Some properties of mixed radial mean bodies on integral transform

英文原文Drying TechnologyThere are three main types of gas-suspension dryers:∙Spray dryers, to convert a liquid solution or suspension to a dry, free-flowing powder∙Fluid-bed dryers, used to dry wet filter cake, or for pastes and sludges with dry product recirculation∙Flash dryers, for a relatively dry, crumbly, non-sticky feedThe type of dryer chosen for any given application depends on both the feed properties and product requirements. Important feed properties are the moisture content, solids, viscosity, and density, as well as any volatile, flammable, or toxic components. Dried product specifications may include average particle size and particle size distribution, density, moisture content, and residual volatiles or solvents. Powder characteristics can be controlled and powder properties maintained constant through continuous operation.Spray DryingSpray drying is a three-step drying process involving both particle formation and drying. (1) The process begins with the atomization of a liquid feed into a spray of fine droplets. (2) Then a heated gas stream suspends the droplets, evaporating the liquid and leaving the solids in essentially their original size and shape. (3) Finally, the dried powder is separated from the gas stream and collected. Spent drying gas is either treated and exhausted to the atmosphere or recirculated to the system. These three steps are accomplished by three components: the atomizer, the disperser, and the drying chamber.The selection and operation of the atomizer is of extreme importance in achieving an optimum operation and production of top-quality powders. There are four main types of atomization:∙Centrifugal atomization, the most common, uses a rotating wheel or disc to break the liquid stream into droplets. The rotational speed determines the mean particle size, while the particle size distribution about the mean remains fairly constant in a system. Centrifugal atomizers are available in a large variety of sizes, from laboratory scale to very large commercial units.∙Hydraulic pressure-nozzle atomization forces pressurized fluid through an orifice. Multiple nozzles are used to increase capacity. The particle size depends on the pressure drop across the orifice, so that the orifice size determines the capacity of the system. This type of atomization is simpler than centrifugal, but cannot be controlled as well. It is not suitable for abrasive materials, or materials that tend to plug the orifices.∙Two-fluid pneumatic atomization uses nozzles, as well, but introduces a second fluid, usually compressed air, into the liquid stream to atomize it. This type of atomization has the advantage of relatively low pressures and velocities and a shorter required drying path. It is most often used in small-scale equipment, laboratory or pilot size.∙Sonic atomization, not yet widely used, passes a liquid over a surface vibrated at ultrasonic frequencies. It can produce very fine droplets at low flow rates. Current limitations are capacity and the range of different product that can be atomized.After atomization, a disperser brings the heated gas into contact with the droplets. The disperser must accomplish three things: mix the gas with the droplets, begin the drying process, and determine the flow paths through the drying chamber. The drying gas may be heated directly by combustion of natural gas, propane, or fuel oil, or indirectly using shell-and-tube or finned heat exchangers. Electric heaters may be used in small dryers. Industrial radial fans move the heated gas through the system.The drying chamber must be sized to allow adequate contact time for evaporation of all of the liquid to produce a dry powder product. Factors that impact the drying time include the temperature difference between the droplets and the drying gas, and their flow rates. The exact shape of the chamber depends on the drying characteristics and product specifications, but most are cylindrical with a cone-shaped lower section to facilitate collection of the product.Finally, proper configuration of the atomizer, disperser, and drying chamber is essential for complete drying and to avoid the deposit of wet material on the interior surfaces of the dryer. Designs may use co-current, counter-current, or mixed flow patterns.The powder is separated from the drying gas at the bottom of the chamber. Most often, the gas exits through an outlet duct in the center of the cone. Heavier or coarser particles will be separated at this point, dropping into the cone to be collected through an air lock. Then either cyclones or fabric filters (or both) remove the remaining powder from the exit gas. In systems producing a very fine powder, most of the collection takes place at this point.Fluid-Bed DryingFluid-bed drying is a process in which a gas is forced upward through a bed of moist particles to achieve a fluidized state. The particles are suspended in the gas stream and dry as they flow along with the gas. Fluid beds can be either cylindrical or rectangular. There are two basic types offluid-bed designs:∙Plug flow fluid beds are used for feeds that are directly fluidizable. Baffles in the bed limit mixing in the horizontal direction to maintain plug flow. This type of bed is ideal for removal of bound volatiles or for heating and cooling. The volatile content and temperature vary uniformly as the solids pass through the bed. Baffle design depends on the shape and size of the bed, with spiral or radial baffles used in circular beds and straight baffles in rectangular.∙Back-mixed fluid beds are used for feeds that cannot be fluidized in their original state, but become fluidizable after a short time in the dryer. The feed is distributed over the bed surface, designed to allow total solids mixing. Product temperature and moisture are uniform across the fluidized layer. Heating surfaces may be immersed in the fluidized layer to improve thermal efficiency and performance.A combination system uses a back-mixed fluid bed to reduce the moisture level of the wet feed, followed by a plug-flow section to achieve final specifications. This type of arrangement is quite common.The advantages of fluidized-bed drying are: relatively long residence times allow highheat-transfer coefficients between the particles and the gas; the ability to closely control product temperature makes fluidized beds ideal for processing temperature-sensitive solids; and they have the highest thermal efficiency of any gas-suspension drying system.Disadvantages are: they can process only a limited range of materials; product particles are relatively large; and there may be difficulty processing needle- or platelet-shaped particles.Flash DryingFlash drying forces drying gas through a heater and upward through a duct or flash tube. The high-velocity gas stream instantly suspends the feed, which enters just after the heater, and carries it to the collection equipment, usually cyclones or bag collectors.Flash dryers are the simplest gas-suspension dryers, and require the least space. Residence time within the dryer is very short, usually less than 3 seconds. Particles must be quite small, and the best feed is reasonably dry, crumbly, and not sticky. There are several ways to obtain the required feed qualities:∙ A cage mill may be used to break up the feed into the required small particles.∙If the feed is too wet or pasty, dry solids may be backmixed to create the proper consistency.∙An agitated design, using a high-speed disintegrating rotor, will keep all particles moving. This design is shorter and larger in diameter than a flash tube, creating a very compact system. Hybrid DryersThere are a number of hydrid systems used in applications where a single system cannot handle the requirements of both the feed and product. The most common are:∙Fluidized spray dryers (FSD™) combine spray with fluid bed drying to produce agglomerated products. The top of the system is a spray dryer, atomizing the liquid and contacting it with heated gas. Additional heated gas is introduced at the bottom to create a fluidized bed portion of the drying chamber. This type of dryer will produce a dustless, free-flowing agglomerated product. It is ideal for products that must dissolve easily, e.g. food colors, dyestuffs, pigments, and some agricultural chemicals.∙ A flash dryer may be used to remove surface moisture, followed by a fluid bed for removal of bound moisture.Niro DryersThe MOBILE MINOR™ is a laboratory-scale spray dryer known for its flexibility and different levels of control systems. It is used to dry small quantities of solutions, suspensions, and emulsions into representative powder samples. Test results provide important information for selecting the design and technical specification of a given drying project.The PRODUCTION MINOR™ is a larger spray dryer that can be used for pilot testing or small-scale production. It has a choice of atomizers, heating systems, and powder discharge. The Fluidized Spray Dryer (FSD™) was invented and patented by Niro in the early 1980s. It combines fluidization and spray-drying technologies to dry a wide variety of products, including many that cannot be dried using conventional equipment. Advantages include easy control of the size and structure of the particles, making it ideal for agglomerated products, and low powder temperatures for thermally sensitive materials. It is also very energy efficient.中文译文干燥技术主要有三种气体悬浮烘干:喷雾干燥器,把液体溶液或悬浮于干燥,自由流动的粉末流化床干燥机,用干,湿滤饼,或浆和污泥干产品再循环闪蒸干燥机,在相当干燥,松软,非饲料粘粘该型干燥器选择任何特定应用取决于双方的饲料性能和产品的要求. 重要饲料性能是水分含量,固形物,粘度,密度,以及任何挥发性,易燃或有毒成分. 木片产品规格可能包括平均粒度分布,密度,含水率,残留挥发或溶剂. 粉末特性可控制粉末特性保持不变,通过连续运行.喷雾干燥.喷雾干燥是一个三步走的干燥过程中,涉及两种粒子形成和干燥. ( 1 )进程始于雾化的液体饲料成喷雾雾滴. ( 2 ) ,然后加热气流暂时飞沫96.3%的液体和离开固体基本上是原来的大小和形状. ( 3)最后,干粉分离气流和收集. 用干燥气体要么是治疗和精疲力竭的气氛或循环使用该系统. 这三个步骤是由三部分组成:雾化,分散,而干燥室.选择和操作的喷雾器,是极端重要性,实现最佳的操作和生产顶级质量粉末. 主要有4种雾化:离心雾化,最常见的,用一个旋转轮或盘打破液体流成液滴. 转速确定的平均粒径, 而粒度分布大约平均维持在相当稳定的系统. 离心式雾化器可有多种尺寸,从实验室规模比较大的商业单位. 液压喷嘴雾化势力加压流体通过一个小孔. 多喷头用来增加容量. 颗粒大小取决于压降过孔板, 使孔大小决定了系统的容量. 这种雾化简单得多离心,但无法控制等. 它是不适合研磨材料,或材料,往往堵塞孔口. 双流体气动雾化喷嘴的用途,以及如何引进,但第二液,通常压缩空气成液体流雾化. 这种雾化的优点在于较低的压力和速度,缩短干燥所需的路径. 这是最常用的小型设备,实验室或中试规模. 声波雾化,尚未广泛使用,在经过了超过液体表面振捣,在超声波的频率. 它可以产生非常细微的动作,在低流率. 电流限制能力,以及各种不同的产品,可雾化.雾化后,使分散的炽热气体接触到液滴. 分散必须完成三件事:混合气体与雾滴,从干燥过程中, 并确定流路径通过干燥室. 干燥气体,可直接加热燃烧天然气,丙烷或燃油或间接使用壳管式或翅片式换热器. 电加热器,可用于小型烘干机. 工业径向球迷提出了激烈的天然气通过该系统. 烘干室必须大小以便有充裕的时间接触蒸发所有的液体产生一个干粉产品. 因素的影响,干燥时间,包括温差的雾滴和干燥气体. 而其流率. 确切庭取决于干燥特性及产品规格, 但大多数是圆柱与锥形下段,以方便收集的产品. 最后,妥善配置的喷雾器,播种机, 和干燥室必须彻底干燥,以避免存款湿材料的内表面在吹干. 设计可利用顺流,逆流或混合流模式. 粉末分离的干燥气室底部. 在多数情况下,出口气体通过一个插座导管中心的锥. 较重或粗颗粒将会分开,在这一点上, 坠入锥可通过收集空锁. 然后要么旋风或织物过滤器(或两者)来清除残留的粉末从出口气. 在系统产生非常微细粉末,大部分的收集发生在这一点.流化床干燥流化床干燥过程中的气体被迫通过向上一床湿颗粒实现沸腾状态. 这些微粒悬浮在气流和干燥,因为他们流随气. 流化床可分为圆柱形或长方形. 有两个基本类型的流化床设计:堵塞流病床被用作饲料,是直接发霉. 挡板床搅拌限制在水平方向上保持堵塞水流. 这种床是理想的搬迁势必挥发或加热和冷却. 挥发量与温度变化一致的固体通过床底下. 挡板的设计取决于形状和尺寸的床, 螺旋或径向隔板采用圆形床和直挡板的长方形. 返混流化床用作饲料,不能流于原始状态, 但成为发霉后,在很短的时间干燥. 饲料派发超过床面,旨在让总固体混合. 产品的温度和湿度都是一刀切流化床层. 受热面,可沉浸在流态化层,以提高热效率和业绩.组合系统采用返混流化床,以减少水分含量的湿饲料其次是一个插件流断面,以达到最终规格. 这种安排是司空见惯. 优点流化床干燥如下: 较长的停留时间,让高传热系数与粒子间的气体; 能密切控制产品温度使得流化床理想的加工温度敏感固体; 他们有最高的热效率气体悬浮干燥系统. 缺点是:它们能过程只是一个范围有限的材料; 产品颗粒较大; 并有可能难以处理针头或血小板形颗粒.速干速干势力干燥气体通过一个加热器,向上通过导管或闪光灯管. 高速气流瞬间停止饲料,其中大部分进入刚刚加热器缥缈,它的采集设备,通常旋风或袋收藏. 闪蒸干燥机是最简单的气体悬浮烘干机,并要求最少的空间. 居留时间内干燥,是非常短,通常小于3秒. 粒子必须相当小,而最好的饲料是合理的干燥,松软,不发粘. 有几种方法,以取得所需的饲料品质: 笼子轧机可用于击破饲料成所需的小颗粒. 如果饲料过于潮湿或糊状,干物质可backmixed 创造适当的一致性. 激动的设计,采用高速粉碎转子,会让所有粒子. 这个设计是较短时间和较大的直径比闪光灯管,创造一个非常紧凑的系统.混合式干燥机有一些氢化系统在应用中,一个单一的系统,不能处理的要求,既饲料和产品. 最常见的有:流化床喷雾干燥器(消防™)结合喷雾流化床干燥制粒生产的产品. 顶级的系统是一个喷雾干燥机,雾化液接触,并与炽热气体. 新增天然气加热介绍,在底部形成流化床部分的干燥室. 这种烘干机将产生一个无尘,自由流动的压块产品. 它是理想的产品,必须解散容易,例如:食用色素,染料,颜料,以及一些农业化学品. 一个旋转闪蒸干燥机,可用于去除表面水分,然后由流化床去除一定水分.Niro干燥移动轻微™是一个实验室规模喷雾干燥机已知的灵活性和不同层次的控制系统. 它是用来干少量溶液,悬浮,乳液为代表的粉末样本. 测试结果提供了重要信息,为选择设计和技术规格,某一干燥工程. 生产小型™是一个较大型喷雾干燥机,可用于试验或小规模生产. 它可以选择雾化器,暖气系统,粉尘排放. 04-0357喷雾干燥机(消防™) ,发明和专利niro在八十年代初期. 它集流和喷雾干燥技术,干燥的多种产品, 其中有许多是不能晒干使用常规设备. 优点包括易于控制的规模和结构的粒子,使之适合压块产品低气温粉热敏感材料. 这也是很有效的能源.。

Analyzing the Properties of ComplexFluidsComplex fluids refer to a broad class of materials that exhibit non-Newtonian behavior, which means that their viscosity changes under different conditions such as shear rate, temperature, and concentration. Examples of complex fluids include polymers, surfactant solutions, colloidal suspensions, and liquid crystals. The properties of these materials are of great interest to a range of industrial applications such as chemical engineering, materials science, and biotechnology.One of the key properties of complex fluids is their viscoelasticity, which describes their ability to behave like a solid under some circumstances and like a liquid under others. This behavior is due to the presence of long, entangled molecular chains or particles in the fluid, which give rise to elastic deformations when the fluid is subjected to stress. At low frequencies or long timescales, these chains or particles can relax and flow like a liquid, resulting in viscous behavior. At high frequencies or short timescales, however, the chains or particles cannot rearrange as quickly, so the fluid behaves more like a solid, exhibiting elastic behavior.Another important property of complex fluids is their rheology, or flow behavior. Unlike Newtonian fluids such as water or oil, which have a constant viscosity at all shear rates, complex fluids exhibit shear-thinning or shear-thickening behavior. Shear-thinning fluids, such as water with added cornstarch, become less viscous when subjected to higher shear rates, while shear-thickening fluids, such as a mixture of cornstarch and water, become more viscous. This behavior is due to the presence of structures or aggregates within the fluid that break up or form under shear, leading to changes in the flow resistance.The microstructure of complex fluids also plays a crucial role in determining their properties. For example, the size and shape of colloidal particles in a suspension can affect its viscosity and stability. When the particles are large and relatively far apart fromeach other, the suspension behaves more like a Newtonian fluid, while when the particles are smaller and closer together, the suspension becomes more viscous and undergoes phase transitions. The concentration of particles also plays a role in determining the behavior of the suspension: at high concentrations, particles may form aggregates that significantly alter the rheological properties of the fluid.Finally, temperature can also affect the behavior of complex fluids. Changes in temperature can cause the particles or chains in the fluid to swell or shrink, leading to changes in the microstructure and rheology. For example, some liquid crystalline materials exhibit a phase transition from an isotropic phase to a nematic phase upon cooling, resulting in an increase in viscosity and elastic behavior. Additionally, changes in temperature can also lead to the formation of more stable or ordered structures within the fluid, resulting in changes in properties such as shear-thinning or shear-thickening.In conclusion, complex fluids are a fascinating and diverse class of materials that exhibit a wide range of properties and behaviors. Understanding the complex interplay between the microstructure, rheology, and temperature of these materials is crucial for designing and optimizing their use in various industrial applications. By studying these properties, researchers can develop new materials and technologies that can improve the performance and efficiency of products ranging from paints to pharmaceuticals.。

Journal of Biotechnology 118(2005)270–277Specific production rate of VHH antibody fragments by Saccharomyces cerevisiae is correlated with growth rate,independent of nutrient limitationYvonne E.Thomassen,Arie J.Verkleij,Johannes Boonstra ∗,C.Theo VerripsDepartment of Molecular Cell Biology and the Institute of Biomembranes,Utrecht University,Padualaan 8,3584CH Utrecht,The Netherlands Received 7September 2004;received in revised form 27April 2005;accepted 2May 2005AbstractSaccharomyces cerevisiae carrying a multicopy integrated expression vector containing the gene encoding a Llama antibody fragment,has been cultivated in continuous cultures both under carbon and nitrogen limiting conditions with galactose as the sole carbon source.VHH-R2expression was under control of the inducible GAL7promoter.Induction however,was independent of the galactose consumption rate and maximal at all growth rates.VHH-R2was secreted with 70%efficiency at all growth rates and under both limitations.The specific production rate increased linear with increasing growth rate in a growth-associated manner.However,when grown under nitrogen limitation at growth rates above 0.09h −1,the extracellular VHH-R2was less active or part of the VHH-R2was in an inactive form.From our results we conclude that to obtain a maximal amount of VHH per kilogram biomass per hour,VHH production should be done in carbon limited continuous cultures at high specific growth rates.©2005Elsevier B.V .All rights reserved.Keywords:Heterologous protein production;Continuous culture;Galactose limited;Nitrogen limited;Carbon limited1.IntroductionAntibodies can be used in a variety of processes.Both at small scale,in research or medicine,and at large scale,like in industrial scale separation processes.InAbbreviations:VHH,variable domain of heavy chain antibody;X,biomass dry weight∗Corresponding author.Fax:+31302513655.E-mail address:J.Boonstra@bio.uu.nl (J.Boonstra).the latter case,large amounts of antibodies are needed at low price bulk quantities.Several attempts have been made to produce antibodies and antibody fragments in different microorganisms (e.g.(Carter et al.,1992;Edqvist et al.,1991;Shusta et al.,1998)).However,this never resulted in a suitable system for high-level secre-tion of antibodies or fragments thereof,which is impor-tant to decrease the downstream processing costs per amount of protein.The discovery of the so-called heavy chain antibodies,devoid of light chains,in Camelidae0168-1656/$–see front matter ©2005Elsevier B.V .All rights reserved.doi:10.1016/j.jbiotec.2005.05.010Y.E.Thomassen et al./Journal of Biotechnology118(2005)270–277271(Hamers-Casterman et al.,1993)enabled construction of a new type of antibody fragments,VHH,which is the variable domain of these antibodies.These small-sized molecules(<15kDa)are well expressed and are stable in adverse environments,which is important for indus-trial applications(van der Linden et al.,1999;Dolk, 2004).They exhibit high specificity towards their cor-responding antigens and can be obtained with affinities comparable to scFvs(Ghahroudi et al.,1997).In this study,we examined the production of VHH-R2,raised against the azo-dye RR6(Frenken et al.,2000;Spinelli et al.,2000).These antibody fragments can be produced in Saccharomyces cerevisiae at a high level(Frenken et al.,2000)and their large-scale fed-batch production has been described(Thomassen et al.,2002).Fed-batch cultivation is the most common method for produc-tion of heterologous proteins.Its origin can be found in the fermentation industry were it was developed to produce baker’s yeasts.First,biomass is produced on inexpensive carbon sources subsequently cells are induced to produce the protein.During this production phase the growth rate is decreased generally using car-bon limitation for growth control.To study the relation between growth rate(in the range of0.03–0.17h−1) and VHH production,continuous culture experiments under carbon and nitrogen limitation were performed using galactose as the sole carbon source.Results showed that induction of the VHH-R2gene was equal under all circumstances tested.The VHH-R2protein production rate increased with the growth rate and was growth associated under both carbon and nitrogen limitation.We therefore concluded that the highest VHH per kilogram biomass per hour can be obtained at high growth rates.2.Methods2.1.StrainsS.cerevisiae CEN.PK111-32D(MAT a leu2-3,112 SUC2GAL MAL2-8c)was used as host for VHH expression.Llama VHH-R2(anti RR-6)(Frenken et al., 2000)was placed under control of the GAL7promoter directed into the secretion route by the invertase sig-nal sequence.To ensure genetic stability,the construct was integrated at the chromosomal ribosomal DNA locus;the construct contained a leu2d gene(Erhart and Hollenberg,1983),which enabled selection on agar plates lacking leucine(van Gemeren et al.,1995; Thomassen et al.,2002).2.2.Medium for cultivationThe media used for batch and continuous cultivation was prepared according to Sierkstra et al.(1992b). The trace element solution and vitamin solution contained the following components:Trace element solution: 5.5g l−1CaCl2·2H2O, 3.75g l−1FeSO4·7H2O,1.4g l−1MnSO4·H2O,2.2g l−1ZnSO4·7H2O,0.4g l−1CuSO4·5H2O,0.45g l−1CoCl2·6H2O, 0.26g l−1Na2MoO4·2H2O,0.4g l−1H3Bo3, 0.26g l−1KI and30g l−1NaEDTA.The pH of the trace element solution was adjusted to 4.00with NaOH and stored at4◦C.Vitamin solution:0.05g l−1 biotin,5g l−1thiamin,47g l−1myoinositol,1.2g l−1 pyridoxin and23g l−1panthotenic acid.After sterile filtration the vitamin solution was stored at4◦C.The medium for batch cultivation and carbon limited continuous cultures had the following composition: 7.63g l−1NH4Cl,2.81g l−1KH2PO4,and0.59g l−1 MgSO4·7H2O,10ml l−1trace element solution,1 ml.l-1vitamin solution and20g l−1galactose.The sugar solution was autoclaved separately from the min-eral medium and subsequently added to the bioreactor or feed vessel,as was the case for the vitamin solu-tion,which was added after sterilefiltration.Medium for nitrogen limited continuous cultures was similar but contained36g l−1galactose and1.5g l−1NH4Cl.2.3.PrecultureAn250ml Erlenmeyerflask containing100ml YP medium(1%(w/v)yeast extract;2%(w/v)bacto-peptone(Difco))and2%(w/v)d-glucose medium was inoculated with a colony of VHH-R2producing yeast and incubated overnight at30◦C at180rpm.Subse-quently,the bioreactor was inoculated.2.4.Fermentation equipmentContinuous cultivations were carried out in a Bioflow3fermenter(New Brunswick Scientific, Nijmegen,The Netherlands)with2l working volume. The pH was controlled with3M KOH at5.0and the temperature was maintained at30◦C.Foaming272Y.E.Thomassen et al./Journal of Biotechnology118(2005)270–277was controlled using antifoam289(Sigma–Aldrich,St. Louis,MO,USA),which was added to the KOH solu-tion.Agitation was set at800rpm and the airflow was 3l min−1.The dissolved oxygen tension maintained above50%.In general steady states were obtained afterfive dilu-tions when exhaust gases were constant.Subsequently, two successive samples were taken and analyzed. Carbon and nitrogen limitations were confirmed by addition of galactose or NH4Cl to the fermenter.2.5.Cell mass determinationCells of10ml of culture were collected by centrifu-gation,washed with H2O and resuspended in2ml H2O. This solution was dried in pre-weighed glassflask for 16h at110◦C.2.6.Exhaust gas analysisFermenter exhaust gases O2and CO2were mea-sured automatically with a paramagnetic and infrared transducer,respectively(1440C,Servomex B.V., Zoetermeer,The Netherlands).Exhaust ethanol was analyzed with an infrared analyzer(Xendos2500,Ser-vomex B.V.,Zoetermeer,The Netherlands).2.7.Analysis of extracellular metabolitesSamples for measurement of extracellular metabo-lites were immediatelyfiltered through a0.45␮m-pore-sizefilter(Millipore,Bedford,MA USA).Thefil-trate was frozen and kept at−80◦C.Residual galactose was determined as described previously(Sillj´e et al., 1997).Ammonium,glycerol and acetate levels were determined according to manufacturers protocol,using enzymatic kits(r-Biopharm,Darmstadt,Germany). 2.8.Analysis of intracellular metabolitesChemostat samples were quickly cooled in10mM HEPES buffered methanol(60%;−40◦C;pH7.5; 1:5dilution).After collecting the cells by centrifuga-tion(5min;4000rpm;−10◦C)3ml70mM HEPES buffered ethanol(75%;80◦C;pH7.5)was added and cells were heated for3min at80◦C.Ethanol was evap-orated with nitrogen gasflow and the metabolites were solved in2ml H2O after which assays were done (Gonzalez et al.,1997).Intracellular trehalose accumulation was deter-mined as described previously(Sillj´e et al.,1997).Internal metabolite concentrations were determinedessentially as described previously(Bergmeyer,1974).2.9.ELISAVHH-R2concentrations were determined withELISA,an activity based assay.Polysorb plates(Nunc,Roskilde,Denmark)were incubated with0.5mM azo-dye RR6in coating buffer(0.1M Na2B4O7·10H2O, 0.15M NaCl pH8.5)at37◦C for16h.Plates wereblocked for1h with3%skim milk powder(Protifar,Nutricia,Zoetermeer,The Netherlands)in phosphatebuffered saline(PBS)(pH7.4).Incubation with sam-ples for1h at room temperature(RT)was followed byextensive washing,once with washing buffer(0.05%tween-20in PBS)and three times with H2O.VHHwere detected with rabbit-anti-llama antibody diluted1:2000in antibody buffer(0.1%BSA,0.05%tween-20in PBS)for1h at RT.Further incubation was donewith goat-anti-rabbit peroxidase(Jackson ImmunoRe-search Inc.,West Grove,PA,USA)diluted1:5000inantibody buffer for30min at RT followed by incubationwith the horseradish peroxidase substrate3.7mM OPD(in50mM Na2PO4,25mM C6H8O7·H2O)for25min in the dark at RT.The reaction was stopped using 50vol%1M H2SO4and spectophotometric readings were performed at490nm using a Microplate Reader (Benchmark,Bio-Rad Laboratories Inc.,Hercules,CA, USA).2.10.Gene expressionTotal RNA was isolated from yeast cells,whichwere disrupted with0.45mm glass beads in a BeadBeater(Biospec Products Inc.,Bartlesville,OK,USA),using phenol/chloroform extraction as described pre-viously(Verwaal et al.,2002).Total RNA(10␮g)wasloaded on a1%denaturing formamide/formaldehydegel and RNA was separated by electrophoresis.RNAwas transferred to Hybond-N membrane(AmershamBiosciences,Freiburg,Germany)and cross-linkedusing UV light in an UV stratalinker(Stratagene,La Jolla,CA,USA).Oligonucleotide probes forACT15 tgtcttggtctacccacgatagatgggaag and VHH-R25 agcctgcaccaatcctccccctgactcctg were labeled with ␥32P-ATP using T4polynucleotide kinase(USB,Y.E.Thomassen et al./Journal of Biotechnology118(2005)270–277273Cleveland,OH,USA).The probes were purified using a nucleotide removal kit(Qiagen,Valencia,CA,USA). Prehybridization and hybridization were done at45◦C in hybridization mixture(1mM EDTA,7%SDS, 0.5M NaPO4pH7.5).The autoradiogram was quanti-fied using a PhosphorImager(Amersham Biosciences, Freiburg,Germany).2.11.Western blottingYeast cells were mechanically disrupted with 0.45mm glass beads in a Bead Beater(Biospec Prod-ucts Inc.,Bartlesville,OK,USA).Cell lysates and medium samples were subjected to SDS-PAGE(12%) and blotted onto PVDF membrane(Roche Mannheim, Germany).The membrane was blocked using3% skim milk powder(Protifar,Nutricia,Zoetermeer,The Netherlands).Primary antibody used,rabbit-anti-llama (Thomassen et al.,2002)was diluted1:1000in wash buffer(0.5%skim milk powder in TBST).The sec-ondary antibody used was goat-anti-rabbit peroxi-dase(Jackson ImmunoResearch Inc.,West Grove,PA, USA)(1:5000dilution).Detection was done using enhanced chemiluminescence(Renaissance,NEN Life Science Products,Boston,MA,USA).The Western blot was quantified using a Fluor-S(Biorad,Hercules, CA,USA).3.Results and discussion3.1.Physiological parametersVHH-R2producing S.cerevisiae was grown in car-bon or nitrogen limited continuous cultures with galac-tose as the sole carbon source.Under these conditions VHH-R2expression was studied as function of the dilution rate,which is equal to the specific growth rate.Duplicate samples were taken at least one volume change after one other,when the exhaust gases,CO2 and O2,were constant and a steady state was reached.Under nitrogen limitation cells were elongated as observed by Gimeno et al.(1992)while the shape of the cells was normal under galactose limitation.The fermentation characteristics are given in Table1A. When cells were grown under carbon limitation,the biomass concentration remained relatively constant, about8.3g l−1,for the different specific growth rates,ranging from0.033h−1to0.172h−1(Table1B).A decrease in the amount of biomass,from8.1g l−1to 5.9g l−1with increasing specific growth rates,rang-ing from0.033h−1to0.147h−1,was found when cells were grown under nitrogen limitation(Table1A).This difference in biomass production as function of the growth rate under carbon and nitrogen limitation was observed previously(Sierkstra et al.,1993,1994)and might be due to a change in biomass composition. It was shown that cells grown under nitrogen limita-tion have higher relative amounts of nitrogen in their biomass when grown at higher dilution rates indicat-ing that this is the cause for a decrease in biomass yield(g g−1nitrogen)(Sierkstra et al.,1994).The accu-mulation of the reserve carbohydrates trehalose and glycogen(Table1)decreased with increasing specific growth rates both when grown under carbon and nitro-gen limiting conditions as has been described both for aerobic and anaerobic nitrogen limited continuous cul-tures(Paalman et al.,2003;Schulze et al.,1996).Under all growth conditions,hardly any acetate (≤0.1mM)and no ethanol(0mM)production was found.When grown under nitrogen limitation some glycerol was produced(Table1).The carbon balances added up to80–120%.The glucose-6-phosphate and ATP levels increased slightly with increased growth rates when cells were grown under nitrogen limitation as was observed for nitrogen limited continuous culture grown on glu-cose(Sierkstra et al.,1994).When cells were grown under carbon limitation glucose-6-phosphate levels decreased with increasing specific growth rates and a decrease in ATP levels was found,also observed for glucose limited cultures(Sierkstra et al.,1992b).The levels of glucose-6-phosphate and ATP found in this study were comparable to the levels found by Sierkstra et al.(1992a).From the fermentation characteristics we conclude that VHH-R2producing S.cerevisiae behaved similar as wild type S.cerevisiae both under carbon and nitro-gen limitation at different growth rates.3.2.Induction of VHH-R2The VHH-R2gene was integrated on the rDNA locus and placed under the control of the GAL7pro-moter of which galactose/ATP is the inducer(Sil et al.,1999).The specific galactose consumption ratesY.E.Thomassen et al./Journal of Biotechnology118(2005)270–277275Fig.1.VHH-R2expressing cells were grown under carbon and nitrogen limiting conditions at different dilution rates.The specific galactose consumption rate(r s;g gX−1h−1)increased linear with the dilution rate(D;h−1)under carbon(circles)and nitrogen limita-tion(squares).X,biomass dry weight.Error bars represent multiple measurements.were determined as function of the specific growth rate (Fig.1).Both for carbon as for nitrogen limited cultures the specific galactose consumption rate increased linear with the specific growth rate.Under nitrogen limitation more galactose is consumed,the feed medium used for the nitrogen limited continuous cultures contained1.5 times as much galactose as compared to the carbon limited continuous cultures(36and20g l−1,respec-tively).In all growth conditions most of the galactose is consumed(Table1).Under carbon limitation the ATP levels decreased with increasing specific growth rates while they remain constant under nitrogen limitation (Table1).So the concentration of inducer molecules differed with growth rate and between nutrient limi-tations.Moreover the integration locus,the ribosomal DNA,changes with growth rate resulting in a higher copy number at higher growth rates(Planta,1997).A difference on the gene expression of VHH-R2can therefore be expected unless at all growth rates a con-stant level of VHH-R2mRNA is produced.To measure the gene expression of VHH-R2,Northern blot analy-sis was performed;ACT1mRNA was used as loading control.As shown in Fig.2,the amounts of VHH-R2mRNA compared to ACT1mRNA levels remained constant at all dilution rates and were equal under car-bon and nitrogen limitation.We thus conclude that the expression system used,the GAL7promoter combined with the multicopy integration of the VHH-R2gene on the rDNA locus ensured a constant(maximal)level of VHH-R2mRNA at all growth rates and under both limitations.Although a decrease in one of theinducer Fig.2.VHH-R2expressing cells were grown under carbon and nitrogen limiting conditions.At different dilution rates(indicated) RNA was isolated.Northern blot analysis of VHH-R2mRNA;ACT1 mRNA was used as a loading control.molecules,namely ATP,was found,the expression VHH-R2mRNA levels were constant indicating that under these growth conditions sufficient ATP is present.It appears that the GAL7promoter system acts like a constitutive promoter under these circumstances. Whether other inducible promoter systems or even con-stitutive promoters would give the same results regard-ing mRNA levels remains unknown since too little data exist on heterologous protein production in continuous cultures to draw any conclusions.3.3.Specific production rate of functional VHHThe VHH-R2specific production rate was deter-mined as the amount of extracellular VHH-R2,mea-sured with ELISA,per amount of biomass per hour.In Fig.3,the VHH-R2specific production rates as a func-tion of the specific growth rate under carbon and nitro-gen limitation are shown.When cells were grown under carbon limiting conditions,an increase in specific pro-duction rates with increasing specific growth rates was found.This indicates a growth-associated type of prod-uct formation(de Hollander,1993)with amaximum Fig.3.Effect of growth rate and nutrient limitation on the specific production rate of VHH determined with ELISA activity assay.Car-bon limitation(circles)and nitrogen limitation(squares).X,biomass. Lines are for guidance.Error bars represent multiple measurements.276Y.E.Thomassen et al./Journal of Biotechnology118(2005)270–277Fig.4.Effect of growth rate and nutrient limitation on the specific production rate of secreted VHH determined with Western blot-ting.Carbon limitation(circles)and nitrogen limitation(squares). X,biomass.Error bars represent multiple measurements.of3.87mg[g X]−1h−1at a specific growth rate of 0.172h−1.Previously expression in S.cerevisiae of wild type fungal cutinase using similar expression con-ditions,i.e.strain,GAL7promotor,integration on the rDNA locus and growth conditions,has been described (Sagt et al.,1998).The specific production rate of this cutinase using carbon limited continuous cultures at a specific growth rate of0.07h−1,was1.75mg[g X]h−1 or81nmol[g X]−1h−1(calculated from Sagt et al., 1998),which corresponds well with the specific pro-duction rate found for VHH-R2at a growth rate of 0.07h−1(under carbon limitation1.73mg[g X]−1h−1 or124nmol[g X]−1h−1).When cells were grown under nitrogen limitation,an optimum in the specific production rate was found at a specific growth rate of0.09h−1.The initial increase in the specific production rate indicates a growth-associated type of product formation also found under carbon limiting conditions.Above a specific growth rate of0.09h−1,the specific production rate decreased.When however the specific production rate of VHH-R2was determined with Western blotting,meaning the total amount of secreted VHH-R2instead of the active VHH-R2,the production rate increased with increasing growth rates both under carbon and nitrogen limita-tion(Fig.4).So independent of the nutrient limitation VHH-R2is produced in growth associated type of prod-uct formation.Apparently when grown under nitrogen limiting conditions at specific growth rates above0.09 h-1the extracellular VHH-R2was less active or part of the VHH-R2was in an inactive form.Inactivation of VHH-R2might be due to incorrect folding.Inactivation due to post-translational modifi-cations can be ruled out since no mass differences were detected using massspectrometry(data not shown). 3.4.Secretion efficiencyGiuseppin et al.(1993)demonstrated that the secre-tion efficiency of␣-galactosidase produced in S.cere-visiae varied with growth rate.Proteins,which remain intracellular,require more expensive downstream pro-cessing and the secretion efficiency is therefore an important factor in production of heterologous pro-teins.We calculated the secretion efficiency as the ratio of extracellular VHH-R2and the total amount of VHH-R2produced(intracellular+extracellular).At all growth rates and under both limitations the secretion efficiency was approximately70%(data not shown), which corresponds with the values found for produc-tion of VHH-R2in shakeflasks(Thomassen et al., 2002).Secretion of VHH-R2is independent of the growth rate and efficient when compared to the secretion of other VHH expressed in S.cerevisiae(Thomassen et al.,2002).4.ConclusionsS.cerevisiae producing VHH has similar fermenta-tion characteristics compared to wild type yeast.VHH-R2mRNA levels were independent of galactose con-sumption rate and apparently maximal at all growth rates.Although induction of the gene was equal at different growth rates,the specific protein production rate increased corresponding with growth rates and was growth associated under both carbon and nitrogen limi-tation.However,when cells were grown at growth rates above0.09h−1under nitrogen limitation the VHH-R2 produced was partially inactive.From our results we conclude that VHH production should be done in carbon limited continuous cultures at high specific growth rates to obtain a maximal amount of VHH per kilogram biomass per hour. 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Math model of metal heating under action by laser beam智慧树知到课后章节答案2023年下11第一章测试1.Steps at the math modeling are（）。

答案:Writing of the differential (and other) equations describing the processunder consideration.2.Which of the following options is the requirement for the numerical method?（）。

答案:All of the above3.The following are applications of laser radiation in the field of physics?（）。

答案:Nanophotonics;Optical data storage(CD, SVD, 5D opticalmemory);Astrophysics4.What fields can laser radiation be used in?（）。

答案:LaserMedicine;LaserBiology;Laser Chemistry;Physics5.What are the properties of laser radiation?（）。

答案:Divergence of laser beam is small.;Coherence (spatial,temporal).;Stimulated emission.;Laser emits monochromatic wave.Usually laser emits single wavelength.;Polarization.6.The one that can explain the experimental curve of blackbody radiationperfectly is （）答案:null7. A concave cavity with a concave mirror of radius R equal to the cavity lengthL is a （）.答案:Critical cavity8.The wavelength of the CO2 laser is（）答案:10.6μm9.The basic structure of the laser consists of electrical working matter, pumpsource and （） three parts.答案:Optical resonant cavity10.Carbon dioxide lasers commonly used gas mixture composition is composedof （）, helium, argon, nitrogen.答案:Carbon dioxide第二章测试1.What type of laser does the carbon dioxide laser belong to?（）答案:Gas laser2.When the pulse energy is certain, the narrower the pulse width, it means thetime energy density with time as the denominator （）.答案:The greater3.For a uniformly broadened medium, the small-signal gain coefficient at thecenter center frequency is G0(v0), and when I=Is, saturation is significant,and the non-small-signal center-frequency gain coefficient is: （）.答案:4.The following statement about the electric field induction formula is correct（）。

2022年考研考博-考博英语-厦门大学考试全真模拟易错、难点剖析AB卷（带答案）一.综合题(共15题)1.单选题Changing from solid to liquid, water takes in heat from all substances near it and this_______produces artificial cold surrounding it.问题1选项A.absorptionB.transitionC.consumptionD.interaction【答案】A【解析】absorption吸收; transition过渡, 转变; consumption消费, 消耗; interaction相互作用。

句意：水从固体变成液体, 会吸收附近所有物质的热量, 这种吸收会在周围产生人工寒潮。

选项A符合句意。

2.单选题The British historian Niall Ferguson speculated that the end of American_______might not fuel an orderly shift to a multipolar system.问题1选项A.domainB.hegemonyC.sovereigntyD.preference【答案】B【解析】domain领地,领域; hegemony霸权; sovereignty主权,君主; preference偏爱, 优先权。

句意：英国历史学家Niall Ferguson推测, 美国霸权主义的终结可能不会推动美国向多极体系的有序转变。

选项B符合句意。

3.翻译题(1). When we talk about the danger of romantic love, we don't mean danger in the obvious heartbreak way—the cheap betrayals, the broken promises—we mean the dark danger that lurks when sensible, educated women fall for the dogmatic idea that romantic love is the ultimate goal for the modern female. Every day, thousands of films, books, articles and TV programs hammer home this message—that without romance, life is somehow barren.However, there are women who entertain the subversive notion, like an intellectual mouse scratching behind the skirting board, that perhaps this higher love is not necessarily the celestial highway to absolute happiness. (2). Their empirical side kicks in. and they observe that couples who marry in a haze of adoration and sex are, ten years later, throwing china and fight bitterly over who gets the dog.(3). But the women who notice these contradictions are often afraid to speak them in case they should be labeled cynics. Surely only the most jaded and damaged would challenge the orthodoxy of romantic love. The received wisdom that there is not something wrong with the modern idea of sexual love as ultimate panacea, but (hat if you don't get it, there is something wrong with you. You freak, go back and read the label. (4).We say the privileging of romantic love over all others, the insistence that it is the one essential, incontrovertible element of human happiness, traced all the way back to the caves, is a trap and a snare. The idea that every human heart, since the invention of the wheel, was yearning for its other half is a myth.(5). Love is a human constant: it is the interpretation of it that changes. The way that love has been expressed, its significance in daily life, have never been immutable or constant. The different kinds of love and what they signify are not fixed, whatever the traditionalists may like to tell you.So the modern idea that romantic love is a woman's highest calling, that she is somehow only half a person without it, that if she questions it she is going against all human history, does not stand up to scrutiny. It is not an imperative carved in stone; it is a human idea, and human beings are frail and suggestible, and sometimes get the wrong end of the stick.Read the passage carefully and translate the underlined sentences into Chinese.【答案】1.当说到浪漫爱情的危险时, 我们并不是指显而易见令人心碎的危险一可耻的背叛、破碎的誓言——而是指当明智的知识女性对教条主义思想信以为真, 即浪漫的爱情是现代女性的终极目标时, 潜伏着的隐秘危险。

标记方法（Labeling method）Tire size marking method with traditional use and two kinds of international standards, the traditional method is two numbers connected with a minus sign to mark the first set of figures shows that the tire section width, the second groups said rim diameter. If it is on the sidewall of the radial tire, the "two" connection of the group numbers is usually replaced by the letter "R". Since the original marking method originated in the United States, the two groups of figures are represented in English units, such as 9.00-20, 11.00R22.5, 13.6-38, 23.5-25 and so on. In addition, some countries adopt metric - inch or metric mixed markers, such as two sets of figures are 260508 mm (mm), 185R15 group (mm), digital mm for the latter inch.Because the tire section contour evolution and development, the traditional method of marking the original has been unable to meet the new requirements, so the international standard for tire section width (mm), tire flat rate (%), tire structure code (such as R for radial tire and rim diameter code) (in) four said.Said the general tire specifications still use traditional labeling methods, represented by the main technical parameters of tyre.(1) bias tireUsually marked with two sets of digital tire connected with a minus sign, the first set of figures shows that the section width of second groups said rim diameter. Since the original marking method originated in the United States, the two groups of figures are represented in English units, such as 9.00-20,11.00R22.5, 13.6-38, 23.5-25 and so on. In addition, some countries adopt metric - inch or metric mixed markers, such as two sets of figures are 260508 mm (mm), 185R15 group (mm), digital mm for the latter inch. This specification is widely used in general, automotive tires, agricultural machinery tires, construction machinery tires are marked with this specification.In addition to the following representation: the "X" is connected with a tire outside diameter and tire section width two sets of figures, D * S, the unit with the British, such as animal vehicle tire 32 x 6, 28 x 6; 18 x 4.4 ultra high pressure air tire, 39 x 13, 56 x 16 specifications. There is also an "X" and "-" a mixture of three groups of digital form, the first set of digital tyre outer diameter, second sets of figures shows tire section width, the third group said rim diameter, and D * Sfd, for example, said aviation tire metric such as 545 x 175 mm 254; with the British code such as 24 * 7.710; metric and imperial hybrid representation such as 360 x 380 x 1504 1356, etc..2, radial tiresRadial tires generally use the "R" letter as the code name, R is the meridian structure Radial prefix, R instead of connecting two groups of "-" symbols, such as 9.00R20, 11R22.5, using the British system. Such as 185R15, the former group is the metric system, the latter is the British system. The French company uses X as the code name, such as 10.00-20X, 175 - 14X; the Soviet Union uses "P" as the code name, such as 155 - 13P, 5.90-15P, Italy uses "Cinturato" as the mark.Because the tire specifications varieties growingtires'section contour have been greatly changed, the original traditional labeling method can not adapt to the new requirements, so the international standard for tire section width (mm), tire flat rate (%), tire structure code (such as R on behalf of meridian tire) and the rim diameter code (in) four said. For example, 175/70SR14, the first set of figures show that the tire section width is 175mm, the second group said the tire section height and width ratio is 70%, namely 70 tyre series, third group number 14 with inch rim diameter, SR, said the rapid stage radial tire, S speed level mark.(3) tubeless tireTubeless tire with deep trough rim, rim diameter change, such as 8 - 22.5 (equivalent to tube tire specifications, 7.50-20) 10 - 22.5 (equivalent to tube tire specifications, using the English 9.00-20). Some tubeless tires are labeled with "tubeless" or "TUBELESS".The size of said tire specifications but said the specifications of the code, not the actual size of the tire, the adjacent two specifications of the difference,Generally no more than 10 to 15%.(4) tractor tiresA. narrow rim tractor tireAlthough this type of tractor tires are being phased out, they still occupy a certain number. Where the width of the wheel rim and tire section width ratio is in the range of 65% narrow rim tractor tires, specification of basic and diagonal tire, using S-d form, only in the section width code with the decimal point for markers, such as 11.45-24, 13.00-28, 9.00-36.B. wide rim tractor tireThe width of the wheel rim and tire section width of the tire rim tractor is about 80%, said the specification method is different from the narrow rim of tractor tire is the tire section width by an integer, such as 10 - 28, 11 - 38, 12 - 38.C. super wide rim tractor tireThe width of the wheel rim and tire section width of ultra wide rim tractor tire than in the 85 to 90% range, the specification method is different from the wide rim tractor tire is the tire section width after the decimal point with only one is not "0" number, such as 11.2-28 (instead of 10 - 28), 12.4-38 (substituted 1138). 13.6-24 (substituted 12-24). At present, the agricultural tire series has developed into super wide rim tractor driven tires.D. low profile agricultural machinery tireTractor steering tire and agricultural machinery tire to low section development, "L" means low cross section, section width value can be integer, also can take decimal point after a number, such as 9.5L-15, 11L-15, 14L- 16.1. Forestry tires, such as30.5L-32. It also uses the "SL" sign, which is only used in agricultural tires, such as 7.50-10SL, 10.00-15SL, etc.. (5) truck tiresLoad and bus tires can be divided into micro, light, medium and heavy tires according to their size. Different types of tires have different specifications and signs.(1) specifications of ISO international standard tireAccording to the ISO international standard, the specifications and specifications of the tire are as follows:255 / 70 R 22.5140 /137 JAmong them:255 tire nominal section width, mm70 tires flat rate,%R tire structure, radial structure;22.5 the nominal diameter of the rim (tubeless rim), in;140 - singleton tire load index, 24.5KN;137 - Twin Load Index, 22.5KN;J speed signs, 100km/h. (two) existing imperial specificationA. mini truck tireA small truck tire with a nominal cross-sectional width of4.50~5.00in and a nominal rim of 10 to 12in. It is usually mounted on a pair of open or deep groove rims:5 - 12 ULTAmong them:5.00 tire nominal section width, in;- hyphen;12 the nominal diameter of the rim, in;ULT vehicle type symbol (Mini).B. light duty truck, trailer and multi purpose passenger car tireThis kind of tire is usually installed in 5. Deep groove or half deep groove rim, mostly on the highway. The rim diameter is generally below 16in, and the nominal tire section is less than 9.00in in diameter. Examples of its specifications are as follows:8.25 - 16 LT8.25 tire nominal section width, in;- hyphen;16 the nominal diameter of the rim, in;LT type sign.C. truck and bus tiresMedium and heavy duty truck and bus tires, typically 18 in 24In in width, and 7.5~14 in width. The tire is mounted on I, II and III rims, and is mainly used for road driving. Such as 9.00-20 bias tire, 11.00R20 and so on. Among them:9 - 209.00 tire nominal section width, in;- hyphen;Especially the nominal diameter of the rim.11 R 2011.00 tire nominal section width, in;R tire marks;Especially the nominal diameter of the rim, in.D. tubeless tires(1) the light weight load of tubeless tires was installed at 15. The nominal diameter of the rim of the deep groove rim is 1.5 in larger than that of the same level, and the width of the cross section is 6.50 in, 1 in larger than that of the same class. And the width of the section after the decimal place is not zero. The specifications and specifications of the tubes with the same level are listed in the table below. The specifications of tubeless tyres for light trucks are presentedTubeless tire specifications corresponding to inner tube tire specifications7-17.5 6.50-168-17.5 7.00-168.5-17.5 7.50-1610-17.5 9.00-16 (2) tubeless tires for heavy truckThe rim diameter of tubeless tire is 2.5 in larger than that of the same level, and the width of the tire section is 8.25 1in larger than that of the same level, except for two specifications of 7.50 and 2. The width of the section is expressed as an integer, and no more zeros are added after the decimal point. The specifications are listed in the following table:Standard Specification for truck and bus tubeless tiresTubeless tire specifications corresponding to inner tube tire specifications8-22.5 7.50-209-22.5 8.25-2010-22.5 9.00-2011-22.5 10.00-2012-22.5 11.00-2013-22.5 12.00-20 E. specifications for other heavy truck tyresML is a heavy truck tire for mines and forestry;HT is a heavy truck tire;MH is a family touring automobile tire;ST is a road running Trailer tire. Signs of car tyresThe logo of car tires includes size and structural features, load and speed characteristics, and other usage characteristics.(1) tyre size and structure markThe specifications of tyres generally indicate the followingitems:A. nominal section width / nominal flat rate;B. tire structure code tire structure code is expressed in the following letters. D stands for skew structures, and R represents meridian structures.C. nominal rim diameter code, assembled on the existing rim of the tire, its rim code is shown in the table below.Table rim diameter and nominal diameterRim code, nominal rim diameter, mm rim code, nominal rim diameter, mm rim code, nominal rim diameter, mm102541333015381123051435616406 (2) use conditional featuresUse condition characteristics include load index and speed mark.A. speed mark speed symbol represents the speed grade that the tire can bear the load corresponding to the load index under the specified conditions. According to the international standard, the speed mark of the car tire is L ~ H, and the corresponding speed grade is 120 ~ 210km/h.The use of other features indicated in the B. characteristics of tire side load and tire pressure, for tubeless, often marked"tubeless", sometimes also with other special markers, such as pattern type and direction of rotation etc..(3) example of tire gauge markThe ratio of height to width of A. ordinary cross section passenger car tire is 0. 96, the section is close to the circle. The width of the tire is marked by 5.20, 5.60, 5.90, 6.40, 6.70, 7.10, 7.60, 8.20. Such as 6.70-13, 7.60-15 and so on.B. low profile rubber car tire (height width ratio is about0.88), the width of the tire section marks the tail for.00 or.50 two kinds. Such as 5, 5.50, 6, 6.50, 7, 7.50, 8. Such as 6.00-15, 7.50-14 and so on.The ratio of height to width of C. super low profile bias passenger car tire is 0.82. The width of the tire is marked by 5.95, 6.15, 6.45, 6.95, 7.35, 7.75, 8.25, 8.55. Such as 6.95-14, 7.35-15 and so on.D. metric tires are measured in metric form, wide in section, inch in English, in rim diameter, with meridian structure in "R", and speed grade in one letter. Such as 155SR13, 215HR15 and so on. Metric car tire section width starts from 125, with 10mm as a level, up to 235.In radial car tire specifications mark, in addition to the use of "R" logo, some brands add other signs in the fetal side. Such as the Michelin tire company with "X", Prelli tire company added "Cinturato", "P" mark the Soviet Union with radial structure, such as 15513P.The e. "70" series tire is a widely used tire, and its specifications are the same as those of metric tires,The nominal flat rate is only 70 before the structure and speed sign. The section width of the tire starts from 145, with 10mm as the first class and up to 215. When the width of the cross section at the same time, the tire load capacity of turbine rim diameter increases."60" series and "50" series of car tires and "70" series of car tire specifications are the same, just the "70" to "60" or "50" can be.F. America's alphabet digital car tires, regardless of their rim diameter and letter code, have the same load capacity. For example, ER70SR14 and ER70SR15 passenger cars have the same load capacity under certain internal pressure. The first letter in the specification represents the load capacity of the tire. In the alphabet digital system, the letters denote the maximum load when the internal pressure is 0.17MPa and 0.22MPa. Specification for aeronautical tyresThere are 7 types of aviation tires.Model I: sleek profile tire; II type: high pressure tire; III type: low pressure tire; type 4: ultra low pressure tire;Type 6: low profile tire; type 7: ultra high pressure tire; type 8: ultra high pressure low profile tire. Among them, 1, 2, 4, 6 are reserved tires.There are 3 specifications for the specifications of aircraft tyres:(1) low pressure tire section width rim diameter, such as: 6.00-6(2) outer diameter, section width, outer diameter, section width and rim diameter of ultra high pressure tire, such as 39 x 13 or 39 x 13-16(3) the outer diameter of the new design, the width of the cross section, the width of the rim diameter, or any letter in the C, B, or H before the specification of the tire:Additional letter C B H without letter in front of tire specificationRim width / tyre section width 0.5~0.6 0.6~0.7 0.6~0.7 0.7 and aboveRim bead seat pitch 151555: H40 * 14.5-19The outer diameter, section width and rim diameter of the tire are 1016mm, 368mm and 483mm respectively;The ratio of rim width to tire section width is 0.6~0.7;The slope of the bead seat of the rim is 5. Specification for motorcycle tyresIn the ISO standard, the tire specifications are mainly composed of section width mark, structure mark and rim diameter mark. Tire section width mark ordinary structure with two decimal numbers, integer bit is 2 to 6, with 0.25 decimal places for a file, respectively, "00", "25", "50" and "75"; structural marker skew matrix "- two" diameter marker is an integer; from 4 to 23, each number for a file, the 4 ~ 12 for scooter tires, motorcycle tires for more than 14 of the general.In order to demonstrate the load capacity of the tire, there is a hierarchy marker behind the specification. Small diameter tires have two levels and four levels, generally motorcycle tires are divided into four levels and six levels. The higher the level, the greater the load capacity, the greater the tire inflation pressure at the prescribed speed. The level of the symbol for the "PR" ("PLY RATING" acronym), such as"2.75-184PR" refers to the new inflated tire section width is 75mm, rim diameter is 458.7mm, the four level skew matrix structure of the general type motorcycle tyre; "2.75-18 6PR" for the heavier motorcycle tire carcass, two the inflated overall size and two diameter are the same. As for the relationship between tire load and air pressure, load and speed, it is stipulated in the relevant standards and the product instructions of the manufacturer. As for the low profile structure of motorcycle tire specifications mark, the section width is marked with a metric, in mm and numerical markers, behind the section width marker, semicolon connection nominal flat rate, then the structure of labeled "-" and such as the common structure of motorcycle tire two diameter marker. In order to indicate the load capacity and the maximum speed of the tire, there are often signs of load index and speed levelsign, such as120/80-18 65SIt means that..:The width of the cross section 120 metric marker;The name of 80 flat rate;- mark structure;18 - rim diameter designation;65 load index, maximum load is 2.84KN;S speed symbol table top speed of 180km/h.The aspect ratio of the low profile motorcycle conjoined body is equal to or less than 1, such as 1, 0.9, 0.8 and so on, so the nominal flat rate is 100, 90, 80 and so on in the specification mark. Low profile structure of motorcycle tires, such as with two decimal digits for the section width mark, its decimal numbers often take 10 or 60, and not marked nominal flat rate, two speed level symbols in structural marker position. For example, 5.10-18 and 4.60H16, the width of the new inflatable section is the same as that of section width 5 and 4.50, respectively.In the American TRA standard, the letter is often used as the width mark method of the motorcycle tire section, which iscompared with the usual wide mark of the section:Table TRA standard section wide mark contrastTRA series F G H J L labeled E M N P R S T 2.25 2.50 2.75 3 section width mark 3.25 3.50 3.75 4 4.25 4.50 4.75 5.10 in the standard portfolio, by the pre marked "sign of motorcycle tire M", followed by code, section width (flat rate), structure mark and rim diameter designation, sometimes with special rim sign suffix. Such as MF-17, MF90-17 and MM90-19T, the former represents a general structure of the 2.50-17 motorcycle tyre, who said the flat rate of 90 2.50-17 low profile motorcycle tires, the latter is represented as a flat rate of 90 3.75-19 low profile motorcycle tyre, and the tyre is installed in the limit of 5. The so-called 2.50CM rim with outer inclination and inner convex core is a deep groove type. In the European ETRTO standard series, the motorcycle tire with low cross section diagonal band structure is labeled as "VB", such as "4.18VB18"". In the JIS standard series of Japan, there is a low profile, ultra low pressure motorcycle tire. Its section width is marked with a decimal number, such as 5.4-6/6.7-10, etc.. The air pressure is between 60 and 120kPa.。

外文原文Bus chassis SummaryBus chassis is the most important part, it has a direct bearing on the performance of bus. China's bus industry started late, so far only 20 or so, on our bus chassis development, can be summarized as: late start, poor foundation, rapid development, and gradually narrow the gap between foreign and other features.Before the 1980s, China's main passenger vehicle chassis modifications. Since slower vehicle speed, vehicle ride is not too high, thus converted into a low-speed bus (maximum 75 kilometers), comfort poor. In 1981 the original factory in Yangzhou Bus (now Yangzhou Yaxing Bus Co., Ltd.) the successful development of the first bus chassis JT663, and its truck chassis compared to the past, Speed (90 km / h), using a wide front axle for Lunju bus, cycle-ball steering gear and dual-circuit brake system pressure, when the system is also a breakthrough has been able to find a "people-oriented" Design concept. JT663 Preparation of success, marking the birth of China's bus chassis, is of epoch-making significance.In the 1990s, the development of China's highway speed of vehicles by the new requirements, the requirements of the largest vehicles more than 120 kilometers per hour, normal driving speed of 90 km above. Although at this time many of the domestic passenger business through joint ventures, cooperation or technology transfer and other means to start producing high-speed bus, but due to high cost of these vehicles only on the strength of passenger traffic, operating in economically developed areas, the economy in underdeveloped regions The number of road mixed lines, the lack of suitable vehicles. At this point buses and chassis business JT66 3 chassis design from the successful experiences of, To reduce the body to relieve themselves, reduce the maximum gross vehicle quality, increased engine power, improve power vehicles than measures such as using integrated power steering and noise, cooling fast, long service life of the radial tire, designed to produce Regular rate is greater than 90 km and a maximum speed reached 10 km above the JS6820 and bus chassis. Because the main assembly of the car were domestic cases, the price of only 30 million, higher cost performance, the general passenger business in about sixmonths to recover the cost, so welcomed by domestic users."9th Five-Year" period, the industrial development of China's passenger by the State attaches great importance to the State Economic and Trade Commission will require high standards of the two passenger buses JT6890 Development as a "9th Five-Year" technology projects. At the same time with the development and bus chassis production capacity of enterprises, for domestic auto parts production lag, and some trains were unable to meet the needs of the actual situation of international procurement, give priority to the forthcoming joint venture in China of products, as well as the domestic auto parts Production enterprises to participate in international economic cooperation matchmaking. Due to international against the procurement methods, and new development of chassis JT6890 control of the lower cost, the price of imports than the same type of chassis low 45 percent. The end of 1998, JT6890 after 30,000 km of the road test, a comprehensive national identification. Although JT6890 chassis assembly were chosen by the United States, Germany, Sweden, Britain and other six countries over 20 kinds of assembly, but a perfect match, it is commendable.Although China-made bus chassis in recent years developed very quickly, but compared with other countries, whether from the design level or from the assembly of the reliability, the gap is still great, particularly the assembly of the quality and reliability of the more prominent issues . With China's accession to the WTO is approaching, international cooperation will be further expanded, this will benefit China's passenger bus chassis design and assembly of raising the level of production, as soon as possible with the advanced world level to narrow differences in opportunities.Since the chassis is the largest body parts, body is good or bad is bound to lead the chassis completely good or bad, a good body is to have high rigidity, the so-called high-rigidity is not deformed. Traffic on the road, with the naked eye looks like no deformation, but in fact will be the impact of the road because of constant deformation, but a body deformation, vehicles will not be obedient, do not think that the 1 ~ 2 mm no deformation, it will You it difficult to control in high-speed vehicles, because in high-speed, you do not control the vehicle to 10 mm, which is why theautomotive media often say that the body rigid for high-speed stability on the absolute nature of the impact.But here referred to the rigid body has nothing to do with security, if really want to make, of course, can make a very good control with no security of the body, and vice versa. Therefore, the manipulation of rigid body is not seen by the impact test, usually rigid body with the manipulation of the distorted rigid test of a fixed endpoint of a body, then the diagonal line endpoint SHI Li, the deformation obtained vehicles Point of view, in units of Nm / deg, this is the depot in the vehicle, often said to the rigid body and raise the number percent of the units of measurement, It is a pity that the world depot for the number of confidentiality home, making relatively rigid body can only be subjective impression of the test, but no scientific data, coupled with the suspension and shock absorbers of the fuzzy, into the old rigid body Wang Maigua traders puff, lies in constantly attacking Jie of the Rashomon.However, regardless of rigid body again, if the suspension arm directly to the car body, also because of stress concentration, and have too many local deformation, so the best equipment on the rigid frame of a higher, will be suspended from The strength of the crane through the frame, distributed to more cars on the body to reduce the deformation, so that the high-priced cars will not mean trailers loaded deputy, to reduce the pressure faced by the body.Chassis suspension system has always been the most volatile areas, because in addition to consider the rigid, point of control is a major challenge, said the first briefing when the steering control, and some cars can be done near real-time responses to some After turning the steering wheel cars only about one second reaction (AOL really tried this car), there is such a major difference between the issue or rigid, less than the rigid body and suspension will absorb deformation out to you the action, and then Rebound out, the car will be open to such people do not have a sense of stability, is actually not trust, Another will be because of early action to be eaten, the driver of the steering wheel will turn some more, leading to the latter part of the centrifugal force caused too much out of control, this car for a long time driving skills will be wrong, leading to vulnerable low-speed out of control.Of course, in addition to the most basic of steering control, suspension systemalso controls the wheels of various point of view, the perspective of many of the wheel, the inclination, after the dip, inclination, the former beam angle. Tire decision, inclination angle of the earth, in theory, the case is 0 °, but the car will roll Guowan, long-term external wear on tires would be more serious, so many negative set point, but also allows car when stability is Guowan As for the plant to see how much experience decision, but not suitable for the original set too conservative or too violent people, according to its own drive demand for tyres will make its own point of view is a better-targeted approach.After the dip is a very important point, it affects you when the vehicle to the impression that after the dip for the role of the former towards the direction of the wheel, which sounds quite vague, with examples to explain! In the column, power forward or North Korea after, so the wheel is Chaoqian Fang, Guowan, Guowan wheels to bear the centrifugal force, the wheels will move towards the direction of centrifugal force, in the tail flick , The front will also move towards the direction of the tail flick, so you know why it has to bend the time may Fangdiao the reasons for the steering wheel. But after the dip is, relative to more people driving force of the rotating wheel, a driving force in front of the vehicle, usually only after the dip 1 ~ 3 °, and then drove usually have a 5 ~ 10 °.Since before the drive after a small dip, it will be less than straight into the stable, so the angle there, the role of the inclination to let the wheels forward, to fill the lack of stability, and this inclination by the Straight power load multiplied by sin (inclination). In addition, with the inclination angle of inclination angle for tolerance, this perspective is not important, it is important to the projection angle to the length of the ground, known as the length of the tyre friction radius, the radius affect the amount of road sense, but too many May cause steering resistance. But changes in tire diameter or round off set box will change the value of friction radius, which is why we say that the front wheels for reasons not to. Before the domestic multi-beam angle as before the beam, because of the previous day for vehicles to mm units, but now almost all in perspective for the unit. Before the beam angle to the role of the wheels on both sides have the strength inside to stable living body, but also to the needs of straight-line stability. Some vehicles, however, before the exhibition angle, so that theinitial response to highly, but relatively rare commercial vehicles to critize. Although there are some perspective did not speak, but will be able to understand these great understanding of the suspension to make things, the control point is to put it bluntly, the most important point of control is not deformation of the suspension system, after all, but a deformation of the pre-set Not the point of view, but now more progress to the point of control, traffic control and better.However, domestic bus chassis in recent years developed very quickly, but compared with other countries, whether from the design level or from the assembly of the reliability, the gap is still great, particularly the assembly of the quality and reliability of the more prominent issues . With China's accession to the WTO is approaching, international cooperation will be further expanded, this will benefit China's passenger bus chassis design and assembly of raising the level of production, as soon as possible with the advanced world level to narrow differences in opportunities.中文译文客车底盘概述底盘是客车最重要部分，它直接关系到客车的性能。

中石油职称英语考试大纲中模拟试题答案及部分试题答案解析模拟试题一参考答案及部分试题答案解析一、答案1-20 ACBBD BBAAC DCCDB DCBCD21-40 ABCCB DDCCB DBACD CDACD41-60 DDCBD ACDDD DDABC DCBAB61-70 CBADC DBACCIV. Translation翻译答案略，翻译参考2013版大纲第47篇 oil。

二、解析I. Vocabulary1.【答案】【译文】我只能看到远处一辆汽车，可是分辨不出汽车的颜色。

【试题分析】词组辨析题。

【详细解答】make out意为“辩认出，理解”，符合句意。

look to“注意，指望，照顾，负责”；look out“当心，提防”；take in“容纳，理解，欺骗（多用于被动态）”，均不符合句意。

【拓展】in the distance在远处look up to sb尊敬某人；尊敬；敬重某人；崇拜某人；look forward to doing期待；盼望；期待做某事；盼望做take part in参加；参与；加入；到场take delight in sth取悦于做某事take stock in购买；相信；注意2.【答案】C【译文】新的科学发现应用于工业生产方法上常使工作更容易做。

【试题分析】此题为形近词辨析题。

【词义辨析】application应用、运用：the application of theory 理论的运用。

A. addition增加，一般用于in addition to”除…之外”结构中，此处不符合句意，科学发现不是“增加到”工业生产方法上，而是“应用到”工业生产技术中。

B. association联系，联想；协会；结交：I'm working in association with another person. 我与另外一个人合伙工作。

D. affection爱情；爱；影响。

专业术语中英文对照表傍河水源地 riverside source field包气带 aeration zone饱和度 degree of saturation饱和流 saturated flow饱水带 saturated zone边界井 boundary well边界条件 boundary condition边界元法 boundary element method标准曲线法（配线法） type-curve method补给区 recharge area补给疏干法 compensation-dewatering method部分排泄型泉 local drainage spring采区充水性图 geologic map of potential flooding in mining area 测压高度 piezometric head层流laminar flow常量元素 common element in groundwater （macroelement ）沉积水（埋藏水） connate water（buried water）成垢作用 boiler scaling成井工艺 well completion technology承压含水层 confined aquifer承压含水层厚度 thickness of confined aquifer承压水 confined water承压水盆地 confined water basin承压水位（头） confining water level持水度 water-holding capacity/ specific retension充水岩层 flooding layer抽水孔 pumping well抽水孔流量 discharge of a pump well抽水孔组 jumping well group抽水量历时曲线图 flow-duration curve抽水试验 pumping test初见（始）水位 initial water level初始条件 initial condition次生盐渍土 secondary salinized soil达西定律Darcy’s law大肠菌群指数 index of coliform organisms大口井 large-diameter wd1大气降水渗入补给量 precipitation infiltration rate单井出水量 yield of single well单孔抽水试验 single well pumping test弹性储存量 elastic storage淡水 fresh groundwater导水系数 transmissivity等降深线 equiodrawdown line等势线 equipotential line等水头面 equipotential surface低频电磁法 very low frequency electromagnetic method 地表疏干 surface draining地表水 surface water地表水补给 surface water recharge地方病 endemic disease地方性氟中毒 endemic fluorosis地面沉降 subsidence地面开裂 land crack地面塌陷 ground surface collapse地下肥水 nutritive groundwater地下集水建筑物 groundwater collecting structure地下径流 underground runoff地下径流模数法 modulus method of groundwater runoff 地下库容 capacity of groundwater reservoir地下卤水 underground brine地下热水 geothermal water地下疏干 underground draining地下水 groundwater地下水补给量 groundwater recharge地下水补给条件 condition of groundwater recharge地下水超采 overdevelopment of groundwater地下水成矿作用 ore-forming process in groundwater地下水储存量（地下水储存资源） groundwater storage地下水的pH值 pH Value of groundwater地下水的碱度 alkalinity of groundwater地下水的酸度 acidity of groundwater地下水的总硬度 total hardness of groundwater地下水等水头线图 map of isopiestic level of confined water地下水等水位线图 groundwater level contour map地下水动力学 groundwater dynamics地下水动态 groundwater regime地下水动态成因类型 genetic types of groundwater regime地下水动态曲线 curve of groundwater regime地下水动态要素 element of groundwater regime地下水分水岭 grot1udwater divide地下水赋存条件 groundwater occurrence地下水化学成分 chemical constituents of groundwater地下水化学类型 chemical type of groundwater地下水环境质量评价groundwater environmental quality assessment 地下水径流量（地下水动储量） groundwater runoff地下水径流流出量 groundwater outflow地下水径流流入量 groundwater inflow地下水均衡 groundwater balance地下水均衡场 experimental field of groundwater balance地下水均衡方程 equation of groundwater balance地下水开采量 groundwater withdrawal地下水开采资源 exploitable groundwater resources地下水可开采量（地下水允许开采量） allowable withdrawal of groundwater 2地下水库 groundwater reservoir地下水埋藏深度 buried depth of groundwater table地下水埋藏深度图 map of buried depth of groundwater地下水模型 groundwater model地下水年龄 age of groundwater地下水年龄测定 dating of groundwater地下水排泄 groundwater discharge地下水盆地 groundwater basin地下水侵蚀性 Corrosiveness of groundwater地下水人工补给 artificial recharge of groundwater地下水人工补给资源 artificial-recharged groundwater resources 地下水设计开采量 designed groundwater withdrawal地下水实际流速 actual velocity of groundwater flow地下水实际流速测定 groundwater actual velocity measurement 地下水数据库 groundwater database地下水数学模型 mathematical model of groundwater地下水水化学图 hydrogeochemical map of groundwater地下水水量模型 groundwater flow model地下水水量评价 evaluation of groundwater quantity地下水水位动态曲线图 hydrograph of groundwater level地下水水质 groundwater quality地下水水质类型 type of groundwater quality地下水水质模型 groundwater quality model地下水天然资源 natural resources of groundwater地下水同位素测定 isotope assaying of groundwater地下水位持续下降 continuously drawndown of groundwater level 地下水污染 groundwater pollution地下水污染评价 groundwater pollution assessment地下水污染物 groundwater pollutants地下水物理模型 physical model of groundwater地下水物理性质 physical properties of groundwater地下水系统 groundwater system地下水预报模型 groundwater prediction model地下水源地 groundwater source field地下水质评价 evaluation of groundwater quality地下水资源 groundwater resources.地下水资源保护 groundwater resources protection地下水资源分布图 map of groundwater resources地下水资源管理区 groundwater resources management地下水资源枯竭 groundwater resources depletion地下水资源评价方法 methods of groundwater resource evaluation地下水总矿化度 total mineralization degree of groundwater地下微咸水 weak mineralized groundwater地下咸水 middle mineralized groundwater地下盐水 salt groundwater地中渗透仪 lysimeter电导率 specific conductance电法测井 electric logging电法勘探 electrical prospecting顶板裂隙带 fissure zone of top wall顶板冒落带 caving zone of top wall定降深抽水试验 constant-drawdown pumping test定解条件 definite condition定流量边界 boundary of fixed flow /constant flow定流量抽水试验 constant-discharge pumping test定水头边界 boundary of fixed water level动水位 dynamic water level断层泉 fault spring断裂带水压导升高度（潜越高度） height of water pressure in fault zone 断面流量 cross-sectional flow对流弥散 convective dispersion多孔抽水试验 multipe wells pumping test多孔介质 porous medium二维流 two-dimensional flow放射性测井 radioactivity logging放射性水文地质图 radio hydrogeological map放射性找水法 radioactive method for groundwater search放水试验 dewatering test非饱和流 unsaturated flow非均匀介质 inhomogeneous medium非均匀流 non-uniform flow非完整井 partially penetrating well非稳定流 unsteady flow非稳定流抽水试验 unsteady-flow pumping test分层抽水试验 separate interval pumping test分层止水 interval plugging分子扩散 molecular diffusion .分子扩散系数 coefficient of molecular diffusion福希海默定律 Forchheimer law辐射井 radial well腐蚀作用 corroding process负均衡 negative balance负硬度 negative hardness富水系数 water content coefficient of mine富水性 water yield property干扰抽水试验 interference-well pumping test干扰井出水量 yield from Interference wells干扰系数（涌水量减少系数） interference coefficient隔水边界 confining boundary隔水层 aquifuge隔水底板 lower confining bed隔水顶板 upper confining bed各向同性介质 isotropic medium各向异性介质 anisotropic medium给水度 specific yield供水水文地质勘查 hydrogeological investigation for water supply 供水水文地质学 water supply hydrogeology拐点法 inflected point method观测孔 observation well管井 tube well灌溉回归系数 irrigation return flow rate灌溉机井 pumping-well for irrigation灌溉系数 irrigation coefficient过水断面 water-carrying section海水入侵 sea-water intrusion3含水层 aquifer含水层储能 energy storage of aquifer含水层弹性释放 elasticity release of aquifers含水层等高线图 contour map of aquifer含水层等厚线图 aquifer impact map含水层等埋深图 isobaths map of aquifer含水层调节能力 regulation capacity of aquifer含水层自净能力 self-purification capability of aquifer含水率 moisture content化学需氧量（COD） chemical oxygen demand环境水文地质勘查 environmental hydrogeological investigation 环境水文地质图 environmental hydyogeologic map环境水文地质学 environmental hydrogeology环境自净作用 environmental self-purification恢复水位 recovering water level回灌井 injection well回灌量 quantity of water recharge回灌水源 recharge water source混合抽水试验 mixed-layer pumping test混合模拟 mixing analog混合作用 mixing hydrochemical action in groundwater激发补给量 induced recharge of groundwater极硬水 hardest water集中供水水源地 well field for concentrated water supply间歇泉 geyser简易抽水试验 simple pumping test降落漏斗 cone of depression降落漏斗法 depression cone method降落曲线 depression curve降水补给 precipitation recharge降水入渗试验 test of precipitation infiltration降水入渗系数 infiltration coefficient of precipitation接触泉 contact spring结构水（化合水） constitutional water （chemical water）结合水 bound water结晶水 crystallization water解逆问题（反演计算） solving of inverse problem解析法 analytic method解正问题（正演计算） solving of direct problem井下供水孔 water supply borehole in mines井中电视（超声成相测井） borehole television（BHTV）径流区 runoff area静止水位（天然水位） static water level （Natural water level）均衡期 balance period均衡区 balance area均匀介质 homogeneous medium均匀流 uniform flow开采模数法 evaluation method of employing groundwater extraction modulus 开采强度法 mining intensity method开采试验法 exploitation pumping test method开采性抽水试验 trail-exploitation pumping test坎儿井 karez空隙 void孔洞 pore space孔隙 pore孔隙比 pore ratio孔隙度（孔隙率） porosity（pore rate）孔隙含水层 porous aquifer孔隙介质 pore medium孔隙水 pore water库尔洛夫式 Kurllov formation矿床充水 flooding of ore deposit矿床充水水源 water source of ore deposit boding矿床充水通道 flooding passage in ore deposit矿床疏干 mine draining矿床疏干深度（疏干水平） dewatering level of mines矿床水文地质 mine hydrogeology矿床水文地质图 mine hydrogeological map矿床水文地质学 mine hydrogeology矿井水文地质调查 survey of mine hydrogeology矿井突水 water bursting in mines矿井涌水 water discharge into mine矿坑水 mine water矿坑突泥 mud gushing in mines矿坑突水量 bursting water quantity of mines矿坑涌砂 sand gushing in mines矿坑涌水量 water yield of mine矿坑正常涌水量 normal water yield of mines矿坑最大涌水量 maximum water yield of mines矿区水文地质勘查 mine hydrogeological investigation 矿泉 mineral spring雷诺数 Reynolds number连通试验 connecting test裂隙 fissure裂隙含水层 fissured aquifer裂隙介质 fissure medium裂隙率 fissure ratio裂隙水 fissure water临界深度 critical depth流量测井 flowmeter logging流量计 flowmeter流网 flow net流线 streamline滤料（填料） gravel pack滤水管（过滤器） screen pipe裸井 barefoot well毛细带 capillary zone毛细管测压水头 capillary piezometric head毛细上升高度 height of capillary rise毛细水 capillary water毛细性 capillarity弥散 dispersion弥散试验 dispersion test钠吸附比（SAR） sodium adsorption ratio拟稳定流 quasi-steady flow凝结水 condensation water凝结水补给 condensation recharge排泄区 discharge area平均布井法 method of well uniform4configuration起泡作用 forming process气体成分分析 gas analysis潜水 phreatic water /unconfined water潜水含水层厚度 thickness of water-table aquifer潜水位 water table潜水溢出量 groundwater overflow onto surface潜水蒸发量 evaporation discharge of phreatic water浅层地震勘探 shallow seismic prospecting强结合水（吸着水） strongly bound water adsorptive water 侵蚀泉 erosional spring侵蚀性二氧化碳 corrosive carbon dioxide裘布依公式 Dupuit formula区域地下水位下降漏斗 regional groundwater depression cone 区域水文地质普查 regional hydrogeological survey区域水文地质学 regional hydrogeology全排泄型泉 complete drainage spring泉 spring泉华 sinter泉流量衰减方程法 method of spring flow attenuation泉水不稳定系数 instability ratio of Spring discharge泉水流量过程曲线 hydrograph of spring discharge泉域 spring area确定性模型 deterministic model扰动土样 disturbed soil sample容积储存量 volumetric storage容水度（饱和含水率） water capacity溶洞 cave cavern溶解他固体总量 total dissolved solids溶解氧（DO） dissolved oxygen溶滤水 lixiviation water溶滤作用 lixiviation软水 soft water弱含水层 aquitard弱结合水（薄膜水） weakly bound water （film water）弱透水边界 weakly-permeable boundary三维流 three-dimensional flow上层滞水 perched water上升泉 ascending spring设汁水位降深 designed drawdown渗流场 seepage field渗流场剖分（单元划分） dissection of seepage field渗流速度 seepage velocity渗入水 infiltration water渗水试验 pit permeability test渗透 seepage渗透率 specific permeability渗透水流（渗流） seepage flow渗透系数（水力传导系数） hydraulic conductivity/ permeability 生化需氧量（BOD） biochemical oxygen demand声波测井 acoustic logging声频大地电场法 audio-frequency telluric method湿地 wet land实井 real well试验抽水 trail pumping手压井 manual-operated pumping well疏干工程排水量 discharge of dewatering excavation疏干巷道 draining tunnel疏干因数 factor of drainage数学模型法 method of mathematical model数学模型检验 verification of mathematical model数学模型识别 calibration d mathematical model数值法 numerical method水文地质勘查报告 report of hydrogeologicai investigation 水动力弥散系数 coefficient of dispersion.水分散晕 water dispersion halo水化学 hydrochemistry水解作用 hydrolytic dissociation水井布局 wafer well arrangement水均衡法 water balance method水均衡方程 equation of water balance水均衡要素 element of water balance水均衡原理 principle of water balance水力坡度 hydraulic gradient水力削减法 hydraulic cut method水流迭加原理 principle of flow superpersitiom水流折射定律 law of seepage flow refraction水圈 hydrosphere水头场 water head field水头场的拟合 fitting of water-head field水头降深场 fieId6f water head drawdown水头降深场的拟合 fitting of water head drawdown field水头损失 water head loss水位计 wellhead water-level gauge水位降深值 drawdown水文地球化学 hydrogeochemistry水文地球化学分带 hydrogeodenml zonality水文地球化学环境 hydrogeochemical environment水文地球化学作用 hydrogeochemical process水文地质比拟法 hydrogeologic analogy method水文地质参数 Hydrogeological parameters水文地质测绘 hydrogeological mapping水文地质单元 hydrogeologic unit水文地质地球物理勘探 hydrogeophysical prospecting水文地质分区 hydrogeological division水文地质概念模型 conceptual hydrogeological model水文地质勘查 hydrogeological investigation水文地质勘查成果 result of hydrogeological investigation 水文地质勘查阶段 hydrogeological investigation stage水文地质勘探孔 hydrogeological exploration borehole水文地质剖面图 hydrogeological profile水文地质试验 hydrogeological test水文地质试验孔 hydrogeological test borehole水文地质条件 hydrogeological condition水文地质学 hydrogeology水文地质学原理 principles of hydrogeology5水文地质钻探 hydrogeological drilling水文水井钻机 hydrogeologic drilling rig水文物探测井 hydrogeological well logging水循环 water cycle水盐均衡 water-salt balance水样 water sample水跃值 hydraulic jump value水质标准 water quality standard水质分析 chemical analysis of water速度水头 velocity head随机模型 stochastic model泰斯公式 Theis formula探采结合孔 exploration-production well同位素水文地质学 isotopic hydrogeology透水边界 permeable boundary透水层 permeable bed透水性 permeability突水水源 source of water bursting突水系数 water bursting coefficient突水预测图 water bursting prediction map土（岩）样 soil （rock）sample土的颗粒分析 grading analysis of soil土壤改良 soil reclamation土壤水 soil water土壤盐渍化 soil salinization脱硫酸作用 desulphidation脱碳酸作用 decarbonation脱硝（氮）作用 denitration完整井 completely penetrating well微量元素 microelement温泉 thermal spring紊流 turbulent flow稳定流 steady flow稳定流抽水试验 steady-flow pumping test稳定水位 steady water level污染通道 pollution channel污染源 pollution source污水资源化 water resources from sewage renewal无压含水层 unconfined aquifer物理模型法 method of physical model细菌总数 bacterial amount下降泉 descending spring咸淡水界面 interface of salt-fresh water相关分析法（回归分析法）correlation analysis method（regression analysis method）硝化作用 nitrification斜井 inclined well虚井 real well悬浮物 suspended solids悬挂泉（季节泉） suspended spring压力传导系数 hydraulic diffusivity压力水头 pressure head雅可布公式 Jacob formula延迟给水（滞后给水） delayed drainage延迟指数 delayed index岩溶含水层 karst aquifer岩溶含水系统 karst water-bring system岩溶介质 karst medium岩溶水 karst water岩石圈 lithosphere岩石渗透性测定 permeability determination of rock盐碱土 saline allkaline soil盐渍土 salinized soil阳离子交替吸附作用cation exchange and adsorption氧化还原电位 oxidation-reduction potential样品采集 sampling遥感技术 remote sensing technology一维流 one-dimensional flow溢流泉 overflow spring影响半径 radius of influence映射法 image method硬水 hard water涌水量方程外推法（试验推断法） discharge equation extrapolation method 游离性二氧化碳 free carbon dioxide有限差分法 finite-difference method有限单元法 finite element method有效降水量 effective precipitation有效孔隙度 effective porosity元素迁移 element migration原生水（初生水） juvenile water（native water）原生盐渍土 primary salinized soil原状土样 undisturbed soil sample越流 leakage越流补给 leakage recharge越流系数 leaky coefficient越流系统 leaky system越流因数（阻越流系数） leaky factor允许水位降深 allowable drawdown蒸发浓缩作用 evaporation-concentration process正均衡 positive balance直线法 linear method重力疏干 gravity drainage重力水 gravity water注水孔 injecting well注水试验 injecting test贮存量变化量 variation of groundwater storage贮水系数（释水系数） storage coefficient专门水文地质学 applied hydrogeology专门性水文地质勘查applied hydrogeclogic investigation专门性水文地质图 special hydrogeological map自流水 artesian water综合水文地质图 synthetic hydrogeoiogical map总水头（渗流水头） total head钻孔流速测 borehole flow-velocity measurement最佳开采量 optimal yield最佳控制水位 optimal controlled water level最佳配水方案 optimal water distribution scheme7.3.2.13斜井 inclined well一般断面尺寸1.8m×2.0 m、倾角20°～40°的倾斜坑道集水工程，适用于开采坚硬岩石、埋深较大的裂隙岩溶水。

Regional mapping of human settlements in southeastern China with multisensor remotely sensed dataDengsheng Lu a ,⁎,Hanqin Tian a ,Guomo Zhou b ,Hongli Ge ba School of Forestry and Wildlife Sciences,Auburn University,602Duncan Drive,Auburn,AL 36849,USA bSchool of Environmental Technology,Zhejiang Forestry University,Lin'An,Zhejiang,ChinaA B S T R A C TA R T I C L E I N F O Article history:Received 6November 2007Received in revised form 16May 2008Accepted 24May 2008Keywords:Human settlements Regional mapping ETM+MODIS NDVI DMSP-OLSPartial unmixing Regression model Southeastern ChinaMapping human settlements from remotely sensed data at regional and global scales has attracted increasingly attention but remains a challenge.The thresholding technique is a common approach for settlement mapping based on the DMSP-OLS data.However,this approach often omits the areas with small proportional settlements such as towns and villages and overestimates urban extents,resulting in information loss of spatial patterns.This paper explored an integrated approach based on a combined use of multiple remotely sensed data to map settlements in southeastern China.Human settlements for selected sites were mapped from Landsat ETM+images with a hybrid approach and they were used as reference data.The DMSP-OLS and Terra MODIS NDVI data were combined to develop a settlement index image.This index image was used to map a pixel-based settlement image with expert rules.A regression model was established to estimate fractional settlements at the regional scale,which the DMSP-OLS and MODIS NDVI data were used as independent variables and the settlement data derived from ETM+images were used as a dependent variable.This research indicated that a combination of DMSP-OLS and NDVI variables provided a better estimation performance than single DMSP-OLS or NDVI variable,and the integrated approach for settlement mapping at the regional scale was pared to the results from the traditional thresholding technique,the estimated fractional settlement image in this paper greatly improved the spatial patterns of settlement distribution and accuracy of settlement areas.This paper provided a rapid and accurate approach to estimate fractional settlements from coarse spatial resolution images at the regional scale by combining a limited number of medium spatial resolution images.This research is especially valuable for timely updating settlement databases at regional and global scales with limited time,labor,and cost.©2008Elsevier Inc.All rights reserved.1.IntroductionHuman settlements are the places where human beings live,work,and recreate,including cities,towns,and villages (Ridd &Hipple,2006).The size,pattern,and spatial distribution of human settlements are a fundamental data source for evaluating impacts of urbanization on environments and for urban management and planning (Milesi et al.,2003a;Pauleit et al.,2005).Human settlements are also closely related to population distribution and economic growth,thus they are an important data source for demographic –economic related studies (Meyer &Turner,1992).With increasing pressure of population and economic growth,the conversion rate of vegetation or agricultural lands to human settlements has been increased sharply during past decades,especially in developing countries such as China (Liu et al.,2005a,b ).The urbanization causing many environmental problems,such as vegetation loss,air pollution,water shortage and contamina-tion,and urban heat island,has been recognized as an important factor affecting the functions of terrestrial ecosystems and climate change (Pickett et al.,2001;Goldewijk &Ramnakutty,2004;Zhou et al.,2004;Foley et al.,2005;Kaufmann et al.,2007).Hence,timely mapping human settlement,especially at regional and global scales,has considerable signi ficance and has already attracted attention in the past decade (Elvidge et al.,1997a,2001;Sudhira et al.,2004;Ridd &Hipple,2006).The urban landscape is a complexity consisting of different land covers,such as trees,lawns,impervious surfaces,and water.In remotely sensed data,especially in coarse spatial resolution images,many different land covers may be mixed in a pixel.This problem often induces dif ficulty in extracting settlements from remotely sensed data.Previous research for mapping human settlements is often based on high or medium spatial resolution images (e.g.,IKONOS,Landsat TM/ETM+)for individual cities (Lu &Weng,2006;Ridd &Hipple,2006).Although many techniques,such as different per-pixel based classi fication approaches and spectral mixture analysis,have been used for mapping settlements or imperviousRemote Sensing of Environment 112(2008)3668–3679⁎Corresponding author.Tel.:+13348441062;fax:+13348441084.E-mail address:LUDS@ (D.Lu).0034-4257/$–see front matter ©2008Elsevier Inc.All rights reserved.doi:10.1016/j.rse.2008.05.009Contents lists available at ScienceDirectRemote Sensing of Environmentj o u r n a l h o m e p a g e :w ww.e l s ev i e r.c o m /l o c a t e /rs esurface areas from medium spatial resolution images(Wu&Murray, 2003;Yang et al.,2003;Lu&Weng,2006;Powell et al.,2007),they are not suitable for regional or global settlement estimation because of the mixed pixel problems and complex landscape.However,mapping human settlements at regional and global scales has become an urgent task because of the increasing pressures from rapid urbanization and associated environmental problems.If high or medium spatial resolution images are used at the regional or global scale,the cost for image purchase,and the time and labor required for processing and interpreting these images could become prohibitive.The frequent cloud conditions in a large area also make it difficult to collect a large number of good-quality images within the same year.It is imperative to develop new approaches to timely and accurately map settlements in a large area with coarse spatial resolution images;however,no suitable approaches are available for mapping settlements at regional and global scales.Hence,this research aims to develop a new approach to map human settlements at the regional scale with the integration of coarse and medium spatial resolution images.In this research,southeastern China was selected as the study area because of its rapid urbanization since the ndsat ETM+ (Enhanced Thematic Mapper Plus)images were used to map settlements in the selected sites at the local scale.Defense Meteor-ological Satellite Program's(DMSP)Operational Line-scan System (OLS)(hereafter,DMSP-OLS)and Terra Moderate Resolution Imaging Spectroradiometer(MODIS)were used to map pixel-based settlement images.A regression model,which was established with the combination of ETM+derived settlements,DMSP-OLS,and MODIS NDVI(Normalized Difference Vegetation Index)data,was used to estimate fractional settlements for the entire study area.2.BackgroundThe DMSP-OLS uses two instruments(i.e.,visible-near infrared and thermal infrared telescopes)to provide both daytime and nighttime images of the Earth(Elvidge et al.,1997b).The visible-near infrared telescope is sensitive to radiation from0.40–1.10µm,and the thermal infrared telescope is sensitive to radiation from10.0–13.4µm and190 to310K.A telescope pixel is0.55km atfine mode and2.7km at smooth mode.Low resolution values are the mean of pixel values at a window size of5by5atfine mode(/dmsp/ sensors/ols.html).Time-series analysis of collected images within a calendar year is used to distinguish stable lights produced by cities and towns from ephemeral lights arising fromfires and lightings,and to remove clouds.The time-series data sets are then composed to generate a city-light image with spatial resolution of1km.Much previous literature has described the characteristics of the DMSP-OLS data(e.g.,Imhoff et al.,1997a,b;Elvidge et al.,1997a,b,c,1999).The DMSP-OLS nighttime image(city lights or stable lights)reflects the existence of human activities.The intensity of the city's nighttime lighting is closely related to population density and economic conditions(Elvidge et al.,2007).Therefore,the DMSP-OLS data are often used to map urban areas or human settlements(Elvidge et al., 1997b;Imhoff et al.,1997a,b;Milesi et al.,2003a;Gallo et al.,2004) and to estimate demographic and socioeconomic variables(Welch, 1980;Sutton et al.,1997;Lo,2001,2002Sutton et al.,2001;Sutton, 2003;Amaral et al.,2005,2006).More applications of DMSP-OLS data were summarized by Elvidge et al.(2007).Two kinds of data formats in the DMSP-OLS images are often used. One is the percent occurrence,or the percentage of time during a grid cell which was lit in the building of the composite(Imhoff et al., 1997b);and the other is the digital number ranging from0to63 (Elvidge et al.,1999).A common application of the DMSP-OLS data is to map urban areas or human settlements with the thresholding technique(Imhoff et al.,1997a,b;Lawrence et al.,2002).A challenge of this technique is to determine appropriate thresholds.No general rules are available for guiding the selection of threshold values.In previous research,when the pixel values of DMSP-OLS stable-light image ranged from0to100%,Imhoff et al.(1997a)used a threshold of 89%to detect urban areas in the continental U.S.;and Amaral et al. (2005)used a threshold of30%to extract a binary image with the nighttime light area and background in the Brazilian Amazonia.When the pixel values of DMSP-OLS image appeared as digital numbers(DN) ranging from0to63,a threshold of50was regarded as optimal in southeastern U.S.(Milesi et al.,2003b).In reality a single threshold could significantly overestimate urban areas,but could omit a large number of towns and villages with a relatively small proportion of settlements.The significant differences of energy availability and consumption,levels of economic development,and density of settlements in a regional or global scale may result in significantly different pixel values in the DMSP-OLS imagery(Small et al.,2005). Thus,the urban distribution derived from a single threshold technique may produce a large error in the spatial pattern.Some previous research has recognized this problem and has used multiple thresh-olds to map settlements at three levels,for instance,urban(N94%), peri-urban(8–94%),and unpopulated places(b8%)in Egypt(Lawrence et al.,2002),or urban(N89%),suburban(25–88%),and rural(b24%)in U.S.Historical Climatology Network(Owen et al.,1998).Depending on the levels of economic development,Henderson et al.(2003) identified the optimal threshold of92%for San Francisco,USA,97% for Beijing,China,and88%for Lhasa,China.Sutton et al.(2001)used three thresholds of40%,80%,and90%for mapping urban areas based on the level of gross domestic product(GDP)per capita in the world.Although previous research with the threshold-based approach has advanced the understanding of settlement mapping from DMSP-OLS data,there remain some problems with the threshold-based approach.First,selecting an appropriate threshold is difficult and seems subjective.No single threshold is appropriate in a large area because of the different levels of socioeconomic development. Secondly,a large uncertainty may be generated by the mixed pixel problem and the impacts of background such as ephemeral light,low-level illumination,and glint of light into adjacent water bodies.Finally, a large number of small settlements may be lost,and the spatial pattern information is reduced significantly.Elvidge et al.(2007) summarized eleven specific shortcomings of the DMSP-OLS data.Fig.1 clearly illustrates some important problems(see the Methods section for the data collection)by examining the images among DMSP-OLS, Terra MODIS color composite,and Landsat ETM+color composite (assigned near infrared,shortwave infrared,and visible bands as red, green and blue).For instance,rivers,lakes,and forests within or nearby Hangzhou,China had similar high DN values to the settlements in the DMSP-OLS image.However,water bodies and forests had significantly different spectral features with settlements in MODIS and ETM+color composites.On the other hand,medium-and low-intensity residential areas had DN values of less than50,thus,they would be lost when a threshold approach was used,resulting in significant underestimation of settlements.Obviously,the threshold-based technique cannot accurately map the spatial pattern of settlements.3.Methods3.1.Study areaSoutheastern China has experienced rapid urbanization since the early1980s.The selected study area covered10provinces and two metropolises—Shanghai and Hong Kong(Fig.2).The study area accounted for15.7%of the total area in China,but the population and gross domestic product(GDP)accounted for44.2%and54.3% according to the China Statistical Yearbook in2006(Bureau of Statistics of China,2006a)[Note:these percentages did not include Hong Kong with a population of6.91million and GDP of$253.1billion in2006according to Wikipedia record(/wiki/3669D.Lu et al./Remote Sensing of Environment112(2008)3668–3679Hong_Kong )].There are three megacities with more than five million inhabitants,23megacities (this number accounts for 45.1%in China)with a population ranging from 1to 5million,and 35cities (accounting for 37.2%)with a population between 0.5to 1million in this study area,according to China City Statistical Yearbook in 2006(Bureau of Statistics of China,2006b ).3.2.Data collection and preprocessingDMSP-OLS stable light,Terra MODIS surface re flectance,multi-temporal MODIS NDVI,and Landsat ETM+images were used in this research and their major characteristics were summarized in Table 1.All the selected data sets were acquired in 2000.The DMSP-OLS nighttime-lights data with 1km spatial resolution were downloaded from the National Geophysical Data Center (NGDC)[/dmsp/global_composites_v2.html (last access on August 7,2007)].The DMSP-OLS image has DN values ranged from 0to 63.The selected DMSP-OLS image was a composite based on time-series archived DMSP-OLS images in the calendar year of 2000.A detailed description of DMSP-OLS data is found in Elvidge et al.(1997b,1999).The stable light data with geographic (Lat/Lon)projection were reprojected to Albers Conical Equal Area projection and the nearest neighbor resampling algorithm was used during the reprojection procedure.Terra MODIS surface re flectance (MOD09A1)and NDVI (MOD13A2)images were downloaded from the USGS (United StateGeographicFig.1.A comparison of human settlements appeared in DMSP-OLS,MODIS,and Landsat ETM+images (Note:a —DMSP-OLS false color image based on sliced DN values;b —DMSP-OLS DN with black and white image;c —Landsat ETM+color composite;and d —MODIS color composite (assigning near infrared,shortwave infrared,and visible bands as red,green and blue).3670 D.Lu et al./Remote Sensing of Environment 112(2008)3668–3679Survey)(Global Visualization Viewer).Previous literature has detailed the description of developing MOD09A1and MOD13A2products (e.g.,Justice et al.,2002).The MODIS data(including surface reflectance and multitemporal NDVI images)with sinusoidal projection were reprojected to Albers Conical Equal Area projection.A bilinear interpolation algorithm was used to resample MODIS surface reflectance images with their original spatial resolution of 463m into a pixel size of1km by1km,and the nearest neighbor resampling algorithm was used to resample multitemporal MODIS NDVI images for keeping the pixel size of1km by1km during the reprojection procedure.Six scenes of Landsat ETM+images were selected within the study area.The ETM+six reflective bands(e.g.,visible,near infrared,and shortwave infrared)with28.5m spatial resolution were used in this research(the thermal band and the panchromatic band were not used).All selected ETM+images with the Universal Transverse Mercator(UTM)coordinate system were reprojected to Albers Conical Equal Area projection.The nearest neighbor algorithm was used to resample the ETM+images into a pixel size of25m by25m.The strategy for mapping human settlements at the regional scale based on a combination of medium and coarse spatial resolution images is illustrated in Fig.3.The ETM+images were used to map settlements at the local scale with a hybrid approach.A combination of MODIS and DMSP-OLS data was used to mask out the pixels with non-settlement land covers.Regression models were then established to calibrate the settlement results at the regional scale.3.3.Settlement mapping from Landsat ETM+imagesAccurate settlement mapping from the selected ETM+images is a prerequisite because this data set is used as a reference for establish-ing regression models and for accuracy assessment.In reality, settlement is a complex combination of different impervious surface materials.Previous research has indicated the difficulty in separating settlements from other land covers based on spectral signatures with traditional per-pixel based classification approaches(Lu&Weng, 2004;2005).One possible approach is to incorporate land surface temperature to separate dark-color impervious surfaces from water based on their differences in land surface temperature(Lu&Weng, 2006).However,the relatively coarse spatial resolution in thermal images(e.g.,120m in TM thermal band vs.28.5m in TM multispectral bands)often resulted in overestimation of impervious surfaces(Lu& Weng,2006).Therefore,in this research,we developed a hybrid approach,which consisted of matchedfiltering(partial unmixing), expert rules,stratification,and unsupervised classification,to map settlements from the ETM+images.The matchedfiltering approach is used tofind the abundance of a user-defined endmember with the partial unmixing technique,which maximizes the response of the selected endmember and suppresses the response of the background(Boardman et al.,1995).This approach provides a rapid way to detect the specific material based on the matches to the selected endmember spectra.The resultant image from matchedfiltering appears as a gray-scale image representing the relative degree of match to the selected spectra.A detailed description of the matchfiltering approach is provided in Boardman et al.(1995). In this research,settlement endmembers was selected on the ETM+ image through visual interpretation of the ETM+color composites. Because of the complexity of settlement materials,it is difficult to identify one settlement to represent all settlements in the study area. Thus,three types of settlements,i.e.,settlements with high-,medium-, and low-spectral signatures,were selected.Matchedfiltering was then used to unmix the ETM+six reflective bands into fraction images based on the selected settlement endmembers.A comparative visual analysis of the three fraction images indicated that the settlement endmember having medium spectral features provided the best results;and thus,Table1Remotely sensed data used in researchSensor Resolution Acquisition dateDMSP-OLS The annual image product with thegrid cell size of1km by1km wasdeveloped from the time-seriesDMSP-OLS images with nominalspatial resolution of0.55km.Theselected DMSP-OLS image has DNvalues ranging from0to63.A cloud-free composite developedfrom all available archived DMSP-OLSdata for the calendar year of2000.MODIS Spatial resolution of500m forMODIS surface reflectance image(MOD09A1).Band5was not used dueto the strip problem.8-day composite,acquired in Sept13–20,2000(MODIS mosaic image based on images of h27v05,h27v06,h28v05,and h28v06scenes).Spatial resolution of1km for multitemporal MODIS NDVI images (MOD13A2).16-day composite;multitemporal NDVI mosaic images were collected between April and October2000.Landsat ETM+Six reflective bands with28.5mspatial resolution(thermal andpanchromatic bands were not used inthis research).Path/row:Acquisition date119/39:Oct11,2000120/37:Sep16,2000122/41:Sep14,2000122/44:Sep14,2000124/45:Oct30,2000122/37:Sep14,2000Fig.2.Study area—southeastern China covering10provinces,Shanghai,and Hong Kong by overlaying a boundary layer at provincial level.3671D.Lu et al./Remote Sensing of Environment112(2008)3668–3679this fraction image was further examined.Analysis of samples of settlements showed that a threshold of0.1was optimal to extract the settlement information from the selected fraction image.Thus,a binary image for the initial settlements was produced based on the rule:if a pixel value in the fraction image was greater than0.1,assigned 1(settlements)to this pixel,otherwise,assigned0(non-settlements) to the pixel.The confusion of some bright-color settlements with bare soils and dark-color settlements with water made the initial settlements overestimated.Therefore,removing non-settlement pixels in the initial settlement image was required.In this research,the spectral signatures of the initial settlement image were extracted from the ETM+reflective bands with an expert rule,i.e.,if the pixel value was1in the initial settlement image,extracted the spectral signatures from the ETM+six reflective bands,otherwise,assigned 0to the pixel.The ISODATA unsupervised classification approach was used to classify the extracted spectral signatures into60 clusters.The cluster image was then overlaid on the ETM+color composite.The analyst was responsible to examine each cluster and to assign each cluster as a settlement or other land cover.The final settlement image was again overlaid on the ETM+color composite to visually examine the success,or not,in mapping the settlements while removing all non-settlements in the image.This procedure for settlement mapping was applied to all selected ETM+ images.Thefinal settlement image was a binary format with1 representing the settlement and0representing other land covers. Finally,the settlement image with25m spatial resolution was aggregated to generate proportional settlement values in a new data set with a pixel size of1km by1km to match the same spatial resolution with MODIS and DMSP-OLS data.3.4.Spectral analysis of settlements from DMSP-OLS dataA total of800sample plots with a window size of1km by1km for each plot were randomly selected from the fractional settlement images which were developed from the ETM+images.The sample plots were linked to the DMSP-OLS image to extract the DN values for examining the relationship between fractional settlements and DMSP-OLS DN values.The fractional settlement values ranging from 0to1.0were separated into10groups with an interval of0.1.The boxplot approach was used to examine DMSP-OLS DN features, representing graphically the distribution of fractional settlements in a pixel against the DMSP-OLS DN value.Fig.4shows the complexity of the relationship between fractions of settlements and DMSP-OLS DN values and indicates the problem using the threshold-based technique in mapping settlements or urban areas because low DN values in the DMSP-OLS image(1km spatial resolution)could contain a certain proportion of settlements in a pixel,as shown in Landsat images (25m spatial resolution here)(see Fig.1).The DN values in the DMSP-OLS image may range from3to63,depending on the proportion of settlements in a pixel.The majority of pixels with fraction values of greater than0.9had DN values of greater than 50.Some pixels with fraction values ranging from0.6and0.9had also DN values of greater than50,but most of them had DN values between15and50.If the fraction values were in0.1–0.5,the DN values ranged from3to30.This implied that similar DN values could contain a significantly different proportion of settlements in a pixel.This problem could result in a large uncertainty in settlement estimation and loss of spatial information based on DMSP-OLS data at the regional scale.3.5.Pixel-based settlement extraction from Terra MODIS and DMSP-OLS imagesPrevious research has indicated that the vegetation index,or vegetation abundance,is closely correlated in a negative mannerwith Fig.3.Framework of developing fractional settlements at regional scale with the combination of medium and coarse spatial resolutionimages.Fig.4.Relationship between DMSP-OLS DN and fractional settlements in a grid cell of1km(note:the fraction value of settlements in a pixel was derived from Landsat ETM+images.This graph was based on the800samples which were randomly selected fromthe settlement images developed from Landsat ETM+images and the correspondingDMSP-OLS DN image).3672 D.Lu et al./Remote Sensing of Environment112(2008)3668–3679impervious surfaces (Weng et al.,2004)and has been used for the estimation of impervious surfaces (Gillies et al.,2003;Bauer et al.,2004).However,bare soils are often a problem when using a single-date vegetation index image.For example,in agricultural lands,different seasons could have different surface covers such as grass,crop,and bare soil.In order to better separate impervious surfaces,or settlements,from bare soils,use of multitemporal NDVI can effectively reduce the impact of bare soils.In a large area,an important role of using multitemporal NDVI images is to remove the impact of cloud contamination.Therefore,multitemporal NDVI images were used in this research to generate a new NDVI composite (i.e.,NDVI max )with the maximum algorithm as expressed in Eq.(1).NDVI max ¼MAX NDVI 1;NDVI 2;N ;NDVI n ½ ;ð1Þwhere NDVI 1,NDVI 2,…,NDVI n are the multitemporal MODIS NDVI images acquired during April and October in 2000.Comparing the settlements from ETM+images with corresponding MODIS NDVI and DMSP-OLS data indicated that high fractional settlements in a pixel had generally high DN values in the DMSP-OLS image and had low values in the NDVI image.Different remotely sensed data have their own characteristics and combined use of them could provide more information than their individuals.Data fusion is the most common approach to integrate multiple sensor data sources (Lu &Weng,2007),and the common data sources include SPOT,Landsat,and radar (Yocky,1996;Haack et al.,2002;Ban,2003).However,rarely has research examined the data fusion approaches for multiple sensors of coarse spatial resolution images.The 6-bit DMSP-OLS data (DN ranges within 0and 63)often resulted in data saturation in urban landscape (Elvidge et al.,2007)and dif ficulty in separating different land covers.As shown in Fig.4,if no city lights exist in a land cover such as forest lands,bare soils,and water bodies,the DMSP-OLS DN values are close to zero.However,because of the different levels of economic development,energy availability and consumption,the similar DN values in the DMSP-OLS image could have a signi ficantly different proportion of settlements in a pixel.Therefore,the traditional thresholding technique cannot be accurately used to map human settlements from DMSP-OLS data,but the DMSP-OLS data can be used first to mask out the non-settlement land covers such as forest,agricultural lands,and water.The 16-bit MODIS data (0–65,535)provided more detail informa-tion for separating different land covers,but MODIS data cannot be directly used for mapping human settlements because of the complexity of settlement materials and the mixture of settlements and other land covers in spectral signatures.In urban landscapes,vegetation distribution is closely related to the patterns of settlements (Weng et al.,2004),thus,the vegetation index can be used to estimate human settlements (Bauer et al.,2004).However,non-vegetation land covers,such as bare soils,water,and human settlements have similar values in the NDVI image;thus,NDVI images are not suitable for directly separating human settlements from water and bare soils.Because of the complexity of human settlements and the mixed pixel problem in the coarse spatial resolution image,the pixel-basedclassi fication approach cannot accurately map human settlements based on the MODIS NDVI images.In theory,NDVI image have values ranging from −1to +1.Because of the coarse spatial resolution in MODIS NDVI,the land surface covers,except large water bodies,have data ranges between 0and 1in the NDVI max image during the growing season.In order to match the data range between NDVI max and DMSP-OLS data sets,it is necessary to convert the DMSP-OLS DN values into a floating format with Eq.(2)so that the data values can be in the range of 0and 1.OLS nor ¼OLS −OLS minOLS max −OLS min;ð2Þwhere OLS nor is the normalized value of the DMSP-OLS DN image.OLS min and OLS max are the minimum and maximum values in the DMSP-OLS image,i.e.,0and 63here.Because of different characteristics between DMSP-OLS and MODIS NDVI max data sets in separating settlements from other land covers as discussed above,a combined use of both data sets could provide new insights for mapping settlements at regional or global scale.Therefore,we developed an index called human settlement index in this paper,as expressed in Eq.(3).Human settlement Index¼1−NDVI max ðÞþOLS nornor ðÞþNDVI max þOLS nor ⁎NDVI maxð3ÞIn general,higher proportion of settlements in a pixel should result in a lower value in MODIS NDVI max and a higher value in DMSP-OLS,thus generating higher value in this index.As different levels of economic development and energy consumption affect the city lights,as shown in Fig.4,similar DMSP-OLS DN values could have signi ficantly different proportion of settlements in various regions.However,in urban landscape,vegetation abundance is highly correlated with impervious surface (Weng et al.,2004).Therefore,incorporation of vegetation information into the city light data set can reduce the effects of external factors such as economic development levels on the DMSP-OLS DN values.Sample plots with a window size of 1km 2were selected based on the ETM+derived settlement images,and these plots were linked to the settlement index image to extract the value for each sample.A threshold was then identi fied,based on a comparative analysis of theTable 2Regression models developed from the combination of coarse and medium spatial resolution images Regression methodVariables usedBest regression model (Y =a +b X 1+c X 2)R 2F testt test ab cLinear and nonlinear regression analysisDMSP FSM =−0.059+0.207Ln(DMSP)0.645916.4−2.8⁎30.3NDVI maxFSM =1.267–1.321NDVI max 0.587716.044.4−26.8Settlement indexFSM =0.657+0.241Ln(index)0.664995.579.831.6Stepwise regression analysis DMSP,Ln(DMSP),DMSP nor ,NDVI max,indexFSM =0.469+0.136Ln(DMSP)−0.588NDVI max0.686550.46.912.6−8.1⁎0.005level.Others at less than 0.0001.Note:FSM represents fractional settlements;R 2represents coef ficient of determination for evaluation of the regression model performance.Table 3Comparison of accuracy assessments among the selected models based on randomly sampled 233samples at pixel level MethodsR RMSE DMSP-OLS 0.810.162NDVI max0.720.194Settlement index0.820.158Both DMSP-OLS and NDVI max0.830.156Note:R represents correlation coef ficient between estimate and reference data.RMSE represents root-mean square error.3673D.Lu et al./Remote Sensing of Environment 112(2008)3668–3679。

铜仁市一次局地大暴雨天气的雷达回波特征分析方标;严小冬;龙俐;罗晓松;陈关清【摘要】为了探明局地大暴雨天气的发生原因和发展过程，降低其给农业生产带来的损失，提高大暴雨天气的预报准确率，利用铜仁市气象局新一代多普勒雷达观测资料结合各县（区）气象观测站的常规气象资料及地面雨量观测记录数据对贵州省铜仁市中东部2013年9月10日的局地大暴雨天气雷达回波特征进行综合分析。

结果表明：1）在混合降水云系中，分散积层混合型回波在较长时间内聚集稳定、少动，并呈“准静止状态”和“列车效应”的回波现象，是导致局地大暴雨天气发生的主要原因。

2）在混合降水回波中存在多个对流回波柱、且强回波核位于云体中下部的回波垂直结构特性是识别、判断局地大暴雨天气的重要特征。

3）在暴雨发生前，对流层的辐合强度和厚度增强，并出现高层辐散；在降水减弱阶段，低层辐合减弱并逐渐变为辐散，高层辐散也逐渐减弱最后转为整体下沉的回波径向速度特征反映了局地暴雨天气的演变发展过程。

%In order to explore the occurrence reason and development prdess of torrential rain,so as to decrease the loss brought by local torrential rain in agricultural production and increase the forecast accuracy of torrential rain,the authors used a new Doppler weather radar data,and combined with conventional meteorological data and rainfall observation records to analyze a local rainstorm weather process on September 10,2013 in the middle part of Tongren ,Guizhou.Results:1)The direct reason for the heavy rain weather in some areas of Tongren was low trough,low vortex deepening,low vortex shear line and the West Pacific subtropical high and stable less dynamic barrier eastward and ground cold air intrusion.2)In the mixture of rainclouds,scattered laminated hybrid echo kept stable,less dynamic, gathered a “quasistationary state”and strong echo rainband constitute the “train effects”in a long tim e was conducive to the heavy rainstorm weather.3)In the mixed precipitation echoes in the presence of multiple convective echo column,strong echo nucleus located in the lower cloud was important to recognize and judge the feature of rainstorm.In the radial velocity,The change of positive and negative velocity and zero velocity line could reflect the development process of the rainstorm weather.4)Before the occurrence of the rainstorm,the intensity and the thickness of convergence of troposphere was enhanced,and divergence emergenced;in the weakening stage,low level convergence weaken and gradually became divergence, divergence was also gradually weakened,and finally into the sinking in the whole.In the radial velocity figure,the variation of plus or minus speed zone and zero velocity curve reflected the evolution process of torrential rain.【期刊名称】《贵州农业科学》【年(卷),期】2014(000)004【总页数】5页(P112-116)【关键词】多普勒雷达;大暴雨天气;雷达回波;列车效应;风廓线;铜仁【作者】方标;严小冬;龙俐;罗晓松;陈关清【作者单位】贵州省铜仁市气象局，贵州铜仁 554300;贵州省铜仁市气象局，贵州铜仁 554300; 贵州省气候中心，贵州贵阳 550002;贵州省气候中心，贵州贵阳 550002;贵州省铜仁市气象局，贵州铜仁 554300;贵州省铜仁市气象局，贵州铜仁 554300【正文语种】中文【中图分类】P458.1+21.1暴雨天气一直是气象防灾减灾的重点，局地暴雨和大暴雨天气常常会造成洪涝灾害，给农业生产和人民生命财产安全带来较大隐患，危害较大。

个人简介1956年1月出生，籍贯：吉林省敦化市，1978.03―1982.01 吉林大学数学系本科生1984.09―1986.08 吉林大学数学所硕士研究生1986.09―1988.12 吉林大学数学所博士研究生1982.01―1988.06 吉林大学数学学院助教1988.07―1990.12 吉林大学数学学院讲师1991.01―1992.09 吉林大学数学学院副教授1992.10―现在吉林大学数学学院教授1994.12―现在吉林大学数学学院博士生导师2001.10―现在吉林大学数学学院长江学者特聘教授四、主要学术贡献主要从事偏微分方程理论及其应用方面的研究。

主持和参加了多项教学和科研项目，于国内外学术刊物发表论文几十篇。

现指导博士研究生人6人，硕士研究生9人(已毕业博士研究生6人，硕士研究生12人).1. 教学项目1) 《数学分析》，教育部基地创名牌课程项目，负责人，2003―2005；2) 《数学分析》，吉林大学百门精品课程，负责人，2001―2006；3) 《新时期应用数学人才培养》，吉林大学新世纪教育教学改革工程，负责人，2 003―2006；4) 《数学物理方程》，吉林大学百门精品课程，负责人，2005―2010；2. 科研项目1)《具退化性和奇异性的非线性扩散方程》，国家杰出青年基金项目，负责人，20 02―2005；2) 《具奇异性的非线性扩散方程》，高等学校博士学科点专项科研基金项目，负责人，2004―2006；3) 《图像处理中的偏微分方程方法及其数值方法》，国家自然科学基金重点项目，负责人，2006―2009.3．获奖励情况(1) 2001年获得香港求是科技基金会“杰出青年学者奖”。

(2) 2001年被教育部评为“长江学者奖励计划”特聘教授。

(3) 1999年获国家教育部科学技术进步一等奖。

(4) 2002年被评为教育部高等学校优秀骨干教师。

(5) 2005年被评为吉林省高级专家。

数学专业英语词汇代数局部1. 有关数x算add，plus 加subtract 减difference 差multiply, times 乘product 积divide 除divisible 可被整除的divided evenly被整除dividend 被除数，红利divisor 因子，除数quotient 商remainder余数factorial 阶乘power 乘方radical sign, root sign 根号round to四舍五入to the nearest 四舍五入2. 有关集合union 并集proper subset 真子集solution set 解集3.有关代数式、方程和不等式algebraic term 代数项like terms, similar terms同类项numerical coefficient 数字系数literal coefficient 字母系数inequality 不等式triangle inequality 三角不等式range 值域original equation 原方程equivalent equation 同解方程，等价方程linear equation 线性方程(e.g. 5x+6=22) 4.有关分数和小数proper fraction真分数improper fraction 假分数mixed number 带分数vulgar fraction，common fraction 一般分数simple fraction简分数complex fraction繁分数numerator 分子denominator 分母(least) common denominator〔最小〕公分母quarter 四分之一decimal fraction 纯小数infinite decimal 无穷小数recurring decimal循环小数tenths unit 十分位5. 根本数学概念arithmetic mean 算术平均值weighted average 加权平均值geometric mean 几何平均数exponent 指数，幂base 乘幂的底数,底边cube 立方数，立方体square root平方根cube root 立方根common logarithm 常用对数digit 数字constant 常数variable 变量inverse function反函数complementary function 余函数linear 一次的，线性的factorization 因式分解absolute value绝对值，e.g.｜-32｜=32 round off四舍五入6.有关数论natural number 自然数positive number 正数negative number 负数odd integer, odd number 奇数even integer, even number 偶数integer, whole number 整数positive whole number 正整数negative whole number 负整数consecutive number 连续整数real number, rational number 实数,有理数irrational〔number〕无理数inverse 倒数composite number 合数 e.g. 4,6,8,9,10,12,14,15……prime number 质数 e.g. 2,3,5,7,11,13,15……注意：全部的质数(2除外)都是奇数，但奇数不肯定是质数reciprocal 倒数common divisor 公约数multiple 倍数(least)common multiple (最小)公倍数(prime) factor (质)因子common factor 公因子ordinary scale, decimal scale 十进制nonnegative 非负的tens 十位units 个位mode众数median 中数common ratio 公比7.数列arithmetic progression(sequence) 等差数列geometric progression(sequence) 等比数列approximate 近似(anti)clockwise (逆) 顺时针方向cardinal 基数ordinal 序数direct proportion 正比distinct 不同的estimation 估量，近似parentheses 括号proportion 比例permutation 排列combination 组合table 表格trigonometric function 三角函数unit 单位,位几何局部1. 全部的角alternate angle 内错角corresponding angle 同位角vertical angle对顶角central angle圆心角interior angle 内角exterior angle 外角supplementary angles补角complementary angle余角adjacent angle 邻角acute angle 锐角obtuse angle 钝角right angle 直角round angle周角straight angle 平角included angle夹角2.全部的三角形equilateral triangle 等边三角形scalene triangle不等边三角形isosceles triangle等腰三角形right triangle 直角三角形oblique 斜三角形inscribed triangle 内接三角形3.有关收敛的平面图形，除三角形外semicircle 半圆concentric circles 同心圆quadrilateral四边形pentagon 五边形hexagon 六边形heptagon 七边形octagon 八边形nonagon 九边形decagon 十边形polygon多边形parallelogram 平行四边形equilateral 等边形plane 平面square 正方形，平方rectangle 长方形regular polygon 正多边形rhombus 菱形trapezoid梯形4.其它平面图形arc 弧line, straight line 直线line segment 线段parallel lines 平行线segment of a circle 弧形5.有关立体图形cube 立方体，立方数rectangular solid 长方体regular solid/regular polyhedron 正多面体circular cylinder 圆柱体cone圆锥sphere 球体solid 立体的6.有关图形上的附属物altitude 高depth 深度side 边长circumference, perimeter 周长radian弧度surface area 外表积volume 体积arm 直角三角形的股cross section 横截面center of a circle 圆心chord 弦radius 半径angle bisector 角平分线diagonal 对角线diameter 直径edge 棱face of a solid 立体的面hypotenuse 斜边included side夹边leg三角形的直角边median of a triangle 三角形的中线base 底边，底数〔e.g. 2的5次方，2就是底数〕opposite直角三角形中的对边midpoint 中点endpoint 端点vertex (复数形式vertices)顶点tangent 切线的transversal截线intercept 截距7.有关坐标coordinate system 坐标系rectangular coordinate 直角坐标系origin 原点abscissa横坐标ordinate纵坐标number line 数轴quadrant 象限slope斜率complex plane 复平面8.其它plane geometry 平面几何trigonometry 三角学bisect 平分circumscribe 外切inscribe 内切intersect相交perpendicular 垂直pythagorean theorem勾股定理congruent 全等的multilateral 多边的1.单位类cent 美分penny 一美分硬币nickel 5美分硬币dime 一角硬币dozen 打〔12个〕score 廿(20个)Centigrade 摄氏Fahrenheit 华氏quart 夸脱gallon 加仑(1 gallon = 4 quart)yard 码meter 米micron 微米inch 英寸foot 英尺minute 分(角度的度量单位，60分=1度) square measure 平方单位制cubic meter 立方米pint 品脱(干量或液量的单位)2.有关文字表达题，主要是有关商业intercalary year(leap year) 闰年(366天) common year 平年(365天)depreciation 折旧down payment 直接付款discount 打折margin 利润profit 利润interest 利息simple interest 单利compounded interest 复利dividend 红利decrease to 减少到decrease by 减少了increase to 增加到increase by 增加了denote 表示list price 标价markup 涨价per capita 每人ratio 比率retail price 零售价tie 打Chapter onefunction notation方程符号函数符号quadratic functions 二次函数quadratic equations 二次方程式二次等式chapter twoEquivalent algebraic expressions 等价代数表达式rational expression 有理式有理表达式horizontal and vertical translation of functions 函数的水平和垂直的平移reflections of functions 函数的倒映映射chapter threeExponential functions 指数函数exponential decay 指数式衰减exponent 指数properties of exponential functions 指数函数的特性chapter fourTrigonometry 三角学Reciprocal trigonometric ratios 倒数三角函数比Trigonometric functions 三角函数Discrete functions 离散函数数学 mathematics, maths(BrE), math(AmE) 公理 axiom定理 theorem计算 calculation运算 operation证明 prove假设 hypothesis, hypotheses(pl.)命题 proposition算术 arithmetic加 plus(prep.), add(v.), addition(n.) 被加数 augend, summand加数 addend和 sum减minus(prep.), subtract(v.), subtraction(n.)被减数 minuend减数 subtrahend差 remainder乘times(prep.), multiply(v.), multiplication(n.)被乘数 multiplicand, faciend乘数 multiplicator积 product除divided by(prep.), divide(v.), division(n.)被除数 dividend除数 divisor商 quotient等于 equals, is equal to, is equivalent to大于 is greater than小于 is lesser than大于等于 is equal or greater than小于等于 is equal or lesser than运算符 operator数字 digit数 number自然数 natural number整数 integer小数 decimal小数点 decimal point分数 fraction分子 numerator分母 denominator比 ratio正 positive负 negative零 null, zero, nought, nil十进制 decimal system二进制 binary system十六进制 hexadecimal system权 weight, significance进位 carry截尾 truncation四舍五入 round下舍入 round down上舍入 round up有效数字 significant digit无效数字 insignificant digit代数 algebra公式 formula, formulae(pl.)单项式 monomial多项式 polynomial, multinomial系数 coefficient未知数unknown, x-factor, y-factor,z-factor等式，方程式 equation一次方程 simple equation二次方程 quadratic equation三次方程 cubic equation四次方程 quartic equation不等式 inequation阶乘 factorial对数 logarithm指数，幂 exponent乘方 power二次方，平方 square三次方，立方 cube四次方the power of four, the fourth powern次方 the power of n, the nth power 开方 evolution, extraction二次方根，平方根 square root三次方根，立方根 cube root四次方根 the root of four, the fourth rootn次方根 the root of n, the nth root 集合 aggregate元素 element空集 void子集 subset交集 intersection并集 union补集 complement映射 mapping函数 function定义域 domain, field of definition值域 range常量 constant变量 variable单调性 monotonicity奇偶性 parity周期性 periodicity图象 image数列，级数 series微积分 calculus微分 differential导数 derivative极限 limit无穷大 infinite(a.) infinity(n.)无穷小 infinitesimal 积分 integral定积分 definite integral不定积分 indefinite integral有理数 rational number无理数 irrational number实数 real number虚数 imaginary number复数 complex number矩阵 matrix行列式 determinant几何 geometry点 point线 line面 plane体 solid线段 segment射线 radial平行 parallel相交 intersect角 angle角度 degree弧度 radian锐角 acute angle直角 right angle钝角 obtuse angle平角 straight angle周角 perigon底 base边 side高 height三角形 triangle锐角三角形 acute triangle直角三角形 right triangle直角边 leg斜边 hypotenuse勾股定理 Pythagorean theorem钝角三角形 obtuse triangle不等边三角形 scalene triangle等腰三角形 isosceles triangle等边三角形 equilateral triangle四边形 quadrilateral平行四边形 parallelogram矩形 rectangle长 length宽 width菱形rhomb, rhombus, rhombi(pl.),diamond正方形 square梯形 trapezoid直角梯形 right trapezoid等腰梯形 isosceles trapezoid 五边形 pentagon六边形 hexagon七边形 heptagon八边形 octagon九边形 enneagon十边形 decagon十一边形 hendecagon十二边形 dodecagon多边形 polygon正多边形 equilateral polygon 圆 circle圆心 centre(BrE), center(AmE) 半径 radius直径 diameter圆周率 pi弧 arc半圆 semicircle扇形 sector环 ring椭圆 ellipse圆周 circumference周长 perimeter面积 area轨迹 locus, loca(pl.)相似 similar全等 congruent四面体 tetrahedron五面体 pentahedron六面体 hexahedron平行六面体 parallelepiped立方体 cube七面体 heptahedron八面体 octahedron九面体 enneahedron十面体 decahedron十一面体 hendecahedron十二面体 dodecahedron二十面体 icosahedron多面体 polyhedron棱锥 pyramid棱柱 prism 棱台 frustum of a prism旋转 rotation轴 axis圆锥 cone圆柱 cylinder圆台 frustum of a cone球 sphere半球 hemisphere底面 undersurface外表积 surface area体积 volume空间 space坐标系 coordinates坐标轴 x-axis, y-axis, z-axis横坐标 x-coordinate纵坐标 y-coordinate原点 origin双曲线 hyperbola抛物线 parabola三角 trigonometry正弦 sine余弦 cosine正切 tangent余切 cotangent正割 secant余割 cosecant反正弦 arc sine反余弦 arc cosine反正切 arc tangent反余切 arc cotangent反正割 arc secant反余割 arc cosecant相位 phase周期 period振幅 amplitude内心 incentre(BrE), incenter(AmE)外心 excentre(BrE), excenter(AmE)旁心 escentre(BrE), escenter(AmE)垂心orthocentre(BrE), orthocenter(AmE)重心 barycentre(BrE), barycenter(AmE) 内切圆 inscribed circle外切圆 circumcircle统计 statistics平均数 average加权平均数 weighted average方差 variance标准差root-mean-square deviation, standard deviation比例 propotion百分比 percent百分点 percentage百分位数 percentile排列 permutation组合 combination概率，或然率 probability分布 distribution正态分布 normal distribution非正态分布 abnormal distribution图表 graph条形统计图 bar graph柱形统计图 histogram折线统计图 broken line graph曲线统计图 curve diagram扇形统计图 pie diagram。

CHAPTER14DIRECT CURRENT(DC)DISCHARGES 14.1QUALITATIVE CHARACTERISTICS OFGLOW DISCHARGESThe dc glow discharge has been historically important,both in applications of weakly ionized plasmas and in studying the properties of the plasma medium.A dc discharge has one obvious feature,its macroscopic time independence,that is simpler than rf discharges.However,the need for the current,which provides the power for the discharge,to be continuous through the dc sheath provides an additional complication to the operation.This complication is not present in rf or microwave discharges where displacement current provides current continuity through the sheath.To understand the glow discharge,we consider the usual con-figuration of a long glass cylinder with the positive anode at one end and a negative cathode at the other.Although not necessarily the configuration used in processing applications,it has the advantage of symmetry and has been well studied.The usual pressure range of operation is between10mTorr and10Torr.Typically,a few hundred volts between cathode and anode is required to maintain the discharge. The approximate characteristics of the discharge are shown in Figure14.1.It is clear from the many light and dark regions identified in Figure14.1a that the beha-vior is quite complicated.The length of the positive column region can be varied by changing the distance between electrodes at a constant pressure and approximately constant voltage drop,while the other regions maintain their lengths.It is therefore Principles of Plasma Discharges and Materials Processing,by M.A.Lieberman and A.J.Lichtenberg. ISBN0-471-72001-1Copyright#2005John Wiley&Sons,Inc.535apparent that the positive column can be analyzed per unit length,while the other features must be analyzed in their entirety.All of the regions are gas,pressure, and voltage dependent in their size and intensity,with some of the smaller features being essentially absent over various parameter ranges.We now describe qualitatively the essential operation of the various regions in maintaining the discharge.The treatment follows most closely that in Cobine (1958)where additional material and references can be found.Positive ColumnThe axially uniform plasma is maintained by the JÁE power integrated over the cross section,which balances the loss of energy per electron–ion pair created, which,in the axially uniform model,is assumed to be radial.The dynamics are very similar to that of the bulk rf discharge,with the power lost per electron–ion pair created going to excitation(the glow),ionization,electron–neutral elastic scat-tering energy losses,and kinetic energy of the electrons and ions striking the walls. The normal glow discharge tends to have a negative voltage–current characteristic (negative differential resistance(d V=d I)which is stabilized by an external resistor, which is varied to adjust the current to the desired value.The power balance deter-mines the(weak)axial Efield required to maintain the positive column.Once E isknown,the drift velocity of the electrons along the column can be found using the dc14.1QUALITATIVE CHARACTERISTICS OF GLOW DISCHARGES537 electron mobility and then,from J,the density can be determined.We use this prescription in Section14.2to calculate the characteristics of the positive column.Cathode SheathThis region,known also as the cathode fall or Crookes dark space,is the region over which most of the voltage drop occurs.The electrons,which carry most of the current in the positive column,are,of course,prevented from reaching the cathode.The massive ions,however,are incapable of carrying the full current. The discharge is maintained by secondary electrons produced at the cathode by the impact of the energetic ions.This process,which is incidental(although often important)in rf discharges,is essential for the operation of the dc discharge.The current is built up by ionization within the sheath,which is generated by the second-ary electrons accelerating in the large electricfields of this region.The electron density andflux grow exponentially from the cathode,with the exponent known as thefirst Townsend coefficient.This mechanism is important,not only for the steady-state discharge,but also for understanding the breakdown that initiates the discharge.In breakdown the entire region between the cathode and the anode par-ticipates in the process,which requires a much higher voltage and therefore leads to hysteresis in the voltage–current characteristic.We analyze this dynamics in Section14.3.Negative Glow and Faraday Dark SpaceThe exponentially increasing density of high-velocity electrons near the cathode leads rapidly to a bright cathode glow in which intense ionization and excitation occurs.The electricfield must decrease rapidly at the end of this region,where the transition to the positive column occurs.However,the high electron velocities must be dissipated by elastic and inelastic collisions before the equilibrium conditions of the positive column can be established.This is done in a rather com-plicated process in which the electronsfirst lose almost all of their energy and then are reaccelerated in a weakfield over approximately a mean free path(the Faraday dark space).We give a simple approximate analysis of this behavior at the end of Section14.3.Anode FallThe drift velocity of the electrons in the weak electricfield of the positive column is typically less than their thermal velocity.This requires a retarding electricfield in the neighborhood of the anode to prevent the full thermal electron current from reaching the anode.However,the anode itself must clearly be positive with respect to the positive column to maintain the current.The result is a double layer,which is also seen in various other types of discharges,for essentially the same reason.Since the total voltage drop in this region is small and plays little role in the overall dynamics,we will not analyze it quantitatively.538DIRECT CURRENT(DC)DISCHARGESOther EffectsThe various other regions indicated in Figure14.1are not of particular significance for an overall understanding of the discharge behavior.In addition to the axial variations there are,of course,radial variations.In a long cylindrical discharge, we shall obtain the usual Bessel function radial variation as part of our solution for the positive column given in Section14.2.We may assume qualitatively similar radial variations of density in other regions,but quantitative calculations are very difficult.Additional radial features exist,such as an incomplete coverage of the cathode surface by the discharge,as we discuss in Section14.3.In the previous discussion we have considered the typical characteristics in the normal glow,which occurs over a range of current densities,typically between 10À5and10À3A=cm2.Considering current density as the controlling variable,the voltage–current characteristic of a dc discharge is shown in Figure14.2.Theflat region with slightly negative slope d V=d I is that of the normal glow.From low currents,the region below I A is called a dark or Townsend discharge.The glow gradually builds up until a transition is reached,with hysteresis,entering the normal glow at a voltage V S.The voltage remains constant as the current increases until I B,at which point there is an increasing voltage–current characteristic called the abnormal glow.A further increase in current results in a rather abrupt transition at I C,again characterized by hysteresis,to a considerably lower voltage discharge known as an arc discharge.The voltage continues to decrease with increasing current,approaching an asymptote.For a typical pressure(say1Torr)and a typical discharge tube of a few centimeters cross section,the transitions might occur at I A%10À6A,I B%10À2A,and I C%10À1A,but these currents dependon various other factors such as gas and electrode surfaces.There areapplications Array FIGURE14.2.Typical voltage–current characteristic of a dc glow discharge.14.2ANALYSIS OF THE POSITIVE COLUMN539 of these various regions,particularly for high current arc discharges,which wedo not consider.The reader canfind further descriptions of the behavior and theapplications in various monographs,for example,in Cobine(1958)and in Roth(1994).In some pressure and voltage ranges there are also interesting time-varyingphenomena,such as moving transverse striations and longitudinalfilaments.Athigh pressures,arc spots can form at the cathode,which correspond to an entirelydifferent range of operation,not considered here,in which the secondary emissionprocess is thermionic.For further study,the interested reader is referred to the litera-ture(Cobine,1958;Franklin,1976;Raizer,1991;Roth,1994).Sputtering and Other ConfigurationsA phenomenon that is not part of the discharge dynamics,but is important bothfor applications and in limiting the use of glow discharges,is cathode sputtering.The potential drop across a cathode sheath is typically several hundred volts.These ion-bombarding voltages lead to severe sputtering of the cathode surfaceand consequently deposit material on other surfaces.We describe physical sput-tering in Section9.3and its application to the deposition of thinfilms in Section16.3.Since there is little control over the large voltage drop in the cathodesheath,the existence of sputtering is important in defining appropriate appli-cations.Low aspect ratio dc discharges have been used for sputtering.Toenhance sputtering efficiency,other configurations of dc discharges have beenemployed.One configuration that has proved to be important for optical radiationsources and for metal-ion lasers is hollow cathode discharges.We treat this con-figuration in Section14.4.Another method of enhancing sputtering,used primar-ily for depositing metallicfilms on substrates,employs a nonuniform dc magneticfield.This configuration is called a dc planar magnetron discharge and is ana-lyzed in Section14.5.14.2ANALYSIS OF THE POSITIVE COLUMNAs in the analysis of rf and microwave discharges,there are various pressureregimes for which different dynamics apply.We will assume the following:(1)The pressure is sufficiently high,l i(T i=T e)R,that a diffusion equation with a constant diffusion coefficient D a applies.The low-pressure(collisionless)limit with freely falling ions,l i&R,was described very early by Tonks and Langmuir(1929);and the intermediate pressure regime,R!l i!(T i=T e)R,is discussed in Godyak(1986).In fact,as described in Section5.3,the radial dis-tributions in the low and intermediate regimes tend to look quite similar.Franklin (1976)describes these various solutions and relations between them.(2)As dis-cussed in Section14.1it is often adequate to assume only radial variation,which we do here.Calculation of T eThe calculation of T e follows from the particle balance as described in Section10.2. Ion particle balance is obtained from the diffusion equation(5.2.21)ÀrÁD a r n¼n iz n(14:2:1) where n¼n e¼n i is the plasma density,D a is the ambipolar diffusion coefficient, and n iz¼K iz n g is the ionization rate as defined in(3.5.1).In cylindrical coordinates (14.2.1)becomesd2n d r2þ1rd nd rþn izD an¼0(14:2:2)Equation(14.2.2)is Bessel’s equation with solution given by(5.2.35)n¼n0J0(b r)(14:2:3) where b¼(n iz=D a)1=2and J0is the usual zero-order Bessel function.If the ion mean free path l i and the sheath thickness s(s%few l De)are both small compared to the column radius R,then the boundary condition n(R)%0can be used,with the solution approximately given by(5.2.36)b¼n izD a1=2¼x01R(14:2:4)where x01%2:405is thefirst zero of the zero-order Bessel function.Although (14.2.4)does not give a completely self-consistent solution,since thefinite ion flux at the wall implies infinite velocity at zero density(see Section5.2),it can give a reasonably accurate value of T e.The reason is that n iz is a very sensitive func-tion of T e of the form(see Chapter3)n iz/p expÀE iz T e(14:2:5) with p the pressure and with the ionization voltage E iz)T e.Thus,T e depends only weakly on all parameters except for E iz.A more accurate solution is obtained by setting the radial particleflux G r equal to n s u B,where,as previously,n s is the density at the sheath edge and u B¼(e T e=M)1=2is the Bohm velocity.For this case,since G r¼ÀD a d n=d r,we can take a derivative of(14.2.3)to obtain a transcendental equation for the electron and ionflux to the wall(see also Section10.2):À(D a n iz)1=2J1(b R)¼J0(b R)u B(14:2:6) 540DIRECT CURRENT(DC)DISCHARGESBecause l i(R for this constant D a solution,(14.2.6)essentially reduces to(14.2.4).In the intermediate-and low-pressure regimes,l i&(T i=T e)R,the radial profile becomes relatively uniform,and the estimate for n iz(5.3.14)applies,n iz%2:2u BR4þRl iÀ1=2(14:2:7)An additional issue at low pressures is the deviation of the electron distribution froma Maxwellian.In using(14.2.5)we have assumed a Maxwellian,thus ignoring theelectron drift motion u e.This motion can readily be included(see Franklin,1976);with u e((e T e=m)1=2this does not appreciably change the results.More important, particularly at low densities,there are various kinetic effects and particle losses,thatcan affect the distribution at high velocities.We discuss these qualitatively at the endof this section.Calculation of E and n0The electricfield E along the z axis(anode-to-cathode)of the discharge is calculatedby equating the input power absorbed to the power lost.In the rf discharge this wasused to determine the density.Here the density cancels,leaving an expression for theelectricfield.However,once thefield is known,a subsidiary condition immediatelygives the density.Equating the ohmic power absorbedP abs¼2p ðRJÁE r d r(14:2:8)to the power lostP loss¼2p R G r e E T(14:2:9) where e E T is the total energy lost per electron–ion pair created,and substituting our radial density solution(14.2.3),we haveen0m e E22p ðRJ0(b r)r d r¼2p R(D a n iz)1=2n0J1(b R)e E T(14:2:10)where we have assumed a constant mobility m e,substituted for the current density J along z usingJ¼en m e E(14:2:11) and have taken E out of the integral by assuming that it is a constant in the long thin approximation.We see that n0cancels from(14.2.10)giving an equation for E14.2ANALYSIS OF THE POSITIVE COLUMN541alone.Performing the integration we find that J 1cancels,and we can solve for E to obtainE ¼n iz E T m e 1=2(14:2:12)Substituting m e ¼e =m n m ,from (5.1.4),then (14.2.12)can also be written in the formE ¼m e n iz n m E T 1=2(14:2:13)We note that n iz and n m are both linearly dependent on pressure,and that the only other dependence on the RHS is T e .Although (14.2.12)gives E as a function of p and as an exponentially sensitive function of T e through its dependence on n iz ,we can eliminate n iz using (14.2.4)to obtainE ¼x 01R D a E T m e 1=2¼x 01R mK m MK mi T e E T 1=2(14:2:14)which shows that E depends only on T e ,independent of p .Integrating (14.2.11)over the discharge cross section yieldsI ¼2p en 0R 2x 01J 1(x 01)m e E (14:2:15)which can be solved to determine n 0for a given discharge current I ,with E given by (14.2.14).Kinetic EffectsAlthough the preceding subsections give a qualitative description of the positive column,various quantitative discrepancies,particularly at lower pressures,have led to more sophisticated treatments.Particular phenomena to be explained are significantly higher average temperatures than predicted from (14.2.7)(with n iz cal-culated for a Maxwellian distribution),higher average energies near the column edge,an excess of local ohmic heating near the column edge compared to the local power dissipated in collisional processes,and a somewhat higher axial electric field.A full kinetic theory including the radial density variation is very complicated,so that various approximate kinetic methods have been employed.One important method is the nonlocal approximation,which we describe in Chapter 18.The basic idea is that,if the pressure is sufficiently low that l E =R .1,where l E isthe electron energy relaxation length,then the total energy e E ¼12m v 2þe F (r )542DIRECT CURRENT (DC)DISCHARGES14.3ANALYSIS OF THE CATHODE REGION543 can be taken to be a constant.For a Maxwellian electron distribution the conserva-tion of total energy is equivalent to the Boltzmann assumption that the temperature is constant and the potential and density are related in the usual logarithmic manner F(r)¼T e ln n(r)=n(0)ðÞ,with F(0)¼0at the plasma center.In this case a local macroscopic theory applies,as it does at high pressure for any distribution. However,we will see in Chapter18that the electron distribution in the positive column tends to be Druyvesteyn-like,falling more rapidly at high energies than a Maxwellian,with the high-energy electrons further truncated by the inelastic processes.Because of the non-Maxwellian distribution the average energy is significantly higher near the plasma edge than in the discharge center,since the lower energy electrons are confined by the potential,while the higher energy electrons can over-come the potential hill.The average energy is significantly higher than predicted by a Maxwellian because overall there are fewer high energy(ionizing)electrons. These effects have been confirmed by comparison with a more complete kinetic theory by Busch and Kortshagen(1995).Because the nonlocal method is limited to low pressures,other methods valid at higher pressure have been proposed(see Ingold,1997for another method of analysis and comparison among various methods).14.3ANALYSIS OF THE CATHODE REGIONConsidering the analysis of the previous section,we take as an example an argon glow discharge at p¼100mTorr and T e¼4V.The current density carried by the electrons in the glow is calculated from(14.2.11)J(r)¼en(r)m e Ewith m e%103m2=(V s)and E¼60V=m.Continuity of current requires the same current at the edge of the cathode sheath region,where the current is carried only by the ions.This can be approximated byJ i(r)¼en s(r)u Bwhere for argon at T e¼4V we calculate u B¼(e T e=M)1=2%3Â103m=s.This is considerably less than the electron drift velocity j u e j¼m e E¼6Â104m=s,and thus,even ignoring the difference between n s and n,it is not possible for the ions to carry the current in the cathode sheath.The resolution of this contradiction is that secondary electrons,created by ion impact at the cathode,are required to sustain the discharge.The process is similar to that involved in vacuum breakdown, and wasfirst analyzed in that context.Wefirst consider the more straightforward case of vacuum breakdown and then discuss the modifications required to treat the cathode sheath.Vacuum BreakdownConsider electrons emitted from a cathode at z ¼0being accelerated by an electric field and ionizing a neutral background.For a flux G e in the z direction (the direction of the field)a differential equation for the increase in flux can be writtend Ge ¼a (z )G e d z(14:3:1)with the solutionG e (z )¼G e (0)exp ðz0a (z 0)d z 0 !(14:3:2)where a (z );1=l iz (z )is the inverse of an “ionization”mean free path,analogous to the collisional mean free path defined in a similar way in Section 3.1.By continuity of total charge (creation of equal numbers of electron–ion pairs)the electron flux leaving the sheath edge at z ¼d ,minus the electron flux emitted at z ¼0,must be equal to the ion flux striking the cathode at z ¼0,minus the ion flux that enters at z ¼d :G i (0)ÀG i (d )¼G e (0)exp ðd0a (z 0)d z 0 !À1&'(14:3:3)where we have substituted for G e (d )from (14.3.2).For breakdown,the discharge must be self-sustaining.That is,setting G e (0)¼g se G i (0)where g se is the secondary electron emission coefficient at the cathode z ¼0,then (14.3.3)must be satisfied with G i (d )¼0.Solving for the exponential,we obtainexpðd0a (z 0)d z 0 ¼1þ1g se (14:3:4)as the self-sustaining condition.For a vacuum region,E is a constant and the electron drift velocity j u e (z )j ¼m e E ¼const.Hence the electron energy is a constant,allowing us to set a ¼const in (14.3.4).Taking the logarithm of both sides,we havea d ¼ln 1þ1g se (14:3:5)the usual form for the breakdown condition of a dc discharge.The quantity a is known as the first Townsend coefficient .As might be expected from our knowledge of cross sections,a is a complicated function of the pressure and the accelerating field,which is very difficult to calculate.However,we might expect a to be 544DIRECT CURRENT (DC)DISCHARGESexpressed in the forma ¼const l e exp ÀE iz E l e(14:3:6)where l e is the mean free path for inelastic (mainly ionization)electron–neutralcollisions,E l e is a typical electron energy gain in the field between collisions,and E iz is an energy for ionization.Here E l e plays the role that T e plays in (14.2.5).Recognizing that l e /p À1,then (14.3.6)can be written in the forma p¼A exp ÀBp E(14:3:7)where A and B are determined experimentally and found to be roughly constantover a restricted range of E =p for any given gas.Some experimental values of a =n g versus E =n g are shown in Figure 14.3.Here the gas density n g (m À3)¼3:25Â1022p (Torr)at room temperature from (2.3.18).The quantity a =n g is a field-intensified ionization cross section.The reduced field E =n g is often specified in units of townsends (1Td ;10À21V m 2).Fitting the form (14.3.7)to data such as shown in Figure 14.3,the coefficients in Table 14.1are constructed.Combining (14.3.7)with (14.3.5),and setting the breakdown voltage V b ¼Ed ,we have the relationApd exp ÀBpd V b ¼ln 1þ1g se(14:3:8)E nnFIGURE 14.3.Field-intensified ionization cross section a =n g versus reduced field E =n g(1Td ;10À21V m 2)(data provided by Petrovic´and Maric ´,2004).14.3ANALYSIS OF THE CATHODE REGION545Solving (14.3.8)for V b ,we obtainV b ¼Bpd ln Apd Àln ln 1þ1=g seÀÁÂÃ(14:3:9)We see that the breakdown voltage is a function of the product pd .For large values of pd ,V b increases essentially linearly with pd .For small pd there is a limiting value of pd ¼A À1ln (1þ1=g se )below which breakdown cannot occur.The breakdown voltage is a minimum V min at some intermediate value pd ¼(pd )min .The curve V b (pd )is called the Paschen curve ,and is a function of the gas and weakly a function of the electrode material.Typical breakdown curves for plane-parallel electrodes are shown in Figure 14.4.As we shall see,the values of V min and (pd )min play an import-ant role in the more complicated problem of the cathode sheath.Cathode SheathWe now consider the cathode sheath region of a discharge for which the electric field,and consequently a ,is not a constant with position.For a large sheath multiplication,we can still take G i (d )¼0in (14.3.3).Taking the logarithm of (14.3.4)we haveðd0a (z )d z ¼ln 1þ1g se (14:3:10)An exact solution for a (z )would involve an integral equation for the field and bevery difficult to solve.A simpler alternative is to measure the electric field distri-bution,which then becomes a known variation in determining a (z ).Somewhat surprisingly (Cobine,1958),it is found that the matrix sheath (constant ion space charge density,see Section 6.3)well approximates the region,giving a linearTABLE 14.1.Constants of the Equation a /p 5A exp(2Bp /E )AB Range of E /p Gas (cm21Torr 21)(V cm21Torr21)(V cm 21Torr 21)He 2.87730–250Ne 4.4111100–400Ar 11.5176100–600Kr 15.6220100–1000Xe 24330200–800H 2 4.813615–600N 211.8325100–600O 2 6.519050–130CH 417300150–1000CF 41121325–200Source :Fits to data supplied by Petrovic´and Maric ´(2004).546DIRECT CURRENT (DC)DISCHARGESfield variationE%E01Àz d(14:3:11)with z¼0at the cathode and z¼d at the sheath edge.Substituting(14.3.11)in (14.3.7)we havea p ¼A expÀBpE0(1Àz=d)!(14:3:12)and substituting(14.3.12)in(14.3.10)we obtainðd0Ap expÀBpE0(1Àz=d)!d z¼ln1þ1gse(14:3:13) FIGURE14.4.Breakdown voltage for plane-parallel electrodes at208C:(a)noble gases;(b)molecular gases(data supplied by Petrovic´and Maric´,2004).14.3ANALYSIS OF THE CATHODE REGION547which can be evaluated to give E0as a function of d.Integrating E in(14.3.11)from 0to d,we can express E0in terms of the cathode sheath(cathode fall)voltage V c as E0¼2V c=d,which when substituted in(14.3.13)givesAB(pd)2 2V c S2V cBpd¼ln1þ1gse(14:3:14)whereS(z)¼ðzeÀ1=y d y(14:3:15)is a known tabulated integral.If one plots V c(pd)for a given gas(given A and B)and given electrode material(given g se)wefind,as expected,curves that have a minimum V c¼V cmin at some(pd)min.We might expect the discharge to adjust itself to this stable value of d,and this is indeed the case in the normal glow region(see Fig.14.2).Some values of the cathode fall voltage are given in Table14.2a,and some corresponding normal glow cathode fall thicknesses are given in Table14.2b.These values are similar to the values for breakdown.We have not quite reached the end of the story.It is also possible to eliminate d in favor of the current density and gain both new insight into the operation of the normal glow region and also understand the abnormal glow operation.The total current density at the cathode is given byJ(0)¼en i(0)v i(0)(1þg se)(14:3:16)TABLE14.2a.Normal Cathode Fall in VoltsCathode Air Ar H2He Hg N2Ne O2Al229100170140245180120311Ag280130216162318233150C240475Cu370130214177447208220Fe269165250150298215150290Hg142340226K18064945917068Mg22411915312518894310Na2001858017875Ni226131211158275197140Pb207124223177210172Pt277131276165340216152364Zn277119184143216354Source:After Cobine(1958).548DIRECT CURRENT(DC)DISCHARGESwhere n i is the ion density,v i is the ion velocity,and g se gives the fraction of the current due to secondary ing Poisson’s equation with the assumption of constant charge density,we can write en i in terms of the cathode fall potential en i (0)¼e 02V c =d 2.Similarly,assuming a collisional sheath,we have v i (0)¼m i 2V c =d ,where m i is the ion mobility.Substituting these values in (14.3.16)we obtainJ (0)¼4e 0m i V 2c (1þg se )d 3(14:3:17)from which we can eliminate d in favor of J (0).Hence we can determine a Paschen-type curve of V c versus J (0).This is shown in Figure 14.5in terms of normalized parameters.It is clear that with a fixed external voltage source V T and resistance R T ,the dashed curve is unstable,such that if J ¼I =A ,J min ,where A is the effective cathode area;that is,ifV T ÀV cminR T A,J min(14:3:18)then the cathode fall area will constrict to a smaller value.This is the normal glow region.On the other hand,forV T ÀV cminR T A.J min(14:3:19)the solution is stable,and V c will increase with increasing current density.It is this region that is called the abnormal glow ,but as we can see,it is just as normal as the normal glow.TABLE 14.2b.Normal Cathode Fall Thickness pd in Torr cm Cathode Air Ar H 2He Hg N 2Ne O 2Al 0.250.290.72 1.320.330.310.640.24C 0.90.69Cu 0.230.80.6Fe 0.520.330.9 1.300.340.420.720.31Hg 0.9Mg 0.61 1.450.350.25Ni 0.90.4Pb 0.84Pt1.0Source :After Cobine (1958).14.3ANALYSIS OF THE CATHODE REGION549。

a r X i v :a s t r o -p h /0010279v 1 14 O c t 2000The Upsilon Andromedae System:Models and StabilityTomasz F.Stepinski(tom@ )Renu Malhotra (renu@ )andDavid C.Black (black@ )Lunar and Planetary Institute,3600Bay Area Blvd.,Houston,TX 77058ABSTRACT Radial velocity observations of the F8V star υAndromedae taken at Lick and at Whipple Observatories have revealed evidence of three periodicities in the line-of-sight velocity of the star.These periodicities have been interpreted as evidence for at least three low mass companions (LMCs)revolving around υAndromedae.The mass and orbital parameters inferred for these companions raise questions about the dynamical stability of the system.We report here results from our independent analysis of the published radial velocity data as well as new unpublished data taken at Lick Observatory.Our results confirm the finding of three periods in the data.Our best fits to the data,on the assumption that these periods arise from the gravitational perturbations of companions in keplerian orbits,is also generally in agreement,but with some differences,from the earlier findings.We find that the available data do not constrain well the orbital eccentricity of the middle companion in a three-companion model of the data.We also find that in order for our best-fit model to the Lick data to bedynamically stable over the lifetime of the star (∼2billion years),the system must have a mean inclination to the plane of the sky greater than 13degrees.The corresponding minimum inclination for the best fit to the Whipple data set is 19degrees.These values imply that the maximum mass for the outer companion can be no greater than about 20Jupiter masses.Our analysis of the stability of the putative systems also places constraints on the relative inclinations of the orbital planes of the companions.We comment on global versus local (i.e.,method of steepest descent)means of finding best-fit orbits from radial velocity data sets.Subject headings:binaries:spectroscopic—planetary systems—stellar dynamics—stars:individual (υAndromedae)1.IntroductionRadial velocity observations of several hundred nearby main-sequence stars have resulted in the detection to date of roughly forty companions with minimum or projected masses(i.e.,m sin i) less than80M J,where M J is the mass of Jupiter(Marcy and Butler1998;Marcy et al.1999; Vogt et al.2000;Mayor et al.1997).Nearly thirty of these companions have m sin i∼<10M J.The evidence to date typically suggests only one companion per star;however,the data from some of the observational studies have suggested that other companions may be present in some cases but will require longer time bases for the observational record beforefirm conclusions can be established (Cumming1999).Evidence for the presence of multiple low mass companions(LMCs)to a star would be signif-icant for several reasons.A key reason is that it would suggest,at least superficially,a similarity of such a system to our planetary system,and by extension,planetary systems in general.Thefirst strong evidence for multiple LMCs to a single star,Upsilon Andromedae(υAnd), was reported recently by Butler et al.(1999)(hereafter referred to as B99).The data presented in that paper are from two independent studies,one conducted at the Lick Observatory and the other conducted at the Whipple Observatory using the Advanced Fiber-Optic Echelle(AFOE) Spectrograph.Earlier observations ofυAnd(Butler et al.1997)had detected a periodicity in the radial velocity data that indicated the presence of a companion with an orbital period of4.6days and a projected mass of∼0.7M J.Those authors noted that the data also contained“evidence for variability in the gamma velocity with timescale of about2yr.”The newer observations(B99) reveal additional periodicities,one in excess of1200days(1269days for the Lick data and1481 days for the AFOE data),as well as one with∼240days.B99have modeled these periodicities as arising from the presence of three LMCs in keplerian orbits aboutυAnd.The eccentricities of the orbits determined by B99are,in order of increasing orbital period,0.042,0.23,and0.36.This three-companion model for the observations raises interesting challenges in understanding the formation and evolution of that system and its possible relationship to systems such as the Solar System.Particular challenges relate to the dynamical stability of such a system and what constraints it might place on physically realizable companion systems,and to how a system consisting of at least three relatively massive objects could form around a star with the orbital structure that is suggested by the data.In an effort to explore these challenges in more detail,we re-examine here the published radial velocity data onυAnd,as well as data taken subsequent to announcement of the results and kindly provided to us by G.Marcy.Section2summarizes the radial velocity data that are used in our analyses.Models for analyzing the radial velocity data are discussed in Section3.The methods that we used forfitting the data and the procedures for assessing the merit of thosefits are described in Section4.The best-fit models,assuming that the periodicities are due to companions(i.e.,thatthe model for describing the data is one comprised of a superposition of Keplerian motion)are presented in Section5.We examine the dynamical stability of candidate model systems in Section 6.A summary of our results and conclusions regarding the possible nature of theυAnd system are given in Section7.2.Radial velocity dataWe use three different data sets to perform our analysis.Thefirst data set was collected at Lick.It contains89observations ofυAnd made between September1987and March1999as part of the Lick survey.We refer to this data set as the original Lick data.The second data set was collected by the AFOE planet search program and contains52observations ofυAnd made between September1994and February1999.We refer to this data set as the AFOE data.Original Lick data and AFOE data are published by B99.Details about these data sets can be found therein. The third data set,referred to as the new Lick data,has been provided to us by G.Marcy.This contains118observations ofυAnd collected at Lick and comprises29observations made between June and August of1999in addition to the original89observations.Note that in this data set the radial velocities for the original89observations have been revised to reflect improvement in the data reduction technique.All three data sets have the same form:each record is a triplet(t,V,σ),where t is the time of observation(in Julian days),V is an unaccounted for component of the star’s radial velocity (hereafter referred to as radial velocity)in(m s−1),andσis a measurement error in(m s−1).Bulk properties of radial velocities are consistent among the three data sets.The range of V is−177m s−1 to165m s−1,the mean value of V is−11m s−1to−5m s−1,and the standard deviation is71m s−1 to82m s−1.Measurement errors are of the order of10m s−1,generally smaller for the Lick data than for the AFOE data.It is useful to think about the radial velocity data fromυAnd as a time series,and to pretend that we have no a priori insight into the mechanism that produces it.Thefirst step is to calculate the signal’s frequency spectrum.Fig.1(left column)shows the frequency spectrum for all three data sets.Because the observations are not evenly spaced,the frequency spectrum cannot be obtained by means of the FFT,instead we used the Lomb-Scargle periodogram technique(Lomb 1976;Scargle1982;Black and Scargle1982)to obtain standard,zero mean periodograms.These spectra indicate the existence of periodic components in the radial velocity signal from υAnd.Spectral features common to all three data sets exist.The most prominent are peaks at ∼4.617d,∼500d,and∼1200–1500d.However,not all significant peaks present in the frequency spectrum actually correspond to real periodicities.A simple test for the reality of periodicities indicated by the frequency spectrum is to fold the signal with suspected periods.Only folds with actual periodicities yield coherent patterns.The fold test provides definitive affirmation,but,in the presence of multiple periodicities it does not necessarily provide definitive disaffiingthe fold test we can confirm the authenticity of the∼4.617d and∼1200–1500d periodicities.The ∼500d feature,which in fact can be shown to be an alias(e.g.B99),fails the fold test.These three features are the only significant periodicities in the frequency spectrum of the original Lick data set.Additional significant features are present in the periodogram of the new Lick data set.The most prominent are located at∼141d,∼14d,and∼230d.They all fail the fold test.The periodogram of the AFOE data set also shows additional significant peaks.The most prominent peak is located at∼29d and is affirmed by the fold test.In addition,peaks at ∼145d and∼245d,the locations close to those identified on the periodogram for the new Lick data set,are present,but they fail the fold test.This preliminary analysis of radial velocity signal fromυAnd indicates existence of two peri-odicities,one at∼4.617d,and another at∼1200to∼1500d.This conclusion holds for all three data sets.Therefore,we can confidently postulate that the radial velocity signal fromυAnd is due to the motion of the star caused by the existence of two companions,having orbital periods of∼4.617d and∼1200−1500d.A model consisting of three companions cannot be confidently postulated on the basis of the frequency spectra of the radial velocity signal.However,if such a model is postulated,the third companion should have a period of either∼145d or∼230–245d in order to be consistent with both the new Lick data and the AFOE data.In the AFOE data set,a periodicity of∼29d can be positively identified,but it is not detected in the other data sets;it would be interesting to understand its origin.3.ModelsAssume a model consisting of a single companion,labeled B,orbitingυAnd.Such a one-companion model predicts the radial velocity,V mod,B(t),at any given instant of time.The radial velocity signal due to the orbital motion of the star caused by gravitational interaction with a companion is given by the following expression,V mod,B=K[cos(f+ω)+e cosω],(1)where e is the eccentricity of the orbit,f is true anomaly,andωis its argument of the periastron. The semi-amplitude K is proportional to the projected mass of the companion,m sin i,where i is the angle between an observer’s line-of-sight to a star and the normal to the orbital plane of the companion.The true anomaly,f,can be expressed in terms of the eccentric anomaly,u,tan f1+e2.(2)In turn,eccentric anomaly,u,can be linked to time by means of Kepler’s equation,2πwhere P is the period of the companion’s orbit,and T peri is the time of periastron passage.Equations(1)to(3)completely define the one-companion model,giving the time dependence (albeit in an implicit form)of radial velocity.There arefive free parameters in this model:K,P, e,T peri,andω.If we assume two companions,labeled B and D,to orbitυAnd,then,in thefirst approximation,the two-companion model is simply given by V mod(t)=V mod,B(t)+V mod,D(t)with individual contributions given by(1).There are10free parameters in the two-companion model. The generalization to a model with an arbitrary number of companions is straightforward.Thus, presupposing that the radial velocity signal fromυAnd is mostly due to gravitational interactions with multiple companions,the N-companion model can be written as followsV mod(t)=Ni=1V mod,i(t)+R(t),(4)where R(t)encapsulates sources of radial velocity signal that cannot be attributed to the presence of companions,but instead are intrinsic to the star.They may,in principle,include pulsation and effects due to the inhomogeneous and dynamic nature of the stellar convective and magnetic patterns.However,in the case ofυAnd,there are arguments against pulsations(B99),leaving convective inhomogeneities as the most likely source of R(t).The surface of a star having a convective zone is inhomogeneous in terms of magneticfield, brightness,as well as vertical motion.These inhomogeneities occur on a variety of length scales and are transient.This phenomenon alone leads to variability of the radial velocity measured from the disk integrated light.Such a variability is referred to as a“jitter.”On short time scales the jitter is intrinsically stochastic.Observations and theoretical arguments can be used to estimate the magnitude of the short-term jitter,but not the actual form of R(t).On long time scales the jitter should be modulated by the dependence of stellar photospheric activity on possible cycles of the large-scale stellar magneticfield.Thus,the long-term character of R(t)should be sinusoidal.ForυAnd,B99quote the magnitude of the short-term jitter to be∼10m s−1.This estimate is based on the work of Saar et al.(1998)who investigated the relationship between the variability of the radial velocity signal(i.e.,jitter,unless the star has companions)and various stellar properties for72stars in the Lick survey.They established empirical relations,defined as the best power-law fits,between the variability,σV,and quantities such as B−V color,stellar rotation period,v sin i, and the fractional Ca II H&Kflux.However,inspection offigures1and2of Saar et al.(1998) shows large scatter of actual data around the empirical relations.Thus,the value10m s−1is only a rough estimate ofυAnd’s jitter;values as large as∼20m s−1cannot be ruled out on the basis of Saar et al.’s diagrams.Keplerian models of the radial velocity signal are defined by R(t)=0.Because the jitter is unavoidable,a keplerian model is always incomplete and does not reflect accurately the reality. Thus,we should not expect the keplerian model tofit the data accurately within the known in-strumental errors.The long-term modulation of the jitter,if present,should be picked up by thekeplerian model as a“companion”,provided that the period of such modulations is short enough and its amplitude is strong enough.4.Fitting methods and proceduresWe assume that the radial velocity signal fromυAnd is caused by the presence of companions and thus adopt a keplerian model given by(4)with R(t)=0.We useχ2as a merit function to determine values of best-fit parameters:χ2=Mk=1 V k−V mod(t k;a1,···,a5N)the GA.Our typical run had a population size of70–100and evolved for5000–10000generations. We ran30–40separate experiments on each model–data set combination.5.Bestfit Keplerian models5.1.Two-companion modelsThe frequency spectra of the radial velocity signal fromυAnd(section2)indicates two periodic components suggesting a two-companion keplerian model.We label the two putative companions B and D,for consistency with B99.In our model each companion is characterized by5parameters, thus the two-companion model has10free parameters to befixed by minimization ofχ2(Eqn.5).Table1summarizes the best-fit two-companion solutions we have found for all three data sets.A description of each best-fit solution is divided into three sections.Thefirst section gives the overall properties of thefit,the other two sections list values of the best-fit parameters for B and D,respectively.For the sake of compactness,we don’t list values of uncertainties of estimated parameters.Uncertainties are generally about the same as those in B99because we tune all solutions using the LM method.In the properties section wefirst list the method used to obtain a given solution.The LM method uses a starting point with orbital periods as indicated by the respective frequency spectra. LM/GA stands for the solution found using the LM method and confirmed using the GA method. In this context,“confirmation”means that the GA method yields the solution“similar”to that obtained by the LM method.Moreover,using the GA solution as a starting point in the LM method recovers the original LM solution.Second,the value ofχ2is listed,together with the value ofχ2red=χ2/L,where L is the number of degrees of freedom(the number of observations,M, minus the number of parameters to befitted);in the case of two-companion models L=M−10. Last,the standard deviation of residuals,labeled as“RMS of residuals”is given.The residuals are the values of V k−V mod(t k),k=1,···,M.Overall the best-fit solutions are quite similar for all three data sets.The LM method failed tofind the best-fit,two-companion solution for the AFOE data.The GA method yields several solutions of comparable“fitness”that can be grouped into two distinct categories.For the AFOE data,Table1lists thefittest solution in each category.There are some systematic differences betweenfits to Lick and AFOE data sets,especially with regard to companion D.Fig.2shows observed radial velocities together with their two-companion best-fit models.For compactness, thisfigure as well as Figs.3–4cover the period between1992and2000,and do not showfive earlier Lick data points.However,all observations are used to obtain the best-fit solutions.It is quite clear from even a visual inspection of Fig.2that the two-companion model does notfit the data well.It is expected that the value ofχ2red≈1for a goodfit.The values ofχ2red in Table1arein the range from6.41to23.66.This seems to suggest that the two-companion model offers a badfit to the data.However,note that theχ2red≈1criterion for the goodness offit assumes completeness of the model.Any keplerian model is an incomplete model because the stellar jitter is not incorporated into it.Thus,the best-fit solution should not be characterized byχ2red≈1, unless theσjitter≤σinst,whereσjitter andσinst are standard deviations of the jitter signal and an average instrumental error,respectively.The RMS of residuals is in the range from28.3m s−1to 35.07m s−1,much higher than∼10m s−1expected if the residuals were due to instrumental errors alone.This indicates a badfit unless the stellar jitter is about26–34m s−1.These are much higher values than10m s−1adopted by B99,but cannot be definitively excluded on the basis of empirical diagrams of Saar et al.(1998)as discussed in Sect.3.Fig.1(right column)shows the frequency spectrum of residuals left after subtracting the best-fit,two-companion model from the signal.Spectral features common to all three data sets exist and indicate the existence of periodic components in the residuals.The prominent peaks are at∼145d and∼240d.Note that frequency spectrum of residuals left after subtracting the formal best-fit model to the AFOE data shows no features and is inconsistent with Lick data sets results.On the other hand,the“good”fit to the AFOE data leaves residuals with frequency spectra consistent with those produced by the bestfits to the Lick data sets,except for an additional periodicity at ∼29d present in the AFOE residuals.The apparent failure of two-companion models tofit well the data does not,by itself,necessarily point out to the existence of the third companion;instead,it may reflect a presence of the large but feasible jitter.It is the existence of periodic component(s)in the residuals of the two-companion model,rather than the large values of the residuals and ofχ2red,that suggests an additional com-panion(s).5.2.Three-companion modelsWe now consider the keplerian model with three companions labeled B,C,and D,from in-nermost to outermost.Such a model is characterized by15parameters.Table2summarizes the assorted three-companion solutions for all three data sets.Allfits were obtained by minimizingχ2 (Eqn.5)with respect to14parameters,the period of the innermost companion,P B,having been fixed for reasons of computational efficiency.This is justified because the periodograms give the value of P B=4.6171d with high accuracy.For each data set four different categories of solutions are listed.Thefirst is obtained by the LM method starting with P D given by the best-fit,two-companion solution,and P C equal to240d as indicated by the highest peak on the periodogram of residuals left after subtracting the best-fit, two-companion model from the data.Solutions in this category are the overall best-fits.Hereafter we refer to them as the BF solutions.The second category(hereafter referred to as the PC145 solutions)is obtained by the LM method starting with P D given by the best-fit,two-companionsolution,and P C equal to145days as indicated by the second highest peak on the periodogram of residuals left after subtracting the best-fit,two-companion model from the data.The third category (labeled as the SE solutions)are the best-fit solutions subject to the condition that eccentricities of all orbits are≤0.1,and the fourth category(labeled as the SEBC solutions)are the best-fit solutions subject to the condition that eccentricities of B and C orbits are≤0.1.The latter two models,SE and SEBC,were motivated by dynamical stability considerations.The description of each solution in Table2is divided into four sections,thefirst section gives the properties of thefit, the remaining three sections list values of parameters for companions B,C and D.Fig.3shows the original Lick data together with the fourfits listed in Table2.Visual inspection of Fig.3suggests that BF,SEBC,and SE solutions offer comparably goodfits to the data,whereas the PC145solution provides a slightly worsefit.This impression is confirmed by the values ofχ2in Table2.The RMS of residuals is in the range from∼16.6m s−1for the BF solution,to∼21m s−1 for other solutions.Thus,the BF solution offers a goodfit providing that the jitter is gaussian withσjitter≥13m s−1,and other solutions offer a goodfit providing thatσjitter≥18.5m s−1.In this context,“goodfit”means thatχ2red,recalculated with weightsσk=The character of the solution in each category is consistent amongst all three data sets.In addition,the only significant difference between the BF,SEBC,and SE solutions are the eccentric-ities.Thefits to the AFOE data systematically yield a longer period and a larger value of K for companion D than thefits to the Lick data.Our bestfit to the original Lick data is very similar to that published in B99,and our bestfit to the the AFOE data is virtually identical to that published in B99.The new Lick data suggests that future data will not support the PC145and SE models; the BF remains the best model and the SEBC remains a viable model.Three-companion models offer goodfits to the data.The periods and amplitudes of all compan-ions,as well as eccentricities for companions B and D,are well constrained by the existing data. However,the eccentricity for companion C is not well constrained by the present data.6.Dynamical stabilityIn a Keplerian model,radial velocity data determinefive parameters for each companion, (K,P,e,T peri,ω).The amplitude K is related to the masses and orbital parameters as follows:K=m sin ia(1−e2)1/2,(6)where M⋆and m are the stellar and companion mass,respectively,G is the universal constant of gravitation,and a is the orbital semimajor axis(related to the orbital period P through Kepler’s third law).From these parameters,we can calculate m sin i and a for each companion,provided the stellar mass M⋆is known.The mass ofυAnd is estimated to be1.2—1.4M⊙(Ford1999);following B99, we adopt M⋆=1.3M⊙.From the best-fit models for the new Lick observations and for the AFOE observations(Table2),the sets of parameters needed for orbital dynamics studies are given in Table3.Note that for each of the companions,two orbital parameters—the inclination and the longitude of ascending node—remain undetermined by the radial velocity data.Although the current estimated orbits of the companions are spatially well separated,the (minimum)masses of the companions and the orbital eccentricities of the two outer companions are sufficiently large that significant perturbation of the orbits can be expected due to the mutual gravitational forces amongst the companions.This is illustrated in Fig.6where we show the results of a numerical integration of the equations of motion for this4-body system including all the(point-mass,Newtonian)gravitational forces amongst them,for the best-fit models to the Lick and the AFOE data.(We used a standard second order mixed variable symplectic integrator(Wisdom and Holman1991),with a step size of0.2days;the total energy error in this integration is quasiperiodic and bounded to a few parts in108.)In this integration,we assumed that the orbits are coplanar and edge-on to the line-of-sight.This assumption is not necessarily realistic but it provides a useful fiducial case for measuring the effect of departures from coplanarity and edge-on orientation(whichwe explore further below).Thefigure shows that the orbital semimajor axes are little perturbed (not unexpected,as all the orbital periods are well separated).However,a remarkable feature of the evolution is that the orbital eccentricities of all companions are perturbed significantly on relatively short timescales.The middle companion,C,exhibits the most dramatic perturbation,its eccentricity varying periodically from a maximum(∼0.35in the Lick best-fit model,∼0.28in the AFOE best-fit model)to a minimum near zero;companion D’s eccentricity exhibits a variation with the same period but much smaller amplitude.The period of these variations is about7000yr for the Lick model,and about3500yr for the AFOE model.These eccentricity variations(and corresponding apsidal variations)arise due to a secular interaction between the outer two companions.(See,for example,Brouwer and Clemence(1961).)This interaction can be described approximately as a superposition of two eigenmodes for the evolution of the“eccentricity vector”,(e cosω,e sinω),for each of the companions C and D.The outer companion D’s apsidal rate is dominated by the slowest frequency mode.For the middle companion C,the two modes have nearly equal amplitudes(so that the magnitude of the eccentricity nearly vanishes periodically),and its apsidal motion is limited to the range–90deg to+90deg relative to the apsidal line of companion D.In this context,it is noteworthy that the radial velocity data do not constrain very well the eccentricity of companion C; goodfits to the data include models with small values of e C(cf.discussion in the previous section). Interestingly,we have found that the large amplitude oscillation of the eccentricity of C persists in the“goodfit”(SEBC)model as well.In Fig.6,we see that in the Lick model the innermost companion,B,also suffers a dramatic eccentricity variation,albeit on a longer timescale;however,we consider that this is not“real”because the proximity of companion B to the star would subject it to general relativistic pre-cession that would dominate its secular evolution,suppressing the amplitude of the eccentricity perturbations(see Riviera and Lissauer(2000)).The outer two companions are the most strongly coupled and companion B provides only a very small perturbation to their orbital evolution.It is important to note that the mutual gravitational interactions of the outer two companions is sensitive to their unknown orbital inclinations and relative orientation of their lines of nodes,i.e.,i C,i D andΩD−ΩC.For given values of these,is given byparameters,the relative inclination of the two orbits,φCD=cos i C cos i D+sin i C sin i D cos(ΩD−ΩC).(7) cosφCDThe uncertainties in the other known parameters will also affect the dynamics and stability of the system.Thus,in principle,there is a very large volume of parameter space that needs to be investigated for dynamical studies.Here we confine our discussion to a subset of this parameter space related to the undetermined parameters only.As the long term dynamics and stability of the system is determined largely by the mutual gravitational interactions of the outer two companions,in the numerical investigations described below,we have neglected the presence of the innermost companion.This allows us to use larger。