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volume of Singular Hyperbolic Sets

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Acta Mathematica Sinica,English Series 2021年第10期37卷 1507-1512页

作者： Dao Fei ZHANG Yun Tao ZANG Mathematics Institute University of WarwickCoventryCV47ALUK School of Mathematical Sciences East China Normal UniversityShanghai 200062P.R.C

Let X be a C^(1+)vector field on a compact Riemannian manifold M with dimension d≥***Λbe a transitive singular hypebolic set with positive *** show thatΛ=M andΛis a uniformly hyperbolic set without singularities.

关键词： Uniformly hyperbolic singular hyperbolic volume

volume of Domains in Symmetric Spaces

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Chinese Annals of Mathematics,Series B 2007年第5期28卷 521-526页

作者： Ximo GUAL-ARNAU Antonio M.NAVEIRA Department of Mathematics Universitat Jaume I 12071-CastellóSpain. Departamento de Geometría y Topología Universidad de Valencia 46100-BurjassotValenciaSpain.

The authors derive a formula for the volume of a compact domain in a symmetric space from normal sections through a special submanifold in the symmetric *** formula generalizes the volume of classical domains as tubes... 详细信息

关键词： Curvature-adapted submanifold Lie triple systematic normal bundle Root decomposable normal bundle Symmetric space volume

A method for calibrating the confocal volume of a confocal three-dimensional micro-x-ray fluorescence setup

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Chinese Physics B 2020年第2期29卷 190-195页

作者： Peng Zhou Xin-Ran Ma Shuang Zhang Tian-Xi Sun Zhi-Guo Liu College of Nuclear Science and Technology Beijing Normal UniversityBeijing 100875China Applied Optics Beijing Key Laboratory Department of PhysicsBeijing Normal UniversityBeijing 100875China Beijing Radiation Center Beijing 100875China Department of Physics Beijing Normal UniversityBeijing 100875China

The measurement of the confocal volume of a confocal three-dimensional micro-x-ray fluorescence(3D-XRF)setup is a key step in the field of confocal 3D-XRF *** the development of x-ray facilities and optical devices,3D-XRF analysis with a micro confocal volume will create a great potential for 2D and 3D microstructural analysis and accurate quantitative ***,the classic measurement method of scanning metal foils of a certain thickness leads to inaccuracy.A method for calibrating the confocal volume is proposed in this *** new method is based on the basic content of the textbook,and the theoretical results and the feasibility are given in detail for the 3D-XRF mono-chromatic x-ray condition and the poly-chromatic x-ray *** obtain a set of experimental confirmation using the poly-chromatic x-ray tube in the *** is proved that the sensitivity factor of the 3D-XRF can be directly and accurately obtained in a real calibration process.

关键词： three-dimensional micro-x-ray fluorescence(3D-XRF) depth analysis confocal volume probe calibrating

Modeling bubble column reactor with the volume of fluid approach:Comparison of surface tension models

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Chinese Journal of Chemical Engineering 2019年第11期27卷 2659-2665页

作者： Qi Liu Zhenghong Luo Department of Chemical Engineering College of Chemistry and Chemical EngineeringState Key Laboratory of Metal Matrix CompositesShanghai Jiao Tong UniversityShanghai 200240China

This work aims at comparing surface tension models in VOF(volume of Fluid) modeling and investigating the effects of gas distributor and gas velocity. Hydrodynamics of a continuous chain of bubbles inside a bubble column reactor was simulated. The grid independence study was first conducted and a grid size of 1.0 mm was adopted in order to minimize the computing time without compromising the accuracy of the results. The predictions were validated by comparing the experimental studies reported in the literature. It was found that all surface tension models can describe the bubble rise and bubble plume in a column with slight deviations.

关键词： Bubble column reactor Computational fluid dynamics volume of fluid method Surface tension models Gas distributor

NUMERICAL SOLUTION OF VISCOUS FLOW PAST A SOLID SPHERE WITH THE CONTROL volume FORMULATION

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Chinese Journal of Chemical Engineering 1997年第2期5卷 13-24页

作者：毛在砂陈家镛 Institute of Chemical Metallurgy Academia Sinica

The control volume formulation with the QUICK finite difference scheme is used to solveincompressible liquid flow past a solid sphere in terms of stream function and *** tech-nical points are addressed on improving the accuracy and efficiency of numerical simulation of similarproblems of fluid *** particular,the importance of suitable specification of the distortion func-tion to enforcing the far field boundarv conditions is emphasized.

关键词： sphere laminar flow numerical simulation control volume formulation QUICK scheme

Visualization of flow structures inside a conical spouted bed by electrical capacitance volume tomography

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Particuology 2019年第1期17卷 15-25页

作者： Hoon Chae Park Hang Seok Choi Department of Environmental Engineering Yonsei UniversityWonju 26493Republic of Korea

Electrical capacitance volume tomography (ECVT) was conducted to measure instantaneous gas–solid flow structures in a conical spouted bed. The sensor has 24 electrodes/channels and was used to make three-dimensional measurements of the solid volume fraction. Flow structures in the conical spouted bed were analyzed using quantitative ECVT images. Three-dimensional images of gas–solid flow structures and time-averaged vertical and radial solid volume fraction profiles are presented. Different fluidization regimes in spouted beds were characterized by analyzing pressure fluctuation signals and ECVT images. ECVT was shown to be robust and powerful for the three-dimensional visualization and quantitative measurement of a gas–solid fluidization system.

关键词： Conical spouted bed Electrical capacitance volume tomography Multiphase flow

Using X-ray computed tomography and micro-Raman spectrometry to measure individual particle surface area, volume, and morphology towards investigating atmospheric heterogeneous reactions

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Journal of Environmental Sciences 2018年第7期30卷 23-32页

作者： Mingjin Wang Nan Zheng Tong Zhu Jing Shang Ting Yu Xiaojuan Song Defeng Zhao Yong Guan Yangchao Tian BIC-ESAT and SKL-ESPCl College of Environmental Sciences and Engineering Peking University Beijing 100871 China National Synchrotron Radiation Laboratory University of Science and Technology of ChinaHefei 230029 China

Heterogeneous reactions on the aerosol particle surface in the atmosphere play important roles in air pollution, climate change, and global biogeochemical cycles. However, the reported uptake coefficients of heterogeneous reactions usually have large variations and may not be relevant to real atmospheric conditions. One of the major reasons for this is the use of bulk samples in laboratory experiments, while particles in the atmosphere are suspended individually. A number of technologies have been developed recently to study heterogeneous reactions on the surfaces of individual particles. Precise measurements on the reactive surface area, volume, and morphology of individual particles are necessary for calculating the uptake coefficient, quantifying reactants and products, and understanding the reaction mechanism better. In this study, for the first time we used synchrotron radiation X-ray computed tomography（XCT） and micro-Raman spectrometry to measure individual CaCO_3 particle morphology, with sizes ranging from 3.5–6.5 μm. Particle surface area and volume were calculated using a reconstruction method based on software threedimensional（3-D） rendering. The XCT was first validated with high-resolution fieldemission scanning electron microscopy（FE-SEM） to acquire accurate CaCO_3 particle surface area and volume estimates. Our results showed an average difference of only 6.1% in surface area and 3.2% in volume measured either by micro-Raman spectrometry or X-ray tomography. X-ray tomography and FE-SEM can provide more morphological details of individual Ca CO3 particles than micro-Raman spectrometry. This study demonstrated that X-ray computed tomography and micro-Raman spectrometry can precisely measure the surface area, volume, and morphology of an individual particle.

关键词： Heterogeneous reactions Individual CaCO3 particle Micro-Raman spectrometry Synchrotron radiation X-ray computed tomography Morphology Surface area volume

Study on the packed volume and the void ratio of idealized human red blood cells using a ?nite-discrete element method

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Applied Mathematics and Mechanics(English Edition) 2019年第5期40卷 737-750页

作者： Dong XU Chunning JI A.MUNJIZA E.KALIVIOTIS E.AVITAL J.WILLAMS State Key Laboratory of Hydraulic Engineering Simulation and Safety Tianjin University School of Engineering & Material Science Queen Mary University of London Faculty of Engineering and Technology Cyprus University of Technology

Numerical simulations are performed to examine the packing behavior of human red blood cells(RBCs). A combined ?nite-discrete element method(FDEM) is utilized, in which the RBCs are modeled as no-friction and no-adhesion solid bodies. The packed volume and the void ratio of a large number of randomly packed RBCs are clari?ed,and the effects of the RBC shape, the mesh size, the cell number, and the container size are investigated. The results show that the packed human RBCs with normal shape have a void ratio of 28.45%, which is slightly higher than that of the ?at or thick cells used in this study. Such information is bene?cial to the further understanding on the geometric features of human RBCs and the research on RBC simulations.

关键词： red blood cell (RBC) void ratio packed volume discrete element method

Predicting the upper stem diameters and volume of a tropical dominant tree species

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Journal of Forestry Research 2022年第6期33卷 1725-1737页

作者： Sunita Ulak Keshav Ghimire Rabindra Gautam Shes Kanta Bhandari Krishna Prasad Poudel Yajna Prasad Timilsina Dhirendra Pradhan Thakur Subedi Forest Research and Training Centre KathmanduNepal Institute of Forestry Tribhuvan UniversityKathmanduNepal School of Biological Sciences The University of Western AustraliaPerthAustralia Department of Forestry Mississippi State UniversityMississippi StatePO Box 9681Starkville 39762USA

Predicting upper stem diameters and individual tree volumes is important for product quantification and can provide important information for the sustainable management of forests of important commercial tree species(Shorea robusta)in *** aim of this study was to develop a taper equation for ***-four trees were selected and felled in the southern low land of Nepal.A mixed effect modelling approach was used to evaluate 17 different taper functions.‘Leave-one-out cross-validation'was used to validate the fitted taper *** variable exponent taper function best fitted our data and described more than 99%of the variation in upper stem *** also showed significant effects of stand density on tree *** tree volume prediction using the local volume model developed in this study was more accurate compared to the volume predicted through the taper function and existing volume *** taper function developed in this study provides the benefit of predicting upper stem diameter and can be used for predicting volume to any merchantable height of individual *** will have implications in estimates of volume,biomass,and carbon and thus may be a potential supporting tool in carbon trade and revenue generation.

关键词： Mixed-model approach Shorea robusta Taper volume Nepal