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分形环轴向衍射特性的小波分析
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作者 廖天河 高穹 《河南师范大学学报(自然科学版)》 CAS CSCD 北大核心 2005年第4期54-57,共4页
对分形环的结构因子做了小波变换,通过模图在不同尺度下的演化,揭示出了相应Cantor集的结构特征.还用WTMM方法计算了轴向衍射强度的多重分形谱,并作了一些比较.
关键词 分形环 小波变换 多重分形
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宽带分形环贴片天线优化分析 被引量:1
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作者 周少波 宋铮 吴伟 《合肥工业大学学报(自然科学版)》 CAS CSCD 北大核心 2010年第12期1897-1902,共6页
文章将基于体-面混合积分方程的矩量法与遗传算法结合,用以优化有限大地板的分形环天线,处理了金属贴片与介质基片接触面的边界条件,并选取RWG面基函数和SWG体基函数计算阻抗矩阵;在保持该天线外围尺寸的情况下,分别得到覆盖整个移动通... 文章将基于体-面混合积分方程的矩量法与遗传算法结合,用以优化有限大地板的分形环天线,处理了金属贴片与介质基片接触面的边界条件,并选取RWG面基函数和SWG体基函数计算阻抗矩阵;在保持该天线外围尺寸的情况下,分别得到覆盖整个移动通信频率的宽带分形环天线和最小频率低至700 MHz的分形环天线。优化过程中采用直接矩阵操作(DMM)的方法,以加快优化计算的速度,减少优化时间。 展开更多
关键词 体-面积分方程 分形环 宽带 遗传算法 直接矩阵操作
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分形在天线雷达散射截面减缩中的应用 被引量:5
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作者 刘英 龚书喜 傅德民 《微波学报》 CSCD 北大核心 2003年第2期28-30,共3页
首次提出利用分形独特的填充性能实现天线雷达散射截面 (RCS)减缩 ,同时 ,分形单元可以减缩单元间的耦合 ,提高阵列的性能。给出了分形天线与常规天线辐射、散射特性的对比 ,表明将分形的概念用于天线设计中 ,不仅可以减小互耦 ,提高天... 首次提出利用分形独特的填充性能实现天线雷达散射截面 (RCS)减缩 ,同时 ,分形单元可以减缩单元间的耦合 ,提高阵列的性能。给出了分形天线与常规天线辐射、散射特性的对比 ,表明将分形的概念用于天线设计中 ,不仅可以减小互耦 ,提高天线阵列的辐射性能 ,而且也可以减小天线的雷达散射截面 ,对天线的隐身有一定的借鉴作用。 展开更多
关键词 分形天线 雷达散射截面 RCS 互耦 填充性 分形环
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具有分形特征的宽带人工磁导体结构 被引量:1
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作者 闫敦豹 高强 +2 位作者 付云起 张国华 袁乃昌 《微波学报》 CSCD 北大核心 2005年第6期36-38,共3页
介绍了一种新型的具有分形特征的宽带 AMC 结构。这种结构是将普通 AMC 结构贴片的边缘用 Minkowski 环代替形成,结果发现使用这种结构可以得到更宽频带的电磁带隙。在3GHz 左右的频率,电磁带隙宽度可提高28%左右。这种结构可用于实际... 介绍了一种新型的具有分形特征的宽带 AMC 结构。这种结构是将普通 AMC 结构贴片的边缘用 Minkowski 环代替形成,结果发现使用这种结构可以得到更宽频带的电磁带隙。在3GHz 左右的频率,电磁带隙宽度可提高28%左右。这种结构可用于实际的宽带电路和天线中。 展开更多
关键词 电磁带隙 人工磁导体 Minkowski分形环 宽带
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多频段兼容复合分形移动通信天线设计 被引量:1
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作者 林斌 《电子科技》 2018年第8期4-8,共5页
针对第二代~第五代移动通信系统对天线的性能要求,文中将矩形环分形结构、康托尔分形结构、谢尔宾斯基分形结构、十字分形结构相结合,设计了一款能够同时覆盖第二代~第五代移动通信频段的复合分形移动通信天线。仿真和实测结果表明,该... 针对第二代~第五代移动通信系统对天线的性能要求,文中将矩形环分形结构、康托尔分形结构、谢尔宾斯基分形结构、十字分形结构相结合,设计了一款能够同时覆盖第二代~第五代移动通信频段的复合分形移动通信天线。仿真和实测结果表明,该天线的工作频带范围为0.751~6.353 GHz,工作带宽为5.602 GHz,天线具有全向辐射特性。该款天线实现了对第二代~第五代移动通信系统的兼容,具有尺寸小、回波损耗低、工作带宽大等优点。 展开更多
关键词 矩形分形 康托尔分形 谢尔宾斯基分形 十字分形 复合分形天线 多频段兼容移动通信天线
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钴铜混合离子-DC^(-)凝胶体系有序结构的FTIR研究
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作者 尹文萱 鲍翰墨 +2 位作者 魏昭君 孙存杰 高庆宇 《光谱学与光谱分析》 SCIE EI CAS CSCD 北大核心 2023年第S01期29-30,共2页
在体外模拟胆结石形成机制的体系,选取混合金属离子Co^(2+)和Cu^(2+)研究其相互耦合,考察Co^(2+)/Cu^(2+)-DC^(-)凝胶体系有序结构的特征,分别用扫描仪及体式显微镜记录体系产生的沉淀的时空图案;傅里叶变换红外谱从凝胶中剥离的沉淀的... 在体外模拟胆结石形成机制的体系,选取混合金属离子Co^(2+)和Cu^(2+)研究其相互耦合,考察Co^(2+)/Cu^(2+)-DC^(-)凝胶体系有序结构的特征,分别用扫描仪及体式显微镜记录体系产生的沉淀的时空图案;傅里叶变换红外谱从凝胶中剥离的沉淀的微观结构。结果显示:Co^(2+)和Cu^(2+)存在相互影响,其混合离子-DC^(-)凝胶体系的沉淀物的时空图案与其单一离子-DC^(-)凝胶体系不同,Co^(2+)-DC^(-)凝胶体系沉淀形貌特征为以粉色花状分形形成周期环;Cu^(2+)-DC^(-)凝胶体系沉淀形貌特征为以蓝色球形颗粒形成周期环;混合金属离子Co^(2+)/Cu^(2+)-DC^(-)凝胶体系沉淀形貌更具复杂性:浅蓝色颗粒组成花状分形再以周期环分布、浅粉色花状分形的枝杈存在颗粒形态分布。FTIR光谱显示,混合离子Co^(2+)/Cu^(2+)-DC^(-)凝胶体系多种沉淀物为Co^(2+),Cu^(2+)-DC^(-)双核配合物,具有非化学计量特征。 展开更多
关键词 胆结石 分形/周期 混合金属离子 FTIR
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LOCAL NONLINEAR CHARACTERISTICS OF GAS LIQUID SOLID THREE PHASE SELF ASPIRATED REVERSED FLOW JET LOOP REACTOR
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作者 闻建平 梁岚 +2 位作者 刘明言 张金利 胡宗定 《Transactions of Tianjin University》 EI CAS 1998年第2期1-5,共5页
Hursts rescaled range (R/S) analysis and Wolfs attractor reconstruction technique have been adopted to estimate the local fractal dimensions and the local largest Lyapunov exponents in terms of the time series pressur... Hursts rescaled range (R/S) analysis and Wolfs attractor reconstruction technique have been adopted to estimate the local fractal dimensions and the local largest Lyapunov exponents in terms of the time series pressure fluctuations obtained from a gas liquid solid three phase self aspirated reversed flow jet loop reactor,respectively.The results indicate that the local fractal dimensions and the local largest Lyapunov exponents in both the jet region and the tubular region inside the draft tube increase with the increase in the jet liquid flowrates and the solid loadings,the local fractal dimension profiles are similar to those of the largest Lyapunov exponent,the local largest lyapunov exponents are positive for all cases,and the flow behavior of such a reactor is chaotic.The local nonlinear characteristic parameters such as the local fractal dimension and the local largest Lyapunov exponent could be applied to further study the flow properties such as the flow regime transitions and flow structures of this three phase jet loop reactor. 展开更多
关键词 three phase self aspirated reversed flow jet loop reactor local fractal dimension local largest Lyapunov exponent
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体外模拟胆结石体系基质调控的FTIR研究
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作者 杨铃 任义 +3 位作者 吕敏莹 崔云佩 王源 尹文萱 《光谱学与光谱分析》 SCIE EI CAS CSCD 北大核心 2018年第S1期13-14,共2页
利用金属离子-脱氧胆酸凝胶体系体外模拟胆结石的化学反应体系,在加入不同的生物基质后体系会有类似胆结石中的周期环/有序分形结构的沉淀产生,利用傅里叶红外光谱表征这些沉淀的微观结构,从而推断胆结石的形成。
关键词 胆结石 生物基质 FTIR 周期/分形
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Complex Dynamics Caused by Torus Bifurcation in Power Systems 被引量:1
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作者 余晓丹 贾宏杰 董存 《Transactions of Tianjin University》 EI CAS 2006年第3期186-192,共7页
Torus bifurcation is a relatively complicated bifurcation caused by a pair of complex conjugate Floquet multipliers coming out of unit circle on the Poincare section. A three-bus system is employed to reveal the relat... Torus bifurcation is a relatively complicated bifurcation caused by a pair of complex conjugate Floquet multipliers coming out of unit circle on the Poincare section. A three-bus system is employed to reveal the relationship between torus bifurcation and some complex dynamics. Based on theoretical analysis and simulation studies, it is found that torus bifurcation is a typical route to chaos in power system. Some complex dynamics usually occur after a torus bifurcation, such as self-organization, deep bifurcations, exquisite structure, coexistence of chaos and divergence. It is also found that chaos has close relationship with various instability scenarios of power systems. Studies of this paper are helpful to understand the mechanism of torus bifurcation in power system and relationship of chaos and power system instabilities. 展开更多
关键词 power system stability torus bifurcation nonlinearity CHAOS
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Explanation for peat-forming environments of coal seam 2 and 9^(-2)based on the maceral composition and aromatic compounds in the Xingtai coalfield,China 被引量:2
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作者 SUN Yu-zhuang QIN Shen-jun +2 位作者 LI Yan-heng LIN Ming-yue DING Shu-li 《Journal of Coal Science & Engineering(China)》 2009年第1期16-23,共8页
Maceral composition and aromatic compounds were determined on columnsamples to study the peat-forming environments of Permian coal seam 2 and Carboniferouscoal seam 9^(-2) from the Xingtai coalfield,China.The macerals... Maceral composition and aromatic compounds were determined on columnsamples to study the peat-forming environments of Permian coal seam 2 and Carboniferouscoal seam 9^(-2) from the Xingtai coalfield,China.The macerals were dominated by inertinitein seam 2 and by vitrinite in seam 9^(-2).Three maceral groups were selected as indicatorsof peat-forming environments.Two triangle diagrams were drawn based on the indicatorsto explicate the peat-forming environments of permian seam 2 and Carboniferousseam 9^(-2).The results indicate that the peat of carboniferous seam 9^(-2) formed dominantlyin wet swamps,whereas the peat of Permian seam 2 formed dominantly in dry swampsand open moor environments. 展开更多
关键词 Xingtai coalfield maceral composition aromatic compounds peat-forming environments PERMIAN CARBONIFEROUS
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Spanning Annuli in 3-manifolds
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作者 董笑咏 雷逢春 《Chinese Quarterly Journal of Mathematics》 CSCD 1997年第4期107-110, ,共4页
An essential annulus A properly imbedded in a 3-manifold M is said to be spanning with respect to a Hereaard splitting VUFW of M if the two components of A are lying in A and separately and A intersects the Heegaard s... An essential annulus A properly imbedded in a 3-manifold M is said to be spanning with respect to a Hereaard splitting VUFW of M if the two components of A are lying in A and separately and A intersects the Heegaard surface F in one circle. In this paper,a sufficient and necessary condition that there is a spanning annulus A in a 3-manifold M with respect to the Heegaard splitting VUFW is given. 展开更多
关键词 Heegaard splitting spanning annulus
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Prediction of Thermophoretic Deposition Efficiency of Particles in a Laminar Gas Flow along a Concentric Annulus: A Comparison of Developing and Fully Developed Flows
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作者 Samira Hashemi Ataallah Soltani Goharrizi 《Chinese Journal of Chemical Engineering》 SCIE EI CAS CSCD 2009年第5期727-733,共7页
Thermophoresis is an important mechanism of micro-particle transport due to temperature gradients in the surrounding medium.It has numerous applications,especially in the field of aerosol technology.This study has num... Thermophoresis is an important mechanism of micro-particle transport due to temperature gradients in the surrounding medium.It has numerous applications,especially in the field of aerosol technology.This study has numerically investigated the thermophoretic deposition efficiency of particles in a laminar gas flow in a concentric annulus using the critical trajectory method.The governing equations are the momentum and energy equations for the gas and the particle equations of motion.The effects of the annulus size,particle diameter,the ratio of inner to outer radius of tube and wall temperature on the deposition efficiency were studied for both developing and fully-developed flows.Simulation results suggest that thermophoretic deposition increases by increasing thermal gradient,deposition distance,and the ratio of inner to outer radius,but decreases with increasing particle size.It has been found that by taking into account the effect of developing flow at the entrance region,higher deposition efficiency was obtained,than fully developed flow. 展开更多
关键词 THERMOPHORESIS thermophoretic deposition efficiency developing flow ANNULUS
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Magnetoelastic Instability in Ring-Shaped Molecule Magnets with Next-Nearest Neighbor Coupling
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作者 LI Peng-Fei CHEN Yu-Guang 《Communications in Theoretical Physics》 SCIE CAS CSCD 2009年第12期1125-1128,共4页
In considering next-nearest neighbor (NNN) coupling, we numerically investigate the magnetoelastic instability in ring-shaped mesoscopic antiferromagnetic Heisenberg spin 1/2 systems with spin-phonon interaction. Th... In considering next-nearest neighbor (NNN) coupling, we numerically investigate the magnetoelastic instability in ring-shaped mesoscopic antiferromagnetic Heisenberg spin 1/2 systems with spin-phonon interaction. The results indicate that, for antiferromagnetic NNN coupling J2, there may be a critical value J2^c, at which the ground state is dimerized for arbitrary lattice spring constant and beyond and below which the magnetoelastic instability behavior is different from each other. The values of J2^c are irrelevant to the system size. For ferromagnetic NNN coupling, only continuous transition is present from dimerized phase to uniform phase as lattice spring constant is increased. 展开更多
关键词 single molecule magnets magnetoelastic instability spin-phonon interaction
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FRACTAL ANALYSIS APPLIED TO SPATIAL STRUCTURE OF CHINA'S VEGETATION
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作者 ZHU Xiao-hua Patel NILANCHAL +1 位作者 ZUO Wei YANG Xiu-chun 《Chinese Geographical Science》 SCIE CSCD 2006年第1期48-55,共8页
Based on the fractal theory, the spatial structure of China's vegetation has been analyzed quantitatively in this paper. Some conclusions are drawn as the following. 1) The relationships between size and frequency o... Based on the fractal theory, the spatial structure of China's vegetation has been analyzed quantitatively in this paper. Some conclusions are drawn as the following. 1) The relationships between size and frequency of patch area and patch shape index exist objectively for China's vegetation. 2) The relationships between perimeter and area exist objectively for China's vegetation. 3) The fractal dimension of evergreen needleleaf forests on mountains in subtropical and tropical zones is the largest, while the smallest for deciduous broadleafand evergreen needleleaf mixed forests in temperate zone, reflecting the most complex spatial structure for evergreen needleleaf forests on mountains in subtropical and tropical zones and the simplest for deciduous broadleaf and evergreen needleleaf mixed forests in temperate zone. 4) The fractal dimensions of China's vegetation types tend to decrease from thc subtropics to both sides. 5) The stability of spatial structure of deciduous broadleaf and evergreen needleleaf mixed forests in temperate zone is the largest, while the smallest for double-cropping rice, or double-cropping rice and temperate-like grain, and tropical evergreen economic tree plantations and orchards, reflecting the steadiest for deciduous broadleaf and evergreen needleleaf mixed forests in temperate zone and the most unstable for double-cropping rice, or double-cropping rice and temperate-like grain, and tropical evergreen economic tree plantations and orchards in spatial structure. 6) The stability of spatial structure of China's vegetation tends to decrease from the temperate zone to both sides, it is significantly pertinent to understand the formation, evolution, dynamics and complexity rule of ecosystem of vegetation. 展开更多
关键词 VEGETATION spatial structure FRACTAL fractal dimension China
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Relationship between ethnic landscape and environment in the Nujiang River basin of Yunnan Province, China
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作者 Jing Ying Huang Chengmin Su Caixiu 《Ecological Economy》 2007年第3期303-311,共9页
Each nationality has formed unique ethnic culture in the long history. Ethnic culture is spatially reflected byethnic distribution. The distribution of nationalities is influenced by ethnic history, culture, society a... Each nationality has formed unique ethnic culture in the long history. Ethnic culture is spatially reflected byethnic distribution. The distribution of nationalities is influenced by ethnic history, culture, society and religion, alsoaffected by regional physical setting. This paper analyzes the relationship between ethnic distribution pattern and naturalsetting with contrast analytical method. The digital elevation model (DEM) is established on basis of contour map on ascale of 1:250,000 in the Nujiang River basin, Yunnan Province by ArcGIS, a Geographic Information System (GIS)software. Based on DEM, the spatial analysis and statistical function of GIS, the landscape patterns of populationdistribution of the selected minorities is described, and 4 sub-regions are divided in the Nujiang River basin of YunnanProvince while the features and disparity of landscape pattern and its forming mechanism are discussed, along withhistorical and archaeological data. The conclusions are as follow: (1) The ethnic distribution is mosaic in the matrix ofother racial distribution, and have a distinct spatial correlation. (2) For the difference in cultivation between differentnationalities, certain nationality lived in the area suitable for production mode of its own and coincident with appropriategeographical setting. (3) The spatial distribution of settlement spots of the minorities is controlled by the convenience ofwater supply. The landscape pattern of ethnic distribution is closely relative to natural environment. 展开更多
关键词 Ethnic group distribution Landscape pattern Nujiang River Basin GIS Natural environmentl
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Ordered Toroid Structures of Nanoparticles in Self-attractive Semiflexible Polymer/Nanoparticle Composites
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作者 杨志勇 柴爱华 +1 位作者 李萍 杨雍福 《Chinese Journal of Chemical Physics》 SCIE CAS CSCD 2016年第3期381-388,I0002,共9页
By employing dynamic Monte Carlo simulations, we investigate a coil-to-toroid transition of self-attractive semiflexible polymers and the spatial distributions of nanoparticles in self- attractive semiflexible polymer... By employing dynamic Monte Carlo simulations, we investigate a coil-to-toroid transition of self-attractive semiflexible polymers and the spatial distributions of nanoparticles in self- attractive semiflexible polymer/nanoparticle composites. The conformation of self-attractive semiflexible polymers depends on bending energy and self-attractive interactions between monomers in polymer chains. A three-stage process of toroid formation for self-attractive semiflexible chains is shown: several isolated toroids, a loose toroid structure, and a compact toroid structure. Utilizing the compact toroid conformations of self-attractive semiflexible chains, we can control effectively the spatial distributions of nanoparticles in self-attractive semiflexible polymer nanocomposites, and an unconventional toroid structure of nanoparti- cles is observed. 展开更多
关键词 Self-attractive semiflexible polymer NANOPARTICLES Toroidal structure
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A Functional-Structural Model of Rice Seedling Coupled with Nitrogen Metabolism 被引量:1
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作者 Zhuoyang Yusang Lifeng Xu +2 位作者 Weilong Ding Zhangyun Yi Yunwei Qiu 《Journal of Agricultural Science and Technology(B)》 2014年第8期652-660,共9页
With the ability of representing the association and inner-feedback between plant morphological structure and physiological functions, functional-structural plant modeling (FSPM) approach has been used in many works... With the ability of representing the association and inner-feedback between plant morphological structure and physiological functions, functional-structural plant modeling (FSPM) approach has been used in many works, trying to better understand the mechanisms of integrating plant functions and its structure, and their communication with environmental factors. To do so, an FSPM of rice seedling was developed in this study, including structural morphogenetic model, photosynthetic model and biomass partitioning module. It can thus describe the developmental course of the rice structure dynamically based on the processes of biomass producing and partitioning. Furthermore, the processes of nitrogen metabolism, which influence the N content and growth dynamics of the virtual rice, were also considered. The model was developed with L-system on a platform established with Java programming language, which took over the parsing and visualization of the L-system strings to 3D objects using Java 3D extended library. The physiological processes in the model can be modified and further improved to gradually meet the needs for modeling the whole life cycle of rice, e.g., considering the respiration, and interaction with other environmental factors like CO2, temperature, etc.. The model was developed to provide a platform to systematically study and understand how plant systems like rice seedling work. The model and the virtualization platform can be expanded to provide decision support on N fertilizer application for the rice seedling and the other crops. 展开更多
关键词 Functional-structural plant model rice seedling nitrogen metabolism L-SYSTEM VISUALIZATION plant model.
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Solid concentration and velocity distributions in an annulus turbulent fluidized bed
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作者 吴诚 高用祥 +2 位作者 成有为 王丽军 李希 《Chinese Journal of Chemical Engineering》 SCIE EI CAS CSCD 2015年第7期1077-1084,共8页
Solid concentration and particle velocity distributions in the transition section of a Ф 200 mm turbulent fluidized bed (TFB) and a q5200 mrn annulus turbulent fluidized bed (A-TFB) with a Ф 50 mm central standp... Solid concentration and particle velocity distributions in the transition section of a Ф 200 mm turbulent fluidized bed (TFB) and a q5200 mrn annulus turbulent fluidized bed (A-TFB) with a Ф 50 mm central standpipe were measured using a PVBD optical probe. It is concluded that in turbulent regime, the axial distribution of solid concentration in A-TFB was similar to that in TFB, but the former had a shorter transition section. The axial solid concentration distribution, probability density, and power spectral distributions revealed that the standpipe hin- dered the turbulence of gas-solid two-phase flow at a low superficial gas velocity. Consequently, the bottom flow of A-TFB approached the bubbling fluidization pattern. By contrast, the standpipe facilitated the turbulence at a high superficial gas velocity, thus making the bottom flow of A-TFB approach the fast fluidization pattern. Both the particle velocity and solid concentration distribution presented a unimodal distribution in A-TFB and TFB. However, the standpipe at a high gas velocity and in the transition or dilute phase section significantly affected the radial distribution of flow parameters, presenting a bimodal distribution with particle concentration higher near the internal and external walls and in downward flow. Conversely, particle concentration in the middle an- nulus area was lower, and particles flowed upward. This result indicated that the standpipe destroyed the coreannular structure of TFB in the transition and dilute phase sections at a high gas velocity and also improved the particle distribution of TFB. In conclusion, the standpipe improved the fluidization quality and flow homogeneity at high gas velocity and in the transition or dilute phase section, but caused opposite phenomena at low gas velocity and in the dense-phase section. 展开更多
关键词 FluidizationAnnulus bedTransition sectionHydrodynamicsTurbulence
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Ring Polymer Molecular Dynamics of the C(^(1)D)+H_(2) Reaction on the Most Recent Potential Energy Surfaces
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作者 Jianwei Cao Yanan Wu Wensheng Bian 《Chinese Journal of Chemical Physics》 SCIE CAS CSCD 2021年第6期833-842,I0003,I0004,共12页
Ring polymer molecular dynamics(RPMD)calculations for the C(^(1)D)+H_(2)reaction are performed on the Zhang-Ma-Bian ab initio potential energy surfaces(PESs)recently constructed by our group,which are unique in very g... Ring polymer molecular dynamics(RPMD)calculations for the C(^(1)D)+H_(2)reaction are performed on the Zhang-Ma-Bian ab initio potential energy surfaces(PESs)recently constructed by our group,which are unique in very good descriptions of the regions around conical intersections and of van der Waals(vdW)interactions.The calculated reaction thermal rate coefficients are in very good agreement with the latest experimental results.The rate coefficients obtained from the ground˜a^(1)A′ZMB-a PES are much larger than those from the previous RKHS PES,which can be attributed to that the vdW saddles on our PESs have very different dynamical effects from the vdW wells on the previous PESs,indicating that the RPMD approach is able to include dynamical effects of the topological structures caused by vdW interactions.The importance of the excited˜b^(1)A′′ZMB-b PES and quantum effects in the title reaction is also underscored. 展开更多
关键词 Rate coefficients Ring polymer molecular dynamics Complex-forming reactions Potential energy surfaces van der Waals interactions
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Mathieu Progressive Waves
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作者 Andrei B.Utkin 《Communications in Theoretical Physics》 SCIE CAS CSCD 2011年第10期733-739,共7页
A new family of exact solutions to the wave equation representing relatively undistorted progressive waves is constructed using separation of variables in the elliptic cylindrical coordinates and one of the Bateman tr... A new family of exact solutions to the wave equation representing relatively undistorted progressive waves is constructed using separation of variables in the elliptic cylindrical coordinates and one of the Bateman transforms. The general form of this Bateman transform in an orthogonal eurvilinear cylindrical coordinate system is discussed and a specific problem of physical feasibility of the obtained solutions, connected with their dependence on the cyclic coordinate, is addressed. The limiting case of zero eccentricity, in which the elliptic cylindrical coordinates turn into their circular cylindrical counterparts, is shown to correspond to the focused wave modes of the Bessel-Gauss type. 展开更多
关键词 wave equation Bateman transform progressive wave Mathieu function
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