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Effect and mechanism of on-chip electrostatic discharge protection circuit under fast rising time electromagnetic pulse
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作者 Mao Xinyi Chai Changchun +3 位作者 Li Fuxing Lin Haodong Zhao Tianlong Yang Yintang 《强激光与粒子束》 CAS CSCD 北大核心 2024年第10期44-52,共9页
The electrostatic discharge(ESD)protection circuit widely exists in the input and output ports of CMOS digital circuits,and fast rising time electromagnetic pulse(FREMP)coupled into the device not only interacts with ... The electrostatic discharge(ESD)protection circuit widely exists in the input and output ports of CMOS digital circuits,and fast rising time electromagnetic pulse(FREMP)coupled into the device not only interacts with the CMOS circuit,but also acts on the protection circuit.This paper establishes a model of on-chip CMOS electrostatic discharge protection circuit and selects square pulse as the FREMP signals.Based on multiple physical parameter models,it depicts the distribution of the lattice temperature,current density,and electric field intensity inside the device.At the same time,this paper explores the changes of the internal devices in the circuit under the injection of fast rising time electromagnetic pulse and describes the relationship between the damage amplitude threshold and the pulse width.The results show that the ESD protection circuit has potential damage risk,and the injection of FREMP leads to irreversible heat loss inside the circuit.In addition,pulse signals with different attributes will change the damage threshold of the circuit.These results provide an important reference for further evaluation of the influence of electromagnetic environment on the chip,which is helpful to carry out the reliability enhancement research of ESD protection circuit. 展开更多
关键词 fast rising time electromagnetic pulse damage effect electrostatic discharge protection circuit damage location prediction
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Hydrodynamic Behavior of a Single Bubble Rising in Viscous Liquids 被引量:7
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作者 CAI Ziqi BAO Yuyun GAO Zhengming 《Chinese Journal of Chemical Engineering》 SCIE EI CAS CSCD 2010年第6期923-930,共8页
The rising behavior of single bubbles has been investigated in six systems with different viscosity and Morton number(Mo) from 3.21×10-11 to 163. Bubbles with maximum equivalent diameter of up to 16 mm were inves... The rising behavior of single bubbles has been investigated in six systems with different viscosity and Morton number(Mo) from 3.21×10-11 to 163. Bubbles with maximum equivalent diameter of up to 16 mm were investigated. The bubble Reynolds number(Re) ranged from 0.02 to 1200 covering 3 regimes in which two func-tions are obtained relating the drag coefficient,CD,with Re and Mo. It has been found that in the high Reynolds number regime the drag coefficient increases until the Reynolds number of about 1200. The classic expression of Jamialahmadi(1994) is improved and extended to high viscosity liquids. A new relationship for the aspect ratio of deformed bubbles in terms of Re,the Etvs number and Mo,applicable to a wide range of system properties,espe-cially in high viscosity liquids,is also suggested. 展开更多
关键词 BUBBLE rising velocity viscous liquid drag coefficient DEFORMATION
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Analysis of deformation and internal flow patterns for rising single bubbles in different liquids 被引量:4
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作者 Xin Li Pan Zhang +2 位作者 Jianlong Li Weiwen Wang Guanghui Chen 《Chinese Journal of Chemical Engineering》 SCIE EI CAS CSCD 2019年第4期745-758,共14页
Gas–liquid multiphase flow is a significant phenomenon in chemical processes. The rising behaviors of single bubbles in the quiescent liquids have been investigated but the internal flow patterns and deformation rule... Gas–liquid multiphase flow is a significant phenomenon in chemical processes. The rising behaviors of single bubbles in the quiescent liquids have been investigated but the internal flow patterns and deformation rules of bubbles, which influence the mass transfer efficiency to a large extent, have received much less attention. In this paper, the volume of fluid method was used to calculate the bubble shapes, pressure, velocity distributions,and the flow patterns inside the bubbles. The rising behavior of the bubbles with four different initial diameters,i.e., 3 mm, 5 mm, 7 mm and 9 mm was investigated in four various liquids including water, 61.23% glycerol,86.73% glycerol and 100% glycerol. The results show that the liquid properties and bubble initial diameters have great impacts on bubble shapes. Moreover, flow patterns inside the bubbles with different initial diameters were analyzed and classified into three types under the condition of different bubble shapes. Three correlations for predicting the maximum internal circulation inside the bubbles in 86.73% glycerol were presented and the R-square values were all bigger than 0.98. Through analyzing the pressure and velocity distributions around the bubbles, four rules of bubble deformation were also obtained to explain and predict the shapes. 展开更多
关键词 MULTIPHASE FLOW Bubble Interface DEFORMATION ANALYSIS INTERNAL FLOW pattern rising behavior
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Effect of rapidly depressurizing and rising temperature on methane hydrate dissociation 被引量:11
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作者 Qingbai Wu Yingmei Wang Jing Zhan 《Journal of Natural Gas Chemistry》 EI CAS CSCD 2012年第1期91-97,共7页
Two methods, rapidly depressurizing to 0.1 MPa at a constant temperature and rising temperature under equilibrium P, T conditions, were used to study the dissociation of pure CH4 hydrate formed below the ice point. At... Two methods, rapidly depressurizing to 0.1 MPa at a constant temperature and rising temperature under equilibrium P, T conditions, were used to study the dissociation of pure CH4 hydrate formed below the ice point. At a constant temperature with rapidly depressurizing to 0.1 MPa, CH4 hydrate dissociated rapidly at initial dissociation and then the dissociation rate gradually decreased. However, the dissociation of CH4 hydrate at temperatures of 261 to 266 K was much faster than that at temperatures of 269 to 272 K, indicating its anomalous preservation. Under an equilibrium P, T conditions, rising temperature had extensively controlling impact on dissociation of CH4 hydrate at equilibrium pressures of 2.31, 2.16 and 1.96 MPa. In this study, we report the effect of pressure on CH4 hydrate dissociation, especially the effect of equilibrium pressure on dissociation at various melting temperatures. And we find that the ice particles size of CH4 hydrate formed may dominant the CH4 hydrate dissociation. Dissociation of CH4 hydrate formed from ice particles of smaller than 250 μm may not have an anomalous preservation below the ice point, while particles larger than 250 μm may have more extensive anomalous preservation. 展开更多
关键词 dissociation of CH4 hydrate method of rapid depressurization method of rising temperature
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A Rising Force for the World-Wide Development of Laser-Induced Breakdown Spectroscopy 被引量:6
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作者 王哲 董凤忠 周卫东 《Plasma Science and Technology》 SCIE EI CAS CSCD 2015年第8期617-620,共4页
Laser-induced breakdown spectroscopy (LIBS) has attracted many academic and industrial interests world-wide due to its unique advantages, such as little or no sample preparation requirement, in-situ/online and multi... Laser-induced breakdown spectroscopy (LIBS) has attracted many academic and industrial interests world-wide due to its unique advantages, such as little or no sample preparation requirement, in-situ/online and multi-elemental analysis, and remote sensing etc., and it has been regarded as a "future super star" for chemical analysis for many years . In China, 展开更多
关键词 LIBS A rising Force for the World-Wide Development of Laser-Induced Breakdown Spectroscopy
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Response of N_2O Emissions of Farmland Ecosystem on Temperature Rising
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作者 刘柳松 施建成 《Agricultural Science & Technology》 CAS 2012年第9期1962-1966,共5页
[Objective] The aim was to study on response of N2O emissions of farm- land ecosystem on temperature rising. [Methed] In farmland ecosystem in Huaibei City in Anhui Province, N2O emission by twelve varieties of crop o... [Objective] The aim was to study on response of N2O emissions of farm- land ecosystem on temperature rising. [Methed] In farmland ecosystem in Huaibei City in Anhui Province, N2O emission by twelve varieties of crop on temperature was researched with DeNitrification-DeComposition (NDC). [Result] Response of dry- land crop on temperature rising can be divided into three categories, as follows: The first category, N2O emission of crop changed little during the temperature increasing, for example, from 0 to 3 %;, the emissions by potatoes, cotton, maize and rapeseed increased little and decreased little when temperature changed from 1.5 to 3 ℃. Crops of the second category declined with temperature increasing in N2O emission, for example, N2O emission decreased by 8.1% with temperature increasing from 0 to 3 ℃, including sugar cane, tobacco, wheat, soybean and pea. In third category, N2O emission of crop grew with temperature increasing, for example, the emission of rice, vegetables and fruit trees increased by 22.8% when the temperature grew from 0 to 3 ℃. [Conclusion] The research indicated that N2O emission in ecosystem of drv farmland increased little with temoerature risina. 展开更多
关键词 Arid land Farmland ecosystem N20 emission Temperature rising
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Effects of rising temperature on growth and energy budget of juvenile Eogammarus possjeticus(Amphipoda:Anisogammaridae) 被引量:1
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作者 Suyan Xue Yuze Mao +2 位作者 Jiaqi Li Jianguang Fang Fazhen Zhao 《Acta Oceanologica Sinica》 SCIE CAS CSCD 2021年第9期82-89,共8页
Growth and energy budget of marine amphipod juvenile Eogammarus possjeticus at different temperatures(20℃,24℃,26℃,28℃,30℃,32℃ and 34℃)were investigated in this study.The results showed that the cumulative morta... Growth and energy budget of marine amphipod juvenile Eogammarus possjeticus at different temperatures(20℃,24℃,26℃,28℃,30℃,32℃ and 34℃)were investigated in this study.The results showed that the cumulative mortality rate increased significantly with rising temperature(p<0.01),and exceeded 50%after 24 h when temperature was above 30℃.With the temperature increasing from 20℃ to 26℃,the ingestion rate and absorption rate increased,but decreased significantly above 28℃(p<0.01),indicating a decline in feeding ability at high temperatures.The specific growth rate increased with rising temperature,but decreased significantly(p<0.01)after reaching the maximum value at 24℃.Similarly,the oxygen consumption and ammonia emission rates also showed a trend of first increase and then decrease.However,the O:N ratio decreased first and then increased with rising temperature,indicating that the energy demand of E.possjeticus juvenile transferred from metabolism of carbohydrate and lipid to protein.In the energy distribution of amphipods,the proportion of each energy is different.With rising temperature,the ratio of the energy deposited for growth accounted for ingested gross energy showing a trend of decrease,while the energy lost to respiration,ammonia excretion,and feces accounted for ingested gross energy being showed a trend of increase.It seemed that rising temperature increased the metabolism and energy consumption of the amphipods and,meanwhile,decreased the energy used for growth,which may be an important reason for the slow growth and small body size of the amphipods during the summer high-temperature period. 展开更多
关键词 Eogammarus possjeticus rising temperature GROWTH respiratory metabolism energy budget
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Auto-Test on Motor Temperature Rising in Electric Vehicles with Mutual MRAS 被引量:1
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作者 王志福 张承宁 《Journal of Beijing Institute of Technology》 EI CAS 2008年第4期395-399,共5页
A new method to calculate the motor temperature rising in electric vehicle (EV) is proposed based on the stator resistance identification. The measure theory of the motor temperature rising with the stator resistanc... A new method to calculate the motor temperature rising in electric vehicle (EV) is proposed based on the stator resistance identification. The measure theory of the motor temperature rising with the stator resistance is discussed at first. An enhanced magnetism motor dynamic math model is built which is the research object. Then the resistance identification system model is built on the mutual model reference adaptive,system (MRAS) theory. The simulation diagram of the mutual MRAS model is constructed and the resistance identification performance is studied in different motor states. Simulation results indicate that the stator resistance identification model with the mutual MRAS is effective. At the same time, the identification of motor temperature rising is possible with the identification of the stator resistance. 展开更多
关键词 electric vehicle (EV) motor's temperature rising model reference adaptive system (MARS) resistance identification
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Effect of pulse voltage rising time on discharge characteristics of a helium-air plasma at atmospheric pressure 被引量:1
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作者 Muyang QIAN Gui LI +4 位作者 Sanqiu LIU Yu ZHANG Shan LI Zebin LIN Dezhen WANG 《Plasma Science and Technology》 SCIE EI CAS CSCD 2017年第6期102-107,共6页
In this paper,the influence of voltage rising time on a pulsed-dc helium-air plasma at atmospheric pressure is numerically simulated.Simulation results show that as the voltage rising time increases from 10 ns to 30 n... In this paper,the influence of voltage rising time on a pulsed-dc helium-air plasma at atmospheric pressure is numerically simulated.Simulation results show that as the voltage rising time increases from 10 ns to 30 ns,there is a decrease in the discharge current,namely 0.052 A when the voltage rising time is 10 ns and 0.038 A when the voltage rising time is 30 ns.Additionally,a shorter voltage rising time results in a faster breakdown,a more rapidly rising current waveform,and a higher breakdown voltage.Furthermore,the basic parameters of the streamer discharge also increase with voltage rise rate,which is ascribed to the fact that more energetic electrons are produced in a shorter voltage rising time.Therefore,a pulsed-dc voltage with a short rising time is desirable for efficient production of nonequilibrium atmospheric pressure plasma discharge. 展开更多
关键词 atmospheric pressure plasma discharge voltage rising time numerical simulation
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Comprehensive tests on rising height of capillary water for coarse grained soil 被引量:4
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作者 GUO Qingsong LI Xin LI Min 《Global Geology》 2013年第1期54-58,共5页
According to the comprehensive tests on the rising height of capillary water for seven kinds of differ- ent coarse grained soil by use of the method of standpipe, the relationship between the rising height of capillar... According to the comprehensive tests on the rising height of capillary water for seven kinds of differ- ent coarse grained soil by use of the method of standpipe, the relationship between the rising height of capillary water and time was obtained, and the influencing factors and rules were analyzed. The data of the steady rising height of capillary water were obtained, and the regression equation of coarse grained soil on steady height and physical indexes (effective grain dl0 and porosity n) was found. Compared with Hazen's and other expressions that could estimate the steady height of capillary water of coarse grained soil, the proposed method is satisfactory and the defects of the latter were pointed out. 展开更多
关键词 method of standpipe coarse grained soil rising height of capillary water degree of compaction
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Can the early bird catch the worm? Effects of early rising on leukocyte subsets via modification of autonomic nervous system and the effect on glucose levels 被引量:1
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作者 Mayumi Watanabe Yiwei Ling +5 位作者 Chikako Tomiyama Kiyoshi Adachi Hidetoshi Mori Kazushi Nishijo Toru Abo Kohei Akazawa 《Natural Science》 2013年第11期1133-1138,共6页
The importance of sleep has been described in proverbs such as “the early bird catches the worm”. However, there are few scientific reports on the effects of early rising. Therefore, early risers (Group E) and late ... The importance of sleep has been described in proverbs such as “the early bird catches the worm”. However, there are few scientific reports on the effects of early rising. Therefore, early risers (Group E) and late risers (Group L) were compared and the number and ratio of leukocytes, body temperature, glucose and its associated hormones were studied. Furthermore, each group was divided into two groups by the duration of sleep and the following four groups were compared: early risers with short sleep (Group E-S);early risers with long sleep (Group E-L);late risers with short sleep (Group L-S);and late risers with long sleep (Group L-L). Then, compared with Group L, Group E showed lower numbers and ratio of granulocytes and a higher ratio of lymphocytes showing parasympathetic nerve dominance. Group E showed higher levels of glucose and its related hormones than Group L, indicating sympathetic nerve dominance. Compared with Groups E-S and L-S, Groups E-L and L-L showed lower glucose and cortisol levels, respectively. These results indicated that early rising might affect leukocyte subsets, and adequate duration of sleep could decrease levels of glucose via modification of the autonomic nervous system. 展开更多
关键词 EARLY rising LEUKOCYTE AUTONOMIC Nervous System (ANS)
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Water-cut rising mechanism and optimized water injection technology for deepwater turbidite sandstone oilfield: A case study of AKPO Oilfield in Niger Delta Basin, West Africa 被引量:1
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作者 YUAN Zhiwang YANG Baoquan +5 位作者 YANG Li GU Wenhuan CHEN Xiao KANG Botao LI Chenxi ZHANG Huilai 《Petroleum Exploration and Development》 2018年第2期302-311,共10页
Through the analysis of the reservoir connection relationship and the water-cut rising rules after water breakthrough in the highly volatile oil AKPO oilfield, a new model of water-cut rising was established, and the ... Through the analysis of the reservoir connection relationship and the water-cut rising rules after water breakthrough in the highly volatile oil AKPO oilfield, a new model of water-cut rising was established, and the timing and strategy of water injection were put forward. The water-cut rising shapes of producers after water breakthrough can be divided into three types, and their water-cut rising mechanism is mainly controlled by reservoir connectivity. For the producers which directly connect with injectors in the single-phase sand body of the single-phase channel or lobe with good reservoir connectivity, the water-cut rising curve is "sub-convex". For the producers which connect with injectors through sand bodies developed in multi-phases with good inner sand connectivity but poorer physical property and connectivity at the overlapping parts of sands, the response to water injection is slow and the water-cut rising curve is "sub-concave". For the producers which connect with injectors through multi-phase sand bodies with reservoir physical properties, connectivity in between the former two and characteristics of both direct connection and overlapping connection, the response to water injection is slightly slower and the water-cut rising curve is "sub-S". Based on ratio relationship of oil and water relative permeability, a new model of water cut rising was established. Through the fitting analysis of actual production data, the optimal timing and corresponding technology for water injection after water breakthrough were put forward. Composite channel and lobe reservoirs can adopt water injection strategies concentrating on improving the vertical sweep efficiency and areal sweep efficiency respectively. This technology has worked well in the AKPO oilfield and can guide the development of similar oilfields. 展开更多
关键词 DEEPWATER field development volatile oil RESERVOIR water-cut rising type RESERVOIR connection relationship water-cut rising MECHANISM optimized WATER injection
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Rising Foreign Investment in China, Despite Trade Tensions 被引量:1
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《China's Foreign Trade》 2018年第6期4-5,共2页
There has been no decline but rather a rise in foreign investment in China since the China-US trade dispute started earlier this year.In the first10months of this year,49,545new foreign-invested enterprises were set u... There has been no decline but rather a rise in foreign investment in China since the China-US trade dispute started earlier this year.In the first10months of this year,49,545new foreign-invested enterprises were set up nationwide,up89.3%over the same period last year,data from the Ministry of Commerce(MOC)showed. 展开更多
关键词 Despite Trade Tensions rising Foreign Investment in China
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Regulating and Controlling the Rising Prices of Geographical Indication Products in Inflation——taking Geographical Indication Products from Chongqing as an Example
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作者 吴茵 《海外英语》 2012年第21期285-288,共4页
Since July 2010,the prices of geographical indication products have risen with the occurrence of inflation.In contrast with other products,geographical indication products are distinct.The increasing prices of geograp... Since July 2010,the prices of geographical indication products have risen with the occurrence of inflation.In contrast with other products,geographical indication products are distinct.The increasing prices of geographical indication goods have their own necessities.From the perspective of the products,they are equipped with appreciation potential due to the cultural pe culiarities.From the historical standpoint,their prices have not been high as well as other agricultural products.Realistically,the increase in their prices results from the costs of labors and raw materials.Therefore,the prices of geographical indication products rise to catch up.Not only are their prices at a reasonable level,but also they are beneficial to increase peasants'income.In con clusion,it is necessary that the strategies which are different from those of other products be adopted to regulate and control the prices of geographical indication products. 展开更多
关键词 INFLATION GEOGRAPHICAL INDICATION PRODUCTS rising
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‘Rising Stars of Light’评选
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《发光学报》 EI CAS CSCD 北大核心 2019年第3期425-426,共2页
投稿截止日期:2019年4月10日背景Light Conference 2019国际学术会议将于2019年7月16日-18日在长春召开。为激励青年学者发表重大创新结果,会议特组织'Rising Stars of Light'评选活动。第1轮通知参选条件学术成果是未发表(2019... 投稿截止日期:2019年4月10日背景Light Conference 2019国际学术会议将于2019年7月16日-18日在长春召开。为激励青年学者发表重大创新结果,会议特组织'Rising Stars of Light'评选活动。第1轮通知参选条件学术成果是未发表(2019年7月18日之前未发表)且与光学研究相关的原创性工作投稿格式论文全文. 展开更多
关键词 rising STARS of LIGHT
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Prediction of Fluid Velocity Distribution near a Rising Bubble
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作者 周弘 周明 《Chinese Journal of Chemical Engineering》 SCIE EI CAS CSCD 2002年第5期545-549,共5页
A model is presented for predicting the fluid velocity distribution around a rising bubble which startsfrom rest on a distillation column tray by considering the unsteady fluid flow based on the method of streamfuncti... A model is presented for predicting the fluid velocity distribution around a rising bubble which startsfrom rest on a distillation column tray by considering the unsteady fluid flow based on the method of streamfunction. Experimental measurement of the velocity distribution by using whole field digitized PIV (particle imagevelocimetry) method is briefly described. The velocity distribution predicted by the present model is in betteragreement with the measurements than the others models published in literature. 展开更多
关键词 rising bubble unsteady flow velocity distribution digital-imagecorrelation method
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Pore structure formation and hydration characteristics of cement paste with temperature rising inhibitor
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作者 ZHAO Hai-tao XIANG Yu +6 位作者 ZHANG Hao SHEN De-jian CHEN Xiao-dong HUANG Jie XU Wen LI Hua WANG Yu-jiang 《Journal of Central South University》 SCIE EI CAS CSCD 2022年第5期1674-1685,共12页
The early-age thermal cracking easily generates and severely impairs the durability of concrete.The temperature rising inhibitor(TRI)was utilized to regulate the temperature evolution by controlling the cement hydrati... The early-age thermal cracking easily generates and severely impairs the durability of concrete.The temperature rising inhibitor(TRI)was utilized to regulate the temperature evolution by controlling the cement hydration process.This paper aimed to investigate the pore structure formation and hydration characteristics of cement paste containing TRI by low-field nuclear magnetic resonance.The experiment showed that the T_(2) peak of cement paste shifted from 7.32 ms to 0.23 ms regardless of TRI addition.But the pattern of pore structure formation was changed with TRI addition,that is,the pore structure formation was delayed,and the pore successively shifted to left in two parts.In addition,TRI addition significantly prolonged the duration of gel pore formation and greatly decreased the increase rate of gel water,which implied that TRI introduction hindered the growth of C-S-H,and subsequently decreased the hydration rates and delayed the main hydration peak.Meanwhile,TRI dissolved and diffused rapidly at 40℃,delaying the hydration of cement paste seriously.Moreover,TRI brought about the C-S-H nucleation homogeneous and the ion concentration uniform,which might reduce the localized curvature occurring on the sheet of C-S-H,and then decreased the T_(2) intensity of capillary water and gel water. 展开更多
关键词 pore structure formation hydration characteristics temperature rising inhibitor low-field nuclear magnetic resonance cement paste
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The Rising Importance of Precision Engineering
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作者 Mark Hoffman Liangchi Zhang 《Engineering》 SCIE EI 2018年第6期759-759,共1页
Precision engineering is the discipline that encompasses the design,development,fabrication,and measurement of parts of a mechanical,optical,or electronic system,in software or in fixtures and other structures.For exa... Precision engineering is the discipline that encompasses the design,development,fabrication,and measurement of parts of a mechanical,optical,or electronic system,in software or in fixtures and other structures.For example,a precision instrument or machine should be able to function or perform at a high accuracy that is many orders of magnitude smaller than the size of the instrument or machine itself.It is critical that such accuracy and accurate performance are repeatable and stable over a designated period.Precision engineering also involves the generation of new knowledge-bases and creation of new technologies which will advance the innovation of such machines,instruments,or systems. 展开更多
关键词 rising IMPORTANCE PRECISION ENGINEERING
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Surface tension effects on the behaviour of a rising bubble driven by buoyancy force
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作者 王含 张振宇 +1 位作者 杨永明 张慧生 《Chinese Physics B》 SCIE EI CAS CSCD 2010年第2期392-400,共9页
In the inviscid and incompressible fluid flow regime,surface tension effects on the behaviour of an initially spherical buoyancy-driven bubble rising in an infinite and initially stationary liquid are investigated num... In the inviscid and incompressible fluid flow regime,surface tension effects on the behaviour of an initially spherical buoyancy-driven bubble rising in an infinite and initially stationary liquid are investigated numerically by a volume of fluid (VOF) method. The ratio of the gas density to the liquid density is 0.001, which is close to the case of an air bubble rising in water. It is found by numerical experiment that there exist four critical Weber numbers We1,~We2,~We3 and We4, which distinguish five different kinds of bubble behaviours. It is also found that when 1≤We2, the bubble will finally reach a steady shape, and in this case after it rises acceleratedly for a moment, it will rise with an almost constant speed, and the lower the Weber number is, the higher the speed is. When We 〉We2, the bubble will not reach a steady shape, and in this case it will not rise with a constant speed. The mechanism of the above phenomena has been analysed theoretically and numerically. 展开更多
关键词 rising bubble surface tension BUOYANCY volume of fluid (VOF) method
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Partial Bell Polynomials, Falling and Rising Factorials, Stirling Numbers, and Combinatorial Identities
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作者 Siqintuya Jin Bai-Ni Guo Feng Qi 《Computer Modeling in Engineering & Sciences》 SCIE EI 2022年第9期781-799,共19页
In the paper,the authors collect,discuss,and find out several connections,equivalences,closed-form formulas,and combinatorial identities concerning partial Bell polynomials,falling factorials,rising factorials,extende... In the paper,the authors collect,discuss,and find out several connections,equivalences,closed-form formulas,and combinatorial identities concerning partial Bell polynomials,falling factorials,rising factorials,extended binomial coefficients,and the Stirling numbers of the first and second kinds.These results are new,interesting,important,useful,and applicable in combinatorial number theory. 展开更多
关键词 Connection EQUIVALENCE closed-form formula combinatorial identity partial Bell polynomial falling factorial rising factorial binomial coefficient Stirling number of the first kind Stirling number of the second kind problem
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