Failure evolution and disaster prediction of rock under uniaxial compression based on non-extensive statistical analysis of electric potential

Rock failure can cause serious geological disasters,and the non-extensive statistical features of electric potential(EP)are expected to provide valuable information for disaster prediction.In this paper,the uniaxial compression experiments with EP monitoring were carried out on fine sandstone,marble and granite samples under four displacement rates.The Tsallis entropy q value of EPs is used to analyze the selforganization evolution of rock failure.Then the influence of displacement rate and rock type on q value are explored by mineral structure and fracture modes.A self-organized critical prediction method with q value is proposed.The results show that the probability density function(PDF)of EPs follows the q-Gaussian distribution.The displacement rate is positively correlated with q value.With the displacement rate increasing,the fracture mode changes,the damage degree intensifies,and the microcrack network becomes denser.The influence of rock type on q value is related to the burst intensity of energy release and the crack fracture mode.The q value of EPs can be used as an effective prediction index for rock failure like b value of acoustic emission(AE).The results provide useful reference and method for the monitoring and early warning of geological disasters.

Damage statistical mechanics model of top coal in steep top caving coal

Damage statistical mechanics model of horizontal section height in the top caving was constructed in the paper. The influence factors including supporting pressure, dip angle and characteristic of coal on horizontal section height were analyzed as well. By terms of the practice project analysis, the horizontal section height increases with the increase of dip angle β and thickness of coal seam M. Dip angle of coal seam β has tremendous impact on horizontal section height, while thickness of coal seam M has slight impact. When thickness of coal seam is below 10m, horizontal section height increases sharply. While thickness exceeds 15m, it is not major factor influencing on horizontal section height any long.

Statistical properties of ideal photons in a two-dimensional dye-filled spherical cap cavity

Within the framework of quantum statistical mechanics,we have proposed an exact analytical solution to the problemof Bose-Einstein condensation(BEC)of harmonically trapped two-dimensional(2D)ideal photons.We utilize this analyticalsolution to investigate the statistical properties of ideal photons in a 2D dye-filled spherical cap cavity.The resultsof numerical calculation of the analytical solution agree completely with the foregoing experimental results in the BEC ofharmonically trapped 2D ideal photons.The analytical expressions of the critical temperature and the condensate fractionare derived in the thermodynamic limit.It is found that the 2D critical photon number is larger than the one-dimensional(1D)critical photon number by two orders of magnitude.The spectral radiance of a 2D spherical cap cavity has a sharppeak at the frequency of the cavity cutoff when the photon number exceeds the critical value determined by a temperature.

CLOSED TRANS-SCALE STATISTICAL MICRODAMAGE MECHANICS

Damage and failure due to distributed microcracks or microvoids are on the challenging frontiers of solid mechanics. This appeals strongly to tools not yet fully developed in continuum damage mechanics, in particular to irreversible statistical thermodynamics and a unified macroscopic equations of mechanics and kinetic equations of microstructural transformations. This review provides the state of the art in statistical microdamage mechanics. (1) It clarifies on what level of approximation continuum damage mechanics works. Particularly,D-level approximation with dynamic function of damage appears to be a proper closed trans-scale formulation of the problem. (2) It provides physical foundation of evolution law in damage mechanics. Essentially, the damage-dependent feature of the macroscopic evolution law is due to the movement of microdamage front, resulting from microdamage growth. (3) It is found that intrinsic Deborah numberD *, a ratio of nucleation rate over growth rate of microdamage, is a proper indication of critical damage in damage mechanics, based on the idea of damage localization. (4) It clearly distinguishes the non-equilibrium damage evolution from equilibrium phase transition, like percolation.

Advances in statistical mechanics of rock masses and its engineering applications

To efficiently link the continuum mechanics for rocks with the structural statistics of rock masses,a theoretical and methodological system called the statistical mechanics of rock masses(SMRM)was developed in the past three decades.In SMRM,equivalent continuum models of stressestrain relationship,strength and failure probability for jointed rock masses were established,which were based on the geometric probability models characterising the rock mass structure.This follows the statistical physics,the continuum mechanics,the fracture mechanics and the weakest link hypothesis.A general constitutive model and complete stressestrain models under compressive and shear conditions were also developed as the derivatives of the SMRM theory.An SMRM calculation system was then developed to provide fast and precise solutions for parameter estimations of rock masses,such as full-direction rock quality designation(RQD),elastic modulus,Coulomb compressive strength,rock mass quality rating,and Poisson’s ratio and shear strength.The constitutive equations involved in SMRM were integrated into a FLAC3D based numerical module to apply for engineering rock masses.It is also capable of analysing the complete deformation of rock masses and active reinforcement of engineering rock masses.Examples of engineering applications of SMRM were presented,including a rock mass at QBT hydropower station in northwestern China,a dam slope of Zongo II hydropower station in D.R.Congo,an open-pit mine in Dexing,China,an underground powerhouse of Jinping I hydropower station in southwestern China,and a typical circular tunnel in Lanzhou-Chongqing railway,China.These applications verified the reliability of the SMRM and demonstrated its applicability to broad engineering issues associated with jointed rock masses.

Non-extensive statistical distributions of charmed meson production in Pb-Pb and pp(p)collisions

The mid-rapidity transverse momentum spectra of charmed mesons in Pb–Pb and pp(p)collisions are analyzed using the Tsallis–Pareto distribution derived from non-extensive statistics.We provide uniform descriptions of both small and large systems over a wide range of collision energies and hadron transverse momenta.By establishing the relationship between the event multiplicity and Tsallis parameters,we observe that there is a signifi-cant linear relationship between the thermal temperature and Tsallis q parameter in Pb–Pb collisions at √sNN=2.76 TeV and 5.02 TeV.Further,the slope of the T–(q-1)parameter plot is positively correlated with the hadron mass.In addition,charmed mesons have a higher thermal temperature than light hadrons at the same q-1,indicat-ing that the charm flavor requires a higher temperature to reach the same degree of non-extensivity as light flavors in heavy-ion collisions.The same fit is applied to the trans-verse momentum spectra of charmed mesons in pp(p)collisions over a large energy range using the Tsallis–Pareto distribution.It is found that the thermal temperature increases with system energy,whereas the q parameter becomes saturated at the pp(p)limit,q-1=0.142±0.010.In addition,the results of most peripheral Pb–Pb collisions are found to approach the pp(p)limit,which suggests that more peripheral heavy-ion collisions are less affected by the medium and more similar to pp(p)collisions.

STATISTICAL MECHANICS MODEL OF LIQUID BINARY ALLOY AND ITS PARAMETERS

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Statistical Mechanics Model of Liquid Binary Ailoy

From the view of chemical short range order and uncomplete random mixing existing in liquid binary al-loy, absorbing the rational part of past statistical mechanics model. a statistical mechanics model of liquidbinary alloy is proposed in this paper. According to the model, the expressions of component activity are obtained.

Wave Mechanics or Wave Statistical Mechanics

By comparison between equations of motion of geometrical optics and that of classical statistical mechanics, this paper finds that there should be an analogy between geometrical optics and classical statistical mechanics instead of geometrical mechanics and classical mechanics. Furthermore, by comparison between the classical limit of quantum mechanics and classical statistical mechanics, it finds that classical limit of quantum mechanics is classical statistical mechanics not classical mechanics, hence it demonstrates that quantum mechanics is a natural generalization of classical statistical mechanics instead of classical mechanics. Thence quantum mechanics in its true appearance is a wave statistical mechanics instead of a wave mechanics.

A statistical mechanics model of carbon nanotube macro-films

Carbon nanotube macro-films are two-dimensional films with micrometer thickness and centimeter by centimeter in-plane dimension.These carbon nanotube macroscopic assemblies have attracted significant attention from the material and mechanics communities recently because they can be easily handled and tailored to meet specific engineering needs.This paper reports the experimental methods on the preparation and characterization of single-walled carbon nanotube macro-films,and a statistical mechanics model on the deformation behavior of this material.This model provides a capability to optimize the synthesis process by comparing with the experiments.

Statistical Mechanics for Weak Measurements and Quantum Inseparability

In weak measurement thought experiment, an ensemble consists of M quantum particles and N states. We observe that separability of the particles is lost, and hence we have fuzzy occupation numbers for the particles in the ensemble. Without sharply measuring each particle state, quantum interferences add extra possible configurations of the ensemble, this explains the Quantum Pigeonhole Principle. This principle adds more entropy to the system;hence the particles seem to have a new kind of correlations emergent from particles not having a single, well-defined state. We formulated the Quantum Pigeonhole Principle in the language of abstract Hilbert spaces, then generalized it to systems consisting of mixed states. This insight into the fundamentals of quantum statistical mechanics could help us understand the interpretation of quantum mechanics more deeply, and possibly have implication on quantum computing and information theory.

Calculation of Vapour Pressure of Metals by Statistical-Mechanical Method With the Debye Model

Statistical expression of vapour pressure equations of metals is derived from the Debye model.The statistical distribution of T_(-p) ensemble is presented in an in-elab- orate mode and the partition function is defined.The vapour pressure of eleven metals have been calculated with the Debye equation and compared with those given by the E- instein equation and empirical equation.Comparison of results of calculation from dif- ferent methods show their evident accordance within the same orders of magnitude.

Variational quantum simulation of thermal statistical states on a superconducting quantum processer

Quantum computers promise to solve finite-temperature properties of quantum many-body systems,which is generally challenging for classical computers due to high computational complexities.Here,we report experimental preparations of Gibbs states and excited states of Heisenberg X X and X X Z models by using a 5-qubit programmable superconducting processor.In the experiments,we apply a hybrid quantum–classical algorithm to generate finite temperature states with classical probability models and variational quantum circuits.We reveal that the Hamiltonians can be fully diagonalized with optimized quantum circuits,which enable us to prepare excited states at arbitrary energy density.We demonstrate that the approach has a self-verifying feature and can estimate fundamental thermal observables with a small statistical error.Based on numerical results,we further show that the time complexity of our approach scales polynomially in the number of qubits,revealing its potential in solving large-scale problems.

Some Concepts on Statistical Models of Relating Mechanical Properties to Chemical Composition

Following the basic principle of modem multivariate statistical analysis theory, the description model, prediction model and control model to relate chemical compositions and mechanical properties of steels are introduced. As an example, the total flowchart of components and structure/properties description, prediction and control model for chemical composition and mechanical properties of 20 and A_2 steel are presented.

Statistical-mechanical analysis of multiuser channel capacity with imperfect channel state information

In this paper, the effect of imperfect channel state information at the receiver, which is caused by noise and other interference, on the multi-access channel capacity is analysed through a statistical-mechanical approach. Replica analyses focus on analytically studying how the minimum mean square error （MMSE） channel estimation error appears in a multiuser channel capacity formula. And the relevant mathematical expressions are derived. At the same time, numerical simulation results are demonstrated to validate the Replica analyses. The simulation results show how the system parameters, such as channel estimation error, system load and signal-to-noise ratio, affect the channel capacity.

Dynamic thermo-mechanical coupled simulation of statistically inhomogeneous materials by statistical second-order two-scale method

In this paper,a statistical second-order twoscale（SSOTS） method is developed to simulate the dynamic thcrmo-mechanical performances of the statistically inhomogeneous materials.For this kind of composite material,the random distribution characteristics of particles,including the shape,size,orientation,spatial location,and volume fractions,are all considered.Firstly,the repre.sentation for the microscopic configuration of the statistically inhomogeneous materials is described.Secondly,the SSOTS formulation for the dynamic thermo-mechanical coupled problem is proposed in a constructive way,including the cell problems,effective thermal and mechanical parameters,homogenized problems,and the SSOTS formulas of the temperatures,displacements,heat flux densities and stresses.And then the algorithm procedure corresponding to the SSOTS method is brought forward.The numerical results obtained by using the SSOTS algorithm are compared with those by classical methods.In addition,the thermo-mechanical coupling effect is studied by comparing the results of coupled case with those of uncoupled case.It demonstrates that the coupling effect on the temperatures,heat flux densities,displacements,and stresses is very distinct.The results show that the SSOTS method is valid to predict the dynamic thermo-mechanical coupled performances of statistically inhomogeneous materials.

Dynamic thermo-mechanical coupled response of random particulate composites:A statistical two-scale method

This paper focuses on the dynamic thermo-mechanical coupled response of random particulate composite materials. Both the inertia term and coupling term are considered in the dynamic coupled problem. The formulation of the problem by a statistical second-order two-scale （SSOTS） analysis method and the algorithm procedure based on the finite-element difference method are presented. Numerical results of coupled cases are compared with those of uncoupled cases. It shows that the coupling effects on temperature, thermal flux, displacement, and stresses are very distinct, and the micro- characteristics of particles affect the coupling effect of the random composites. Furthermore, the coupling effect causes a lag in the variations of temperature, thermal flux, displacement, and stresses.

Decomposition mechanisms of nuclear-grade cationic exchange resin by advanced oxidation processes:Statistical molecular fragmentation model and DFT calculations

The treatment and disposal of radioactive waste are presently facing great challenges.Spent ion exchange resins have become a focus of attention due to their high production and serious environmental risks.In this paper,a simplified model of cationic exchange resin is proposed,and the degradation processes of cationic resin monomer initiated by hydroxyl radicals(·OH)are clarified by combining statistical molecular fragmentation(SMF)model and density functional theory(DFT)calculations.The prediction of active sites indicates that the S-O bonds and the C-S bond of the sulfonic group are more likely to react during the degradation.The meta-position of the sulfonic group on the benzene ring is the most active site,and the benzene ring without the sulfonic group has a certain reactivity.The C11-C14 and C17-C20 bonds,on the carbon skeleton,are the most easily broken.It is also found that dihydroxy addition and elimination reactions play a major role in the process of desulfonation,carbon skeleton cleavage and benzene ring separation.The decomposition mechanisms found through the combination of physical models and chemical calculations,provide theoretical guidance for the treatment of complex polycyclic aromatic hydrocarbons.

Application of artificial intelligence to rock mechanics:An overview

Different artificial intelligence(AI)methods have been applied to various aspects of rock mechanics,but the fact that none of these methods have been used as a standard implies that doubt as to their generality and validity still exists.For this,a literature review of application of AI to the field of rock mechanics is presented.Comprehensive studies of the researches published in the top journals relative to the fields of rock mechanics,computer applications in engineering,and the textbooks were conducted.The performances of the AI methods that have been used in rock mechanics applications were evaluated.The literature review shows that AI methods have successfully been used to solve various problems in the rock mechanics field and they performed better than the traditional empirical,mathematical or statistical methods.However,their practical applicability is still an issue of concern as many of the existing AI models require some level of expertise before they can be used,because they are not in the form of tractable mathematical equations.Thus some advanced AI methods are still yet to be explored.The limited availability of dataset for the AI simulations is also identified as a major problem.The solutions to the identified problems and the possible future research focus were proposed in the study subsequently.

Statistical analysis of aggregation in freeway traffic

We restudy the master-equation approach to aggregation in freeway traffic based on the theory of birth-death process, in which the clustering behaviour in one-lane freeway traffic model is investigated. The transition probabilities for the jump processes are reconstructed by using Greenshields＇ model, and the equation of the mean size of the cluster at any time t is derived from the birth^death equation. Numerical experiments show the clustering behaviours varying with time very well.