Biomedical subjects

J B Rundle

Publications and source records attributed to J B Rundle.

7 recordsLinked to original sources

PubMed2005

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. These results have important implications for our understanding of earthquakes and other driven dissipative systems.

Algorithms↗

PubMed2005

A simulation-based approach to forecasting the next great San Francisco earthquake.

In 1906 the great San Francisco earthquake and fire destroyed much of the city. As we approach the 100-year anniversary of that event, a critical concern is the hazard posed by another such earthquake. In this article, we examine the assumptions presently used to compute the probability of occurrence of these earthquakes. We also present the results of a numerical simulation of interacting faults on the San Andreas system. Called Virtual California, this simulation can be used to compute the times, locations, and magnitudes of simulated earthquakes on the San Andreas fault in the vicinity of San Francisco. Of particular importance are results for the statistical distribution of recurrence times between great earthquakes, results that are difficult or impossible to obtain from a purely field-based approach.

Disasters↗

PubMed2003

Ergodic dynamics in a natural threshold system.

Numerical simulations suggest that certain driven, dissipative mean-field threshold systems, including earthquake models, can be characterized by statistical properties often associated with ergodic dynamics, in the same sense as stochastic Brownian motion. We applied a fluctuation metric proposed by Thirumalai and Mountain [Phys. Rev. E 47, 479 (1993)]] for statistically stationary systems and find that the natural earthquake fault system in California demonstrates similar ergodic dynamics.

Computer Simulation↗

PubMed2002

Precursory dynamics in threshold systems.

A precursory dynamics, motivated by the analysis of recent experiments on solid-on-solid friction, is introduced in a continuous cellular automaton that mimics the physics of earthquake source processes. The resulting system of equations for the interevent cycle can be decoupled and yields an analytical solution in the mean-field limit, exhibiting a smoothing effect of the dynamics on the stress field. Simulation results show the resulting departure from scaling at the large-event end of the frequency distribution, and support claims that the field leakage may parametrize the superposition of scaling and characteristic regimes observed in real earthquake faults.

Journal Article↗

PubMed2002

Self-organization in leaky threshold systems: the influence of near-mean field dynamics and its implications for earthquakes, neurobiology, and forecasting.

Threshold systems are known to be some of the most important nonlinear self-organizing systems in nature, including networks of earthquake faults, neural networks, superconductors and semiconductors, and the World Wide Web, as well as political, social, and ecological systems. All of these systems have dynamics that are strongly correlated in space and time, and all typically display a multiplicity of spatial and temporal scales. Here we discuss the physics of self-organization in earthquake threshold systems at two distinct scales: (i) The "microscopic" laboratory scale, in which consideration of results from simulations leads to dynamical equations that can be used to derive the results obtained from sliding friction experiments, and (ii) the "macroscopic" earthquake fault-system scale, in which the physics of strongly correlated earthquake fault systems can be understood by using time-dependent state vectors defined in a Hilbert space of eigenstates, similar in many respects to the mathematics of quantum mechanics. In all of these systems, long-range interactions induce the existence of locally ergodic dynamics. The existence of dissipative effects leads to the appearance of a "leaky threshold" dynamics, equivalent to a new scaling field that controls the size of nucleation events relative to the size of background fluctuations. At the macroscopic earthquake fault-system scale, these ideas show considerable promise as a means of forecasting future earthquake activity.

Animals↗

PubMed2001

Nonlinear network dynamics on earthquake fault systems.

Earthquake faults occur in interacting networks having emergent space-time modes of behavior not displayed by isolated faults. Using simulations of the major faults in southern California, we find that the physics depends on the elastic interactions among the faults defined by network topology, as well as on the nonlinear physics of stress dissipation arising from friction on the faults. Our results have broad applications to other leaky threshold systems such as integrate-and-fire neural networks.

Journal Article↗

PubMed1999

Spinodals, scaling, and ergodicity in a threshold model with long-range stress transfer.

We present both theoretical and numerical analyses of a cellular automaton version of a slider-block model or threshold model that includes long-range interactions. Theoretically we develop a coarse-grained description in the mean-field (infinite range) limit and discuss the relevance of the metastable state, limit of stability (spinodal), and nucleation to the phenomenology of the model. We also simulate the model and confirm the relevance of the theory for systems with long- but finite-range interactions. Results of particular interest include the existence of Gutenberg-Richter-like scaling consistent with that found on real earthquake fault systems, the association of large events with nucleation near the spinodal, and the result that such systems can be described, in the mean-field limit, with techniques appropriate to systems in equilibrium.

Journal Article↗