We study the failure properties of fiber bundles with a finite lower cutoff of the strength disorder varying the range of interaction between the limiting cases of completely global and completely local load sharing. Computer simulations revealed that at any range of load redistribution there exists a critical cutoff strength where the macroscopic response of the bundle becomes perfectly brittle, i.e. linearly elastic behavior is obtained up to global failure, which occurs catastrophically after the breaking of a small number of fibers. As an extension of recent mean field studies [Phys. Rev. Lett. 95, 125501 (2005)], we demonstrate that approaching the critical cutoff, the size distribution of bursts of breaking fibers shows a crossover to a universal power law form with an exponent 3/2 independent of the range of interaction.PACS numbers: 46.50.+a, 62.20.Mk, 81.40.Np In engineering constructions solids are subjected to various types of external loads and typically fail when the load exceeds a critical value. Monitoring stressed systems and forecasting an imminent failure event is of enormous importance due to the possible material and human costs. In spite of the large amount of experimental and theoretical efforts that has been undertaken over the past decades, there is no comprehensive understanding of failure phenomena, which is also reflected by the absence of reliable prediction methods. Materials of low disorder typically fail in a "one-crack" way, where the main problem is to prevent crack initiation and propagation. However, the failure of highly disordered materials proceeds in bursts of local breaking events which can be recorded in form of acoustic signals. Experiments on a large variety of materials have revealed that in crackle noise spectra accompanying quasi-static fracture of disordered materials, the amplitude and duration of signals and the waiting time between them are characterized by power law distributions over a broad range [1,2,3]. Quantitative changes of the burst activity when approaching the critical load could be precursors of catastrophic failure and may serve as the basis for forecasting techniques.In the framework of discrete models of the fracture of disordered materials, bursts can be identified as trails of correlated breakings of the microscopic constituents of the model. Fiber bundle models consist of a parallel bundle of fibers with identical linearly elastic behavior and randomly distributed breaking thresholds [4,5,6]. Under an increasing external load, each fiber breaking is followed by a load redistribution over the remaining intact fibers, which may trigger avalanches of correlated breaking events analogous to crackling noise in experiments. Assuming global load sharing (GLS), it has been * Electronic address:raischel@ica1.uni-stuttgart.de shown that the distribution of avalanche sizes has a universal power law behavior with an exponent 5/2 [7]. In the other extreme of local load sharing (LLS), redistributing the load solely over the closest neighborhood of fibers,...

During the last decade, lattice-Boltzmann (LB) simulations have been improved to become an efficient tool for determining the permeability of porous media samples. However, well known improvements of the original algorithm are often not implemented. These include for example multirelaxation time schemes or improved boundary conditions, as well as different possibilities to impose a pressure gradient. This paper shows that a significant difference of the calculated permeabilities can be found unless one uses a carefully selected setup. We present a detailed discussion of possible simulation setups and quantitative studies of the influence of simulation parameters. We illustrate our results by applying the algorithm to a Fontainebleau sandstone and by comparing our benchmark studies to other numerical permeability measurements in the literature.

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We apply recent methods in stochastic data analysis for discovering a set of few stochastic variables that represent the relevant information on a multivariate stochastic system, used as input for artificial neural networks models for air quality forecast. We show that using these derived variables as input variables for training the neural networks it is possible to significantly reduce the amount of input variables necessary for the neural network model, without considerably changing the predictive power of the model. The reduced set of variables including these derived variables is therefore proposed as optimal variable set for training neural networks models in forecasting geophysical and weather properties. Finally, we briefly discuss other possible applications of such optimized neural network models.

We present an extension of fiber bundle models considering that failed fibers still carry a fraction 0 < or = alpha < or = 1 of their failure load. The value of alpha interpolates between the perfectly brittle failure (alpha = 0) and perfectly plastic behavior (alpha = 1) of fibers. We show that the finite load bearing capacity of broken fibers has a substantial effect on the failure process of the bundle. In the case of global load sharing it is found that for alpha --> 1 the macroscopic response of the bundle becomes perfectly plastic with a yield stress equal to the average fiber strength. On the microlevel, the size distribution of avalanches has a crossover from a power law of exponent approximately 2.5 to a faster exponential decay. For localized load sharing, computer simulations revealed a sharp transition at a well-defined value alpha(c) from a phase where macroscopic failure occurs due to localization as a consequence of local stress enhancements, to another one where the disordered fiber strength dominates the damage process. Analyzing the microstructure of damage, the transition proved to be analogous to percolation. At the critical point alpha(c), the spanning cluster of damage is found to be compact with a fractal boundary. The distribution of bursts of fiber breakings shows a power-law behavior with a universal exponent approximately 1.5 equal to the mean-field exponent of fiber bundles of critical strength distributions. The model can be relevant to understand the shear failure of glued interfaces where failed regions can still transmit load by remaining in contact.