Simulation of crack growth during fracture of heterogeneous materials

A cellular automaton model for describing the fracture of mechanically loaded heterogeneous materials has been constructed. Two extreme scenarios of the fracture process have been revealed, i.e., the dispersion (percolation) scenario, according to which defects accumulate uniformly throughout the volume of the material, and the correlated scenario (growth of predominantly a single source), which have been observed during the fracture of real materials. It has been shown that, in the case of the correlated fracture, a crack grows through the mechanism of ejection of double kinks of its front. In the intermediate case, the process occurs according to both scenarios: first, the slow accumulating (percolation) fracture and, then, the rapid correlated fracture; by the time the latter process begins, a self-organized critical state with a power-law size distribution of cracks typical of it has been formed.     

Structure of a Deformed Inhomogeneous Material on the Data of Acoustic Emission and X-Ray Computer Microtomography

Accumulation of defects at various stages of the deformation of a structurally inhomogeneous material (granite) has been studied using two nondestructive methods: acoustic emission (AE) and X-ray computer microtomorgaphy (CT). The quasi-static testing of cylindrical samples of a Westerly granite was carried out under uniaxial compression. The control of the defect formation was realized using the real-time monitoring of acoustic emission. For each sample under study, several steps of the loading and tomographic imaging have been performed. We have found that an exponential or power-law function of the energy distribution of the AE signals makes it possible to select a sample region, in which the system of defects has transited into a self-organized criticality state and large cracks have been formed. This result coincides with the data of the X-ray tomography Computer Microtomography.     

Effect of Correlations on the Exponents for the Power-Law Distributions in Self-Organized Criticality

The origin of power-law distributions in self-organized criticality is investigated by treating the variation of the number of active sites in the system as a stochastic process. An avalanche is mapped to a first-return random-walk process in a one-dimensional lattice. In order to understand the reason of variant exponents for the power-law distributions in different self-organized critical systems, we introduce the correlations among evolution steps. Power-law distributions of the lifetime and spatial size are found when the random walk is unbiased with equal probability to move in opposite directions. It is found that the longer the correlation length, the smaller values of the exponents for the power-law distributions.     

Effect of Correlations on the Exponents for the Power-Law Distributions in Self-Organized Criticality

The origin of power-law distributions in self-organized criticality is investigated by treating the variation of the number of active sites in the system as a stochastic process. An avalanche is mapped to a first-return random-walk process in a one-dimensional lattice. In order to understand the reason of variant exponents for the power-law distributions in different self-organized critical systems, we introduce the correlations among evolution steps. Power-law distributions of the lifetime and spatial size are found when the random walk is unbiased with equal probability to move in opposite directions. It is found that the longer the correlation length, the smaller values of the exponents for the power-law distributions.     

Self-organized critical limit of autocatalytic surface reactions

We argue that the autocatalytic surface reaction 2CO+O₂→2CO₂ on Pt(110) may show self-organized critical behavior if the appropriate range of parameter values is investigated. Such a self-organized critical state is characterized by a power-law distribution of reconstructed surface regions.     

The critical properties of the agent-based model with environmental-economic interactions

The steady-state and nonequilibrium properties of the model of environmental-economic interactions are studied. The interacting heterogeneous agents are simulated on the platform of the emission dynamics of cellular automaton. The diffusive emissions are produced by the factory agents, and the local pollution is monitored by the randomly walking (mobile) sensors. When the threshold concentration is exceeded, a feedback signal is transmitted from the sensor to the nearest factory that affects its actual production rate. The model predicts the discontinuous phase transition between safe and catastrophic ecology. Right at the critical line, the broad-scale power-law distributions of emission rates have been identified. The power-law fluctuations are triggered by the screening effect of factories and by the time delay between the environment contamination and its detection. The system shows the typical signs of the self-organized critical systems, such as power-law distributions and scaling laws. The text was submitted by the authors in English.     

The critical properties of the agent-based model with environmental–economic interactions

The steady-state and nonequilibrium properties of the model of environmental–economic interactions are studied. The interacting heterogeneous agents are simulated on the platform of the emission dynamics of cellular automaton. The model possesses the discontinuous transition between the safe and catastrophic ecology. Right at the critical line, the broad-scale power-law distributions of emission rates have been identified. Their relationship to Zipf's law and models of self-organized criticality is discussed.     

Evolution of avalanche conducting states in electrorheological liquids

Charge transport in electrorheological fluids is studied experimentally under strongly nonequilibrium conditions. By injecting an electrical current into a suspension of conducting nanoparticles we are able to initiate a process of self-organization which leads, in certain cases, to formation of a stable pattern which consists of continuous conducting chains of particles. The evolution of the dissipative state in such a system is a complex process. It starts as an avalanche process characterized by nucleation, growth, and thermal destruction of such dissipative elements as continuous conducting chains of particles as well as electroconvective vortices. A power-law distribution of avalanche sizes and durations, observed at this stage of the evolution, indicates that the system is in a self-organized critical state. A sharp transition into an avalanche-free state with a stable pattern of conducting chains is observed when the power dissipated in the fluid reaches its maximum. We propose a simple evolution model which obeys the maximum power condition and also shows a power-law distribution of the avalanche sizes.     

Black swans,power laws,and dragon-kings: Earthquakes,volcanic eruptions,landslides, wildfires,floods, and SOC models

Extreme events that change global society have been characterized as black swans. The frequency-size distributions of many natural phenomena are often well approximated by power-law (fractal) distributions. An important question is whether the probability of extreme events can be estimated by extrapolating the power-law distributions. Events that exceed these extrapolations have been characterized as dragon-kings. In this paper we consider extreme events for earthquakes, volcanic eruptions, wildfires, landslides and floods. We also consider the extreme event behavior of three models that exhibit self-organized criticality (SOC): the slider-block, forest-fire, and sand-pile models. Since extrapolations using power-laws are widely used in probabilistic hazard assessment, the occurrence of dragon-king events have important practical implications.     

Avalanche dynamics of magnetic flux in a two-dimensional discrete superconductor

The critical state of a two-dimensional discrete superconductor in an external magnetic field is studied. This state is found to be self-organized in the generalized sense, i.e., is a set of metastable states that transform to each other by means of avalanches. An avalanche is characterized by the penetration of a magnetic flux to the system. The sizes of the occurring avalanches, i.e., changes in the magnetic flux, exhibit the power-law distribution. It is also shown that the size of the avalanche occurring in the critical state and the external magnetic field causing its change are statistically independent quantities.     

On Origin of Power-Law Distributions in Self-Organized Criticality from Random Walk Treatment

The origin of power-law distributions in self-organized criticality is investigated by treating the variation of the number of active sites in the system as a stochastic process. An avalanche is then regarded as a first-return random walk process in a one-dimensional lattice. We assume that the variation of the number of active sites has three possibilities in each update： to increase by 1 with probability f1, to decrease by 1 with probability f2, or remain unchanged with probability 1 - f1 - f2. This mimics the dynamics in the system. Power-law distributions of the lifetime are found when the random walk is unbiased with equal probability to move in opposite directions. This shows that power-law distributions in self-organized criticality may be caused by the balance of competitive interactions.     

Kinetic theory of strength and a self-organized critical state in the process of fracture of materials

The basic principles of the Zhurkov kinetic approach are analyzed in light of the modern idea of self-organization of nonlinear systems under nonequilibrium conditions. It is indicated that the final state before fracture can be described in terms of the model of a self-organized critical state.     

Local structural transformations in the fcc lattice in various contact interaction. Molecular dynamics study

The work is a molecular dynamics study of the peculiarities of local structural transformations in a copper crystallite at the atomic level in contact interaction of various types: shear loading of perfectly conjugate surfaces, local shear loading and nanoindentation. Interatomic interaction is described in the framework of the embedded atom method. It is shown that initial accommodation of the loaded crystallite proceeds through local structural transformations giving rise to higher-rank defects such as dislocations, stacking faults, interfaces, etc. In further plastic deformation, the structural defects propagate from the contact zone to the crystallite bulk. The egress of structural defects to a free surface causes deformation of the model crystallite. The deformation pattern can evolve, depending on the loading conditions, with a change in crystallographic orientation of the crystallite near the contact zone, generation of misoriented nano-sized regions, and eventually formation of a stable nanostructural state. The obtained results allow conceptually new understanding of the nature of defect generation in a crystalline structure during the nucleation and development of plastic deformation in loaded materials.     

Structure of the critical state in a discrete superconductor for different values of the SQUID parameter

The critical state of a 1D multijunction SQUID with intrinsic spatial randomness has been studied. It is shown that the system behavior is independent of the SQUID parameter and the critical state under consideration is self-organized.     

Direct evidence of Cd vacancies in CdSe nanoparticles: positron annihilation studies

Poly vinyl alcohol (PVA) capped CdSe nanoparticles having size in the range of 7–17 nm have been synthesized through chemical route and characterized using X-ray diffraction (XRD) and transmission electron microscopy (TEM). Positron coincidence Doppler broadening (CDB) measurements have been carried out in these nanoparticles. It is observed that the electron momentum distributions show a variation in the core electron momentum region with the particle size. In order to examine the influence of defects, first principle calculations of electron momentum distributions in bulk CdSe and in the presence of Cd as well as Se vacancy defects have been performed. Comparison of experimental data with the calculated momentum distribution reveals the presence of Cd vacancy defects, the concentration of which decreases with the increase in the particle size. The present study also indicates possible Se enrichment on the surface of the nanoparticles with the decrease in the particle size.     

Formation of different surface reliefs of metallic glasses under mechanical stress

The micro- and nanoreliefs of loaded lateral surfaces and fracture surfaces of foils of the Fe₇₇Ni₁Si₉B₁₃, Fe₅₈Ni₂₀Si₉B₁₃, and Fe₇₀Cr₁₅B₁₅ amorphous alloys have been investigated using scanning tunneling and atomic force microscopy. The isotropic and anisotropic surface reliefs have been examined. The fractal dimensions of the surfaces of loaded specimens and the fracture surfaces along and across the direction of crack propagation have been estimated using the box counting method. Fractal characteristics of the surfaces, such as the Hölder exponent and the half-width of the singularity spectrum, have been calculated using the wavelet transform method. It has been found that, on the topographies with a clearly pronounced anisotropy of the relief, the surface is fractal in only one direction, and the surface is fractal in two directions on the topographies with a less pronounced anisotropy of the relief. The fractal characteristics of the lateral surfaces and the fracture surfaces with allowance made for their anisotropy have close values. It has been shown that the formation of two types of fracture surfaces is adequately described in terms of the model of a cellular automaton.     

Blow-up Modes in Fracture of Rock Samples and Earth’s Crust Elements

It is well known that the final stage of macroscopic fracture develops as a catastrophe in a superfast blow-up mode. However, the specific features of this stage are well studied only on large scales of earthquakes. Of particular interest for fracture prediction are both the stage of superfast catastrophic fracture and the mechanical behavior of the medium in the state of self-organized criticality prior to transition of fracture to the blow-up mode in order to reveal precursors of fracture transition to the catastrophic stage. This paper studies experimentally and theoretically the mechanical behavior of the medium prior to the catastrophic stage and transition to the blow-up mode. Rock samples (marble and artificial marble) were tested in three-point bending and uniaxial compression tests. The lateral surface velocities of loaded samples were recorded using a laser Doppler vibrometer. The recording frequency in measurements was 48 kHz, and the determination accuracy of the velocity amplitude was 0.1 μm/s. The estimated duration of the blow-up fracture stage is 10–20 ms. The mechanical behavior of samples in the experimental conditions, including the catastrophic fracture stage, is simulated numerically. The damage accumulation model parameters are determined from a comparison with the experimental data. Certain features of the mechanical response prior to catastrophic fracture are revealed which can be interpreted as fracture precursors.     

Flat-head power-law, size-independent clustering, and scaling of coevolutionary scale-free networks

Scale-free topology and high clustering coexist in some real networks, and keep invariant for growing sizes of the systems. Previous models could hardly give out size-independent clustering with selforganized mechanism when succeeded in producing power-law degree distributions. Always ignored, some empirical statistic results display flat-head power-law behaviors. We modify our recent coevolutionary model to explain such phenomena with the inert property of nodes to retain small portion of unfavorable links in self-organized rewiring process. Flat-head power-law and size-independent clustering are induced as the new characteristics by this modification. In addition, a new scaling relation is found as the result of interplay between node state growth and adaptive variation of connections.     

Effects of Aging and Self-organized Criticality in a Pulse-Coupled Integrate-and-Fire Neuron Model Based on Small World Networks

Effects of aging and self-organized criticality in a pulse-coupled integrate-and-fire neuron model based on small world networks have been studied. We give the degree distribution of aging network, average shortest path length, the diameter of our network, and the clustering coefficient, and find that our neuron model displays the power-law behavior, and with the number of added links increasing, the effects of aging become smaller and smaller. This shows that if the brain works at the self-organized criticality state, it can relieve some effects caused by aging.     

脆性金属玻璃断面上的奇妙图案

文章简要介绍了脆性块体金属玻璃(简称BMG)断裂面上几种主要的图案花样:河流花样、"韧窝"结构花样和自组装条纹结构花样,并总结了目前对上述各种形貌形成机理的可能的物理解释.对BMG断裂面上形貌的研究可以揭示材料的断裂机理,有助于更深刻地理解材料的力学性能,开发高性能金属玻璃材料,并为工程选材提供安全标准.