A damage model based on failure threshold weakening

A variety of studies have modeled the physics of material deformation and damage as examples of generalized phase transitions, involving either critical phenomena or spinodal nucleation. Here we study a model for frictional sliding with long range interactions and recurrent damage that is parameterized by a process of damage and partial healing during sliding. We introduce a failure threshold weakening parameter into the cellular-automaton slider-block model which allows blocks to fail at a reduced failure threshold for all subsequent failures during an event. We show that a critical point is reached beyond which the probability of a system-wide event scales with this weakening parameter. We provide a mapping to the percolation transition, and show that the values of the scaling exponents approach the values for mean-field percolation (spinodal nucleation) as lattice size $L$ is increased for fixed $R$. We also examine the effect of the weakening parameter on the frequency-magnitude scaling relationship and the ergodic behavior of the model

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.

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

Structure of neodymium sulfate octahydrate

The problems of X-ray crystal structure determination require some type of automatic computing machinery. An evaluation of these problems has lead to the conclusions that a parallel channel relay digital computer operating in conjunction with the standard I. B. M. units will meet the calculation needs of a structure determination and greatly shorten the time and labor involved. A brief description of a relay computer designed to meet these needs has been given. The computer will be able to perform all of the calculations required with the exception of the Patterson and electron density calculations. The latter may be carried out efficiently on standard I. B. M. units

Earthquake forecasting and its verification

No proven method is currently available for the reliable short time prediction of earthquakes (minutes to months). However, it is possible to make probabilistic hazard assessments for earthquake risk. These are primarily based on the association of small earthquakes with future large earthquakes. In this paper we discuss a new approach to earthquake forecasting. This approach is based on a pattern informatics (PI) method which quantifies temporal variations in seismicity. The output is a map of areas in a seismogenic region (``hotspots'') where earthquakes are forecast to occur in a future 10-year time span. This approach has been successfully applied to California, to Japan, and on a worldwide basis. These forecasts are binary--an earthquake is forecast either to occur or to not occur. The standard approach to the evaluation of a binary forecast is the use of the relative operating characteristic (ROC) diagram, which is a more restrictive test and less subject to bias than maximum likelihood tests. To test our PI method, we made two types of retrospective forecasts for California. The first is the PI method and the second is a relative intensity (RI) forecast based on the hypothesis that future earthquakes will occur where earthquakes have occurred in the recent past. While both retrospective forecasts are for the ten year period 1 January 2000 to 31 December 2009, we performed an interim analysis 5 years into the forecast. The PI method out performs the RI method under most circumstances.Comment: 10(+1) pages, 5 figures, 2 tables. Submitted to Nonlinearl Processes in Geophysics on 5 August 200

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

Crystal structure and magnetic properties of LiCuCl3-2H2O

Interest in the study of the effect of cation size upon the configuration assumed by a complex anion led to the determination of the crystal structure of LiCuCl3 • 2H2O. A unique (Cu2Cl6)= dimer ion was discovered in the structure that was determined by conventional X-ray diffraction techniques. These dimer ions are linked together into a zigzag chain by means of long Cu-Cl bonds between the dimers. The chains in any given unit cell of the crystal are related to each other by a two-fold screw axis. Each dimer has two water molecules associated with it through long Cu-O interactions, giving a distorted octahedral array about each copper ion. There are two additional water molecules per dimer ion which are lattice waters and which, along with one of the other oxygens and a chlorine ion, form a tetrahedral hole in which the lithium ion is probably located