Estimation of fracture size and azimuth in the universal elliptical disc model based on trace information

The geometric characteristics of fractures within a rock mass can be inferred by the data sampling from boreholes or exposed surfaces.Recently,the universal elliptical disc(UED)model was developed to represent natural fractures,where the fracture is assumed to be an elliptical disc and the fracture orientation,rotation angle,length of the long axis and ratio of short-long axis lengths are considered as variables.This paper aims to estimate the fracture size-and azimuth-related parameters in the UED model based on the trace information from sampling windows.The stereological relationship between the trace length,size-and azimuth-related parameters of the UED model was established,and the formulae of the mean value and standard deviation of trace length were proposed.The proposed formulae were validated via the Monte Carlo simulations with less than 5%of error rate between the calculated and true values.With respect to the estimation of the size-and azimuth-related parameters using the trace length,an optimization method was developed based on the pre-assumed size and azimuth distribution forms.A hypothetical case study was designed to illustrate and verify the parameter estimation method,where three combinations of the sampling windows were used to estimate the parameters,and the results showed that the estimated values could agree well with the true values.Furthermore,a hypothetical three-dimensional(3D)elliptical fracture network was constructed,and the circular disc,non-UED and UED models were used to represent it.The simulated trace information from different models was compared,and the results clearly illustrated the superiority of the proposed UED model over the existing circular disc and non-UED models。

A universal elliptical disc(UED)model to represent natural rock fractures

Since natural fractures are often non-equidimensional,the circular disc model still has great limitations.By contrast,the elliptical disc model is more applicable to representing natural fractures,especially for slender ones.This paper developed a universal elliptical disc(UED)model by incorporating the center point,size,and azimuth of fractures as variables.Specifically,with respect to the azimuth of elliptical fractures in three-dimensional(3D)space,we proposed a paradigm to construct its probability density function(PDF)by coupling the orientation and rotation angle of long axis based on three coordinate transformations.To illustrate the construction process of the PDF of the fracture azimuth,we took the orientation following the Fisher distribution and the rotation angle following Von Mises distribution as an example.A rock slope is used to show the use of the developed UED model,and the 3D DFNs for the slope rock mass are generated by Monte Carlo simulation.In addition,the DFNs for the rock mass are also generated based on the existing circular disc model and non-universal elliptical disc model.The comparison results from the three models clearly illustrate the superiority of the UED model over the existing circular and non-universal elliptical disc models.

Effective electroelastic constants for three-phase confocal elliptical cylinder model in piezoelectric quasicrystal composites

A three-phase confocal elliptical cylinder model is proposed to analyze micromechanics of one-dimensional hexagonal piezoelectric quasicrystal （PQC） compos- ites. Exact solutions of the phonon, phason, and electric fields are obtained by using the conformal mapping combined with the Laurent expansion technique when the model is subject to far-field anti-plane mechanical and in-plane electric loadings. The effective elec- troelastic constants of several different composites made up of PQC, quasicrystal （QC）, and piezoelectric （PE） materials are predicted by the generalized self-consistent method. Numerical examples are conducted to show the effects of the volume fraction and the cross-sectional shape of inclusion （or fiber） on the effective electroelastic constants of these composites. Compared with other micromechanical methods, the generalized self- consistent and Mori-Tanaka methods can predict the effective electroelastic constants of the composites consistently.

An Elliptical Wind Field Model of Typhoons

An elliptical wind field model of typhoons is put forward based on the characteristics of the typhoon wind fields occurring in the Yellow Sea and Bohai Sea. By contrasting it with the circular typhoon wind field model, it is found that the elliptical model can adequately represent the real wind field and trace the process of a typhoon storm surge. The numerically simulated results of storm surges by using the elliptical model are in good agreement with the observations and markedly better than those by using the circular model.

Application of the Static Headland-Bay Beach Concept to a Sandy Beach: A New Elliptical Model

The headland-bay beach is one of the most common coastal types in the world.Its morphology reflects the changes that occurred during long-term evolution of the sandy coast.Several headland-bay beach models have been proposed to simulate the coastline’s configuration in equilibrium.In this paper,a new elliptical model is proposed,described,and applied.On the east coast of Laizhou Bay in Shandong Province from Longkou Port to Diaolongzui,four typical headland-bay beaches have developed,and four headland-bay beach models are used in this paper to simulate the morphology of these beaches to assess the applicability of each model.The simulation results of the elliptical model verify that it is applicable to the study area.In addition,the elliptical model is easy to use.Through simulation and field investigations,we concluded that most of the coastal segments in this area will remain in an erosion state,and the human activity has a significant impact on the shoreline’s evolution.

Spatiotemporal patterns and drivers of cultivated land conversion in Inner Mongolia Autonomous Region,northern China

Protection and optimization of cultivated land resources are of great significance to national food security.Cultivated land conversion in northern China has increased in recent years due to the industrialization and urbanization of society.However,the assessment of cultivated land conversion in this area is insufficient,posing a potential risk to cultivated land resources.This study evaluated the evolution and spatiotemporal patterns of cultivated land conversion in Inner Mongolia Autonomous Region,China,and the driving factors to improve rational utilization and to protect cultivated land resources.The spatiotemporal patterns of cultivated land conversion in Inner Mongolia were analyzed using the cultivated land conversion index,kernel density analysis,a standard deviation ellipse model,and a geographic detector.Results showed that from 2000 to 2020,the trends in cultivated land conversion area and rate in Inner Mongolia exhibited fluctuating growth,with the total area of cultivated land conversion reaching 7307.59 km^(2) at a rate of 6.69%.Spatial distribution of cultivated land conversion was primarily concentrated in the Hetao Plain,Nengjiang Plain,Liaohe Plain,and the Hohhot-Baotou-Ordos urban agglomeration.Moreover,the standard deviational ellipse of cultivated land conversion in Inner Mongolia exhibited a directional southwest-northeast-southwest-northeast distribution,with the northeast-southwest direction identified as the main driving force of spatial change in cultivated land conversion.Meanwhile,cultivated land conversion exhibited an increase-decrease-increase change process,indicating that spatial distribution of cultivated land conversion in Inner Mongolia became gradually apparent within the study period.The geographic detector results further revealed that the main driving factors of cultivated land conversion in Inner Mongolia were the share of secondary and tertiary industries and per-unit area yield of grain,with explanatory rates of 57.00%,55.00%,and 51.00%,respectively.Additionally,improved agricultural production efficiency and the coordinated development of population urbanization and industry resulted in cultivated land conversion.Collectively,the findings of this study indicated that,from 2000 to 2020,the cultivated land conversion in Inner Mongolia was significant and fluctuated in time,and had strong spatial heterogeneity.The primary drivers of these events included the effects of agriculture,population,and social economy.

Space-time correlations in turbulent Rayleigh–Bnard convection

The recent development of the elliptic model （He, et al. Phy. Rev. E, 2006）, which predicts that the space-time correlation function Cu（r, r） in a turbulent flow has a scaling form Cu（rE, 0） with re being a combined space-time separa- tion involving spatial separation r and time delay T, has stimulated considerable experimental efforts aimed at testing the model in various turbulent flows. In this paper, we review some recent experimental investigations of the space-time correlation function in turbulent Rayleigh-Benard convection. The experiments conducted at different representative locations in the convection cell confirmed the predictions of the elliptic model for the velocity field and passive scalar field, such as local temperature and shadowgraph images. The understanding of the functional form of Cu（r, v） has a wide variety of applications in the analysis of experimental and numerical data and in the study of the statistical properties of small-scale turbulence. A few examples are discussed in the review.

TRPIV investigation of space-time correlation in turbulent flows over flat and wavy walls

The present experimental work is devoted to in- vestigate a new space-time correlation model for the turbulent boundary layer over a flat and a wavy walls. A turbulent boundary layer flow at Reo = 2460 is measured by tomographic time-resolved particle image velocimetry （Tomo-TRPIV）. The space-time correlations of instantaneous streamwise fluctuation velocity are calculated at 3 different wall-normal locations in logarithmic layer. It is found that the scales of coherent structure increase with moving far away from the wall. The growth of scales is a manifestation of the growth of prevalent coherent structures in the turbulent boundary layer like hairpin vortex or hairpin packets when they lift up. The resulting contours of the space-time correlation exhibit elliptic-like shapes rather than straight lines. It is suggested that, instead of Taylor hypothesis, the elliptic model of the space-time correlation is valid for the wallbounded turbulent flow over either a flat wall or a wavy wall. The elliptic iso-correlation curves have a uniform preferred orientation whose slope is determined by the convection velocity. The convection velocity derived from the space-time correlation represents the velocity at which the large-scale eddies carry small-scale eddies. The sweep velocity rep- resents the distortions of the small-scale eddies and is intimately associated with the fluctuation velocity in the logarithmic layer of turbulent boundary layers. The nondimensionalized correlation curves confirm that the elliptic model is more proper for approximating the space-time correlation than Taylor hypothesis, because the latter can not embody the small-scale motions which have non-negligible distortions. A second flow over a wavy wall is also recorded using TRPIV. Due to the combined effect of shear layers and the adverse pressure gradient, the space-time correlation does not show an elliptic-like shape at some specific heights over the wavy wall, but in the outer region of the wavy wallbounded flow, the elliptic model remains valid.

Yield modeling of elliptical defect

Physical defects have always played an important role in integrated circuit(IC)yields,and the design sensitivity to these physical elements has continued to increase in today’s nanometer technologies.The modeling of defect out-lines that exhibit a great variety of defect shapes is usually modeled as a circle,which causes the errors of critical area estimation.Since the outlines of 70%defects approximate to elliptical shapes,a novel yield model associated with elliptical outlines of defects is presented.This model is more general than the circular defects model as the latter is only an instance of the proposed model.Comparisons of the new and circular models in the experiment show that the new model can predict yield caused by real defects more accurately than what the circular model does,which is of significance for the prediction and improvement of the yield.

EA模型在海洋的速度横向时空互相关函数中的应用

椭圆近似(EA)模型是从单个点的时间波动数据中推断空间波动数据的重要方法,它已在室内实验剪切场的纵向时空互相关函数C(r,τ)得到验证并被广泛应用.在这里,我们研究了EA模型在海洋流场中的有效性,并介绍了其在横向时空互相关函数G(r,τ)中的应用.结果表明,EA模型在海洋的速度场中是有效的,即G(r,τ)具有G(r_(E),0)的尺度形式,其中r_(E)=[(r-Uτ)^(2)+(Vτ)^2]^(1/2),U和V是与内波垂直相速度相关的两个特征速度.基于EA模型,我们可以获得海洋的垂直波数能谱,并估计海洋的泰勒微尺度和雷诺数.

Geometrical statistical channel model arisen from scatterers around the mobile with an inverted-parabolic spatial distribution

In this paper, firstly presented a geometrically based statistical channel model with scatterers that are with an inverted parabolic spatial distribution around mobile station （MS） within a circle wherein the base station （BS） and MS are included. This paper proposed a technique to simply derive probability density functions （PDFs） of angle of arrival （AOA）, time of arrival （TOA） and Doppler spectra to characterize the outdoor macrocell and microcell environments by employing various distances between BS and MS, or different size of circular region. Employing this channel model, we analyze the impacts of a directional antenna at BS with the main-lobe width 2~z on the fading and the Doppler spectra.

Estimation of Net Surface Shortwave Radiation from Land Surface Temperature in Regional Scale

The method to estimate NSSR （net surface shortwave radiation） from LST （land surface temperature） in regional scale is discussed. First, an elliptical model between the time series of normalized LST and NSSR was developed using the daily evolution of LST and NSSR. Second, time series of LST and NSSR were simulated by common land model （CoLM） and were proved to be of high accuracy. On the basis of these, a non-linear least square ellipse fitting using the genetic algorithm method was used to fit the normalized LST and NSSR. Finally, LST was inverted using MODIS （moderate resolution imaging spectroradiometer） data with the split-window algorithm, and the regional NSSR was then estimated with LST and an elliptical model. The validation result shows that the derived average NSSR of 50×50 pixels of MODIS data was quite close to the observed data, and the distribution was reasonable, which indicates that the proposed method was capable of estimating NSSR on a regional scale.