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

Tension on JAM-A activates RhoA via GEF-H1 and p115 RhoGEF

Junctional adhesion molecule A (JAM-A) is a broadly expressed adhesion molecule that regulates cell–cell contacts and facilitates leukocyte transendothelial migration. The latter occurs through interactions with the integrin LFA-1. Although we understand much about JAM-A, little is known regarding the protein’s role in mechanotransduction or as a modulator of RhoA signaling. We found that tension imposed on JAM-A activates RhoA, which leads to increased cell stiffness. Activation of RhoA in this system depends on PI3K-mediated activation of GEF-H1 and p115 RhoGEF. These two GEFs are further regulated by FAK/ERK and Src family kinases, respectively. Finally, we show that phosphorylation of JAM-A at Ser-284 is required for RhoA activation in response to tension. These data demonstrate a direct role of JAM-A in mechanosignaling and control of RhoA and implicate Src family kinases in the regulation of p115 RhoGEF

Near mean-field behavior in the generalized Burridge-Knopoff earthquake model with variable range stress transfer

Simple models of earthquake faults are important for understanding the mechanisms for their observed behavior in nature, such as Gutenberg-Richter scaling. Because of the importance of long-range interactions in an elastic medium, we generalize the Burridge-Knopoff slider-block model to include variable range stress transfer. We find that the Burridge-Knopoff model with long-range stress transfer exhibits qualitatively different behavior than the corresponding long-range cellular automata models and the usual Burridge-Knopoff model with nearest-neighbor stress transfer, depending on how quickly the friction force weakens with increasing velocity. Extensive simulations of quasiperiodic characteristic events, mode-switching phenomena, ergodicity, and waiting-time distributions are also discussed. Our results are consistent with the existence of a mean-field critical point and have important implications for our understanding of earthquakes and other driven dissipative systems.Comment: 24 pages 12 figures, revised version for Phys. Rev.

Missing physics in stick-slip dynamics of a model for peeling of an adhesive tape

It is now known that the equations of motion for the contact point during peeling of an adhesive tape mounted on a roll introduced earlier are singular and do not support dynamical jumps across the two stable branches of the peel force function. By including the kinetic energy of the tape in the Lagrangian, we derive equations of motion that support stick-slip jumps as a natural consequence of the inherent dynamics. In the low mass limit, these equations reproduce solutions obtained using a differential-algebraic algorithm introduced for the earlier equations. Our analysis also shows that mass of the ribbon has a strong influence on the nature of the dynamics.Comment: Accepted for publication in Phys. Rev. E (Rapid Communication

Rain, power laws, and advection

Localized rain events have been found to follow power-law size and duration distributions over several decades, suggesting parallels between precipitation and seismic activity [O. Peters et al., PRL 88, 018701 (2002)]. Similar power laws are generated by treating rain as a passive tracer undergoing advection in a velocity field generated by a two-dimensional system of point vortices.Comment: 7 pages, 4 figure

Space-Time Clustering and Correlations of Major Earthquakes

Earthquake occurrence in nature is thought to result from correlated elastic stresses, leading to clustering in space and time. We show that occurrence of major earthquakes in California correlates with time intervals when fluctuations in small earthquakes are suppressed relative to the long term average. We estimate a probability of less than 1% that this coincidence is due to random clustering.Comment: 5 pages, 3 figures. Submitted to PR

A Cellular Automaton Model of Damage

We investigate the role of equilibrium methods and stress transfer range in describing the process of damage. We find that equilibrium approaches are not applicable to the description of damage and the catastrophic failure mechanism if the stress transfer is short ranged. In the long range limit, equilibrium methods apply only if the healing mechanism associated with ruptured elements is instantaneous. Furthermore we find that the nature of the catastrophic failure depends strongly on the stress transfer range. Long range transfer systems have a failure mechanism that resembles nucleation. In short range stress transfer systems, the catastrophic failure is a continuous process that, in some respects, resembles a critical point.Comment: 11 pages, 11 figures (2 in color). Various corrections as recommended by referees. This is the final version for publication in Phys. Rev.

Self-Similarity of Friction Laws

The change of the friction law from a mesoscopic level to a macroscopic level is studied in the spring-block models introduced by Burridge-Knopoff. We find that the Coulomb law is always scale invariant. Other proposed scaling laws are only invariant under certain conditions.}Comment: Plain TEX. Figures not include

Transition from synchronous to asynchronous superfluid phase slippage in an aperture array

We have investigated the dynamics of superfluid phase slippage in an array of apertures. The magnitude of the dissipative phase slips shows that they occur simultaneously in all the apertures when the temperature is around 10 mK below the superfluid transition, and subsequently lose their simultaneity as the temperature is lowered. We find that when periodic synchronous phase slippage occurs, the synchronicity exists from the very first phase slip, and therefore is not due to mode locking of interacting oscillators. When the system is allowed to relax freely from a given initial energy, the total number of phase slips that occur and the energy left in the system after the last phase slip depends reproducibly on the initial energy. We find the energy remaining after the final phase slip is a periodic function of the initial system energy. This dependence directly reveals the discrete and dissipative nature of the phase slips and is a powerful diagnostic for investigation of synchronicity in the array. When the array slips synchronously, this periodic energy function is a sharp sawtooth. As the temperature is lowered and the degree of synchronicity drops, the peak of this sawtooth becomes rounded, suggesting a broadening of the time interval over which the array slips. The underlying mechanism for the higher temperature synchronous behavior and the following loss of synchronicity at lower temperatures is not yet understood. We discuss the implications of our measurements and pose several questions that need to be resolved by a theory explaining the synchronous behavior in this quantum system. An understanding of the array phase slip process is essential to the optimization of superfluid `dc-SQUID' gyroscopes and interferometers.Comment: 10 pages, 4 figure