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.

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.

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.

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.

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.

A Framework for Non-Equilibrium Statistical Ensemble Theory

Since Gibbs synthesized a general equilibrium statistical ensemble theory, many theorists have attempted to generalized the Gibbsian theory to non-equilibrium phenomena domain, however the status of the theory of non-equilibrium phenomena can not be said as firm as well established as the Gibbsian ensemble theory. In this work, we present a framework for the non-equilibrium statistical ensemble formalism based on a subdynamic kinetic equation (SKE) rooted from the Brussels-Austin school and followed by some up-to-date works. The constructed key is to use a similarity transformation between Gibbsian ensembles formalism based on Liouville equation and the subdynamic ensemble formalism based on the SKE. Using this formalism, we study the spin-Boson system, as cases of weak coupling or strongly coupling, and obtain the reduced density operators for the Canonical ensembles easily.

Non-equilibrium statistical theory about microscopic fatigue cracks of metal in magnetic field

This paper develops the non-equilibrium statistical fatigue damage theory to study the statistical behaviour of micro-crack for metals in magnetic field. The one-dimensional homogeneous crack system is chosen for study. To investigate the effect caused by magnetic field on the statistical distribution of micro-crack in the system, the theoretical analysis on microcrack evolution equation, the average length of micro-crack, density distribution function of microcrack and fatigue fracture probability have been performed. The derived results relate the changes of some quantities, such as average length, density distribution function and fatigue fracture probability, to the applied magnetic field, the magnetic and mechanical properties of metals. It gives a theoretical explanation on the change of fatigue damage due to magnetic fields observed by experiments, and presents an analytic approach on studying the fatigue damage of metal in magnetic field.

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.

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.

A Mixed-control Mechanism Model of Proeutectoid Ferrite Growth under Non-equilibrium Interface Condition in Fe-C Alloys

By combining the α/γ interface migration and the carbon diffusion at the interface in Fe-C alloys, a mathematical model is constructed to describe the mixed-control mechanism for proeutectoid ferrite formation from austenite. In this model, the α/γ interface is treated as non-equilibrium interface, i.e., the carbon concentration of austenite at γ/α interface is obtained through theoretical calculation, instead of that assumed as the local equilibrium concentration. For isothermal precipitation of ferrite in Fe-C alloys, the calculated results show that the rate of interface migration decreases monotonically during the whole process, while the rate of carbon diffusion from γ/α interface into austenite increases to a peak value and then decreases. The process of ferrite growth may be considered as composed of three stages: the period of rapid growth, slow growth and finishing stage. The results also show that the carbon concentration of austenite at γ/α interface could not reach the thermodynamic equilibrium value even at the last stage of ferrite growth.

Statistical Constitutive Equation of Aramid Fiber Bundles

Tensile impact tests of aramid (Twaron) fiber bundles were carried out under high strain rates with a wide range of 0. 01/s -1 000/s by using MTS and bar-bar tensile impact apparatus. Based on the statistical constitutive model of fiber bundles, statistical constitutive equations of aramid fiber bundles are derived from statistical analysis of test data at different strain rates. Comparison between the theoretical predictions and experimental data indicates statistical constitutive equations fit well with the experimental data, and statistical constitutive equations of fiber bundles at different strain rates are valid.