Origin of the universal roughness exponent of brittle fracture surfaces:stress-weighted percolation in the damage zone

We suggest that the observed large-scale universal roughness of brittle fracture surfaces is due to the fracture propagation being a damage coalescence process described by a stress-weighted percolation phenomenon in a self-generated quadratic damage gradient. We use the quasistatic 2D fuse model as a paradigm of a mode I fracture model. We measure for this model, which exhibits a correlated percolation process, the correlation length exponent nu approximately 1.35 and conjecture it to be equal to that of classical percolation, 4/3. We then show that the roughness exponent in the 2D fuse model is zeta=2nu/(1+2nu)=8/11. This is in accordance with the numerical value zeta=0.75. Using the value for 3D percolation, nu=0.88, we predict the roughness exponent in the 3D fuse model to be zeta=0.64, in close agreement with the previously published value of 0.62+/-0.05. We furthermore predict zeta=4/5 for 3D brittle fractures, based on a recent calculation giving nu=2. This is in full accordance with the value zeta=0.80 found experimentally.     

Nonextensive statistical analysis of the data on the high-speed impact fracture of solids

The high-speed detection of impact-induced cracks in samples of materials that differ strongly in their degree of homogeneity (fused quartz and granite) has been performed by the acoustic emission method. The experimental energy distributions of the acoustic emission signals that correspond to the energy distribution in the events of the nucleation, growth, and coalescence of the microcracks have been interpreted in terms of the Tsallis statistics, which has been developed to generalize classical thermodynamics over the case of nonequilibrium systems. This allowed us to estimate the degree of correlation in the process of crack formation and to compare the energy release densities in various materials and at various stages of the impact fracture.     

Experimental and numerical analysis of the high-speed deformation and erosion damage of the titanium alloy VT-6

The temporal characteristics of the dynamic fracture of the titanium alloy VT-6 have been investigated under high-speed loading conditions. A relationship has been established between the process of dynamic tension of the specimen according to the Kolsky method and the surface erosion damage. A numerical analysis of the experimental data has been carried out. The method of erosion loading has been further developed as a tool for the dynamic testing of strength properties of materials.     

延性材料动态拉伸断裂早期连通过程的逾渗描述

 借鉴逾渗理论,提出了新的应力松弛函数,简称PR函数（Percolation-Release Function）,用以描述断裂发生前由于微孔洞连通而引起的快速应力松弛过程,具有较为明确的物理意义。通过其与损伤度函数模型进行耦合,对无氧铜和45钢平板撞击层裂进行了数值模拟。结果表明：数值计算不仅有效地再现了界面的应力历史和自由面速度历史,而且再现了靶中的损伤分布;新的逾渗松弛函数具有较好的适用性。     

Study of the magnetic microstructure of Ni/NiO nanogranular samples above the electric percolation threshold by magnetoresistance measurements

Magnetoresistance measurements have been exploited to gain information on the magnetic microstructure of two Ni/NiO nanogranular materials consisting of Ni nanocrystallites (mean size of the order of 10 nm) embedded in a NiO matrix and differing in the amount of metallic Ni, ~33 and ~61 vol%. The overall conductance of both samples is metallic in character, indicating that the Ni content is above the percolation threshold for electric conductivity; the electric resistivity is two orders of magnitude smaller in the sample with higher Ni fraction (10(-5) Ωm against 10(-3) Ωm). An isotropic, spin-dependent magnetoresistance has been measured in the sample with lower Ni content, whereas both isotropic and anisotropic magnetoresistance phenomena coexist in the other material. This study, associated with magnetization loop measurements and the comparison with the exchange bias effect, allows one to conclude that in the sample with lower Ni content neither the physical percolation of the Ni nanocrystallites nor the magnetic percolation (i.e., formation of a homogeneous ferromagnetic network) are achieved; in the other sample physical percolation is reached while magnetic percolation is still absent. In both behaviors, a key role is played by the NiO matrix, which brings about a magnetic nanocrystallite/matrix interface exchange energy term and rules both the direct exchange interaction among Ni nanocrystallites and the magnetotransport properties of these nanogranular materials.     

Tricritical point in heterogeneous k-core percolation

k-core percolation is an extension of the concept of classical percolation and is particularly relevant to understanding the resilience of complex networks under random damage. A new analytical formalism has been recently proposed to deal with heterogeneous k-cores, where each vertex is assigned a local threshold k(i). In this Letter we identify a binary mixture of heterogeneous k-cores which exhibits a tricritical point. We investigate the new scaling scenario and calculate the relevant critical exponents, by analytical and computational methods, for Erd?s-Rényi networks and 2D square lattices.     

Broadband dielectric spectroscopy of inhomogeneous and composite weak conductors

ABSTRACT

In this paper, we discuss broadband dielectric spectroscopy from mHz up to the infrared range mainly for materials with inhomogeneous weak conductivity, including conductor-dielectric nanocomposites. Our discussion is based on the effective medium approximation (EMA) and experiments modeled by this approach are reviewed. We discuss core–shell composites modeled by coated-spheres (Hashin–Shtrikman model) and normal composites with a possible percolation of the conductor component resulting in sharp or smeared percolation threshold of the DC conductivity and diverging static permittivity in the former case. The sharp percolation threshold is modeled by the Bruggeman EMA or by general EMA with arbitrary percolation threshold and arbitrary critical exponents of the DC conductivity and static permittivity. For the case of smeared percolation threshold in the case of complex topologies, we use the Lichtenecker model allowing for partial percolation of both the components. Finally, numerous papers reporting negative permittivity in weakly conducting materials are criticized and concluded to be due to spurious effects.     

The origins of dragon-kings and their occurrence in society

A society is a medium with a complex structure of one-to-one relations between people. Those could be relations between friends, wife–husband relationships, relations between business partners, and so on. At a certain level of analysis, a society can be regarded as a gigantic maze constituted of one-to-one relationships between people. From a physical standpoint it can be considered as a highly porous medium. Such media are widely known for their outstanding properties and effects like self-organized criticality, percolation, power-law distribution of network cluster sizes, etc. In these media supercritical events, referred to as dragon-kings, may occur in two cases: when increasing stress is applied to a system (self-organized criticality scenario) or when increasing conductivity of a system is observed (percolation scenario). In social applications the first scenario is typical for negative effects: crises, wars, revolutions, financial breakdowns, state collapses, etc. The second scenario is more typical for positive effects like emergence of cities, growth of firms, population blow-ups, economic miracles, technology diffusion, social network formation, etc. If both conditions (increasing stress and increasing conductivity) are observed together, then absolutely miraculous dragon-king effects can occur that involve most human society. Historical examples of this effect are the emergence of the Mongol Empire, world religions, World War II, and the explosive proliferation of global internet services. This article describes these two scenarios in detail beginning with an overview of historical dragon-king events and phenomena starting from the early human history till the last decades and concluding with an analysis of their possible near future consequences on our global society. Thus we demonstrate that in social systems dragon-king is not a random outlier unexplainable by power-law statistics, but a natural effect. It is a very large cluster in a porous percolation medium. It occurs as a result of changes in external conditions, such as supercritical load, increase in system elements’ sensitivity, or system connectivity growth.     

工程陶瓷崩碎损伤的声发射逾渗特征

为研究工程陶瓷崩碎损伤演化过程中的逾渗行为,揭示其损伤机理,以氧化铝陶瓷为研究对象,构建了工程陶瓷崩碎损伤实验系统,建立了基于声发射的逾渗理论模型。通过对崩碎损伤过程中声发射信号分析可得:声发射计数率/能量释放率能实时反映陶瓷崩碎损伤过程中裂纹激活率的逾渗行为;基于声发射累积计数/累积能量的破坏比率反映了损伤累积对材料内部性能的影响,可从损伤积累的角度描述陶瓷崩碎损伤过程中的逾渗行为;声发射持续时间反映了陶瓷崩碎过程中逾渗行为的团簇变化规律。研究结果表明:基于声发射的逾渗理论模型可较好的描述陶瓷崩碎损伤演化过程的逾渗特征。      

First-Passage Percolation, Semi-Directed Bernoulli Percolation, and Failure in Brittle Materials

We present a two-dimensional, quasistatic model of fracture in disordered brittle materials that contains elements of first-passage percolation, i.e., we use a minimum-energy-consumption criterion for the fracture path. The first-passage model is employed in conjunction with a semi-directed Bernoulli percolation model, for which we calculate critical properties such as the correlation length exponent v ^sdir and the percolation threshold p _c ^sdir . Among other results, our numerics suggest that v ^sdir is exactly 3/2, which lies between the corresponding known values in the literature for usual and directed Bernoulli percolation. We also find that the well-known scaling relation between the wandering and energy fluctuation exponents breaks down in the vicinity of the threshold for semi-directed percolation. For a restricted class of materials, we study the dependence of the fracture energy (toughness) on the width of the distribution of the specific fracture energy and find that it is quadratic in the width for small widths for two different random fields, suggesting that this dependence may be universal.     

Chaotic sources and percolation of strings in heavy ion collisions

The chaoticity parameter of Bose–Einstein correlations is studied as a tool for analyzing the interaction between color strings in multiparticle production at high energies. Different scenarios of this interaction lead to a different behavior of with energy and atomic number of the participants. Comparison to the present experimental data favors the percolation of strings scenario. The one of its versions in which shows a peculiar dependence on the string density, very similar to the dependence of the fractional average cluster size, looks particularly attractive. Received: 19 February 2001 / Revised version: 5 July 2001 / Published online: 10 August 2001     

Two Different Bifurcation Scenarios in Neural Firing Rhythms Discovered in Biological Experiments by Adjusting Two Parameters

Two different bifurcation scenarios, one is novel and the other is relatively simpler, in the transition procedures of neural firing patterns are studied in biological experiments on a neural pacemaker by adjusting two parameters. The experimental observations are simulated with a relevant theoretical model neuron. The deterministic non-periodic firing pattern lying within the novel bifurcation scenario is suggested to be a new case of chaos, which has not been observed in previous neurodynamical experiments.     

Percolation thresholds of a group of anisotropic three-dimensional fracture networks

Percolation thresholds (average number of connections per object) of two models of anisotropic three-dimensional (3D) fracture networks made of mono-disperse hexagons have been calculated numerically. The first model is when the fracture networks are comprised of two groups of fractures that are distributed in an anisotropic manner about two orthogonal mean directions, i.e., Z- and X-directions. We call this model bipolar anisotropic fracture network (BFN). The second model is when three groups of fractures are distributed about three orthogonal mean directions, that is Z-, X-, and Y-directions. In this model three families of fractures about three orthogonal mean directions are oriented in 3D space. We call this model tripolar anisotropic fracture network (TFN). The finite-size scaling method is used to predict the infinite percolation thresholds. The effect of anisotropicity on percolation thresholds in X-, Y-, and Z-directions is investigated. We have revealed that as the anisotropicity of networks increases, the percolation thresholds in X-, Y-, and Z-directions span the range of 2.3 to 2.0, where 2.3 and 2.0 are extremums of percolation thresholds for isotropic and non-isotropic orthogonal fracture networks, respectively.     

Channeling and percolation in two-dimensional chaotic dynamics

The Hamiltonian dynamics of a particle moving in a nearly periodic two-dimensional (2-D) potential of square symmetry is analyzed. The particle undergoes two types of unbounded stochastic or random walks in such a system: a quasi-1-D motion (a "stochastic channeling") and a 2-D motion which results from a sort of stochastic percolation. A scenario for the onset of this stochastic percolation is analyzed. The threshold energy for percolation is found as a function of the perturbation parameter. Each type of random walk has the property of intermittency. The particle transport is anomalous in certain energy intervals.     

Current challenges for statistical physics in fracture and plasticity

Statistical physics has been applied in the last decades to several problems in mechanics, including fracture and plasticity. Concept drawn from percolation, fractal geometry, phase-transitions, and interface depinning have been used with varying degrees of success to understand these problems. In this colloquium, I describe recent successes and current challenging problems for statistical physics in fracture and plasticity, focusing on the roughness of cracks, fracture size effects and micron-scale plasticity.     

Two—phase flow in correlated pore—throat random porous media

We have constructed a porous media model in which there are percolation clusters with varying percolation probability P and correlated site-bonds. Taking into account both the pore and the throat geometry, the viscous fingering (VF) in porous media has been investigated by using the standard over-relaxed Gauss-Seidel scheme. The simulation results show that the VF structure varies with the correlation parameter ε, the viscosity ratio M and the percolation probability P. The smaller the correlation parameter ε, the greater the deviation of the normalized size distribution of the invaded throat N_inv(r) from the truncated Rayleigh distribution. For a larger viscosity ratio M, the VF pattern looks like a diffusion-limited-aggregation structure in percolation clusters. The fractal dimension D increases with the increase of the percolation probability P and the correlation parameter ε. The velocity distribution f(α) of VF in percolation clusters is of a parabola-like curve. The tail of the distribution (large α) is longer for a larger correlation parameter ε. For a smaller ε, the distribution is very sharp. The sweep efficiency E decreases along with the decrease of the correlation parameter ε and the increase of the network size L_nz. E has a minimum as L_nz increases up to the maximum no matter what the values of P, M and ε. The E～ L_nz curve has a frozen zone and an active zone. The geometry and the topology of the porous media have strong effects on the displacement processes and the structure of VF.     

Explaining DAMPE results by dark matter with hierarchical lepton-specific Yukawa interactions

We propose to interpret the DAMPE electron excess at 1.5 Te V through scalar or Dirac fermion dark matter(DM) annihilation with doubly charged scalar mediators that have lepton-specific Yukawa couplings. The hierarchy of such lepton-specific Yukawa couplings is generated through the Froggatt-Nielsen mechanism, so that the dark matter annihilation products can be dominantly electrons. Stringent constraints from LEP2 on intermediate vector boson production can be evaded in our scenarios. In the case of scalar DM, we discuss one scenario with DM annihilating directly to leptons and another scenario with DM annihilating to scalar mediators followed by their decays. We also discuss the Breit-Wigner resonant enhancement and the Sommerfeld enhancement in the case where the s-wave annihilation process is small or helicity-suppressed. With both types of enhancement, constraints on the parameters can be relaxed and new ways for model building can be opened in explaining the DAMPE results.     

Scaling behaviour in the fracture of fibrous materials

We study the existence of distinct failure regimes in a model for fracture in fibrous materials. We simulate a bundle of parallel fibers under uniaxial static load and observe two different failure regimes: a catastrophic and a slowly shredding. In the catastrophic regime the initial deformation produces a crack which percolates through the bundle. In the slowly shredding regime the initial deformations will produce small cracks which gradually weaken the bundle. The boundary between the catastrophic and the shredding regimes is studied by means of percolation theory and of finite-size scaling theory. In this boundary, the percolation density scales with the system size L, which implies the existence of a second-order phase transition with the same critical exponents as those of usual percolation. Received 24 June 1999     

The Effects of Tachyonic and Phantom Fields in the Intermediate and Logamediate Scenarios of the Anisotropic Universe

In this work, we have analyzed two scenarios namely, “intermediate” and “logamadiate” scenarios for closed, open and flat anisotropic universe in presence of phantom field, normal tachyonic field and phantom tachyonic field. We have assumed that there is no interaction between the above mentioned dark energy and dark matter. In these two types of the scenarios of the Universe, the nature of the scalar fields and corresponding potentials have been investigated. In intermediate scenario, (i) the potential for normal tachyonic field decreases, (ii) the potentials for phantom tachyonic field and phantom field increase with the corresponding fields. Also in logamediate scenario, (i) the potential for normal tachyonic field increases, (ii) the potentials for phantom tachyonic field and phantom field decrease with the corresponding fields.     

Finite-size scaling in extreme statistics

We study the deviations from the limit distributions in extreme value statistics arising due to the finite size (FS) of data sets. A renormalization method is introduced for the case of independent, identically distributed (iid) variables, showing that the iid universality classes are subdivided according to the exponent of the FS convergence, which determines the leading order FS shape correction function as well. It is found that, for the correlated systems of subcritical percolation and 1/f;(alpha) stationary (alpha<1) noise, the iid shape correction compares favorably to simulations. Furthermore, for the strongly correlated regime (alpha>1) of 1/f;(alpha) noise, the shape correction is obtained in terms of the limit distribution itself.