Six core issues for vortex definition and identification concern with (1) the absolute strength,(2) the relative strength,(3) the rotational axis,(4) the vortex core center,(5) the vortex core size, and (6) the vortex...Six core issues for vortex definition and identification concern with (1) the absolute strength,(2) the relative strength,(3) the rotational axis,(4) the vortex core center,(5) the vortex core size, and (6) the vortex boundary (Liu C. 2019). However, most of the currently popular vortex identification methods, including the Q criterion, the criterion and the Acj criterion etc., are Eulerian local region-type vortex identification criteria and can only approximately identify the vortex boundary by somewhat arbitrary threshold. On the other hand, the existing Eulerian local line-type methods, which seek to extract line-type features such as vortex core line, are not entirely satisfactory since most of these methods are based on vorticity or pressure minimum that will fail in many cases. The key issue is the lack of a reasonable mathematical definition for vortex core center. To address this issue, a Liutex (previously named Rortex) based definition of vortex core center is proposed in this paper. The vortex core center, also called vortex rotation axis line here, is defined as a line where the Liutex magnitude gradient vector is aligned with the Liutex vector, which mathematically implies that the cross product of the Liutex magnitude gradient vector and the Liutex vector on the line is equal to zero. Based on this definition, a novel three-step method for extracting vortex rotation axis lines is presented. Two test cases, namely the Burgers vortex and hairpin vortices, are examined to justify the proposed method. The results demonstrate that the proposed method can successfully identify vortex rotation axis lines without any user-specified threshold, so that the proposed method is very straightforward, robust and efficient.展开更多
The spatial structures of China’s Major Function Zoning are important constraining indicators in all types of spatial planning and key parameters for accurately downscaling major functions.Taking the proportion of ur...The spatial structures of China’s Major Function Zoning are important constraining indicators in all types of spatial planning and key parameters for accurately downscaling major functions.Taking the proportion of urbanization zones,agricultural development zones and ecological security zones as the basic parameter,this paper explores the spatial structures of major function zoning at different scales using spatial statistics,spatial modeling and landscape metrics methods.The results show:First,major function zones have spatial gradient structures,which are prominently represented by latitudinal and longitudinal gradients,a coastal distance gradient,and an eastern-central-western gradient.Second,the pole-axis system structure and core-periphery structure exist at provincial scales.The general principle of the pole-axis structure is that as one moves along the distance axis,the proportion of urbanization zones decreases and the proportion of ecological security zones increases.This also means that the proportion of different function zones has a ring-shaped spatial differentiation principle with distance from the core.Third,there is a spatial mosaic structure at the city and county scale.This spatial mosaic structure has features of both spatial heterogeneity,such as agglomeration and dispersion,as well as of mutual,adjacent topological correlation and spatial proximity.The results of this study contribute to scientific knowledge on major function zones and the principles of spatial organization,and it acts as an important reference for China’s integrated geographical zoning.展开更多
Gradient cemented carbides with nano-TiN were prepared by the common powder metallurgical procedure. The formation of gradient zone and the microstructure, properties of the alloys were investigated using scanning ele...Gradient cemented carbides with nano-TiN were prepared by the common powder metallurgical procedure. The formation of gradient zone and the microstructure, properties of the alloys were investigated using scanning electron microscope（SEM）, energy dispersive spectroscopy（EDS） and other performance testing apparatus. Moreover, the effect of nano-TiN on the gradient cemented carbide was studied. It is found that gradient zone width increases slightly with nano-TiN introduction. Both cobalt and titanium concentrations reach the maximum near the gradient border. Tungsten concentration shows fluctuation from the surface to the bulk. （Ti ,W）C phase grains are refined for nitrogen introduction. Core-rim structure has been observed under the SEM back-scattered mode. The core appears as dark due to more titanium in it and the rim with more tungsten appears as grey. In addition, the hardness and transverse rupture strength of gradient cemented carbide are enhanced with nano-TiN introduced.展开更多
基金supported by the National Natural Science Foundation of China (Grant No. 91530325).
文摘Six core issues for vortex definition and identification concern with (1) the absolute strength,(2) the relative strength,(3) the rotational axis,(4) the vortex core center,(5) the vortex core size, and (6) the vortex boundary (Liu C. 2019). However, most of the currently popular vortex identification methods, including the Q criterion, the criterion and the Acj criterion etc., are Eulerian local region-type vortex identification criteria and can only approximately identify the vortex boundary by somewhat arbitrary threshold. On the other hand, the existing Eulerian local line-type methods, which seek to extract line-type features such as vortex core line, are not entirely satisfactory since most of these methods are based on vorticity or pressure minimum that will fail in many cases. The key issue is the lack of a reasonable mathematical definition for vortex core center. To address this issue, a Liutex (previously named Rortex) based definition of vortex core center is proposed in this paper. The vortex core center, also called vortex rotation axis line here, is defined as a line where the Liutex magnitude gradient vector is aligned with the Liutex vector, which mathematically implies that the cross product of the Liutex magnitude gradient vector and the Liutex vector on the line is equal to zero. Based on this definition, a novel three-step method for extracting vortex rotation axis lines is presented. Two test cases, namely the Burgers vortex and hairpin vortices, are examined to justify the proposed method. The results demonstrate that the proposed method can successfully identify vortex rotation axis lines without any user-specified threshold, so that the proposed method is very straightforward, robust and efficient.
基金National Natural Science Foundation of China,No.41630644Innovative Think-tank Foundation for Young Scientists of China Association for Science and Technology,No.DXB-ZKQN-2017-048。
文摘The spatial structures of China’s Major Function Zoning are important constraining indicators in all types of spatial planning and key parameters for accurately downscaling major functions.Taking the proportion of urbanization zones,agricultural development zones and ecological security zones as the basic parameter,this paper explores the spatial structures of major function zoning at different scales using spatial statistics,spatial modeling and landscape metrics methods.The results show:First,major function zones have spatial gradient structures,which are prominently represented by latitudinal and longitudinal gradients,a coastal distance gradient,and an eastern-central-western gradient.Second,the pole-axis system structure and core-periphery structure exist at provincial scales.The general principle of the pole-axis structure is that as one moves along the distance axis,the proportion of urbanization zones decreases and the proportion of ecological security zones increases.This also means that the proportion of different function zones has a ring-shaped spatial differentiation principle with distance from the core.Third,there is a spatial mosaic structure at the city and county scale.This spatial mosaic structure has features of both spatial heterogeneity,such as agglomeration and dispersion,as well as of mutual,adjacent topological correlation and spatial proximity.The results of this study contribute to scientific knowledge on major function zones and the principles of spatial organization,and it acts as an important reference for China’s integrated geographical zoning.
基金Funded by Research Funds for the Central Universities(No.2011SCU11038)Chengdu Science and Technology Project(Nos.10GGZD080GX-268 and 11DXYB096JH-027)
文摘Gradient cemented carbides with nano-TiN were prepared by the common powder metallurgical procedure. The formation of gradient zone and the microstructure, properties of the alloys were investigated using scanning electron microscope（SEM）, energy dispersive spectroscopy（EDS） and other performance testing apparatus. Moreover, the effect of nano-TiN on the gradient cemented carbide was studied. It is found that gradient zone width increases slightly with nano-TiN introduction. Both cobalt and titanium concentrations reach the maximum near the gradient border. Tungsten concentration shows fluctuation from the surface to the bulk. （Ti ,W）C phase grains are refined for nitrogen introduction. Core-rim structure has been observed under the SEM back-scattered mode. The core appears as dark due to more titanium in it and the rim with more tungsten appears as grey. In addition, the hardness and transverse rupture strength of gradient cemented carbide are enhanced with nano-TiN introduced.
