Positive Feedback, Memory and the Predictability of Earthquakes

We review the "critical point" concept for large earthquakes and enlarge it in the framework of so-called "finite-time singularities". The singular behavior associated with accelerated seismic release is shown to result from a positive feedback of the seismic activity on its release rate. The most important mechanisms for such positive feedback are presented. We introduce and solve analytically a novel simple model of geometrical positive feedback in which the stress shadow cast by the last large earthquake is progressively fragmented by the increasing tectonic stress. Finally, we present a somewhat speculative figure that tends to support a mechanism based on the decay of stress shadows. This figure suggests that a large earthquake in Southern California of size similar to the 1812 great event is maturing.Comment: PostScript document of 18 pages + 2 eps figure

Modeling singular mineralization processes due to fluid pressure fluctuations

Mineralization in the Earth's crust can be regarded as a singular process resulting in large amounts of mass accumulation and element enrichment over short time or space scales. The elemental concentrations modeled by fractals and multifractals show self-similarity and scale-invariant properties. We take the view that fluid-pressure variations in response to earthquakes or fault rupture are primarily responsible for changes in solubility and trigger transient physical and chemical variations in ore-forming fluids that enhance the mineralization process. Based on this general concept, we investigated mineral precipitation processes driven by rapid fluid pressure reductions by coupling mineralization to a cellular automaton model to reveal the nonlinear mechanism of the orogenic gold mineralization process using simulation. In the model, fluid pressure can increase to the rock failure condition, which was set as lithostatic pressure at a depth of 10 km (270 MPa), due to either porosity reduction or dehydration reactions. Rapid drops in pressure resulting from fault rupture or local hydrofracture may induce repeated gold precipitation. The geochemical patterns generated by the model evolve from depletion to enrichment patterns, and from spatially random to spatially clustered structures quantified by multifractal models and geostatistics. Results show how metal elements self-organize to form high metal concentration patterns displaying self-similarity and scale-invariance. These transitions are attributed to the growth and coalescence of sub-networks with different fluid pressures up to the percolation threshold, resulting in a wide range of fluid pressure reductions and gold precipitation in the form of clusters. The results suggest that cyclic evolution of fluid pressure and its effects on gold precipitation systems can effectively mimic the repeated mineralization superposition process, and generate complex geochemical patterns characterized by a multifractal model. The nonlinear behavior exhibits scale-invariance and self-organized critical threshold, where mineral phase separations result from fluid pressure reductions associated with fault failure

Rupture by damage accumulation in rocks

The deformation of rocks is associated with microcracks nucleation and propagation, i.e. damage. The accumulation of damage and its spatial localization lead to the creation of a macroscale discontinuity, so-called "fault" in geological terms, and to the failure of the material, i.e. a dramatic decrease of the mechanical properties as strength and modulus. The damage process can be studied both statically by direct observation of thin sections and dynamically by recording acoustic waves emitted by crack propagation (acoustic emission). Here we first review such observations concerning geological objects over scales ranging from the laboratory sample scale (dm) to seismically active faults (km), including cliffs and rock masses (Dm, hm). These observations reveal complex patterns in both space (fractal properties of damage structures as roughness and gouge), time (clustering, particular trends when the failure approaches) and energy domains (power-law distributions of energy release bursts). We use a numerical model based on progressive damage within an elastic interaction framework which allows us to simulate these observations. This study shows that the failure in rocks can be the result of damage accumulation

Development of a formalism of discrete element method to study mechanical response of geological materials and media at different scales

A general approach to realization of models of elasticity, plasticity and fracture of heterogeneous materials within the framework of particle-based discrete element method is proposed in the paper. The approach is based on constructing many-body forces of particle interaction, which provide response of particle ensemble correctly conforming to the response (including elastic-plastic behavior and fracture) of simulated solids. For correct modeling of inelastic deformation and failure of geological materials and media at "high" structural scales (relative to the scale of grains) an implementation of dilatational Nikolaevsky's model of plasticity of rocks within the framework of mathematical formalism of discrete element method is proposed. Perspectives of multiscale modeling of geological materials from grainrelated scale up to macroscopic scale within the same numerical technique (DEM) are discussed

Probabilistic approach for analysis of strength of ceramics with different porous structure based on movable cellular automaton modeling

Movable cellular automaton method which is a computational method of particle mechanics is applied to simulating uniaxial compression of 3D porous ceramic specimens. Pores were considered explicitly by removing automata selected randomly from the original fcc packing. Distribution of pores in space, their size and the total fraction were varied. For each values of porosity there were generated several represented specimens with individual pore position in space. The resulting values of elastic modulus and strength of the specimens were scattered and well described by the Weibull distribution. We showed that to reveal dependence of the elastic and strength properties on porosity it is much better to consider not average of the values for the specimens of the same porosity, but the mathematical expectation of the corresponding Weibull distribution. It is shown that relation between mechanical properties of the material and its porosity depends significantly on pore structure. Namely, percolation transition from closed porosity to interconnected pores strongly manifests itself on strength dependence on porosity. Thus, the curve of strength versus porosity fits different equations for different kind of pore structure. Composite ceramics which pores are filled by plastic filler shows the similar behavior

Cellular Automaton for Realistic Modelling of Landslides

A numerical model is developed for the simulation of debris flow in landslides over a complex three dimensional topography. The model is based on a lattice, in which debris can be transferred among nearest neighbors according to established empirical relationships for granular flows. The model is then validated by comparing a simulation with reported field data. Our model is in fact a realistic elaboration of simpler ``sandpile automata'', which have in recent years been studied as supposedly paradigmatic of ``self-organized criticality''. Statistics and scaling properties of the simulation are examined, and show that the model has an intermittent behavior.Comment: Revised version (gramatical and writing style cleanup mainly). Accepted for publication by Nonlinear Processes in Geophysics. 16 pages, 98Kb uuencoded compressed dvi file (that's the way life is easiest). Big (6Mb) postscript figures available upon request from [email protected] / [email protected]

Decentralized and adaptive sensor data routing

Wireless sensor network (WSN) has been attracting research efforts due to the rapidly increasing applications in military and civilian fields. An important issue in wireless sensor network is how to send information in an efficient and adaptive way. Information can be directly sent back to the base station or through a sequence of intermediate nodes. In the later case, it becomes the problem of routing. Current routing protocols can be categorized into two groups, namely table-drive (proactive) routing protocols and source-initiated on-demand (reactive) routing. For ad hoc wireless sensor network, routing protocols must deal with some unique constraints such as energy conservation, low bandwidth, high error rate and unpredictable topology, of which wired network might not possess. Thus, a routing protocol, which is energy efficient, self-adaptive and error tolerant is highly demanded. A new peer to peer (P2P) routing notion based on the theory of cellular automata has been put forward to solve this problem. We proposed two different models, namely Spin Glass (Physics) inspired model and Multi-fractal (Chemistry) inspired model. Our new routing models are distributed in computation and self-adaptive to topological disturbance. All these merits can not only save significant amount of communication and computation cost but also well adapt to the highly volatile environment of ad hoc WSN. With the cellular automata Cantor modeling tool, we implemented two dynamic link libraries (DLL) in C++ and the corresponding graphic display procedures in Tcl/tk. Results of each model’s routing ability are discussed and hopefully it will lead to new peer to peer algorithms, which can combine the advantages of current models

Review of Methods to Solve Desiccation Cracks in Clayey Soils

This paper reviews numerical methods used to simulate desiccation cracks in clayey soils. It examines five numerical approaches: Finite Element (FEM), Lattice Boltzmann (LBM), Discrete Element (DEM), Cellular Automaton (CAM), and Phase Field (PFM) Methods. The paper presents a simplified description of the methods, including their basic numerical formulations. Several factors such as the multiphase nature of soils, heterogeneity, nonlinearities, coupling, scales of analysis, and computational aspects are discussed. The review highlights the characteristics, strengths, and limitations of each method. FEM shows a good capacity to deal with the thermo-hydromechanical behavior of clays when drying that complement well with the ability of DEM to deal with particle interactions as well as LBM, PFM, and CAM to deal with complex crack patterns. The article concludes by reviewing the integration of multiple numerical methods to enhance the simulation of desiccation cracks in clayey soils and proposing what is the best option to continue improving the study of this problem

Application of symbiotic cellular automaton method to describe the contrast media

The method of symbiotic cellular automaton, which combines two approaches to describe the simulated media – the method of conventional cellular automaton and method of movable cellular automaton, has been developed for modeling and study of heterogeneous materials. Verification of the method has been carried out by comparing the simulation results of sorption of carbon dioxide in the lignite with experimental data. Possibilities of the method are exemplified by results of numerical study of the influence of the gas phase on strength and fracture of the lignite specimens

Development of a formalism of movable cellular automaton method for numerical modeling of fracture of heterogeneous elastic-plastic materials

A general approach to realization of models of elasticity, plasticity and fracture of heterogeneousmaterials within the framework of particle-based numerical methods is proposed in the paper. It is based onbuilding many-body forces of particle interaction, which provide response of particle ensemble correctlyconforming to the response (including elastic-plastic behavior and fracture) of simulated solids. Implementationof proposed approach within particle-based methods is demonstrated by the example of the movable cellularautomaton (MCA) method, which integrates the possibilities of particle-based discrete element method (DEM)and cellular automaton methods. Emergent advantages of the developed approach to formulation of manybodyinteraction are discussed. Main of them are its applicability to various realizations of the concept ofdiscrete elements and a possibility to realize various rheological models (including elastic-plastic or visco-elasticplastic)and models of fracture to study deformation and fracture of solid-phase materials and media.Capabilities of particle-based modeling of heterogeneous solids are demonstrated by the problem of simulationof deformation and fracture of particle-reinforced metal-ceramic composites