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.

Comparing Complex Fitness Surfaces: Among-Population Variation in Mutual Sexual Selection in Drosophila serrata

The problem of synchronization of metacommunities is investigated in this article with reference to a rather general model composed of a chaotic environmental compartment driving a biological compartment. Synchronization in the absence of dispersal (i.e., the so-called Moran effect) is first discussed and shown to occur only when there is no biochaos. In other words, if the biological compartment is reinforcing environmental chaos, dispersal must be strictly above a specified threshold in order to synchronize population dynamics. Moreover, this threshold can be easily determined from the model by computing a special Lyapunov exponent. The application to prey-predator metacommunities points out the influence of frequency and coherence of the environmental noise on synchronization and agrees with all experimental studies performed on the subject

Genetic Constraints and the Evolution of Display Trait Sexual Dimorphism by Natural and Sexual Selection.

The evolution of sexual dimorphism involves an interaction between sex-specific selection and a breakdown of genetic constraints that arise because the two sexes share a genome. We examined genetic constraints and the effect of sex-specific selection on a suite of sexually dimorphic display traits in Drosophila serrata. Sexual dimorphism varied among nine natural populations covering a substantial portion of the species range. Quantitative genetic analyses showed that intersexual genetic correlations were high because of autosomal genetic variance but that the inclusion of X-linked effects reduced genetic correlations substantially, indicating that sex linkage may be an important mechanism by which intersexual genetic constraints are reduced in this species. We then explored the potential for both natural and sexual selection to influence these traits, using a 12-generation laboratory experiment in which we altered the opportunities for each process as flies adapted to a novel environment. Sexual dimorphism evolved, with natural selection reducing sexual dimorphism, whereas sexual selection tended to increase it overall. To this extent, our results are consistent with the hypothesis that sexual selection favors evolutionary divergence of the sexes. However, sex-specific responses to natural and sexual selection contrasted with the classic model because sexual selection affected females rather than males

Nonlinear Network Dynamics on Earthquake Fault Systems

Earthquake faults occur in networks that have dynamical modes not displayed by single isolated faults. Using simulations of the network of strike-slip faults in southern California, we find that the physics depends critically on both the interactions among the faults, which are determined by the geometry of the fault network, as well as on the stress dissipation properties of the nonlinear frictional physics, similar to the dynamics of integrate-and-fire neural networks.Comment: 12 pages, 4 figure

Will People With Type 2 Diabetes Speak to Family Members About Health Risk?

OBJECTIVE—This study aimed to assess the potential for communication of familial risk by patients with type 2 diabetes

Avalanches in Breakdown and Fracture Processes

We investigate the breakdown of disordered networks under the action of an increasing external---mechanical or electrical---force. We perform a mean-field analysis and estimate scaling exponents for the approach to the instability. By simulating two-dimensional models of electric breakdown and fracture we observe that the breakdown is preceded by avalanche events. The avalanches can be described by scaling laws, and the estimated values of the exponents are consistent with those found in mean-field theory. The breakdown point is characterized by a discontinuity in the macroscopic properties of the material, such as conductivity or elasticity, indicative of a first order transition. The scaling laws suggest an analogy with the behavior expected in spinodal nucleation.Comment: 15 pages, 12 figures, submitted to Phys. Rev. E, corrected typo in authors name, no changes to the pape

Analytic approach to stochastic cellular automata: exponential and inverse power distributions out of Random Domino Automaton

Inspired by extremely simplified view of the earthquakes we propose the stochastic domino cellular automaton model exhibiting avalanches. From elementary combinatorial arguments we derive a set of nonlinear equations describing the automaton. Exact relations between the average parameters of the model are presented. Depending on imposed triggering, the model reproduces both exponential and inverse power statistics of clusters.Comment: improved, new material added; 9 pages, 3 figures, 2 table

Heat kernel regularization of the effective action for stochastic reaction-diffusion equations

The presence of fluctuations and non-linear interactions can lead to scale dependence in the parameters appearing in stochastic differential equations. Stochastic dynamics can be formulated in terms of functional integrals. In this paper we apply the heat kernel method to study the short distance renormalizability of a stochastic (polynomial) reaction-diffusion equation with real additive noise. We calculate the one-loop {\emph{effective action}} and its ultraviolet scale dependent divergences. We show that for white noise a polynomial reaction-diffusion equation is one-loop {\emph{finite}} in $d=0$ and $d=1$, and is one-loop renormalizable in $d=2$ and $d=3$ space dimensions. We obtain the one-loop renormalization group equations and find they run with scale only in $d=2$.Comment: 21 pages, uses ReV-TeX 3.

Fluctuations and correlations in sandpile models

We perform numerical simulations of the sandpile model for non-vanishing driving fields $h$ and dissipation rates $\epsilon$. Unlike simulations performed in the slow driving limit, the unique time scale present in our system allows us to measure unambiguously response and correlation functions. We discuss the dynamic scaling of the model and show that fluctuation-dissipation relations are not obeyed in this system.Comment: 5 pages, latex, 4 postscript figure