Study on the Relationship between Fracture Morphology and Splitting Strength of Granite Based on Fabric Distribution

Because of the requirement of the mechanical properties of the damaged surrounding granite rock and the existence of the fracture water in hydraulic fracturing engineering, the strength of granite is related to the fabric, and the roughness of the section is also related to the liquid flow rate, a method of roughly determining the strength of the specimen by observing the failure mode of rock is needed. Considering that the physical and mechanical properties of granite are obviously affected by the fabric, the discrete element numerical simulation method was used to reconstruct the granite fabric based on the spatial correlation function to simulate the splitting experiment to investigate the failure mode of the specimen. The relationship between strength, the fractal value of cross-section, and the fabric was analyzed, which was verified through experiment. The results show that (1) the Voronoi GBM model with spatial correlation function of the discrete element can effectively simulate the controllable granite fabric and carry out micromechanical analysis. (2) The strength of the granite specimen and the fractal value of the cross-section have an obvious linear relationship with the fabric; besides, there is also a certain linear relationship between the strength of the specimen and the fractal value, which is influenced by granite fabric. (3) The predicted strength of the specimen according to the fractal value of the section is in good agreement with the actual strength with the error rate of 30%. In a word, this method can predict the strength of the specimen through the failure section and analyze the hydraulic fracture section and water pressure.

Experimental Investigation of the Unsteady Stator/Rotor Wake Characteristics Downstream of an Axial Air Turbine

A feasibility study of velocity field measurements using the Particle Image Velocimetry (PIV) method in an axial air turbine model is presented. The wakes past the blades of the rotor wheel were observed using the PIV technique. Data acquisition was synchronized with the shaft rotation; thus, the wakes were phase averaged for statistical analysis. The interaction of the rotor blade wakes with the stator ones was investigated by changing the stator wheel’s angle. The measurement planes were located just behind the rotor blades, covering approximately 3 cm × 3 cm in axial × tangential directions. The spatial correlation function suggests that the resolution used is sufficient for the large-scale flow-patterns only, but not for the small ones. The scales of fluctuations correspond to the shear layer thickness at the mid-span plane but, close to the end-wall, they contain larger structures caused by the secondary flows. The length-scales of the fluctuations under off-design conditions display a dependence on the area of the stator and rotor wakes cross-sections, which, in turn, depend on their angle. The obtained experimental data are to be used for the validation of mathematical simulation results in the future.

Сhanges of the Structure Indicators and the Salinity Field Average Value in the Sea of Azov

Purpose. The work is aimed at continuing the started in the previous papers investigations of structure of the Azov Sea salinity field based on the oceanographic survey data collected since 2000. Interest in studying this parameter is conditioned by its anomalous increase after 2006. Methods and Results. The data of 49 seasonal oceanographic surveys carried out in the Sea of Azov by the Azov-Black Sea Branch of "VNIRO" ("AzNIIRKH") from 2001 to 2016 permitted to calculate the following: the radii in the concentration region of the field spatial correlation function in the meridional and zonal directions for the surface and bottom layers (the characteristic of the field homogeneity); the ratio between these radii; the sea-average values of salinity field for the surface and bottom layers. The time graphical and the paired correlation analyses of the calculated indicators’ series were done. The average values of the meridional and zonal radii of the concentration region of the spatial correlation function (42.5 and 47.1 km) testify presence of two relatively isolated zones in the sea related to the water circulation. These zones are formed under the conditions of the eastern winds dominating in the region. The average values of the above-mentioned radii the near-bottom sea layer were approximately equal, whereas in the surface layer, the average zonal radii exceeded the meridional ones. In spring and summer, the meridional radius in the bottom layer surpassed the zonal one. Long-term variability shows that in the surface layer, the meridional radius values tend to increase, and in the bottom layer, the zonal radius ones – to decrease. These trends demonstrate a change in the nature of water exchange in the sea, namely from predominance of the zonal transport to that of the meridional one. Conclusions. Since 2006, the changes in the structure of the Azov Sea water salinity field (trends towards decrease of the zonal radii and increase of the meridional ones in the concentration region of the field spatial correlation function) resulted from decrease in the river water inflow and increase of water exchange with the Kerch Strait, and were accompanied by growth of average salinity. Water exchange with the Kerch Strait in the bottom layer was the most active in spring and summer. The anticipatory shift of the field structural characteristics by 1 and 2 years relative to its average values makes it possible to forecast them with a two-year advance time.

Сhanges of the Structure Indicators and the Salinity Field Average Value in the Sea of Azov

Purpose. The work is aimed at continuing the started in the previous papers investigations of structure of the Azov Sea salinity field based on the oceanographic survey data collected since 2000. Interest in studying this parameter is conditioned by its anomalous increase after 2006. Methods and Results. The data of 49 seasonal oceanographic surveys carried out in the Sea of Azov by the Azov-Black Sea Branch of "VNIRO" ("AzNIIRKH") from 2001 to 2016 permitted to calculate the following: the radii in the concentration region of the field spatial correlation function in the meridional and zonal directions for the surface and bottom layers (the characteristic of the field homogeneity); the ratio between these radii; the sea-average values of salinity field for the surface and bottom layers. The time graphical and the paired correlation analyses of the calculated indicators’ series were done. The average values of the meridional and zonal radii of the concentration region of the spatial correlation function (42.5 and 47.1 km) testify presence of two relatively isolated zones in the sea related to the water circulation. These zones are formed under the conditions of the eastern winds dominating in the region. The average values of the above-mentioned radii in the near-bottom sea layer were approximately equal, whereas in the surface layer, the average zonal radii exceeded the meridional ones. In spring and summer, the meridional radius in the bottom layer surpassed the zonal one. Long-term variability shows that in the surface layer, the meridional radius values tend to increase, and in the bottom layer, the zonal radius ones – to decrease. These trends demonstrate a change in the nature of water exchange in the sea, namely from predominance of the zonal transport to that of the meridional one. Conclusions. Since 2006, the changes in the structure of the Azov Sea water salinity field (trends towards decrease of the zonal radii and increase of the meridional ones in the concentration region of the field spatial correlation function) resulted from decrease in the river water inflow and increase of water exchange with the Kerch Strait, and were accompanied by growth of average salinity. Water exchange with the Kerch Strait in the bottom layer was the most active in spring and summer. The anticipatory shift of the field structural characteristics by 1 and 2 years relative to its average values makes it possible to forecast them with a two-year advance time.

On the three-dimensional spatial correlations of curved dislocation systems

Coarse-grained descriptions of dislocation motion in crystalline metals inherently represent a loss of information regarding dislocation-dislocation interactions. In the present work, we consider a coarse-graining framework capable of re-capturing these interactions by means of the dislocation-dislocation correlation functions. The framework depends on a convolution length to define slip-system-specific dislocation densities. Following a statistical definition of this coarse-graining process, we define a spatial correlation function which will allow the arrangement of the discrete line system at two points—and thus the strength of their interactions at short range—to be recaptured into a mean field description of dislocation dynamics. Through a statistical homogeneity argument, we present a method of evaluating this correlation function from discrete dislocation dynamics simulations. Finally, results of this evaluation are shown in the form of the correlation of dislocation densities on the same slip-system. These correlation functions are seen to depend weakly on plastic strain, and in turn, the dislocation density, but are seen to depend strongly on the convolution length. Implications of these correlation functions in regard to continuum dislocation dynamics as well as future directions of investigation are also discussed.

Coupling effects among elementary polarization properties

In this work, we propose that there exist coupling effects among birefringence, dichroism and off-diagonal depolarization parameters of differential Mueller matrix of random anisotropic media. An anisotropic spatial correlation function of anisotropic random medium is proposed to explain this phenomenon. The consequences of these effects are then pointed out. The idea in this work is very helpful for accurate interpretation of the measured Mueller matrices of optically anisotropic depolarizing medium. In addition, the concept of the anisotropic spatial correlation function of anisotropic random medium will open a new door and will play a central role for analyzing polarized light scattering by anisotropic random media.

Correction: Abramov, R. The Random Gas of Hard Spheres. J 2019, 2, 162–205

In the published paper [1], we used the spatial correlation function R(σ) of two spheres, each of diameter σ, to construct a closure to the BBGKY hierarchy of hard spheres [...]

Households Health Status in Saudi Arabia: Spatial Distribution and Association With Socioeconomic Factors

This paper examines the spatial relationship between Saudi and non-Saudi people's health status and the socioeconomic composition of the neighbourhoods in which they live. Data were recorded from the National Population Health Survey (NPHS) performed by the Saudi General Authority for Statistics (GAS) in 2018. The survey counts 23,980,846 inhabitants grouped into 24,012 households who assessed their health status by gender and administrative region. Only people who are fifteen years of age and over and claiming poor health status were retained in the analysis. We used a Generalized Linear Spatial Model (GLSM) to study the relationship between Saudi and non-Saudi household’s health status and socioeconomic factors. A Gaussian process with a powered exponential spatial correlation function was introduced on the right-hand side of the model to consider the unexplained spatial variation in the data. The statistical results show the progressive increase in the number of Saudi and non-Saudi households claiming poor health status with the high Saudi unemployment rate, low average monthly income and high current daily smokers. The results of the statistical analyses show the wider potential of GLSM for analyzing data of this kind and the important risk of misleading interpretations when the non-spatial analysis is used on spatially structured data. The method of inference was Bayesian using Markov Chain Monte Carlo Implementation.