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Formation Mechanisms of Some Features in Siliceous Upper Cretaceous-Lower Tertiary Beds of Jordan-Undulations, Geodes, Boudinages
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作者 Elias Salameh Hani Khoury 《Open Journal of Geology》 CAS 2024年第4期569-577,共9页
Geode, boudinage, and undulation structures are widely distributed in the siliceous beds of the Upper Cretaceous/Tertiary rocks in Jordan. Their formation was attributed to tectonic forces, syngenetic processes, organ... Geode, boudinage, and undulation structures are widely distributed in the siliceous beds of the Upper Cretaceous/Tertiary rocks in Jordan. Their formation was attributed to tectonic forces, syngenetic processes, organic disintegration processes, subaquatic gliding, compaction and settlement, and meteoritic impacts. In this work, the structural features in the siliceous beds of Jordan are attributed to an interplay of load and directed pressures, and mineralogical transformation processes (opal-A to opal-CT to quartz), governed by pH changes. Tectonic directed pressure was acting in an ESE-WSW direction and is common in the silicified limestone of Upper Cretaceous. 展开更多
关键词 undulationS Geodes Boudinages Opal-A Porcelanite Chert Transformations pH Changes Stress Fields JORDAN
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极小长高比腔体内混合流体Undulation行波对流 被引量:11
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作者 齐昕 宁利中 +2 位作者 刘嘉夫 王卓运 王娜 《力学季刊》 CSCD 北大核心 2014年第2期253-261,共9页
通过二维流体力学基本方程组模拟了具有较强Soret效应(分离比ψ=-0.47)的混合流体在极小长高比(Γ=4)腔体内的Rayleigh-Benard对流运动.研究了极小长高比行波对流的动力学特性,得到了稳定的Undulation行波存在的r值范围,给出了稳定后的U... 通过二维流体力学基本方程组模拟了具有较强Soret效应(分离比ψ=-0.47)的混合流体在极小长高比(Γ=4)腔体内的Rayleigh-Benard对流运动.研究了极小长高比行波对流的动力学特性,得到了稳定的Undulation行波存在的r值范围,给出了稳定后的Undulation行波摆动周期Tp的变化规律,分析了极小长高比行波对流的r依赖性及稳定性.首次发现极小长高比Γ=4时,与长高比Γ=12和Γ=8时相比,在腔体两端的滚动生成和消失的现象不再出现.讨论了长高比对Undulation行波向行波过渡的影响. 展开更多
关键词 RAYLEIGH-BENARD对流 行波 undulation行波 稳定性 混合流体
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中等长高比腔体内的混合流体Undulation行进波 被引量:5
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作者 齐昕 宁利中 +2 位作者 刘嘉夫 张淑芸 周倩 《西安理工大学学报》 CAS 北大核心 2010年第3期271-276,共6页
通过二维流体力学基本方程组模拟了具有较强Soret效应(分离比ψ=-0.47)的混合流体在中等长高比(Γ=12)腔体内的Rayleigh-Benard对流运动。研究了不同瑞利数情况下腔体内出现的各种行进波状态,详细地探讨了Undulation行进波(UTW)的特性... 通过二维流体力学基本方程组模拟了具有较强Soret效应(分离比ψ=-0.47)的混合流体在中等长高比(Γ=12)腔体内的Rayleigh-Benard对流运动。研究了不同瑞利数情况下腔体内出现的各种行进波状态,详细地探讨了Undulation行进波(UTW)的特性、时空结构及稳定性。 展开更多
关键词 RAYLEIGH-BENARD对流 行进波 undulation行进波 稳定性
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具有强SORET效应的混合流体Undulation行进波对流斑图 被引量:3
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作者 宁利中 齐昕 +1 位作者 余荔 周洋 《力学季刊》 CSCD 北大核心 2008年第4期521-529,共9页
本文通过流体力学基本方程组的数值模拟,探讨了具有强Soret效应(分离比ψ=-0.6)的混合流体Un-dulation行进波对流斑图的动力学特性。在相对瑞利数r<6.436时,首次发现一种没有源缺陷的左右相对传播的CPW(Counter propagating waves)... 本文通过流体力学基本方程组的数值模拟,探讨了具有强Soret效应(分离比ψ=-0.6)的混合流体Un-dulation行进波对流斑图的动力学特性。在相对瑞利数r<6.436时,首次发现一种没有源缺陷的左右相对传播的CPW(Counter propagating waves)状态向行进波状态的过渡形式。在r=6.436—10.8的范围内,发现了两种不同结构的Undulation行进波对流斑图。当6.436<r<10时,出现了腔体内的平均波数在时间上变化且局部波数或当地波数在空间和时间上连续变化的Undulation行进波对流斑图。当r=10—10.8时,出现了腔体内的平均波数在时间上保持为常数而局部波数或当地波数在空间和时间上连续变化的Undulation行进波斑图。在两种状态下,Undulation行进波的摆动周期随瑞利数r增大而减小,它的对流振幅和Nusselt数随瑞利数r增大而增加。在Undulation行进波斑图形成以前,存在以中心为对称的Undulation行进波斑图,它的存活时间依赖于r。当r增加到11.0时,Undulation行进波过渡到定常对流状态。 展开更多
关键词 混合流体 undulation行进波 对流 斑图
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Topography of the Moho Undulation in Cameroon from Gravity Data:Preliminary Insights into the Origin,the Age and the Structure of the Crust and the Upper Mantle across Cameroon and Adjacent Areas 被引量:1
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作者 Albert Eyike Francoise Enyegue A.Nyam Charles Antoine Basseka 《Open Journal of Geology》 2018年第1期65-85,共21页
In this paper, the complete Bouguer anomaly data from Cameroon and part of the neighboring countries has been examined to compute the topography of the Moho undulations. This work is based on an improved filtering tec... In this paper, the complete Bouguer anomaly data from Cameroon and part of the neighboring countries has been examined to compute the topography of the Moho undulations. This work is based on an improved filtering technique and an appropriate density contrast between the crust and the upper mantle. Comparison with seismic data shows that our Moho map defines better the continuity and morphology of the crust-mantle interface than the scattered seismic data in Cameroon. The present relief map, although may not give real depths at some areas provides a better surface correlation with the surface geology better than seismic techniques. Comparison between the Moho undulations and the topography maps reveals that the crust in Cameroon seems to not be in isostatic equilibrium. The Moho in the Central African Shear Zone (CASZ) must be linked with different dextral movements during the opening of the south Atlantic in the Cretaceous time. In the Chad basin, the Moho is associated to the opening of the central and south Atlantic ~130 Ma. In the case of the Congo basin, the Moho undulations are related to the post rift subsidence. The correlation between the Moho undulations map with the surface geology indicates that the actual morphology of the crust mantle interface in Cameroon can be related to the build-up of the West and Central African rift system dating back to the Early Cretaceous to Palaeogene, where the presence of intraplate tensional stresses reactivated previous shear zones of lithospheric weakness during the break up of Gondwana. 展开更多
关键词 Crustal Instabilities Gravity Anomaly Moho undulations Cameroon
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Numerical simulation of fluctuation and undulation of the thermo-cline under tide (tidal current) action in the Bohai Sea
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作者 Zhang Yanting and Wang Yijiao First Institute of Oceanography, State Oceanic Administration, Qingdao 266003, China 《Acta Oceanologica Sinica》 SCIE CAS CSCD 1993年第3期347-357,共11页
Besides seasonal variation, instantaneous variation of thermal layer will occur under the effects of tide, tidal current and wind disturbance. In this study the numerical simulation has been first carried out on fluct... Besides seasonal variation, instantaneous variation of thermal layer will occur under the effects of tide, tidal current and wind disturbance. In this study the numerical simulation has been first carried out on fluctuation and undulation of thermal layer under influence of tide (simultaneous input of 8 tidal components). The study reveals the geographic distribution of thermal layer fluctuation in the entire study region and temporal and spatial variations of the undulation in tidal period superposing on the fluctuation. Especially, the wave with large amplitude simulated is consistent with observation in the channal and the sea areas with a convex coastline and complex variation of depth, internal relations of tide, tidal current, residual current as well as the factors such as geography, and the fluctuation of thermal layer is induced by residual current due to unsymmetry which occurs as a result of the tidal movement in lower layer influenced by friction and geography, meanwhile, analysis indicates that the fluctuation of thermal layer and tidal oscillation are different undulations in character. 展开更多
关键词 line In action in the Bohai Sea Numerical simulation of fluctuation and undulation of the thermo-cline under tide tidal current
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Calculation of geoid undulations and gravity anomaliesin the Northwest Pacific by using the Topex/Poseidonand Geosat altimeter data
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作者 Pan Jiayi Wang Junqin +1 位作者 Wang Yanfeng Zhang XinmeiYuan Yeli (First Institute of Oceanography State Oceanic Adminitration,Qingdao 266003 China)Zheng Quan’an (Center for Remote Sensing College of Marine Studies University of Delaware Newaerk DE 19716 USA 《Acta Oceanologica Sinica》 SCIE CAS CSCD 1999年第4期523-533,共11页
The geoid undulations in the Northwest Pacific were calculated by usingtheTopex/Poseidon and Geosataltimeter data. Firstly the bias between two types of the altimeter data was removed and the geoid undulations in the... The geoid undulations in the Northwest Pacific were calculated by usingtheTopex/Poseidon and Geosataltimeter data. Firstly the bias between two types of the altimeter data was removed and the geoid undulations in theNorthwest Pacific were acquired by a long wave bias diminishing model with a resolution of 30 km and precision of 14cm. Then an algorithm of inversion of gravity anomalies was derived , and the gravity anomalies in the East China Seawere calculated by using the algorithm and the geoid undulations. The rms of difference between the in situ measure-ments the gravity anomalies from altimeter data was 3 .8× 10-5 m/s2. A method to colculate the gravity anomaliesin a larger area was developed which combined gravity anomalies in four subregions overlapping each other into one data set in a larger region. The error analysys shaws that the model and result of the inversion of gravity anomalies were reliable. 展开更多
关键词 Geoid undulations gravity anomalies Northwest Pacific Topex/Poseidon and Geosat altimeter data
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Enchanting Undulations
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作者 Fran?is Dubé 《ChinAfrica》 2017年第10期50-51,共2页
WHEN Sammia Du took her first step on stage in a Cairo five-star hotel, the public looked a bit ambivalent. Her Asian features were unlike those of any other Egyptian belly dancers who performed that night, But as she... WHEN Sammia Du took her first step on stage in a Cairo five-star hotel, the public looked a bit ambivalent. Her Asian features were unlike those of any other Egyptian belly dancers who performed that night, But as she closed her eyes and began to ripple to the rhythm of the drums, the young Chinese dancer was quick to dispel any doubts. 展开更多
关键词 Enchanting undulations
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EVOLUTIONARY CHARACTERISTICS OF LAKES AND PALAEOCLIMATIC UNDULATION IN THE Q AID AM BASIN,CHINA 被引量:1
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作者 黄麒 Teh-Lung Ku Fred M.Phillips 《Chinese Journal of Oceanology and Limnology》 SCIE CAS CSCD 1993年第1期34-45,共12页
The Qaidam Basin is. a tectonically controlled depression at 2700 m altitude on the northern margin of the Tibet Plateau. A succession of Neogene clastic sediments indicates lake depocentre migration from NW to SE. To... The Qaidam Basin is. a tectonically controlled depression at 2700 m altitude on the northern margin of the Tibet Plateau. A succession of Neogene clastic sediments indicates lake depocentre migration from NW to SE. Towards late Pliocene, evaporative conditions developed with formation of gypsum, halite, celestite, mirabilite and bloedite. Continued deformation through Pleistocene developed a series of NW- SE trending domes and troughs. This setting continued to exert a controlling influence on basin and brine evolution and the progressive development of sulfate to chloride brines as, dry conditions intensified in late Pleistocene, at the end of which, extensive flat floors were formed in Dalangtan, Qarhan and other playas.The, model, which was set up based on the synthetic analyses, divides the fluctuating palaeoclimate since 750ka,B. P. into 11 warm and humid stages and 10 dry and cold stages. The water of the lakes evaporated during the dry-cold periods and were freshened during the warm-humid 展开更多
关键词 evolution of salt LAKES organic carbon STRATIGRAPHY undulating model of PALEOCLIMATE
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Enhancing undulation of soft robots in granular media:A numerical and experimental study on the effect of anisotropic scales
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作者 Longchuan Li Chaoyue Zhao +3 位作者 Shuqian He Qiukai Qi Shuai Kang Shugen Ma 《Biomimetic Intelligence & Robotics》 EI 2024年第2期63-70,共8页
Generating efficient locomotion in granular media is important,although it is difficult for robots.Inspired by the fact that sand vipers usually have saw-like scales,in this study,we design a soft undulation robot wit... Generating efficient locomotion in granular media is important,although it is difficult for robots.Inspired by the fact that sand vipers usually have saw-like scales,in this study,we design a soft undulation robot with tangential anisotropic friction to enhance the undulation performance of soft robots in granular media.A mathematical model was derived and numerical simulations were conducted accordingly to investigate the effectiveness of tangential friction anisotropy for undulation gait generation in granular media.In particular,we introduce a pseudo-rigid-body dynamics model consisting of links and joints while simulating the pneumatic actuation method to more closely approximate the response of soft robots.Moreover,a soft snake-like robot was fabricated,and its forward and reverse undulations were compared in two sets of controlled experiments.The consistency between the experimental results and the numerical simulations confirms that tangential anisotropic friction induces a propulsive effect in undulation,thereby increasing the robot's locomotion speed.This discovery provides new insights into the design of undulation robots in granular environments.2024 The Author(s).Published by Elsevier B.V.on behalf of Shandong University.This is an open access articleunder the CCBY license(http://creativecommons.org/licenses/by/4.0/). 展开更多
关键词 Granular media Anisotropicity Pseudo-rigid-body model Soft robot undulation
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Enchanting Undulations
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作者 Fran?ois Dubé 《Beijing Review》 2017年第46期44-45,共2页
Chinese belly dance enthusiasts reignite the popularity of the ancient Egyptian tradition When Sammia Du took her first step on stage in a Cairo five-star hotel,the public looked a bit ambivalent.Her Asian features we... Chinese belly dance enthusiasts reignite the popularity of the ancient Egyptian tradition When Sammia Du took her first step on stage in a Cairo five-star hotel,the public looked a bit ambivalent.Her Asian features were unlike those of any other Egyptian belly dancers who 展开更多
关键词 Enchanting undulations
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Numerical studies of undulation control on dynamic stall for reverse flows 被引量:1
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作者 Biao Wang Jian Liu +1 位作者 Yunjun Yang Zhixiang Xiao 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2020年第2期290-305,共16页
The delayed detached-eddy simulation with adaptive coefficient(DDES-AC)method is used to simulate the baseline and leading-edge undulation control of dynamic stall for the reverse flow past a finite-span wing with NAC... The delayed detached-eddy simulation with adaptive coefficient(DDES-AC)method is used to simulate the baseline and leading-edge undulation control of dynamic stall for the reverse flow past a finite-span wing with NACA0012 airfoil.The numerical results of the baseline configuration are compared with available measurements.DDES and DDES-AC perform differently when predicting the primary and secondary dynamic stalls.Overall,DDES-AC performs better owing to the decrease of grey area between the strong shear layer and the fully three-dimensional separated flow.Moreover,the effects of the undulating leading-edge on the forces,lift gradients,and instantaneous flow structures are explored.Compared with the uncontrolled case,the lift gradient in the primary dynamic stall is reduced from 18.4 to 8.5,and the secondary dynamic stall disappears.Therefore,periodic unsteady air-loads are also reduced.Additionally,the control mechanism of the wavy leading edge(WLE)is also investigated by comparison with the straight leading edge(SLE).No sudden breakdown of strong vortices is the main cause for WLE control. 展开更多
关键词 DDES-AC model Dynamic stall Reverse flow Undulating leading edge Flow control
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Performance of the merged APPLE-Knot undulator for soft x-ray beamline in medium energy ring
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作者 成锐 张发远 +1 位作者 查鹤鸣 乔山 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第11期240-246,共7页
APPLE-Knot undulator can effectively solve the on-axis heat load problem and is proven to perform well in VUV beamline and soft x-ray beamline in high energy storage ring. However, for soft x-ray beamline in a medium ... APPLE-Knot undulator can effectively solve the on-axis heat load problem and is proven to perform well in VUV beamline and soft x-ray beamline in high energy storage ring. However, for soft x-ray beamline in a medium energy ring,whether the APPLE-Knot undulator excels the APPLE undulator is still a question. Here, a merged APPLE-Knot undulator is studied to generate soft x-ray in a medium energy ring. Its advantages and problems are discussed. Though the on-axis heat load of the APPLE-Knot undulator is lower in linear polarization modes compared to the APPLE undulator, its flux is lower. The APPLE-Knot undulator shows no advantage when only fundamental harmonic is needed. However, in circular polarization mode, the APPLE-Knot undulator shows the ability to cover a broader energy range which can remedy the notable shortcoming of the APPLE undulator. 展开更多
关键词 synchrotron radiation APPLE-Knot undulator soft x-ray
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波纹唇鱼染色体核型分析 被引量:12
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作者 霍蕊 张本 +3 位作者 陈国华 尹绍武 王世锋 齐兴柱 《海洋科学》 CAS CSCD 北大核心 2009年第4期94-97,共4页
为了解波纹唇鱼(Cheilinus undulates)的细胞生物学特征,采用植物血凝集素PHA、秋水仙素腹腔注射和空气干燥制片法以头肾组织为材料,对波纹唇鱼的染色体核型进行了研究。结果表明,波纹唇鱼具有染色体48条,核型公式为2n=48=6m+42t,NF=54... 为了解波纹唇鱼(Cheilinus undulates)的细胞生物学特征,采用植物血凝集素PHA、秋水仙素腹腔注射和空气干燥制片法以头肾组织为材料,对波纹唇鱼的染色体核型进行了研究。结果表明,波纹唇鱼具有染色体48条,核型公式为2n=48=6m+42t,NF=54,未发现随体、次溢痕及性染色体,其核型符合典型的高位类群鱼类核型特征。 展开更多
关键词 波纹唇鱼(Cheilinus undulates) 染色体 核型
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野生波纹唇鱼Cheilinus undulates营养成分分析与评价 被引量:12
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作者 区又君 李加儿 《热带海洋学报》 CAS CSCD 北大核心 2010年第3期97-102,共6页
该研究测定了野生波纹唇鱼Cheilinus undulates肌肉的营养成分。结果显示,波纹唇鱼肌肉(鲜样)的水分、粗蛋白、粗脂肪和粗灰分的含量分别为80.97%、18.38%、0.10%和0.49%。肌肉中含有18种氨基酸,总量为15.70%(鲜重),必需氨基酸含量占氨... 该研究测定了野生波纹唇鱼Cheilinus undulates肌肉的营养成分。结果显示,波纹唇鱼肌肉(鲜样)的水分、粗蛋白、粗脂肪和粗灰分的含量分别为80.97%、18.38%、0.10%和0.49%。肌肉中含有18种氨基酸,总量为15.70%(鲜重),必需氨基酸含量占氨基酸总量的39.37%,必需氨基酸的组成符合FAO/WHO的标准。氨基酸的支/芳值为2.5654,接近正常人的支/芳值;依据氨基酸评分(AAS)结果,第一限制性氨基酸为苏氨酸(Thr),第二限制性氨基酸为色氨酸(Trp);必需氨基酸指数(EAAI)为68.46;4种鲜味氨基酸(SAA)的总量为31.85%。脂肪酸中二十碳五烯酸(EPA)+二十二碳六烯酸(DHA)的含量为21.86%。含有人体所必需的钠、钾、钙、镁、铁、铜、锌等元素,表明波纹唇鱼具有较高的营养价值。 展开更多
关键词 波纹唇鱼Cheilinus undulates 生化组成 氨基酸 脂肪酸 矿物质和微量元素
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Parametric Research of Experiments on a Carangiform Robotic Fish 被引量:13
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作者 Qin Yan Zhen Han Shi-wu Zhang Jie Yang 《Journal of Bionic Engineering》 SCIE EI CSCD 2008年第2期95-101,共7页
In this paper, a carangiform robotic fish with 4-DoF (degree of freedom) tail has been developed. The robotic fish has capability of swimming under two modes that are radio control and autonomous swimming. Experimen... In this paper, a carangiform robotic fish with 4-DoF (degree of freedom) tail has been developed. The robotic fish has capability of swimming under two modes that are radio control and autonomous swimming. Experiments were conducted to investigate the influences of characteristic parameters including the frequency, the amplitude, the wave length, the phase difference and the coefficient on forward velocity. The experimental results shown that the swimming performance of the robotic fish is affected mostly by the characteristic parameters observed. 展开更多
关键词 BIOMIMETIC robotic fish experimental parameter matrix undulation equation body length velocity
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波纹巴非蛤小分子肽在水剂化妆品中的稳定性 被引量:1
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作者 陈得科 陈忻 +4 位作者 陈华 潘剑宇 陈晓刚 刘少余 孙恢礼 《湖北农业科学》 2015年第13期3208-3212,共5页
试验考察了含量、空气暴露时长、光照、pH、化妆品常用防腐剂等因素对波纹巴非蛤(Paphi0 Undu-Zctte)小分子肽抗氧化活性的影响,并研究了其在化妆品体系中的稳定性。结果表明.波纹巴非蛤小分子肽在含量为0.2%~1.0%(m/V)时... 试验考察了含量、空气暴露时长、光照、pH、化妆品常用防腐剂等因素对波纹巴非蛤(Paphi0 Undu-Zctte)小分子肽抗氧化活性的影响,并研究了其在化妆品体系中的稳定性。结果表明.波纹巴非蛤小分子肽在含量为0.2%~1.0%(m/V)时对自由基的清除能力随含量增大而增强,当含量达到1.0%时,羟自由基清除率为66%,超氧阴离子自由基清除率为70%,且24h空气暴露对自由基清除能力无影响:波纹巴非蛤小分子肽的光和pH稳定性良好;常用化妆品防腐剂对其稳定性基本无影响,但避免加入量过大。波纹巴非蛤小分子肽作为抗氧化活性物质适于与大部分水剂化妆品原料进行配伍. 展开更多
关键词 波纹巴非蛤(Paphia undulate)小分子肽 化妆品 稳定性 自由基 抗氧化
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Understanding the Rayleigh instability in humping phenomenon during laser powder bed fusion process 被引量:2
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作者 Wenxuan Zhang Wenyuan Hou +1 位作者 Luc Deike Craig Arnold 《International Journal of Extreme Manufacturing》 SCIE EI 2022年第1期85-92,共8页
The periodic undulation of a molten track’s height profile in laser-based powder bed fusion of metals(PBF-LB/M)is a commonly observed phenomena that can cause defects and building failure during the manufacturing pro... The periodic undulation of a molten track’s height profile in laser-based powder bed fusion of metals(PBF-LB/M)is a commonly observed phenomena that can cause defects and building failure during the manufacturing process.However a quantitative analysis of such instabilities has not been fully established and so here we used Rayleigh–Plateau theory to determine the stability of a single molten track in PBF-LB/M and tested it with various processing conditions by changing laser power and beam shape.The analysis discovered that normalized enthalpy,which relates to energy input density,determines whether a molten track is initially unstable and if so,the growth rate for the instability.Additionally,whether the growth rate ultimately yields significant undulation depends on the melt duration,estimated by dwell time in our experiment. 展开更多
关键词 additive manufacturing powder bed fusion dual lasers undulation humping
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Thermokinetic Behaviour Degenerated from Limit Cycle Oscillation of Isothermal B-Z Reaction System due to Temperature Controlling of Heat Compensation Type 被引量:2
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作者 WenHuaZHANG JiuLiLUO 《Chinese Chemical Letters》 SCIE CAS CSCD 2004年第9期1075-1078,共4页
The thermokinetic behavior of the B-Z reaction system was influenced by both the chemical reaction-heat conduction coupling and the temperature undulation due to temperature controlling of heat compensation type. Qua... The thermokinetic behavior of the B-Z reaction system was influenced by both the chemical reaction-heat conduction coupling and the temperature undulation due to temperature controlling of heat compensation type. Quantitative research indicated that this kind of temperature fluctuation will lead to limit cycle degeneration and the periodic or quasi-periodic response behavior of the focus near a supercritical Hopf bifurcation . 展开更多
关键词 Temperature undulation thermokinetic behavior B-Z reaction system.
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Entropic force between biomembranes 被引量:1
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作者 Long Li Fan Song 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2016年第5期970-975,共6页
Undulation force, an entropic force, stems from thermally excited fluctuations, and plays a key role in the essential interactions between neighboring surfaces of objects. Although the characteristics of the undulatio... Undulation force, an entropic force, stems from thermally excited fluctuations, and plays a key role in the essential interactions between neighboring surfaces of objects. Although the characteristics of the undulation force have been widely studied theoretically and experimentally,the distance dependence of the force, which constitutes its most fundamental characteristic, remains poorly understood.In this paper, first, we obtain a novel expression for the undulation force by employing elasticity and statistical mechanics and prove it to be in good agreement with existing experimental results. Second, we clearly demonstrate that the two representative forms of the undulation force proposed by Helfrich and Freund were respectively the upper and lower bounds of the present expression when the separation between membranes is sufficiently small, which was intrinsically different from the existing results where Helfrich's and Freund's forms of the undulation force were only suitable for the intermediate and small separations. The investigations show that only in a sufficiently small separation does Helfrich's result stand for the undulation force with a large wave number and Freund's result express the force with a small wave number. Finally, a critical acting distance of the undulation force, beyond which the entropic force will rapidly decay approaching zero, is presented. 展开更多
关键词 undulation force Flexible membrane Entropic force Confined fluctuations
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