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[1]. 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[2]: 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[5]. Our study urges re-evaluations and re-interpretations of those results.
A spring-block model of earthquakes was introduced in [6]. It incorporates more realistic force-displacement relations than in previous models, especially the well-known OFC model[7]. 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[7].
Last revised October 7, 2002 ©KtL