Transient and stationary behavior of the Olami-Feder-Christensen earthquake model

Using long-term computer simulations and mean-field like arguments, we investigate the transient time and the properties of the stationary state of the Olami-Feder-Christensen earthquake model as function of the coupling parameter $\alpha$ and the system size $N$. The most important findings are that the transient time diverges nonanalytically when $\alpha$ approaches zero, and that the avalanche-size distribution will not approach a power law with increasing system size.Comment: 10 pages, 8 figure

Slip avalanches in a fiber bundle model

We study slip avalanches in disordered materials under an increasing external load in the framework of a fiber bundle model. Over-stressed fibers of the model do not break, instead they relax in a stick-slip event which may trigger an entire slip avalanche. Slip avalanches are characterized by the number slipping fibers, by the slip length, and by the load increment, which triggers the avalanche. Our calculations revealed that all three quantities are characterized by power law distributions with universal exponents. We show by analytical calculations and computer simulations that varying the amount of disorder of slip thresholds and the number of allowed slips of fibers, the system exhibits a disorder induced phase transition from a phase where only small avalanches are formed to another one where a macroscopic slip appears.Comment: 6 pages, 6 figure

Periodicity and criticality in the Olami-Feder-Christensen model of earthquakes

Characteristic versus critical features of earthquakes are studied on the basis of the Olami-Feder-Christensen model. It is found that the local recurrence-time distribution exhibits a sharp $\delta$-function-like peak corresponding to rhythmic recurrence of events with a fixed ``period'' uniquely determined by the transmission parameter of the model, together with a power-law-like tail corresponding to scale-free recurrence of events. The model exhibits phenomena closely resembling the asperity known in seismology

Constant angular velocity of the wrist during the lifting of a sphere.

The primary objective of the experiments was to investigate the wrist motion of a person while they were carrying out a prehensile task from a clinical hand function test. A sixcamera movement system was used to observe the wrist motion of 10 participants. A very light sphere and a heavy sphere were used in the experiments to study any mass effects. While seated at a table, a participant moved a sphere over a small obstacle using their dominant hand. The participants were observed to move their wrist at a constant angular velocity. This phenomenon has not been reported previously. Theoretically, the muscles of the wrist provide an impulse of force at the start of the rotation while the forearm maintains a constant vertical force on a sphere. Light–heavy mean differences for the velocities, absolute velocities, angles and times taken showed no significant differences (p¼0.05)

Seismic cycles, size of the largest events, and the avalanche size distribution in a model of seismicity

We address several questions on the behavior of a numerical model recently introduced to study seismic phenomena, that includes relaxation in the plates as a key ingredient. We make an analysis of the scaling of the largest events with system size, and show that when parameters are appropriately interpreted, the typical size of the largest events scale as the system size, without the necessity to tune any parameter. Secondly, we show that the temporal activity in the model is inherently non-stationary, and obtain from here justification and support for the concept of a "seismic cycle" in the temporal evolution of seismic activity. Finally, we ask for the reasons that make the model display a realistic value of the decaying exponent $b$ in the Gutenberg-Richter law for the avalanche size distribution. We explain why relaxation induces a systematic increase of $b$ from its value $b\simeq 0.4$ observed in the absence of relaxation. However, we have not been able to justify the actual robustness of the model in displaying a consistent $b$ value around the experimentally observed value $b\simeq 1$.Comment: 11 pages, 10 figure

The complex scaling behavior of non--conserved self--organized critical systems

The Olami--Feder--Christensen earthquake model is often considered the prototype dissipative self--organized critical model. It is shown that the size distribution of events in this model results from a complex interplay of several different phenomena, including limited floating--point precision. Parallels between the dynamics of synchronized regions and those of a system with periodic boundary conditions are pointed out, and the asymptotic avalanche size distribution is conjectured to be dominated by avalanches of size one, with the weight of larger avalanches converging towards zero as the system size increases.Comment: 4 pages revtex4, 5 figure

Simulation of the Burridge-Knopoff Model of Earthquakes with Variable Range Stress Transfer

Simple models of earthquake faults are important for understanding the mechanisms for their observed behavior, such as Gutenberg-Richter scaling and the relation between large and small events, which is the basis for various forecasting methods. Although cellular automaton models have been studied extensively in the long-range stress transfer limit, this limit has not been studied for the Burridge-Knopoff model, which includes more realistic friction forces and inertia. We find that the latter model with long-range stress transfer exhibits qualitatively different behavior than both the long-range cellular automaton models and the usual Burridge-Knopoff model with nearest neighbor springs, depending on the nature of the velocity-weakening friction force. This result has important implications for our understanding of earthquakes and other driven dissipative systems.Comment: 4 pages, 5 figures, published on Phys. Rev. Let

First motions from seismic sources near a free surface

The radiation patterns of first motions are calculated for the sudden occurrence of an arbitrarily oriented fault (dislocation) at the surface of a half space; the dislocation in the fault plane is also arbitrarily oriented and is assumed to occur over a very small area of the fault plane. Initially the source is considered at a finite depth and the solution is obtained by allowing the depth to tend to zero. In general the results show a surprising directionality for the radiation of SV. In the focal plane projection the first motions of P and SH for a strike-slip fault show the familiar four-lobed radiation patterns. The first motions of SV show some reversals in polarity with angular distance from the source. The first motions for all components of motion for a dip-slip fault have characteristics governed strongly by the presence of the free surface, and hence differ markedly from the usual radiation patterns for a deeply imbedded source