti-persistent fractional Gaussian noise source. An essential element of the theory is re-scaling to obtain a proper thermodynamic limit, and it captures all temporal features of the toppling process obtained by numerical simulation of the Bak-Tang-Wiesenfeld sandpile in this limit.Comment: 9 pages, 4 figure

Burst statistics of fluctuations in a simple magnetized torus configuration

In a toroidal plasma confined by a purely toroidal magnetic field the plasma transport is governed by electrostatic turbulence driven by the flute interchange instability on the low-field side of the torus cross section. In this paper we revisit experimental data obtained from the Blaamann torus at the University of Tromso. On time-scales shorter than the poloidal rotation time, the time series of potential and electron density fluctuations measured on stationary Langmuir probes essentially reflect the spatial poloidal structure of the turbulent field (Taylor hypothesis). On these time scales the signals reveals an intermittent character exposed via analysis of probability density functions and computation of multifractal dimension spectra in different regimes of time scales. This intermittency is associated with the shape and distribution of pronounced spikes in the signal. On time scales much longer than the rotation period there are strong global fluctuations in the plasma potential which are shown to to be the result of low-dimensional chaotic dynamics

Modeling temporal fluctuations in avalanching systems

We demonstrate how to model the toppling activity in avalanching systems by stochastic differential equations (SDEs). The theory is developed as a generalization of the classical mean field approach to sandpile dynamics by formulating it as a generalization of Itoh's SDE. This equation contains a fractional Gaussian noise term representing the branching of an avalanche into small active clusters, and a drift term reflecting the tendency for small avalanches to grow and large avalanches to be constricted by the finite system size. If one defines avalanching to take place when the toppling activity exceeds a certain threshold the stochastic model allows us to compute the avalanche exponents in the continum limit as functions of the Hurst exponent of the noise. The results are found to agree well with numerical simulations in the Bak-Tang-Wiesenfeld and Zhang sandpile models. The stochastic model also provides a method for computing the probability density functions of the fluctuations in the toppling activity itself. We show that the sandpiles do not belong to the class of phenomena giving rise to universal non-Gaussian probability density functions for the global activity. Moreover, we demonstrate essential differences between the fluctuations of total kinetic energy in a two-dimensional turbulence simulation and the toppling activity in sandpiles.Comment: 14 pages, 11 figure

E-pile model of self-organized criticality

The concept of percolation is combined with a self-consistent treatment of the interaction between the dynamics on a lattice and the external drive. Such a treatment can provide a mechanism by which the system evolves to criticality without fine tuning, thus offering a route to self-organized criticality (SOC) which in many cases is more natural than the weak random drive combined with boundary loss/dissipation as used in standard sand-pile formulations. We introduce a new metaphor, the e-pile model, and a formalism for electric conduction in random media to compute critical exponents for such a system. Variations of the model apply to a number of other physical problems, such as electric plasma discharges, dielectric relaxation, and the dynamics of the Earth's magnetotail.Comment: 4 pages, 2 figure

Organization of the magnetosphere during substorms

The change in degree of organization of the magnetosphere during substorms is investigated by analyzing various geomagnetic indices, as well as interplanetary magnetic field z-component and solar wind flow speed. We conclude that the magnetosphere self-organizes globally during substorms, but neither the magnetosphere nor the solar wind become more predictable in the course of a substorm. This conclusion is based on analysis of five hundred substorms in the period from 2000 to 2002. A minimal dynamic-stochastic model of the driven magnetosphere that reproduces many statistical features of substorm indices is discussed