Nonequilibrium Statistical Theory of Fracture

Nonequilibrium statistical theory of fracture is a theory of fracture that macromechanical quantities can be derived from the microscopic atomic mechanism of microcrack(or microvoid)evolution kinetcs by means of nonequilibrium statistical physical concepts and methods. The microcrack evolution equation is the central equation in the theory.The coefficents of the equation, the microcrack growth rate and the microcrack nucleation rate,come from microscopic atomic mechanism.The solution of the equation connects with macromechanical quantities by the model of the weakest chain. All the other formulas and quantities, for instance, distribution function,fracture probability, reliability, failure rate and macromechanical quantities such as strength, toughness, life etc. and their statistical distribution function and statistical fluctuation are derived in a unified fashion and expressed by a few physical parameters. This theory can be widely applied to various kinds of fracture, such as the brittle, fatigue, delayed and environmental fracture of metals and structural ceramics. The theoretical framework of this theory is given in this paper.

Correlation of ^1H NMR Chemical Shift for Aqueous Solutions by Statistical Associating Fluid Theory Association Model

1H NMR chemical shifts of binary aqueous mixtures of acylamide, alcohol, dimethyl sulphoxide (DMSO), and acetone are correlated by statistical associating fluid theory (SAFT) association model. The comparison between SAPT association model and Wilson equation shows that the former is better for dealing with aqueous solutions. Finally, the specialties of both models are discussed.

Construction of a Comprehensive Soundscape Evaluation System in Forest Parks Based on Grey Statistical Theory

Based on collection and arrangement of evaluation indicators of soundscape in a forest park,24 primary evaluation indicators are chosen by grey statistical theory.The results show that there are 5 main factors influencing soundscape in a forest park,including water soundscape,wind soundscape,animal soundscape,recreation soundscape,and artificial soundscape,which contain 13 evaluation indicators.Among these factors,natural sound elements account for 84.6%.Thus a comprehensive evaluation indicator system of soundscape(including natural and unnatural soundscape) in a forest park is constructed by the selected evaluation indicators,and it is expected to provide a reference for scientific and systematic construction and development of forest parks in future.

Statistical Theory of Turbulence by the Late Lamented Dr. Shunichi TsugéCase Study on Flow through a Grid in Wind Tunnel

This paper is concerned with statistical theory of turbulence by the late lamented Dr. Shunichi Tsugé.? The theory has been applied to the primary flow through a grid fixed vertically with respect to the horizontal axis of the wind tunnel.?The first analytical solution has been obtained and explained the well-known “the inverse-linear decay law” of the turbulent intensity.? It is believed that the present result is the first exact solution in the theory of turbulence.

Integration of Ideological and Political Education into the Probability Theory and Mathematical Statistics Course:A Teaching Design Based on Estimation and Hypothesis Testing

With the rapid development of higher education in China,colleges and universities are facing new challenges and impacts in talent training.Probability Theory and Mathematical Statistics is one of the important courses in higher education for science and engineering majors and economics and management majors.Its critical role in cultivating students’thinking skills and improving their problem-solving skills is self-evident.Course ideological and political education construction is an important link in college talent training work.Combining ideological and political education with course teaching can help students establish correct value concepts and play a certain role in improving their comprehensive ability and quality.At present,the construction of ideological and political education in the Probability Theory and Mathematical Statistics course still faces some problems,mainly manifested in the lack of attention paid by teachers to course ideological and political education,insufficient exploitation of ideological and political elements,and the simplification of ideological and political education implementation methods.In order to comprehensively deepen the construction of course ideological and political education in line with the actual needs of Probability Theory and Mathematical Statistics course teaching,we should strengthen the construction of teacher teams,improve teachers’ability to carry out course ideological and political education,integrate educational resources,develop educational resources for ideological and political education,and innovate teaching methods to improve the overall effect of ideological and political education integration.

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.

Calculation of the Canonical Rate Constant for the Nonadiabatic Trapping Model Based on Unified Statistical Theory:A Test on The Exchange Reaction H_2+H

A new approach was employed to calculate the canonical (thermal) rate constant basedon unified statistical theory. All information for the calculation was obtained from ab initio meth-ods. The flux integral for any point of reaction coordinate was calculated by counting the numberof quantum states and applied to determine the dividing surfaces along the intrinsic reaction coor-dinate (IRC). The classical exchange reaction H2+H, as an example, was investigated. The IRC forthe reaction has been traced and detailed information of IRC was carried out at the QCISD/6-311 G** level .The calculated rate constants are well consistent with the experimental results.

Statistical Gauge Theory for Relativistic Finite Density Problems

A relativistic quantum field theory is presented for finite density problems based on the principle of locality. It is shown that, in addition to the conventional ones, a local approach to the relativistic quantum field theories at both zero and finite densities consistent with the violation of Bell-like inequalities should contain and provide solutions to at least three additional problems, namely, i) the statistical gauge invariance; ii) the dark components of the local observables; and iii) the fermion statistical blocking effects, based upon an asymptotic nonthermal ensemble. An application to models is presented to show the importance of the discussions.

A Statistical Rate Theory of Interface Concentration during Solution ZeoliteCrystal Growth

A theoretical model is developed using statistical rate theory to determine the rate of molecular transport across the interface of a growing spherical zeolite crystal. The model is expressed in terms of the interface concentration. Two model constants appear in the expression for the equilibrium exchange rate. In order to validate the model, zeolite crystallization is investigated for a system for which experimental data exist. The model constants were first established using the measured growth rates at a specific temperature. Then the model was used to predict the growth rate at other temperatures.

Nonequilibrium Statistical Modeling of Fatigue Crack Growth Behaviour

In order to study the influence of microstructural texture on the growth of short fatigue cracks in metals, the nonequilibrium statistical theory of fatigue fracture correlating a microscopic mechanism with the macroscopic properties is modified to take into consideration the microstructural features of a material, thereby allowing a rationalisation of the experimental data of short fatigue crack growth and long fatigue crack growth. The nonequilibrium statistical theory thus developed relates the growth of cracks with a dislocation mechanism to simulate short fatigue crack growth with the long fatigue crack growth behaviour and predicts the fatigue crack growth rates throughout the fatigue lifetime. The results is finally compared with that of other fatigue theories.

Application of Statistical Tools for Data Analysis and Interpretation in Rice Plant Pathology

There has been a significant advancement in the application of statistical tools in plant pathology during the past four decades. These tools include multivariate analysis of disease dynamics involving principal component analysis, cluster analysis, factor analysis, pattern analysis, discriminant analysis, multivariate analysis of variance, correspondence analysis, canonical correlation analysis, redundancy analysis, genetic diversity analysis, and stability analysis, which involve in joint regression, additive main effects and multiplicative interactions, and genotype-by-environment interaction biplot analysis. The advanced statistical tools, such as non-parametric analysis of disease association, meta-analysis, Bayesian analysis, and decision theory, take an important place in analysis of disease dynamics. Disease forecasting methods by simulation models for plant diseases have a great potentiality in practical disease control strategies. Common mathematical tools such as monomolecular, exponential, logistic, Gompertz and linked differential equations take an important place in growth curve analysis of disease epidemics. The highly informative means of displaying a range of numerical data through construction of box and whisker plots has been suggested. The probable applications of recent advanced tools of linear and non-linear mixed models like the linear mixed model, generalized linear model, and generalized linear mixed models have been presented. The most recent technologies such as micro-array analysis, though cost effective, provide estimates of gene expressions for thousands of genes simultaneously and need attention by the molecular biologists. Some of these advanced tools can be well applied in different branches of rice research, including crop improvement, crop production, crop protection, social sciences as well as agricultural engineering. The rice research scientists should take advantage of these new opportunities adequately in adoption of the new highly potential advanced technologies while planning experimental designs, data collection, analysis and interpretation of their research data sets.

Prestack seismic stochastic inversion based on statistical characteristic parameters

In the conventional stochastic inversion method,the spatial structure information of underground strata is usually characterized by variograms.However,effectively characterizing the heterogeneity of complex strata is difficult.In this paper,multiple parameters are used to fully explore the underground formation information in the known seismic reflection and well log data.The spatial structure characteristics of complex underground reservoirs are described more comprehensively using multiple statistical characteristic parameters.We propose a prestack seismic stochastic inversion method based on prior information on statistical characteristic parameters.According to the random medium theory,this method obtains several statistical characteristic parameters from known seismic and logging data,constructs a prior information model that meets the spatial structure characteristics of the underground strata,and integrates multiparameter constraints into the likelihood function to construct the objective function.The very fast quantum annealing algorithm is used to optimize and update the objective function to obtain the fi nal inversion result.The model test shows that compared with the traditional prior information model construction method,the prior information model based on multiple parameters in this paper contains more detailed stratigraphic information,which can better describe complex underground reservoirs.A real data analysis shows that the stochastic inversion method proposed in this paper can effectively predict the geophysical characteristics of complex underground reservoirs and has a high resolution.

A Fuzzy Adaptive Algorithm Based on“Current”Statistical Model for Maneuvering Target Tracking

The basic"current"statistical model and adaptive Kalman filter algorithm can not track a weakly maneuvering target precisely,though it has good estimate accuracy for strongly maneuvering target.In order to solve this problem,a novel nonlinear fuzzy membership function was presented to adjust the upper and lower limit of target acceleration adaptively,and then the validity of the new algorithm for feeblish maneuvering target was proved in theory.At last,the computer simulation experiments indicated that the new algorithm has a great advantage over the basic"current"statistical model and adaptive algorithm.

Statistical Analyses for Quality of English Grammar Paper

Context Theory have been extensively used in the teaching of minority English majors. Meanwhile, teachers of English in China have been inevitably involved in language testing of various types, either to choose an appropriate existing language test or design by themselves. Therefore it is of practical significance to testify whether the course taken under the Context Theory has enabled teachers to become competent in the design, development, and use of language tests. The main purpose of the present study is to analyze the quality of English grammar paper to check whether minority English majors' management of English grammar have been improved.

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.

Hypothetical Dark Matter Explains the Origin of Subatomic Universe: FEP-Theory

Although the standard model provides a suitable pattern based on observable experimental data, it cannot explain dark matter, gravitation, the structural nature of the fundamental particles, and charges. In this paper, a new theory about the nature of charges, particles and proposed structures for atoms were presented. This theory explains how an ideal quantum fluid (IQF) including hypothetical dark matter or fundamental elementary particles (FEPs) can produce the building blocks of matter. This theory describes quadruple blocks with two types of independent charges that can create different characteristics for these building blocks. Quadruple blocks have similarities and differences with the fundamental particles in standard model. This theory also explains the possible mechanism of creation the next generation of particles such as protons and neutrons.

Time Sequence Change-Point Model of Electrostatic State Parameters of Aircraft Engine

Electrostatic monitoring technology of particle charging information can facilitate online monitoring of aero-engine,which effectively enhances engine fault diagnosis and health managements.Unlike traditional engine state monitoring technologies,aircraft engine monitoring by gas path electrostatic monitoring not only covers the predicted information source itself,but also detects the information that can provide an early warnings for initial fault states through gas path charging levels.This paper establishes a non-stationary time sequence change-point model for anomaly recognition of electrostatic signals based on change-point theory combined with difference method of non-stationary time series.Finally,electrostatic induction data were utilized by the engine life test for a particular aircraft to validate the proposed algorithm.The results indicate that the activity level and the event rate were0.5—0.8(nc)and 50%,respectively,which were far greater than 4—12(pc)and 0—4% under normal working conditions of the engine.

Quantization of light energy directly from classical electromagnetic theory in vacuum

It is currently believed that light quantum or the quantization of light energy is beyond classical physics, and the picture of wave-particle duality, which was criticized by Einstein but has attracted a number of experimental researches, is necessary for the description of light. It is shown in this paper, however, that the quantization of light energy in vacuum, which is the same as that in quantum electrodynamics, can be derived directly from the classical electromagnetic theory through the consideration of statistics based on classical physics. Therefore, the quantization of energy is an intrinsic property of light as a classical electromagnetic wave and has no need of being related to particles.

A Measurement Theoretical Foundation of Statistics

It is a matter of course that Kolmogorov’s probability theory is a very useful mathematical tool for the analysis of statistics. However, this fact never means that statistics is based on Kolmogorov’s probability theory, since it is not guaranteed that mathematics and our world are connected. In order that mathematics asserts some statements concerning our world, a certain theory (so called “world view”) mediates between mathematics and our world. Recently we propose measurement theory (i.e., the theory of the quantum mechanical world view), which is characterized as the linguistic turn of quantum mechanics. In this paper, we assert that statistics is based on measurement theory. And, for example, we show, from the pure theoretical point of view (i.e., from the measurement theoretical point of view), that regression analysis can not be justified without Bayes’ theorem. This may imply that even the conventional classification of (Fisher’s) statistics and Bayesian statistics should be reconsidered.

Incomplete nonextensive statistics and the zeroth law of thermodynamics

On the basis of the entropy of incomplete statistics （IS） and the joint probability factorization condition, two controversial problems existing in IS are investigated： one is what expression of the internal energy is reasonable for a composite system and the other is whether the traditional zeroth law of thermodynamics is suitable for IS. Some new equivalent expressions of the internal energy of a composite system are derived through accurate mathematical calculation. Moreover, a self-consistent calculation is used to expound that the zeroth law of thermodynamics is also suitable for IS, but it cannot be proven theoretically. Finally, it is pointed out that the generalized zeroth law of thermodynamics for incomplete nonextensive statistics is unnecessary and the nonextensive assumptions for the composite internal energy will lead to mathematical contradiction.