Size-dependent vibration and buckling of porous functionally graded microplates based on modified couple stress theory in thermal environments by considering a dual power-law distribution of scale effects

In this study,the thermodynamic behaviors of the intrinsic frequency and buckling temperature of rectangular plates of functionally graded materials(FGMs)are explored based on the modified couple stress theory(MCST)and the novel dual powerlaw scale distribution theory.The effects of linear,homogeneous,and non-homogeneous temperature fields on the frequency and buckling temperature of FGM microplates are evaluated in detail.The results show that the porosity greatly affects the mechanical properties of FGM plates,reducing their frequency and flexural temperature compared with non-porous plates.Different temperature profiles alter plate frequencies and buckling temperatures.The presence and pattern of scale effect parameters are also shown to be crucial for the mechanical response of FGM plates.The present research aims to provide precise guidelines for the micro-electro-mechanical system(MEMS)fabrication by elucidating the complex interplay between thermal,material,and structural factors that affect the performance of FGM plates in advanced applications.

Distribution law and susceptibility of geohazards across a gradient belt of the Western Sichuan Plateau

Across a gradient belt of the Western Sichuan Plateau,geohazards have seriously limited economic and social development.According to incomplete statistics,15,673 geohazards have been recorded in the study area.In order to mitigate the threat of geohazards to human engineering activities in the region,an overall understanding of the distribution pattern of geohazards and susceptibility assessment are necessary.In this paper,a gradient belt of the Western Sichuan Plateau and its zoning criteria were defined.Subsequently,on the basis of relief amplitude,distance to faults,rainfall,and human activities,three indicators of endogenic process were introduced:Bouguer gravity anomaly gradient,vertical deformation gradient,and horizontal deformation gradient.Thereafter,the distribution patterns of geohazards were investigated through mathematical statistics and ArcGIS software.By randomly selecting 10,449 hazards,a geohazard susceptibility map was generated using the Information Value(IV)model.Finally,the IV model was validated against 5224 hazards using the Area Under Curve(AUC)method.The results show that 47.6%of the geohazards were distributed in the zone of steep slope.Geohazards showed strong responses to distance to faults,human activities,and annual rainfall.The distribution of geohazards in the gradient belt of the Western Sichuan Plateau is more sensitive to vertical internal dynamics factors(such as vertical deformation gradient and Bouguer gravity anomaly gradient)without any apparent sensitivity to horizontal internal dynamics factors.The areas of high and very-high risk account for up to 32.22%,mainly distributed in the Longmenshan and Anning River faults.According to the AUC plot,the success rate of the IV model for generating the susceptibility map is 76%.This susceptibility map and geohazard distribution pattern can provide a reference for geological disaster monitoring,preparation of post-disaster emergency measures,and town planning.

Prediction Based on Generalized Order Statistics from a Mixture of Rayleigh Distributions Using MCMC Algorithm

This article considers the problem in obtaining the maximum likelihood prediction (point and interval) and Bayesian prediction (point and interval) for a future observation from mixture of two Rayleigh (MTR) distributions based on generalized order statistics (GOS). We consider one-sample and two-sample prediction schemes using the Markov chain Monte Carlo (MCMC) algorithm. The conjugate prior is used to carry out the Bayesian analysis. The results are specialized to upper record values. Numerical example is presented in the methods proposed in this paper.

Power Law Distributions in the Experiment for Adjustment of the Ion Source of the NBI System

The experiential adjustment process in an experiment on the ion source of the neutral beam injector system for the HT-7 Tokamak is reported in this paper. With regard to the data obtained in the same condition, in arranging the arc current intensities of every shot with a decay rank, the distributions of the arc current intensity correspond to the power laws, and the distribution obtained in the condition with the cryo-pump corresponds to the double Pareto distribution. Using the similar study method, the distributions of the arc duration are close to the power laws too. These power law distributions are formed rather naturally instead of being the results of purposeful seeking.

Power Law Exponents for Vertical Velocity Distributions in Natural Rivers

While log law is an equation theoretically derived for near-bed region, in most cases, power law has been researched by experimental methods. Thus, many consider it as an empirical equation and fixed power law exponents such as 1/6 and 1/7 are generally applied. However, exponent of power law is an index representing bed resistance related with relative roughness and furthermore influences the shapes of vertical velocity distribution. The purpose of this study is to investigate characteristics of vertical velocity distribution of the natural rivers by testing and optimizing previous methods used for determination of power law exponent with vertical velocity distribution data collected with ADCPs during the years of 2005 to 2009 from rivers in South Korea. Roughness coefficient has been calculated from the equation of Limerinos. And using theoretical and empirical formulae, and representing relationships between bed resistance and power law exponent, it has been evaluated whether the exponents suggested by these equations appropriately reproduce vertical velocity distribution of actual rivers. As a result, it has been confirmed that there is an increasing trend of power law exponent as bed resistance increases. Therefore, in order to correctly predict vertical velocity distribution in the natural rivers, it is necessary to use an exponent that reflects flow conditions at the field.

Parameter Estimations of Rayleigh Distribution

设随机变量X服从Rayleigh分布，其密度函数为p(x;β)=2x/βe-x^2/β，x＞0,β＞0为参数，对变换群G={gc;gc(x)=c^2x,c＞0}，本文分别在平方损失和熵损失下研究了β在G上的最优同变估计；当β有先验信息时，给出了β的Bayes估计。

A Study on Mixture of Exponentiated Rayleigh and Exponentiated Exponential Distributions Based on Order Statistics

Mixtures of lifetime distributions occur when two different causes of failure arc present, each with the same parametric form of lifetime distributions. This paper is considered with the mixture model of exponentiated Rayleigh and exponentiated exponential distributions. The author＇s objectives are finding the statistical properties of the model and estimating the parameters of the model by using point estimation and interval estimation methods. First, some properties of the model with some graphs of the density function are discussed. Next, the maximum likelihood method of estimation is used for estimating scale and shape parameters of the model. Estimating the parameters is studied under complete and type II censored samples for different sample sizes. Asymptotic Fisher information matrix of the estimators for complete samples is founded with different sample sizes. The asymptotic variances of the maximum likelihood estimates are derived. Based on the asymptotic variances of the maximum likelihood estimates, interval estimates of the parameters are obtained. Some of the equations in this paper are solved by using numerical iteration such as Newton Raphson method by using Mathematica 7.0. The performance of findings in the paper is showed by demonstrating some numerical illustrations through Monte Carlo simulation study based on absolute relative bias and mean square error.

Kumaraswamy-Odd Rayleigh-G Family of Distributions with Applications

We propose a new generator of continuous distributions with at least four positive parameters called the Kumaraswamy-Odd Rayleigh-G family. Some special cases were presented. The plots of the Kumaraswamy Odd Rayleigh Log-Logistic (KORLL) distribution indicate that the distribution can take many shapes depending on the parameter values. The negative skewness and kurtosis indicates that the distribution has lighter tails than the normal distribution. The Monte Carlo simulation results indicate that the estimated biases decrease when the sample size increases. Furthermore, the root mean squared error estimates decay towards zero as the sample size increases. This part shows the consistency of the maximum likelihood estimators. From the considered analytical measures, the new KORLL provides the best fit to the analysed five real data sets indicating that this new model outclasses its competitors.

Heavy-Tailed Distributions Generated by Randomly Sampled Gaussian, Exponential and Power-Law Functions

A simple stochastic mechanism that produces exact and approximate power-law distributions is presented. The model considers radially symmetric Gaussian, exponential and power-law functions inn= 1, 2, 3 dimensions. Randomly sampling these functions with a radially uniform sampling scheme produces heavy-tailed distributions. For two-dimensional Gaussians and one-dimensional exponential functions, exact power-laws with exponent –1 are obtained. In other cases, densities with an approximate power-law behaviour close to the origin arise. These densities are analyzed using Padé approximants in order to show the approximate power-law behaviour. If the sampled function itself follows a power-law with exponent –α, random sampling leads to densities that also follow an exact power-law, with exponent -n/a – 1. The presented mechanism shows that power-laws can arise in generic situations different from previously considered specialized systems such as multi-particle systems close to phase transitions, dynamical systems at bifurcation points or systems displaying self-organized criticality. Thus, the presented mechanism may serve as an alternative hypothesis in system identification problems.

The abundance,distribution,and enrichment mechanism of harmful trace elements in coals from Guizhou,Southwestern China

Coal seams can enrich a variety of harmful trace elements under specific geological conditions.The spatial distribution of harmful trace elements in coal is extremely uneven,and the distribution characteristics of each element content are different.The harmful elements released in the process of coal mining and utilization will cause serious harm to the environment and the human body.It is of great resource significance to study the geochemistry of coal that affects the enrichment and distribution characteristics of harmful trace elements.Based on the domestic and foreign literature on coal geochemistry in Guizhou published by previous investigators,this study counted 1097 sample data from 23 major coal-producing counties in Guizhou Province,systematically summarized the relevant research results of harmful trace elements in the coal of Guizhou,and revealed the overall distribution and enrichment characteristics of harmful trace elements in the coal of Guizhou.The results show that the average contents of Cd,Pb,Se,Cu,Mo,U,V,As,Hg,and Cr in coal of Guizhou are higher than those in Chinese coal and world coal.A variety of harmful trace elements in the coal of Guizhou have high background values,especially in Liupanshui,Xingyi and Qianbei coalfield.The enrichment of various harmful trace elements in the Late Permian coal in Guizhou is mainly related to the combined action of various geological and geochemical factors.The supply of terrigenous debris and sedimentary environment may be the basic background of the enrichment of harmful elements in western Guizhou,while low-temperature hydrothermal activity and volcanic ash deposition may be the main reasons for the enrichment of harmful elements in southwestern Guizhou.

Hydrocarbon accumulation and orderly distribution of whole petroleum system in marine carbonate rocks of Sichuan Basin,SW China

Based on the situation and progress of marine oil/gas exploration in the Sichuan Basin,SW China,the whole petroleum system is divided for marine carbonate rocks of the basin according to the combinations of hydrocarbon accumulation elements,especially the source rock.The hydrocarbon accumulation characteristics of each whole petroleum system are analyzed,the patterns of integrated conventional and unconventional hydrocarbon accumulation are summarized,and the favorable exploration targets are proposed.Under the control of multiple extensional-convergent tectonic cycles,the marine carbonate rocks of the Sichuan Basin contain three sets of regional source rocks and three sets of regional cap rocks,and can be divided into the Cambrian,Silurian and Permian whole petroleum systems.These whole petroleum systems present mainly independent hydrocarbon accumulation,containing natural gas of affinity individually.Locally,large fault zones run through multiple whole petroleum systems,forming a fault-controlled complex whole petroleum system.The hydrocarbon accumulation sequence of continental shelf facies shale gas accumulation,marginal platform facies-controlled gas reservoirs,and intra-platform fault-and facies-controlled gas reservoirs is common in the whole petroleum system,with a stereoscopic accumulation and orderly distribution pattern.High-quality source rock is fundamental to the formation of large gas fields,and natural gas in a whole petroleum system is generally enriched near and within the source rocks.The development and maintenance of large-scale reservoirs are essential for natural gas enrichment,multiple sources,oil and gas transformation,and dynamic adjustment are the characteristics of marine petroleum accumulation,and good preservation conditions are critical to natural gas accumulation.Large-scale marginal-platform reef-bank facies zones,deep shale gas,and large-scale lithological complexes related to source-connected faults are future marine hydrocarbon exploration targets in the Sichuan Basin.

CONCEPT, DISTRIBUTION LAW AND FORMATION MACHANISM OF INLAND SALINE ALKALINE WETLAND─ ─ Taking Songliao Plain for Example

The paper, taking Songliao Plain for example, studied the concept, distribution law and formation mechanism of inland saline alkaline wetland. The inland saline alkaline wetland is distributed over the inland region of arid or semi arid climate; it is the wet or slightly stagnant environment, forming saline alkaline soil and salt vegetation and making the geogra phical environment fonming complex with an ecosystem of saline alkaline wetland. The laws of zone nature and non zone nature control the distribution of the inland saline alkaline wetland that extensively spreads in north part of China and other countries. The inland saline alkaline wetland is formed jointly by atmosphere, hydrosphere, lithosphere and biosphere including intellectual sphere. Under the special condition, the artificial activity is possibly the key function. In order to improve the human environment, it is a great duty confronting the whole world to rationally transform the inland saline alkaline wetland. Therefore, we presented an anti inland theory to promote the environment transformation.

Group velocity distribution of Rayleigh waves and crustal and upper mantle velocity structure of the Chinese mainland and its vicinity

Based on the long period digital surface wave data recorded by 11 CDSN stations and 11 IRIS stations, the dispersion curves of the group velocities of fundamental mode Rayleigh waves along 647 paths, with the periods from 10 s to 92 s, were measured by multi-filter. Their distribution at 25 central periods within the region of 18~54N, 70~140E was inverted by Dimtar-Yanovskaya method. Within the period from 10 s to 15.9 s, the group velocity distribution is laterally inhomogeneous and is closely related to geotectonic units, with two low velocity zones located in the Tarim basin and the East China Sea and its north regions, respectively. From 21 s to 33 s, the framework of tectonic blocks is revealed. From 36.6 s to 40 s, the lithospheric subdivision of the Chinese mainland is obviously uncovered, with distinct boundaries among the South-North seismic belt, the Tibetan plateau, the North China, the South China and the Northeast China. Four cross-sections of group velocity distribution with period along 30N, 38N, 90E and 120E, are discussed, respectively, which display the basic features of the crust and upper mantle of the Chinese mainland and its neighboring regions. There are distinguished velocity differences among the different tectonic blocks. There are low-velocity-zones (LVZ) in the middle crust of the eastern Tibetan plateau, high velocity featured as stable platform in the Tarim basin and the Yangtze platform, shallow and thick low-velocity-zone in the upper mantle of the North China. The upper mantle LVZ in the East China Sea and the Japan Sea is related to the frictional heat from the subduction of the Philippine slab and the strong extension since the Himalayan orogenic period.

A Research of the Finding and Distribution Law of Taisui in Modern China

The academic world is still uncertain about the classification of Taisui. It is debating whether Taisui is living or not, myxomycete complex or fungi. The passage studies the 228 finding reports of Taisui in modern China. It confirms that the first finding time of Taisui in modern China is 1963, and the first reported time is 1992. Taisui has been found in 25 administrative divisions. Taisui occurs the most times in Shandong Province. Besides, provinces where Taisui has been found most times are in northern China. Finding locations of Taisui vary from place to place. Taisui is most often found in normal earth layer, with different burying depth. Taisui is mainly found through seeing, tramping, and digging. Taisui findings lack subjective motivations and are connected with the life and production of the finders. Conclusion: Taisui is an object growing in earth layer.

Plastic zone distribution laws and its types of surrounding rock in large-span roadway

In order to study the distribution laws and types of plastic zone of surrounding rock in large-span roadway, we analyzed the distribution laws with different spans and lateral pressures using FLAC3D numerical calcu- lation software. Based on the roadway support difficulty and distribution laws of the plastic zone of sur- rounding rock, we defined the large-span roadway and classified the types of large-span rectangular roadways. As a result, the distribution laws of the plastic zone on surrounding rock in a rectangular roadway with different spans and lateral pressures were obtained. The results show that the area of the plastic zone on surrounding rock increased with the increase of the spans and lateral pressures, and the plastic zone was symmetrical to the center line of roadway. At λ=0.5, 1.0, 1.5, and 2.0, the plastic zone presented ＂addle- shape＂ distribution, ＂ellipse＂ distribution, ＂thin and high＂ distribution and ＂inverse trapezium＂ distribu- tion, respectively. In addition, we classified the roadways into four types according to the different lateral pressures and spans, including small-span, moderate-span, large-span and extreme-large-span roadways.

Seepage field distribution and water inflow laws of tunnels in water-rich regions

Currently,the water inrush hazards during tunnel construction,the water leakage during tunnel operation,and the accompanying disturbances to the ecological environment have become the main problems that affect the structural safety of tunnels in water-rich regions.In this paper,a tunnel seepage model testing system was used to conduct experiments of the grouting circle and primary support with different permeability coefficients.The influences of the supporting structures on the water inflow laws and the distribution of the water pressure in the tunnel were analyzed.With the decrease in the permeability coefficient of the grouting circle or the primary support,the inflow rate of water into the tunnel showed a non-linear decreasing trend.In comparison,the water inflow reduction effect of grouting circle was much better than that of primary support.With the increase of the permeability coefficient of the grouting ring,the water pressure behind the primary lining increases gradually,while the water pressure behind the grouting ring decreases.Thus,the grouting of surrounding rock during the construction of water-rich tunnel can effectively weaken the hydraulic connection,reduce the influence range of seepage,and significantly reduce the decline of groundwater.Meanwhile,the seepage tests at different hydrostatic heads and hydrodynamic heads during tunnel operation period were also conducted.As the hydrostatic head decreased,the water pressure at each characteristic point decreased approximately linearly,and the water inflow rate also had a gradual downward trend.Under the action of hydrodynamic head,the water pressure had an obvious lagging effect,which was not conducive to the stability of the supporting structures,and it could be mitigated by actively regulating the drainage rate.Compared with the hydrostatic head,the hydrodynamic head could change the real-time rate of water inflow to the tunnel and broke the dynamic balance between the water pressure and water inflow rate,thereby affecting the stress state on the supporting structures.

Estimation of the Unknown Parameters for the Compound Rayleigh Distribution Based on Progressive First-Failure-Censored Sampling

This article considers estimation of the unknown parameters for the compound Rayleigh distribution (CRD) based on a new life test plan called a progressive first failure-censored plan introduced by Wu and Kus (2009). We consider the maximum likelihood and Bayesian inference of the unknown parameters of the model, as well as the reliability and hazard rate functions. This was done using the conjugate prior for the shape parameter, and discrete prior for the scale parameter. The Bayes estimators hav been obtained relative to both symmetric (squared error) and asymmetric (LINEX and general entropy (GE)) loss functions. It has been seen that the symmetric and asymmetric Bayes estimators are obtained in closed forms. Also, based on this new censoring scheme, approximate confidence intervals for the parameters of CRD are developed. A practical example using real data set was used for illustration. Finally, to assess the performance of the proposed estimators, some numerical results using Monte Carlo simulation study were reported.

Statistical Inference for the Parameter of Rayleigh Distribution Based on Progressively Type-I Interval Censored Sample

In this paper, the estimation of parameters based on a progressively type-I interval censored sample from a Rayleigh distribution is studied. Different methods of estimation are discussed. They include mid-point approximation estima- tor, the maximum likelihood estimator, moment estimator, Bayes estimator, sampling adjustment moment estimator, sampling adjustment maximum likelihood estimator and estimator based on percentile. The estimation procedures are discussed in details and compared via Monte Carlo simulations in terms of their biases.

Applicability of law of mass action to distribution of manganese between slag melts and liquid iron

According to the law of mass action and the coexistence theory of slag structure, the distribution of manganese between MnO FeO SiO 2 and MgO MnO FeO SiO 2 slag melts as well as liquid iron was analyzed. It is shown that K ′ Mn and K MnO are only dependent on temperature and don’t change with basicities and compositions of slag melts. So the distribution of manganese between the above mentioned slag melts and molten iron obeys the law of mass action. But analysis of experimental results from other sources shows that K ′ Mn and K MnO really change with basicities of slag, which is probably arisen from not approaching equilibrium under low basicity slag melts.

Leak Detection in Water Distribution Systems Using Bayesian Theory and Fisher’s Law

A leak detection method based on Bayesian theory and Fisher’s law was developed for water distribution systems. A hydraulic model was associated with the parameters of leaks (location, extent). The randomness of parameter values was quantified by probability density function and updated by Bayesian theory. Values of the parameters were estimated based on Fisher’s law. The amount of leaks was estimated by back propagation neural network. Based on flow characteristics in water distribution systems, the location of leaks can be estimated. The effectiveness of the proposed method was illustrated by simulated leak data of node pressure head and flow rate of pipelines in a test pipe network, and the leaks were spotted accurately and renovated on time.