Absolute summation of Fourier integrals with multiplier by G.F. Voronoi method

We provide the theorem that is connected with functional method of G.F. Voronoi. We establish sufficient conditions for a function that generates the summation method of G.F. Voronoi, on function-multiplier, and on function $f(t)$, under which the Fourier integral of this function with multiplier is absolutely summable by the functional method of G.F. Voronoi.

Fine-Scale Dasymetric Population Mapping with Mobile Phone and Building Use Data Based on Grid Voronoi Method

Fine-scale population mapping is of great significance for capturing the spatial and temporal distribution of the urban population. Compared with traditional census data, population data obtained from mobile phone data has high availability and high real-time performance. However, the spatial distribution of base stations is uneven, and the service boundaries remain uncertain, which brings significant challenges to the accuracy of dasymetric population mapping. This paper proposes a Grid Voronoi method to provide reliable spatial boundaries for base stations and to build a subsequent regression based on mobile phone and building use data. The results show that the Grid Voronoi method gives high fitness in building use regression, and further comparison between the traditional ordinary least squares (OLS) regression model and geographically weighted regression (GWR) model indicates that the building use data can well reflect the heterogeneity of urban geographic space. This method provides a relatively convenient and reliable idea for capturing high-precision population distribution, based on mobile phone and building use data.

Numerical Study of Fracture Behavior of Gradient Nano-Grained Metals by Molecular Dynamics Simulations

Benefit from the gradient distribution of microstructure, gradient nanograined (GNG) metals have broad application prospect owing to their advantages of both high strength and good tensile ductility. Meanwhile, the fracture behavior of gradient nanograined metals is different from that of traditional homogeneous materials. Using molecular dynamics (MD) method, we simulated the propagation of a crack in a pre-cracked GNG Cu. Voronoi method was adopted to generate the polycrystalline topology with gradient grain size, and FCC copper atoms were filled into the topological structure. The crack was introduced by removing three layers of atoms. Then, the MD specimen was loaded to simulate the crack growth and/or blunting. The micro-defects were identified by the common neighbor analysis parameter. The effects of the grain size gradient and the crack tip initial position on the crack growth were also investigated.

Urban Commercial Spatial Structure Optimization in the Metropolitan Area of Beijing: A Microscopic Perspective

Urban commercial districts (UCDs) are the concentrated areas for commercial activities in a city, which provide shopping, leisure, business, and other functions. Urban planners usually face problems in how to plan and design UCDs. The layout of UCDs should not only be appropriately concentrated to realize economic benefits, but should also be properly dispersed to accommodate the distribution of the population. Using Beijing as a case study, this study conducted research into UCDs from a microscopic perspective by utilizing open source big data. A recognition and classification method of UCDs was proposed based on the data of POI and road networks. The proposed model combines Huff’s model and the Voronoi method to analyze how various UCDs should be distributed within a city according to the spatial pattern of the population. The results showed that different kinds of UCDs had different spatial distribution features. Problems were also found, for example, UCDs on the urban outskirts served a large population; there were limitations to the spatial distribution of UCDs in the downtown area; and there was incongruity between the UCD types and the population layout. Based on these findings, suggestions regarding the optimization of the urban commercial spatial structure were also put forward.

Numerical Investigation into Evolution of Crack and Stress in Residual Coal Pillars under the Influence of Longwall Mining of the Adjacent Underlying Coal Seam

Longwall mining of the adjacent coal seam with the presence of residual coal pillars overlying the seam can result in abnormal strata pressure and severe overburden failure, which poses a significant threat to mining safety. The threat is mainly manifested in the form of intense coal or rock burst and hazardous interconnection between gobs. This study employed the universal distinct element code (UDEC) to investigate the microscopic failure mechanism of the overlying residual coal pillars under the influence of longwall mining of an adjacent underlying coal seam in Yuanbaowan coal mine, China. Using the Voronoi method, we innovatively visualized the evolution of cracks in residual pillars, revealed the mechanism behind the failure of pillars, and explored the evolution and distribution of abutment stress. Also, strata movement characteristics during underlying panel extraction have been surveyed. Based on the modeling results, effective measures are proposed to ensure safe mining under residual coal pillars. This study might provide a certain reference for safe extraction of multiple seams in Datong Coalfield, China, and also in the central and western Appalachian Basin, United States, where many mining activities are carried out under residual pillars.

Understanding Vasomotion of Lung Microcirculation by In Vivo Imaging

The balance of lung extravascular water depends upon the control of blood flow in the alveolar distribution vessels that feed downstream two districts placed in parallel, the corner vessels and the alveolar septal network. The occurrence of an edemagenic condition appears critical as an increase in extravascular water endangers the thinness of the air–blood barrier, thus negatively affecting the diffusive capacity of the lung. We exposed anesthetized rabbits to an edemagenic factor (12% hypoxia) for 120 min and followed by in vivo imaging the micro-vascular morphology through a “pleural window” using a stereo microscope at a magnification of 15× (resolution of 7.2 μm). We measured the change in diameter of distribution vessels (50–200 μm) and corner vessels (<50 μm). On average, hypoxia caused a significant decrease in diameter of both smaller distribution vessels (about ~50%) and corner vessels (about ~25%) at 30 min. After 120 min, reperfusion occurred. Regional differences in perivascular interstitial volume were observed and could be correlated with differences in blood flow control. To understand such difference, we modelled imaged alveolar capillary units, obtained by Voronoi method, integrating microvascular pressure parameters with capillary filtration. Results of the analysis suggested that at 120 min, alveolar blood flow was diverted to the corner vessels in larger alveoli, which were found also to undergo a greater filtration indicating greater proneness to develop lung edema.

FEM Analysis on a Tensile Loaded Copper Plate in Meso and Macro Scale

Under ABAQUS plateform, a tensile loaded pure copper plate is analyzed by FEM in mesoscale by means of Voronoi method and in macro scale by traditional method in statistical meaning. This conduct follows that, in the uniaxial tensile loaded plate, an uneven stress and strain field are produced with maximum stresses on the grain boundaries in mesoscale, compared with the stress and strain fields distributed continuously in macrostace as usually predicted. This reflects some of objective properties of polycrystalline material.

Size effects on the Mechanical Behavior of Nanometric W/Cu Multilayers

The mechanical behavior of nanostructured stratified W/Cu composites prepared by ion beam sputtering has been investigated using a method combining X-ray diffraction and tensile testing. Tests were performed on a synchrotron light source to analyze the elastic response of the tungsten phase. Three different microstructures have been analyzed: the specimen composed of the thinner tungsten layers reveals an elastic behavior different from the one expected assuming bulk elastic constants. However, Transmission Electron Microscopy (TEM) and Grazing-Incidence Small-Angle X-ray Scattering (GISAXS) measurements reveal discontinuities in the copper layers. As the strain in the related copper clusters as well grains boundary contributions are not experimentally accessible, atomistic calculation are of utmost importance. Polycrystalline materials have already been constructed through the Voronoï method and thanks to TEM observations. Atomistic simulation and calculation are underway to validation.