Self-organized criticality (SOC) is a concept that explains the appearance of scale invariance and power laws without parameter tuning in slowly driven, dissipative systems. Through a series of papers, we addressed SOC-related issues in stick-slip models. It is generally accepted for stick-slip models that criticality is achieved by a marginal phase locking mechanism: Due to inhomogeneities or open boundaries, phase locking is frustrated throughout the system leading to long-range correlations in the phase and a broad range of avalanche sizes, and hence SOC.
We discovered that this mechanism is less general than thought; it does not apply to a class of multiplicatively driven models[3,4]. Instead, phase locking was found to be replaced by coarsening. Surprisingly, contrary to previous understanding boundary conditions become irrelevant. Although non-equilibrium steady state has long been regarded as necessary for the appearance of SOC, our results show that a punctuated approach to equilibrium suffices. In retrospect, there exists a host of experimental systems which have been claimed to exhibit SOC but dismissed on the ground of non-stationarity. Our study urges re-evaluations and re-interpretations of those results.
A spring-block model of earthquakes was introduced in . It incorporates more realistic force-displacement relations than in previous models, especially the well-known OFC model. To our knowledge, this is the first examination of the effects of internal stresses, vectorial forcing and nonlinear force-displacement relationship in those models. We emphasized the key role of internal stresses in the tuning of critical exponents, and pointed out certain pitfalls in the setup of previous models.
Last revised October 7, 2002 ©KtL