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.

On Origin of Power-Law Distributions in Self-Organized Criticality from Random Walk Treatment

在自我组织的 criticality 的幂定律分布的起源被在系统把活跃地点的数字的变化当作一个随机的过程调查。雪崩然后在一个一个维的格子被认为是一个第一回来的随机的散步过程。我们假设活跃地点的数字的变化在每更改有三可能性：与概率 f 1, 增加 1 与概率 f 2, 在 1 减少或与概率 1-f 1-f2 仍然保持未改变。这在系统模仿动力学。当随机的散步与相等的概率是不偏的搬到相反的方向时，一生的幂定律分布被发现。这证明在自我组织的 criticality 的幂定律分布可以被竞争相互作用的平衡引起。

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.

Relativistic Corrections to the Maxwellian Distribution for Astrophysical and Fusion Plasmas

We present calculations and improvement inspired by the work of Lorenzo Zaninetti, published in 2020, it concerns a problem whose origin dates back 1911 with so called Maxwell-Jüttner distribution these lies on the Lorentz factor , with . This work uses powerful modern software for a reconstruction of Zaninetti work, which computes with special functions, these are included in the Mathematica software, as by instance Bessel and Meijer G-functions ready to manipulate. A progress is made, it is possible to perform an integral that is not computed in Zaninetti paper. This author connects the correct relativistic probability law: the Maxwell-Jüttner to the synchrotron emissivity with a magnetic B field, this work generalize these results, using the linear Stark effect and deals with an electric field E.

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.

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.

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 FLAC 3D numerical calculation software. Based on the roadway support difficulty and distribution laws of the plastic zone of surrounding 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 k = 0.5, 1.0, 1.5, and 2.0, the plastic zone presented "addleshape" distribution, "ellipse" distribution, "thin and high" distribution and "inverse trapezium" distribution, 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.

S-curve networks and an approximate method for estimating degree distributions of complex networks

In the study of complex networks almost all theoretical models have the property of infinite growth, but the size of actual networks is finite. According to statistics from the China Internet IPv4 （Internet Protocol version 4） addresses, this paper proposes a forecasting model by using S curve （logistic curve）. The growing trend of IPv4 addresses in China is forecasted. There are some reference values for optimizing the distribution of IPv4 address resource and the development of IPv6. Based on the laws of IPv4 growth, that is, the bulk growth and the finitely growing limit, it proposes a finite network model with a bulk growth. The model is said to be an S-curve network. Analysis demonstrates that the analytic method based on uniform distributions （i.e., Barabasi-Albert method） is not suitable for the network. It develops an approximate method to predict the growth dynamics of the individual nodes, and uses this to calculate analytically the degree distribution and the scaling exponents. The analytical result agrees with the simulation well, obeying an approximately power-law form. This method can overcome a shortcoming of Barabasi-Albert method commonly used in current network research.

VOICE ACTIVITY DETECTION UNDER RAYLEIGH DISTRIBUTION

This paper presents an improved Voice Activity Detection (VAD) algorithm which uses the Signal-to-Noise Ratio (SNR) measure. We assume that noise Power Spectral Density (PSD) in each spectral bin follows a Rayleigh distribution. Rayleigh distributions with its asymmetric tail charac- teristics give a better description of the noise PSD distribution than Gaussian distribution. Under this assumption, a new threshold updating expression is derived. Since the analytical integral of the false alarm probability, the threshold updating expression can be represented without the inverse comple- mentary error function and low computational complexity is achieved in our system. Experimental results show that the proposed VAD outperforms or at least is comparable with the VAD scheme presented by Davis under several noise environments and has a lower computational complexity.

Power-law Distribution of Normal Fault Displacement and Length and Estimation of Extensional Strain due to Normal Faults:A Case Study of the Sierra de San Miguelito, Mexico

The Sierra de San Miguelito is a relatively uplifted area and is constituted by a large amount of silicic volcanic rocks with ages from middle to late Cenozoic. The normal faults of the Sierra de San Miguelito are Domino-style and nearly parallel. The cumulative length and displacement of the faults obey power-law distribution. The fractal dimension of the fault traces is -1.49. Using the multi-line one-dimensional sampling, the calculated exponent of cumulative fault displacements is -0.66. A cumulative curve combining measurements of all four sections yielded a slope of -0.63. The displacement-length plot shows a non-linear relationship and large dispersion of data. The large dispersion in the plot is mainly due to the fault linkage during faulting. An estimation of extensional strain due to the normal faults is ca. 0.1830. The bed extension strain is always less than or equal to the horizontal extension strain. The deformation in the Sierra de San Miguelito occurred near the surface, producing pervasive faults and many faults are too small to appear in maps and sections at common scales. The stretching produced by small faults reach ca. 33% of the total horizontal elongation.