E.J. Ding

BURST-SIZE DISTRIBUTION IN FIBER-BUNDLES WITH LOCAL LOAD-SHARING

Abstract A critical load x c is introduced into the fiber-bundle model with local load-sharing. The critical load is defined as the average load per fiber that causes the final complete failure. It is shown that x c →0 when the size of the system N →∞. A power law for the burst-size distribution, D (Δ)σΔ -ξ , is approximately correct. The exponent ξ is not universal, since it depends on the strength distribution as well as the size of the system.

THE LYAPUNOV EXPONENT NEAR THE CRITICALITY OF TYPE-V INTERMITTENCY

Abstract With a piecewise linear map, we show both analytically and numerically that the Lyapunov exponent forms a complete devils staircase, and that its value follows a 1/In ∈ law when the driving parameter ∈ changes in the vicinity of the criticality of type V intermittency. These conclusions are in good agreement with the experimental observations in an electronic relaxation oscillator.

Universal scaling behavior in the weakly coupled map lattice

Abstract The first Lyapunov exponent for a unimodal map lattice with very weak coupling strength is calculated. The numerical results show that there is a universal scaling relation between the first Lyapunov exponent and the coupling strength, independent of the dimension of the lattice.

NUMERICAL SIMULATIONS OF BURST PROCESSES IN FIBRE BUNDLES

We discuss a very effective numerical method for simulating fibre-bundle models with equal load-sharing and with local load-sharing. Particular attention is paid to the case of the local load-sharing model, in which the critical load xc is defined as the average load per fibre that causes the final complete failure. It is shown that xc to 0 when the size of the system N to infinity . We also show analytically that the power law of the burst size distribution, D( Delta ) varies as Delta - xi , is approximately correct. The exponent xi in the local load-sharing case is not universal, since it depends on the strength distribution as well as on the size of the system.

Predictions of large events on a spring-block model

We study the predictability of a theoretical model for earthquakes, using a pattern recognition algorithm similar to the CN and M8 algorithms known in seismology. The model, which is a stochastic spring-block model with both global correlation and local interaction, becomes more predictable as the strength of the global correlation or the local interaction is increased.

The Lyapunov exponents in a periodic window for a weak-coupled map lattice

The first Lyapunov exponent in a period window for a weak-coupled map lattice is calculated. Within the windows the behaviour of the coupled map lattice could be recovered by considering a small number of modes. The depth of the windows is well defined.

Critical processes, Langevin equation and universality

Abstract In nature there are ubiquitous systems that can naturally approach critical states. The Langevin equation in the discrete version can be used to describe a class of critical processes, which are characterized by power-law behaviors and scaling relations. As an example, we present a simple model for a clinical thermometer, whose reading cannot fall even when its temperature decreases. The fibers bundle model and the spring-block model are also shown to belong to such a class.

One-dimensional sandpile model with stochastic slide

A new kind of theoretical one-dimensional sandpile model is proposed. In contrast to the models studied previously, the sliding process in this model is assumed to be of stochastic nature. Numerical simulations show that the behavior of this model is apparently closer to the reality of true sandpile than the models considered previously. The universality and scaling of this model is also discussed.

Scaling relation in the burst process of fibre bundles

The burst process in a load-carrying bundle of fibres is considered. For a bundle of finite total number of fibres, large bursts near complete failure are shown to exhibit scaling behaviour.

NOISE, ORDER, AND SPATIOTEMPORAL INTERMITTENCY

In a large array of globally coupled random bistable units, an ordered phase can appear at an intermediate noise strength. In company with the appearance of the ordered phase, super transients and spatiotemporal intermittencies can be found. The analysis based on a mean-field theory shows that the appearance of a fascinating ordered phase is caused by a phenomenon named the array enhanced tunnel crisis resulting from the nontrivial cooperative effect of the noise, the nonlinearity, and the coupling among units.