176 research outputs found
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
Scale-free vortex cascade emerging from random forcing in a strongly coupled system
The notions of self-organised criticality (SOC) and turbulence are
traditionally considered to be applicable to disjoint classes of phenomena.
Nevertheless, scale-free burst statistics is a feature shared by turbulent as
well as self-organised critical dynamics. It has also been suggested that
another shared feature is universal non-gaussian probability density functions
(PDFs) of global fluctuations. Here, we elucidate the unifying aspects through
analysis of data from a laboratory dusty plasma monolayer. We compare analysis
of experimental data with simulations of a two-dimensional (2D) many-body
system, of 2D fluid turbulence, and a 2D SOC model, all subject to random
forcing at small scales. The scale-free vortex cascade is apparent from
structure functions as well as spatio-temporal avalanche analysis, the latter
giving similar results for the experimental and all model systems studied. The
experiment exhibits global fluctuation statistics consistent with a
non-gaussian universal PDF, but the model systems yield this result only in a
restricted range of forcing conditions
Is there long-range memory in solar activity on time scales shorter than the sunspot period?
The sunspot number (SSN), the total solar irradiance (TSI), a TSI
reconstruction, and the solar flare index (SFI), are analyzed for long-range
persistence (LRP). Standard Hurst analysis yields , which
suggests strong LRP. However, solar activity time series are non-stationary due
to the almost periodic 11 year smooth component, and the analysis does not give
the correct for the stochastic component. Better estimates are obtained by
detrended fluctuations analysis (DFA), but estimates are biased and errors are
large due to the short time records. These time series can be modeled as a
stochastic process of the form , where
is the smooth component, and is a stationary fractional noise
with Hurst exponent . From ensembles of numerical solutions to the
stochastic model, and application of Bayes' theorem, we can obtain bias and
error bars on and also a test of the hypothesis that a process is
uncorrelated (). The conclusions from the present data sets are that
SSN, TSI and TSI reconstruction almost certainly are long-range persistent, but
with most probable value . The SFI process, however, is either
very weakly persistent () or completely uncorrelated. Some differences
between stochastic properties of the TSI and its reconstruction indicate some
error in the reconstruction scheme.Comment: 23 pages, 12 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
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