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We study the local load sharing fiber bundle model and its energy burst statistics. While it is known that the avalanche size distribution of the model is exponential, we numerically show here that the avalanche size ($s$) and the corresponding energy burst ($E$) in this version of the model have a non-linear relation ($Esim s^{gamma}$). Numerical results indicate that $gammaapprox 2.5$ universally for different failure threshold distributions. With this numerical observation, it is then possible to show that the energy burst distribution is a power law, with a universal exponent value of $-(gamma+1)$.
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Mapping a complex network to an atomic cluster, the Anderson localization theory is used to obtain the load distribution on a complex network. Based upon an intelligence-limited model we consider the load distribution and the congestion and cascade failures due to attacks and occasional damages. It is found that the eigenvector centrality (EC) is an effective measure to find key nodes for traffic flow processes. The influence of structure of a WS small-world network is investigated in detail.
Statistical models are essential to get a better understanding of the role of disorder in brittle disordered solids. Fiber bundle models play a special role as a paradigm, with a very good balance of simplicity and non-trivial effects. We introduce here a variant of the fiber bundle model where the load is transferred among the fibers through a very compliant membrane. This Soft Membrane fiber bundle mode reduces to the classical Local Load Sharing fiber bundle model in 1D. Highlighting the continuum limit of the model allows to compute an equivalent toughness for the fiber bundle and hence discuss nucleation of a critical defect. The computation of the toughness allows for drawing a simple connection with crack front propagation (depinning) models.
We investigate the size scaling of the macroscopic fracture strength of heterogeneous materials when microscopic disorder is controlled by fat-tailed distributions. We consider a fiber bundle model where the strength of single fibers is described by a power law distribution over a finite range. Tuning the amount of disorder by varying the power law exponent and the upper cutoff of fibers strength, in the limit of equal load sharing an astonishing size effect is revealed: For small system sizes the bundle strength increases with the number of fibers and the usual decreasing size effect of heterogeneous materials is only restored beyond a characteristic size. We show analytically that the extreme order statistics of fibers strength is responsible for this peculiar behavior. Analyzing the results of computer simulations we deduce a scaling form which describes the dependence of the macroscopic strength of fiber bundles on the parameters of microscopic disorder over the entire range of system sizes.
We generalize the recent study of random space-filling bearings to a more realistic situation, where the spacing offset varies randomly during the space-filling procedure, and show that it reproduces well the size-distributions observed in recent studies of real fault gouges. In particular, we show that the fractal dimensions of random polydisperse bearings sweep predominantly the low range of values in the spectrum of fractal dimensions observed along real faults, which strengthen the evidence that polydisperse bearings may explain the occurrence of seismic gaps in nature. In addition, the influence of different distributions for the offset is studied and we find that the uniform distribution is the best choice for reproducing the size-distribution of fault gouges.
In a recent publication [Phys. Rev. Lett. 97, 227402 (2006), cond-mat/0611411], it has been demonstrated numerically that a long-range disorder potential in semiconductor quantum wells can be reconstructed reliably via single-photon interferometry of spontaneously emitted light. In the present paper, a simplified analytical model of independent two-level systems is presented in order to study the reconstruction procedure in more detail. With the help of this model, the measured photon correlations can be calculated analytically and the influence of parameters such as the disorder length scale, the wavelength of the used light, or the spotsize can be investigated systematically. Furthermore, the relation between the proposed angle-resolved single-photon correlations and the disorder potential can be understood and the measured signal is expected to be closely related to the characteristic strength and length scale of the disorder.
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