Formation of Space-Time Structure in a Forest-Fire Model

We present a general stochastic forest-fire model which shows a variety of different structures depending on the parameter values. The model contains three possible states per site (tree, burning tree, empty site) and three parameters (tree growth probability $p$, lightning probability $f$, and immunity $g$). We review analytic and computer simulation results for a quasideterministic state with spiral-shaped fire fronts, for a percolation-like phase transition and a self-organized critical state. Possible applications to excitable systems are discussed.Comment: 20 pages REVTEX, 9 figures upon reques

Different hierarchy of avalanches observed in the Bak-Sneppen evolution model

We introduce a new quantity, average fitness, into the Bak-Sneppen evolution model. Through the new quantity, a different hierarchy of avalanches is observed. The gap equation, in terms of the average fitness, is presented to describe the self-organization of the model. It is found that the critical value of the average fitness can be exactly obtained. Based on the simulations, two critical exponents, avalanche distribution and avalanche dimension, of the new avalanches are given.Comment: 5 pages, 3 figure

Exact equqations and scaling relations for f-avalanche in the Bak-Sneppen evolution model

Infinite hierarchy of exact equations are derived for the newly-observed f-avalanche in the Bak-Sneppen evolution model. By solving the first order exact equation, we found that the critical exponent which governs the divergence of the average avalanche size, is exactly 1 (for all dimensions), confirmed by the simulations. Solution of the gap equation yields another universal exponent, denoting the the relaxation to the attractor, is exactly 1. We also establish some scaling relations among the critical exponents of the new avalanche.Comment: 5 pages, 1 figur

Exact Results for the One-Dimensional Self-Organized Critical Forest-Fire Model

We present the analytic solution of the self-organized critical (SOC) forest-fire model in one dimension proving SOC in systems without conservation laws by analytic means. Under the condition that the system is in the steady state and very close to the critical point, we calculate the probability that a string of $n$ neighboring sites is occupied by a given configuration of trees. The critical exponent describing the size distribution of forest clusters is exactly $\tau = 2$ and does not change under certain changes of the model rules. Computer simulations confirm the analytic results.Comment: 12 pages REVTEX, 2 figures upon request, dro/93/

Replicating financial market dynamics with a simple self-organized critical lattice model

We explore a simple lattice field model intended to describe statistical properties of high frequency financial markets. The model is relevant in the cross-disciplinary area of econophysics. Its signature feature is the emergence of a self-organized critical state. This implies scale invariance of the model, without tuning parameters. Prominent results of our simulation are time series of gains, prices, volatility, and gains frequency distributions, which all compare favorably to features of historical market data. Applying a standard GARCH(1,1) fit to the lattice model gives results that are almost indistinguishable from historical NASDAQ data.Comment: 20 pages, 33 figure

Crossover from Percolation to Self-Organized Criticality

We include immunity against fire as a new parameter into the self-organized critical forest-fire model. When the immunity assumes a critical value, clusters of burnt trees are identical to percolation clusters of random bond percolation. As long as the immunity is below its critical value, the asymptotic critical exponents are those of the original self-organized critical model, i.e. the system performs a crossover from percolation to self-organized criticality. We present a scaling theory and computer simulation results.Comment: 4 pages Revtex, two figures included, to be published in PR

Celebrating the Physics in Geophysics

As 2005, the International Year of Physics, comes to an end, two physicists working primarily in geophysical research reflect on how geophysics is not an applied physics. Although geophysics has certainly benefited from progress in physics and sometimes emulated the reductionist program of mainstream physics, it has also educated the physics community about some of the generic behaviors of strongly nonlinear systems. Dramatic examples are the insights we have gained into the ``emergent'' phenomena of chaos, cascading instabilities, turbulence, self-organization, fractal structure, power-law variability, anomalous scaling, threshold dynamics, creep, fracture, and so on. In all of these examples, relatively simple models have been able to explain the recurring features of apparently very complex signals and fields. It appears that the future of the intricate relation between physics and geophysics will be as exciting as its past has been characterized by a mutual fascination. Physics departments in our universities should capitalize on this trend to attract and retain young talent motivated to address problems that really matter for the future of the planet. A pressing topic with huge impact on populations and that is challenging enough for both physics and geophysics communities to work together like never before is the understanding and prediction of extreme events.Comment: 6 pages, final version to appear in EOS-AGU Transactions in November 200

Stochastic modeling of Congress

We analyze the dynamics of growth of the number of congressmen supporting the resolution HR1207 to audit the Federal Reserve. The plot of the total number of co-sponsors as a function of time is of "Devil's staircase" type. The distribution of the numbers of new co-sponsors joining during a particular day (step height) follows a power law. The distribution of the length of intervals between additions of new co-sponsors (step length) also follows a power law. We use a modification of Bak-Tang-Wiesenfeld sandpile model to simulate the dynamics of Congress and obtain a good agreement with the data

Word Processors with Line-Wrap: Cascading, Self-Organized Criticality, Random Walks, Diffusion, Predictability

We examine the line-wrap feature of text processors and show that adding characters to previously formatted lines leads to the cascading of words to subsequent lines and forms a state of self-organized criticality. We show the connection to one-dimensional random walks and diffusion problems, and we examine the predictability of catastrophic cascades.Comment: 6 pages, LaTeX with RevTeX package, 4 postscript figures appende

Randmoness and Step-like Distribution of Pile Heights in Avalanche Models

The paper develops one-parametric family of the sand-piles dealing with the grains' local losses on the fixed amount. The family exhibits the crossover between the models with deterministic and stochastic relaxation. The mean height of the pile is destined to describe the crossover. The height's densities corresponding to the models with relaxation of the both types tend one to another as the parameter increases. These densities follow a step-like behaviour in contrast to the peaked shape found in the models with the local loss of the grains down to the fixed level [S. Lubeck, Phys. Rev. E, 62, 6149, (2000)]. A spectral approach based on the long-run properties of the pile height considers the models with deterministic and random relaxation more accurately and distinguishes the both cases up to admissible parameter values.Comment: 5 pages, 5 figure