Example Of Self-organized Criticality Research Articles

Forest fires: An example of self-organized critical behavior

Despite the many complexities concerning their initiation and propagation, forest fires exhibit power-law frequency-area statistics over many orders of magnitude. A simple forest fire model, which is an example of self-organized criticality, exhibits similar behavior. One practical implication of this result is that the frequency-area distribution of small and medium fires can be used to quantify the risk of large fires, as is routinely done for earthquakes.

Energy avalanches in a rice-pile model

We investigate a one-dimensional rice-pile model. We show that the distribution of dissipated potential energy decays as a power law with an exponent α = 1.53. The system thus provides a one-dimensional example of self-organized criticality. Different driving conditions are examined in order to allow for comparisons with experiments.

Dynamic complexity inPhysarum polycephalum shuttle streaming

The nature of the oscillator controlling shuttle streaming inPhysarum polycephalum is not well understood. To examine the possibility of complex behavior in shuttle streaming, the time between reversal of streaming direction was measured over several hours in an intact plasmodium to produce a time series. Time series data were then used to analyze shuttle streaming dynamics. Complexity in shuttle streaming is revealed by an inverse frequency (1/f) power spectrum where the amplitude of reversals is plotted against their frequency. The complex dynamics of shuttle streaming is also shown by a trajectory in phase space typical of a strange attractor. Finally, shuttle streaming time series data have a dominant Lyapunov exponent of approximately zero. Dynamic systems with a Lyapunov exponent of zero exist in a state at the edge of chaos. Systems at the edge exhibit self-organized criticality, which produces complex behavior in many physical and biological systems. We propose that complex dynamics inPhysarum shuttle streaming is an example of self-organized criticality in the cytoplasm. The complex behavior ofPhysarum is an emergent phenomenon that probably results from the interaction of actin filaments, myosin, ATP, and other components involved in cell motility.

Phase transitions near the "game of Life"

Whether or not the cellular automaton (CA) game of is an example of self-organized criticality has been a controversial question. Here we view the problem from a different perspective by introducing probabilities into the rules. Thereby we extend the discrete space of deterministic CA to a hypercubic space of stochastic CA, where each corner represents a deterministic CA. We examine the scaling structure near the game of corner and identify a phase-transition line separating Life and Death. The transition line ends very close to but not in the game of Life.

Effect of self-organized criticality on magnetic-flux creep in type-II superconductors: A time-delayed approach.

Bean's original model successfully explained the phenomenon of irreversible magnetization in type-II superconductors and revealed the threshold behavior of flux motion. The latter has similarities to the sliding of sand grains in a pile of sand, an example of self-organized criticality (SOC) initiated by P. Bak [ital et] [ital al]. However, the effect of thermal relaxation was not considered in the SOC context. We have generalized Kim and Anderson's derivation of flux creep by incorporating the effects of avalanches on the relaxation of magnetization close to the self-organized critical state using a time-delayed diffusion equation approach. We predict qualitative changes in the nature of flux creep when measured close to the critical state.

FRACTAL TECTONICS AND EROSION

Tectonic processes build landforms that are subsequently destroyed by erosional processes. Landforms exhibit fractal statistics in a variety of ways; examples include (1) lengths of coast lines; (2) number-size statistics of lakes and islands; (3) spectral behavior of topography and bathymetry both globally and locally; and (4) branching statistics of drainage networks. Erosional processes are dominant in the development of many landforms on this planet, but similar fractal statistics are also applicable to the surface of Venus where minimal erosion has occurred. A number of dynamical systems models for landforms have been proposed, including (1) cellular automata; (2) diffusion limited aggregation; (3) self-avoiding percolation; and (4) advective-diffusion equations. The fractal statistics and validity of these models will be discussed. Earthquakes also exhibit fractal statistics. The frequency-magnitude statistics of earthquakes satisfy the fractal Gutenberg-Richter relation both globally and locally. Earthquakes are believed to be a classic example of self-organized criticality. One model for earthquakes utilizes interacting slider-blocks. These slider block models have been shown to behave chaotically and to exhibit self-organized criticality. The applicability of these models will be discussed and alternative approaches will be presented. Fragmentation has been demonstrated to produce fractal statistics in many cases. Comminution is one model for fragmentation that yields fractal statistics. It has been proposed that comminution is also responsible for much of the deformation in the earth’s crust. The brittle disruption of the crust and the resulting earthquakes present an integrated problem with many fractal aspects.

Self-organized criticality in 4He with a heat current.

In the presence of a small heat current and appropriate boundary conditions, [sup 4]He will reach the superfluid critical point without fine tuning the temperature. This provides a physical example of self-organized criticality via the mechanism of singular diffusion proposed by Carlson [ital et] [ital al]. [Phys. Rev. Lett. 65, 2547 (1990)].

SELF-ORGANIZED CRITICALITY AND THE BARKHAUSEN EFFECT IN AMORPHOUS AND POLYCRYSTALLINE METALS

An investigation of the possibility that the Barkhausen effect in amorphous and polycrystalline ferromagnets is an example of self-organized criticality is described. Since the theory of self-organized criticality was introduced by Bak, Tang, and Weisenfeld to explain the behavior of spatially extended, dissipative, dynamical systems the Barkhausen effect is a natural candidate for such a description. The data are consistent with self-organized critical behavior: the power spectral densities depend on frequency f as 1/fa and the distribution of pulse energies are well described by a power law analogous to the Gutenberg-Richter law for earthquakes. Alternative explanations for power law dependences are also presented.

A cellular-automata, slider-block model for earthquakes II. Demonstration of self-organized criticality for a 2-D system

SUMMARY It has been suggested that distributed seismicity is an example of self-organized criticality. If this is the case, the Earth’s crust in an active tectonic zone is in a near-critical state and faults can interact over large distances. Observed seismicity and earthquake statistics are consequences of the dynamical interaction of seismic faulting over a wide range of scales. We address this problem by considering a two-dimensional array of slider blocks with static/dynamic friction. The twodimensional system is treated as a cellular automaton such that only one slider block is allowed to slip at a given time and interacts only with its nearest neighbours through connecting springs. Because of this treatment, the amount of slip for each failed block can be obtained analytically, and the system is deterministic with no stochastic inputs or spatial heterogeneities. In many cases, the slip of one block induces the slip of adjacent blocks. The size of an event is specified by the number of blocks that participate in the event. The number of small events with a specified size has a power-law dependence on the size with a power close to -1.36. The distributions of normalized recurrence times for most events are close to a Poisson process, and gradually deviate towards periodicity for large events. The recurrence time statistics are generally insensitive to parameter variations. Large events may occur at stress levels considerably lower than the failure strength of an individual block, and the stress drops associated with large events are generally small. This may provide an explanation for observed low stress levels in tectonically active

Acoustic emission from volcanic rocks: An example of self-organized criticality

Experimental evidence of ultrasonic emission from volcanic rocks has been produced for the first time by a survey of the Strombolian activity. The statistical analysis of the recorded acoustic wave bursts show that the notion of self-organized criticality applies well to the mechanism responsible for the observed emission phenomenon.