Mechanically amplified large displacement piezoelectric actuators

Evaporation induced self-assembly of zeolite A micropatterns dueto the stick –slip dynamics of contact lineU ğursoy Olgun ⁎,Vahdettin SevínçDepartment of Chemistry,Faculty of Arts and Sciences,Sakarya University,Esentepe,Sakarya,54187,TurkeyReceived 15March 2007;received in revised form 17July 2007;accepted 23July 2007Available online 3August 2007AbstractIn this study,a new surfactant –solvent system was described for the preparation of periodic stripe patterns of zeolite A on solid substrates.The evaporation induced self-assembly of zeolite A particles was due to the stick –slip dynamics of the three-phase contact line of the colloid solutions in acetone containing 10%(v/v)poly(dimethylsiloxane)(PDMS)fluid (2cst.).In order to investigate the possible effects of particle size and the particle concentration on the stick –slip dynamics,three types of zeolite A samples with different particle sizes (zeolite A-I:250–500nm,zeolite A-II:100–250nm and zeolite A-III:0–100nm)were utilized to prepare 0.007–0.06%(w/v)colloidal dispersions.Zeolite A micropatterns were self-assembled on the surface of glass,high density polyethylene (HDPE)and poly(tetrafluoroethylene)(PTFE)substrates,which were placed vertically inside the colloid solutions and held against the wall of the cylindrical vial during the evaporation of acetone.The stripe patterns of zeolite A particles were analyzed with field emission scanning electron microscope (FE-SEM)and optical microscope.The widths of microstripes and the distance between the stripes were found as 2–20μm and 40–60μm respectively depending on the particle concentration.By using the stick –slip dynamics of colloids,the linear micropatterns of zeolite A nanocrystals were prepared with low cost and low energy.©2007Elsevier B.V .All rights reserved.Keywords:Self-assembly;Stick –slip dynamics;Zeolite A;Micropattern;Nanoparticle1.IntroductionOver the last decade,considerable efforts have been directed toward the preparation of functional zeolite nanoparticles be-cause of their potential applications in membranes,catalytic coating reactors,chemical sensors and biomedical materials.Furthermore,the use of zeolite micropatterns for biological applications [1],the incorporation of zeolites in microchemical systems [2]and the fabrication of zeolite-based microreactors [3]found growing interest.Micropatterning of oriented zeolite monolayers on glass by covalent linkage [4]and patterning of continuous zeolite films on glass by direct dipping in synthesis gel [5]have been studied.Extensive studies are being conducted on micropatterning of colloidal nanoparticles.Micropatterns made of ceramic powders have been prepared from colloidal suspensions using self-as-sembled monolayers (SAM)on gold and silicon wafer substrates[6].It was reported that the aqueous colloidal dispersions of aluminum oxide and tin oxide adhered only to the hydrophilic micropatterns whereas they repelled from the hydrophobic areas in a simple dip coating process.The maximum resolution of ceramic micropatterns was in the order of 5μm.In another study,photolithographed self-assembled monolayers of (3-mercapto-propyl)-trimethoxysilane were utilized in the fabrication of col-loidal gold micropatterns on SiO 2-coated Si substrates [7].It was pointed out that this approach could be applicable to the assembly of microelectronic circuits and microbiosensors.To demonstrate the potential application areas,some ex-amples of other micropatterning techniques are also reviewed below.For instance,the fabrication of TiO 2micro-patterns on Si wafers was demonstrated using laser direct writing and post-annealing [8].A nickel micropattern with a 9μm line width and 12μm line intervals was obtained on an insulating board via anodizing aluminum,laser irradiation,nickel electroplating,insulating board attachment and aluminum substrate dissolution [9].Chemical etching was used to pattern tin oxide film on silicon substrate up to 5μm width for the fabrication of two-Available online at Powder Technology 183(2008)207–212/locate/powtec⁎Corresponding author.Tel.:+902642956060;fax:+902642955950.E-mail address:ugursoyolgun@ (U.Olgun).0032-5910/$-see front matter ©2007Elsevier B.V .All rights reserved.doi:10.1016/j.powtec.2007.07.028dimensional micro-gas sensor array[10].Micropatterns with sizes of10–100μm were created in poly(dimethylsiloxane) using laminar flows of liquids in capillaries[11].Application of micropatterning techniques to the fabrication of scaffolds spe-cifically designed to support chondrogenesis was studied[12]. It was demonstrated that the surface-patterned scaffolds pro-mote adhesion,restrict spreading and maintain key aspects of the chondrogenic phenotype.Although the importance of zeolites in micro-and nano-scale systems has been demonstrated in the literature,a limited number of studies have been performed about the formation of zeolite micropatterns directly from the solution phase.Here,in our study,in the light of recent developments in colloid science, the spontaneous deposition of zeolite A micropatterns from the colloidal dispersions of nanoparticles in10%(v/v)PDMS–ac-etone system was demonstrated without using any pretreatment of substrate surface.Micropatterning of zeolite nanocrystals on the surface of substrate was due to the stick–slip dynamics of contact line of PDMS–acetone system during the evaporation process.In a similar procedure,the formation of ZSM-5zeolite films from nanosuspensions has been investigated by using high polarity solvents,such as water and formaldehyde[13]. However,the direct micropattern formation and the stick–slip dynamics have not been reported previously for any other col-loidal zeolite–solvent system.2.Experimental2.1.Preparation of nanosized zeolite A samplesZeolite A-I(250–500nm)was prepared from commercial zeolite A powder(Ege Kimya)by means of grinding in poly (dimethylsiloxane)(PDMS,2cst)(ABCR Inc.).The other zeolite A nanopowders,zeolite A-II(100–250nm)and zeolite A-III(0–100nm),were prepared by using the hydrothermal crystallization method.Sodium aluminate solution was pre-pared by using Al foil(1.2753g),anhydrous NaOH(Aldrich) (4.1497g)and deionized water(35.1768g).Sodium sili-cate solution was prepared from Na2SiO3(d=1.37kg/L, Na2O=7.5–8.5%,SiO2=25.5–26.5%)(Merck)(7.0593g),an-hydrous NaOH(1.5034g)and deionized water(66.7350g). Filtered clear solutions were used immediately after preparation.The hydrothermal crystallization experiments were carried out in a polypropylene vessel(250mL),which was placed in a temperature controlled oven kept at75°C.Sodium aluminate solution was heated up to75°C under stirring and then the sodium silicate solution was added gradually within10min. About3mL0.26%(w/v)seed solution of commercial zeolite A was added after30min of mixing.Zeolite crystals were allowed to grow for5h.In order to terminate the growth process,a part of reaction mixture(50mL)was removed from the reaction vessel and filtered.Produced zeolite A-III(0–100nm)powder was washed with excess amount of water and dried at110°C for 4h.Another part of synthesis mixture(10mL)were removed from the crystallization vessel and placed in a tightly closed polypropylene bottle and kept at75°C for14h.At the end of crystallization,prepared zeolite A-II(100–250nm)powder was also washed with excess amount of deionized water and dried at 110°C for4h.The purity of zeolite A nanopowders,zeolite A-I (250–500nm),zeolite A-II(100–250nm)and zeolite A-III(0–100nm)were analyzed by x-ray diffraction technique.2.2.Preparation of zeolite A colloidsZeolite A nanopowders(about0.02g)were dispersed in liquid PDMS(2mL)and stirred for10min before the addition of acetone(Merck)(10mL).Grinding of powder samples in PDMS was also performed for better dispersion.Colloid solutions were decanted with the aim of separating possibly agglomerated and large particles,which were settled to the bottom of the beaker.In order to prepare different concentrations of colloids,some part of colloid solution(5mL)was taken in each step and diluted to the half concentration by adding proper amount of acetone(5mL). The particle concentrations of zeolite A colloid solutions were also determined from the measurement of turbidity at420nm. The calibration graph of turbidity for each zeolite sample was generated using the turbidity measurements of the colloids of known particle concentrations.2.3.Preparation of zeolite A micropatternsThe preparation of periodic stripe micropatterns of zeolite A was carried out as shown in Fig.1by using the evaporation-induced self-assembly process.Glass micro slides(26×76mm2) (Iso Lab.)were used as the substrates and they were placed in polyethylene vials(R=30mm,h=50mm)containing the col-loid solutions of zeolite A powders(5mL)and hold against to the wall of the container.The linear micropatterns of zeolite A nanocrystals were allowed to self-assemble on glass substrates for1h during the evaporation of acetone at20°C(the rate of acetone evaporation:6.9mg/min).The self-assembly of zeolite A-III(0–100nm)nanoparticles on the surface of glass(Iso Lab),HDPE and PTFE(Penn Fibre,Ft-Washington,PA,U.S.) substrates was also performed at25°C for1h(the rate of acetone evaporation:9.2mg/min)and at50°C for15min(the rate of acetone evaporation:31.6mg/min).The substrates were dipped into3mL colloid solution of zeolite A-III in a glass vial (R=20mm,h=28mm,5mL)and the formation of micro-patterns wasobserved.Fig.1.Evaporation induced self-assembly of zeolite A stripe patterns from colloids.208U.Olgun,V.Sevínç/Powder Technology183(2008)207–2122.4.CharacterizationPrepared zeolite samples were characterized as pure zeolite A by using the X-ray powder diffraction patterns obtained from X-ray diffractometer (Shimadzu XRD-6000).Turbidity mea-surements were performed at 420nm by UV –visible spectro-photometer (Shimadzu UV-2401PC)in order to estimate the concentrations of zeolite A particles in colloid solutions during the self-assembly process.The surface characterizations of self-assembled micropat-terns were carried out using field emission scanning electron microscope (FE-SEM)(JEOL JSM-6335F)and optic micro-scopes (Olympus and Motic).FE-SEM images were obtained after Au spray coating of zeolite A samples by using a sputter coater (Edwards S150B).Contact angle measurements were carried out by using the microscope setup with online camera attachment connected to the computer.3.Results and discussion3.1.Self-assembly of zeolite A micropatternsThe preparation of zeolite A stripe patterns was performed as shown in Fig.1.As acetone evaporated from the solutions,zeolite A micropatterns were self-assembled on the surface of glass substrates,which were placed vertically inside the colloids of 0.06–0.007%(w/v)zeolite A.The self-assembly process was allowed to take place for 1h and the substrates were removed from the colloid solutions.The images of prepared micro-patterns were analyzed by scanning electron microscope.The uniform stripe micropatterns of zeolite A-I,zeolite A-II and zeolite A-III are demonstrated in Fig.2.3.2.Effects of particle size and concentrationSelf-assembled stripe micropatterns of zeolite A-I,zeolite A-II and zeolite A-III are shown in Fig.2.The surface mor-phologies of stripes are also exhibited in Fig.2for different size zeolite A particles.The formation of zeolite A stripes was studied at various particle concentrations for different size zeolite A samples.Optical microscopy images of micropatterns prepared from 0.06,0.03and 0.015%(w/v)zeolite A-I colloid solutions are demonstrated in Fig.3(a –c).Decrease in particle concentration resulted in greater number of self-assembled stripes with smaller distances between them.Micropattern formation was not observed at very low particle concentrations of 0.007%(w/v)zeolite A-I.The experimental results demonstrated that 0.06%(w/v)zeolite A-I,0.03%(w/v)zeolite A-II and 0.007%(w/v)zeolite A-III are suitable to prepare 15stripes of zeolite A on glass substrates under these experimental conditions after 1h.Reducing the particle concentration of zeolite A-I from about 0.06%(w/v)to 0.015%(w/v),the number of stripes was almost doubled.3.3.Effects of substrate and temperatureThe formation of microstripes of zeolite A-III particles on the surface of glass,HDPE and PTFE substrates was investigated at 25°C and at 50°C.The microscope images of microstripes prepared at 25°C are demonstrated in Fig.3d for glass,in Fig.3e for HDPE and in Fig.3f for PTFE.The uniform widths of stripes were reduced significantly on HDPE and PTFE surface compared to the glass surface.The distance between the stripes was increased in the case of PTFE surface.As the critical surface tension of substrate reduced from 31dyn/cm forHDPEFig.2.Self-assembled stripe patterns of a)zeolite A-I,b)zeolite A-II and c)zeolite A-III on glass substrates.Surface microstructures of stripes demonstrating d)zeolite A-(I),e)zeolite A-II and f)zeolite A-III particles.209U.Olgun,V .Sevínç/Powder Technology 183(2008)207–212to 18dyn/cm for PTFE,the immobilization of nano zeolite A particles at contact line was decreased.The contact angle values of 10%(v/v)PDMS –acetone solutions were measured as 21°for glass,20°for HDPE and 30°for PTFE.Contact angle values were reduced about 5–7°during the deposition of zeolite A particles from colloid solutions.The images of microstripes prepared at 50°C are shown in Fig.3g for glass,in Fig.3h for HDPE and in Fig.3i for PTFE.In general,the increase in temperature resulted in large increases in stripe widths.3.4.Zeolite microgrid preparationIn order to construct more complex micropatterns of zeolite A,such as the grid microstructure,we have attempted to coat a second layer of micropattern on top of first stripe pattern in crossing direction.Thus,the glass substrate was rotated 90°during the self-assembly of second layer of micropattern.The microgrid pattern of zeolite A-II was produced as seen in Fig.4by using this two-step self-assembly process.The width of zeolite A stripes was about 20μm and the empty distance between the stripes was about 60–80μm.It was also interesting to note that the second step of micropatterning had no de-forming effect on the first layer of zeolite A stripes.3.5.Stick –slip dynamics of contact lineThe mechanism of self-assembly of stripes from colloids was explained with the proposed steps of stick –slip dynamics of three-phase contact line as drawn in Fig.1.It was observed that the contact line on the substrate surface repeatedly jumped to a new position where the nanoparticles started to form the next stripe.It was proposed that the wetting of both thesubstrateFig.3.Micropatterns of zeolite A-I prepared on glass substrates from a)0.06%(w/v),b)0.03%(w/v)and c)0.015%(w/v)colloid solutions.Micropatterns of zeolite A-III prepared on d)glass,e)HDPE and f)PTFE substrates at 25°C from 0.03%(w/v)colloid solutions.Micropatterns of zeolite A-III prepared on g)glass,h)HDPE and i)PTFE substrates at 50°C from 0.03%(w/v)colloid solutions.210U.Olgun,V .Sevínç/Powder Technology 183(2008)207–212surface and the self-assembled stripe became energetically unfavorable after a specific time due to the reduced contact angle,and therefore,the contact line jumped to its new equi-librium position.The changes in the nature of zeolite A powders and the particle size had significant effects on the self-assembly of zeolite A particles.However,all of the zeolite A particles exhibited similar patterning behavior during the contact line dynamics possibly because of the adsorption of PDMS chains to the particle surfaces in colloid solutions.It was concluded that the wetting of self-assembled stripe becomes energetically unfavorable at some point due to the experimental observation of the contraction of solution into the center.Furthermore,the instant drop of fluid level from a low contact angle point to an equilibrium point requires an increase in contact angle simply because of the mass transfer of solvent from wall surface to the center.The entrapment of solvent molecules and the PDMS polymer chains between the deposited particles was evidenced from the observed regular defects on the surface of stripes of very fine zeolite A-III particles (Fig.2f).Considering the low surface free energy of PDMS,it is pre-dicted that the formation of a thin layer of PDMS as deposited together with the particles along the contact line destabilizes the wetting of substrate surface by an acetone rich solvent.There-fore,the adhesive failure between deposited stripe and the colloid solution was observed at this critical point.The stick –slip dynamics was also sensitive to the concen-tration of zeolite A particles in colloid solutions.The stripe patterns resulting from the stick –slip dynamics are shown in Fig.3(a –c)for 0.06,0.03and 0.015%(w/v)colloidal disper-sions of zeolite A-I.Decrease in zeolite A particle concentra-tion increased the number of stripes and reduced the empty distance between the stripes.In other words,the time interval spent between the consecutive slips (or the jumps)of the solution on the substrate surface was increased linearly as a function of zeolite A-I particle concentration in the range of 0.015–0.06%(w/v).Therefore,it was concluded that the number of stick –slip positions of contact line was reduced for a given period of time at higher concentrations of zeolite A particles.The results shown in Fig.3(d –f)indicated that the decrease in the critical surface tension of substrate from 31dyn/cm for HDPE to 18dyn/cm for PTFE,the width of stripes were reduced significantly,while the distance between the slip points was increased.The increase in temperature during the stick –slip dynamics led to increase in stripe widths as seen in Fig.3(g –i).The increase of PDMS%from 10%to 20%and 40%resulted in a gradual increase in the stripe widths of zeolite A-III particles on glass surface.Therefore,it was concluded that the PDMS chains increased the accumulation of nanoparticles from so-lution to the three-phase contact line and it helped their im-mobilization on the surface of substrate.The other advantages of using PDMS were identified as the stabilization of colloids and the formation of smooth three phase contact line.4.ConclusionIn this study,it was demonstrated that the formation of periodic stripe patterns of zeolite A was due to the stick –slip dynamics of the contact line of colloidal solutions of zeolite A particles in PDMS –acetone system.The patterning process is simple compared to the previous techniques in the field and does not require any external energy,molded patterns or photo mask for micropattern formation.Although,we have used a hydrophilic zeolite A particles,the nanoparticles does not need to be hydrophilic and the patterns of hydrophobic zeolites were also produced.As shown in Fig.2,the micropatterns of zeolite A-II particles had better surface coverage without any defects on the stripe surface.Thus,the optimum particle size of zeolite A to achieve the best micro stripe quality was predicted as 100–250nm.Also,the optimum particle concentration was de-termined as 0.015–0.06%(w/v)for these zeolite samples.It was also concluded that the stick –slip dynamics of contact line was slow at higher concentrations of zeolite A particles.PDMS provided a stable environment for the particles with its low viscosity,low surface tension and good wetting pro-perties.However,the key role of PDMS was to induce the formation of the stick –slip dynamics of the contact line in its dilute solutions in acetone.The pattern formation from dilute polymer solutions [14]and the evaporation induced deposition of Ag nanowires at the solvent –substrate contact line due to the stick –slip motion [15]have been reported recently.In this study,however,we have utilized liquid PDMS to stabilize zeolite A nanoparticles in solution and self-assembled them into micro-stripe patterns due to the stick –slip motion of contact line.The process of contact line dynamics is suitable to produce two-dimensional micropatterns of nanoparticles with a broad range of periodicity.Processing of nanoparticles to form predictable bulk structures has a great technological importance and we hope that the understanding of this versatile patterning pro-cedure may lead to the development of new nano-scale patterning methods.AcknowledgementThis work was supported by Sakarya University under Project No.BAPK2004-2.Fig. 4.Zeolite A-II microgrid structure produced by using two-step self-assembly process (glass substrate was rotated 90°in the second step)and imaged in transmission (left)and reflection (right)modes.211U.Olgun,V .Sevínç/Powder Technology 183(2008)207–212References[1]W.Sun,m,L.W.Wong,K.L.Yeung,mun.(2005)4911.[2]J.L.H.Chau,Y.S.S.Wan,A.Gavriilidis,K.L.Yeung,Chem.Eng.88(2002)187.[3]Y.S.S.Wan,J.L.H.Chau, A.Gavriilidis,K.L.Yeung,MicroporousMesoporous Mater.42(2001)157.[4]K.Ha,Y.J.Lee,D.Y.Jung,J.H.Lee,K.B.Yoon,Adv.Mater.12(2000)1614.[5]K.Ha,Y.J.Lee,Y.S.Chun,Y.S.Park,G.S.Lee,K.B.Yoon,Adv.Mater.13(2001)594.[6]M.Heule,U.P.Schönholzer,L.J.Gauckler,J.Euro.Ceram.Soc.24(2004)2733.[7]J.F.Liu,L.G.Zhang,N.Gu,J.Y.Ren,Y.P.Wu,Z.H.Lu,P.S.Mao,D.Y.Chen,Thin Solid Films176(1998)327.[8]K.Kordás,A.E.Pap,S.Leppävuori,Surf.Coat.Technol.176(2003)84.[9]T.Kikuchi,M.Sakairi,H.Takahashi,Y.Abe,N.Katayama,Surf.Coat.Technol.199(2003)169.[10]W.Y.Chung,J.W.Lim,Curr.Appl.Phys.3(2003)413.[11]S.Takayama,E.Ostuni,X.Qian,J.C.McDonald,X.Jiang,P.LeDuc,M.H.Wu,D.E.Ingber,G.M.Whitesides,Adv.Mater.13(2001)570.[12]E.F.Petersen,R.G.S.Spencer,E.W.McFarland,Biotech.Bioeng.78(2002)802.[13]K.T.Jung,Y.G.Shul,J.Membr.Sci.191(2001)189.[14]H.Yabu,M.Shimomura,Adv.Funct.Mater.15(2005)575.[15]J.Huang,R.Fan,S.Connor,P.Yang,Angew.Chem.Int.Ed.46(2007)2414.212U.Olgun,V.Sevínç/Powder Technology183(2008)207–212。

【高分子专业英语翻译】第五课乳液聚合大部分的乳液聚合都是由自由基引发的并且表现出其他自由基体系的很多特点,最主要的反应机理的不同源自小体积元中自由基增长的场所不同。

乳液聚合不仅允许在高反应速率下获得较高分子量,这在本体聚合中是无法实现或效率低下的,,同时还有其他重要的实用优点。

水吸收了大部分聚合热且有利于反应控制,产物在低粘度体系中获得,容易处理,可直接使用或是在凝聚,水洗,干燥之后很快转化成固体聚合物。

在共聚中,尽管共聚原理适用于乳液体系,单体在水相中溶解能力的不同也可能导致其与本体聚合行为不同,从而有重要的实际意义。

乳液聚合的变化很大,从包含单一单体,乳化剂,水和单一引发剂的简单体系到这些包含有2,3个单体,一次或分批添加,,混合乳化剂和助稳定剂以及包括链转移剂的复合引发体系。

单体和水相的比例允许变化范围很大,但是在技术做法上通常限制在30/70到60/40。

单体和水相比更高时则达到了直接聚合允许的极限,只有通过分批添加单体方法来排除聚合产生的大量的热。

更复杂的是随着胶体数的增加粘度也大大增加,尤其是当水溶性的单体和聚合物易容时,反应结束胶乳浓度降低。

这一阶段常常伴随着通过聚集作用或是在热力学不稳定时凝结作用而使胶粒尺寸增大。

第十课高分子的构型和构象本课中我们将使用根据经典有机化学术语而来的构型和构象这两个词。

构型异构是由于分子中存在一个或多个不对称中心,以最简单的C原子为例,每一碳原子的绝对构型为R型和S型,当存在双键时会有顺式和反式几何异构。

以合成聚合物为例,构型异构的典型问题和R.S型不对称碳原子在主链上的排布有关。

这些不对称碳原子要么来自不对称单体,如环氧丙烷,要么来自对称单体,如乙烯单体,,这些物质的聚合,在每个单体单元中形成至少一个不对称碳原子。

大分子中的构型异构源于侧链上存在不对称的碳原子,例如不对称乙烯单体的聚合,也是可能的,现今已经被广泛研究。

和经典有机化学术语一致,构象,旋转体,旋转异构体,构象异构体,指的是由于分子单键的内旋转而形成的空间排布的不同。

UNIT 1一、材料根深蒂固于我们生活的程度可能远远的超过了我们的想象，交通、装修、制衣、通信、娱乐（recreation）和食品生产，事实上（virtually），我们生活中的方方面面或多或少受到了材料的影响。

历史上，社会的发展和进步和生产材料的能力以及操纵材料来实现他们的需求密切（intimately）相关，事实上，早期的文明就是通过材料发展的能力来命名的（石器时代、青铜时代、铁器时代）。

二、早期的人类仅仅使用（access）了非常有限数量的材料，比如自然的石头、木头、粘土（clay）、兽皮等等。

随着时间的发展，通过使用技术来生产获得的材料比自然的材料具有更加优秀的性能。

这些性材料包括了陶瓷（pottery）以及各种各样的金属，而且他们还发现通过添加其他物质和改变加热温度可以改变材料的性能。

此时，材料的应用（utilization）完全就是一个选择的过程，也就是说，在一系列有限的材料中，根据材料的优点来选择最合适的材料，直到最近的时间内，科学家才理解了材料的基本结构以及它们的性能的关系。

在过去的100年间对这些知识的获得，使对材料性质的研究变得非常时髦起来。

因此，为了满足我们现代而且复杂的社会，成千上万具有不同性质的材料被研发出来，包括了金属、塑料、玻璃和纤维。

三、由于很多新的技术的发展，使我们获得了合适的材料并且使得我们的存在变得更为舒适。

对一种材料性质的理解的进步往往是技术的发展的先兆，例如：如果没有合适并且没有不昂贵的钢材，或者没有其他可以替代（substitute）的东西，汽车就不可能被生产，在现代、复杂的（sophisticated）电子设备依赖于半导体（semiconducting）材料四、有时，将材料科学与工程划分为材料科学和材料工程这两个副学科（subdiscipline）是非常有用的，严格的来说，材料科学是研究材料的性能以及结构的关系，与此相反，材料工程则是基于材料结构和性能的关系，来设计和生产具有预定性能的材料，基于预期的性能。

Centro de Investigaci´o n y de Estudios Avanzados del IPN Departamento de Ingenier´ıa El´e ctrica2nd International Conference on Electrical and Electronics Engineering(ICEEE)XI Conference on Electrical Engineering(CIE2005)Mexico City,MexicoSeptember7-9,2005Final Program&Abstract BookThis book was elaborated using L A T E X2e. CINVESTAV,August2005ContentsMessage from the conference chair4 Message from the Head of the EED5 2nd ICEEE-CIE Organizing Committee7 Topic Chairs8 Reviewers9 Final Program11 Courses19 Round table sessions21 General Information21 Keynote Speakers22 Plenary Conferences Abstracts23 Abstract Book27 Autor Index63Message from the conference chairWe begin our joint Conference,namely ICEEE-CIE2005,with the desire to meet col-leagues and friends from Mexico and abroad.We mean students,professors and pro-fessionals that design,develop and propose technological and engineering solutions for electrical and electronics systems,whether as research work or immediate application. Certainly,this Conference is an opportunity to do so.It is worth pointing out that it is the second time this technical forum is presented as an international event and whose diffusion has been excellent due to the means of the prestigious institution:the Institute of Electrical and Electronics Engineers,IEEE.In this respect,we are also grateful to Cinvestav by its support providing facilities andfinances.Looking at the ICEEE-CIE2005program,we can mention that the technical topics cover a wide spectrum of areas,namely in computer science,bioelectronics,communica-tion systems,solid-state electronics,VLSI design,electronic materials and mechatronics. They reflect modern engineering techniques and methods,which belong to those proposed by experienced experts that work in academia,laboratories and industry,in collaboration with students and specialized technicians.In summary,we are going to witness relevant results that might help ours,fulfilling the early objectives of this Conference.We realize that the quality of the selected papers for oral presentation is high due in part to the participation of foreign reviewers,who kindly accepted the silent task of eval-uating the original manuscripts in collaboration with national ones.We recognize that the participation of keynote speakers is a cornerstone on which this Conference builds its success.In particular,five full professors,each one invited by the Sections of the host Electrical Engineering Department,enhance this issue.Some words for visitors from abroad follow.Mexico is a modern Spanish-speaker coun-try,where the friendship is a distinctive gesture that foreigners always appreciate,there-fore,this event is a vehicle to try.Our city,which is taken into account as the largest in the world,is also warm even though its thoughtful people and Cinvestav is not the exception to the rule.In the context of both the initial preparation and thefinal process of setting details of the Conference,we want to thank to Mrs.Carmen Quintero,Judith Esparza,Anabel D´ıaz,Miguel-Angel Velasco,Emilio Espinosa,Gabriel Vega Mart´ınez and student Victor Ponce for offering their timely and valuable skills.Finally,on behalf of the ICEEE-CIE2005organizing committee I welcome to everyone attending this fruitful three-day academic meeting.Likewise,enjoy your stay in our city! Sincerely,Felipe G´o mez-Casta˜n edaICEEE-CIE2005Conference Chair.Message from the Head of the EEDDear Coleagues:On behalf of the Electrical Engineering Department(EED)at the Center of Research and Advanced Studies(Cinvestav),it is my privilege to welcome you to the Second In-ternational Conference on Electrical and Electronics Engineering(ICEEE)and the XI Conference on Electrical Engineering(CIE).This occasion is quite special since we are celebrating eleven years of the CIE which has been organized as an annual event by the EED.Furthermore,we are initiating today a new adventure:The ICEEE organized for the this time in the EED’s Mexico city main campus.As you know,this time our venue is M´e xico,City where we expect an intensive interaction among scholars and electrical engineering practitioners from all over the world,especially,from the Americas.One of the main objectives of the ICEEE is to provide a forum to spread and promote the disciplines cultivated by the EED,namely:Bioelectronics,Communications,Com-puter Science,Mechatronics and Solid State Electronics.Likewise,this event represents an opportunity to make known scientific and technological contributions achieved by other Mexican institutes.Throughout its forty two years of existence and as its most important reason to be, the EED faculty has strived to promote science and technology in Mexico.Such task has not been only limited to pure academic developments but also has decisively con-tributed to improvements and developments in a variety of national industry products and applications.That is why the ICEEE and CIE-2005conferences have always had the presence of industry representatives whose participation we welcome.In this sense,the ICEEE comes to crown and consecrate the entire academic and research efforts of the EED faculty during all these years.Given the rich diversity of Electrical Engineering disciplines cultivated by the EED,an international and national committee in different specialties was assembled together to perform a rigorous review process of the submitted papers.In this way,we are in the position to guarantee both,the quality of the conference and the benefit that all delegates can obtain from attending our ICEEE/CIEEE-2005conference.Attendees willfind that there is a lot to learn from the scientific and technological exchange to be provided by this forum.Assistance willfind an opportunity to increase their awareness of nowadays most relevant electrical engineering problems.For all the aforementioned,this even constitutes a high priority means to promote the technological advanced of our countries.Another milestone achieved recently by Cinvestav was our graduate student number 5324.Out of this number,the EED alone has contributed with824graduated students,be-ing the highest number ever obtained by any Electrical Engineering post-graduate school in Mexico.Finally,on behalf of all the faculty member of the EED,I would like to thank all those who have worked so hard to make these conferences possible.Particularly,we are grateful to our director,Rosalinda Contreras,to IEEE and to our sponsors for all the support given to us towards the organization of this event.We hope that you will enjoy the Conferences and that you willfind some free time to relax and get to know the Mexico city.Ernesto SuasteHead of the EED2nd ICEEE-CIE Organizing Committee Dr.Felipe G´o mez-Casta˜n eda(Conference Chairman)Dr.Carlos Alvarado-Serrano(Proceedings Editor)Dr.Rafael Castro-Linares(Tutorials)Dr.Luis Gerardo de la Fraga(Technical Program)Dr.Felipe Alejandro Cruz-P´e rez(Advertising)Dr.Ernesto Suaste-G´o mez(Industrial Relations and Exhibit)Dra.Xiaoou Li Zhang(Logistics)Technical SupportJudith Esparza(System and On-Line Submission)Ma.del Carmen Quintero(Administrative Assistant)Ricardo G´o mez(Exhibiting Assistant)Conference Management System CINVESTAV(On-Line Paper Submission and Reviewing System)Topic Chairs Bioengineering and Medical Electronics Electrical PowerElectronic CircuitsCarlos Alvarado SerranoCINVESTAV-IPN. Communication SystemsMauricio Lara-Barr´o nCINVESTAV-IPN.Computer ScienceXiaoou Li ZhangCINVESTAV-IPN.Solid-State Electronics and VLSI Semiconductor MaterialsMar´ıa de la Luz Olvera-AmadorCINVESTAV-IPN.Automatic Control and Mechatronics Rafael Castro-LinaresCINVESTAV-IPN.ReviewersAbraham Claudio S´a nchez.........................................CENIDET,M´e xico Aldo Orozco...............................................CINVESTAV-IPN,M´e xico Alfonso Guti´e rrez Aldana...........................................CIC-IPN,M´e xico Andr´e s Iv´a n Oliva Arias...................................CINVESTAV-IPN,M´e xico Ante Salcedo Gonz´a lez.................................................ITAM,M´e xico Antonio F Mondragon Torres..............................Texas Instruments,U.S.A. Arturo Escobosa...........................................CINVESTAV-IPN,M´e xico Arturo Hern´a ndez Aguirre............................................CIMAT,M´e xico Arturo Morales-Acevedo...................................CINVESTAV-IPN,M´e xico Arturo Veloz Guerrero...................................................Intel,M´e xico Arturo Vera Hern´a ndez....................................CINVESTAV-IPN,M´e xico Carlos A.Coello Coello....................................CINVESTAV-IPN,M´e xico Carlos Alberto Cruz Villar.................................CINVESTAV-IPN,M´e xico Carlos Alvarado Serrano...................................CINVESTAV-IPN,M´e xico Carlos Arist´o teles De La Cruz Blas...........Universidad P´u blica de Navarra,Espa˜n a Christopher Druzgalski...............................................CSULB,U.S.A. Claude Moog........................................................IRCCyN,France David H.Covarrubias Rosales.......................................CICESE,M´e xico Demetrio Villanueva Ayala.................................CINVESTAV-IPN,M´e xico Deni L.Torres Rom´a n.....................................CINVESTAV-IPN,M´e xico Dominique boratoire LSR Logiciels Systemes Resea,France Edgar Ch´a vez.............Universidad Michoacana de San Nicol´a s de Hidalgo,M´e xico Eduardo Moreno.............................................ICIMAF,CITMA,Cuba Ernesto Suaste.............................................CINVESTAV-IPN,M´e xico Felipe Alejandro Cruz P´e rez...............................CINVESTAV-IPN,M´e xico Felipe G´o mez Casta˜n eda...................................CINVESTAV-IPN,M´e xico Fernando Ram´ırez Mireles.............................................ITAM,M´e xico Francisco Javier Garc´ıa Ugalde................Facultad de Ingenier´ıa,UNAM,M´e xico Francisco J.Garc´ıa S´a nchez....................Universidad Sim´o n Bol´ıvar,Venezuela Francisco J.Ruiz-S´a nchez..................................CINVESTAV-IPN,M´e xico Francisco Rodr´ıguez-Henr´ıquez.............................CINVESTAV-IPN,M´e xico Gabriel Romero Paredes Rubio............................CINVESTAV-IPN,M´e xico Giselle M.Galv´a n-Tejada..................................CINVESTAV-IPN,M´e xico Guang-Bin Huang.......................Nanyang Technological University,Singapore Guillermo Morales-Luna...................................CINVESTAV-IPN,M´e xico Henri Huijberts................................University of London,United Kingdom Horacio Soto Ortiz..................................................CICESE,M´e xico Ieroham Baruch...........................................CINVESTAV-IPN,M´e xico Isaac Rudomin.................................................ITESM-CEM,M´e xico Javier E.Gonz´a lez Villarruel.........................................ITESM,M´e xico Jes´u s Carrillo L´o pez...........................................BUAP,Puebla,M´e xico Joaquin Alvarez.....................................................CICESE,M´e xico Jorge Carlos Mex Perera.........................ITESM,Campus Monterrey,M´e xicoJos´e Alfredo´Alvarez-Ch´a vez.............University of Southampton,United Kingdom Jos´e Luis Medina Monroy...........................................CICESE,M´e xico Jos´e Luis Ramos Quirarte........................Universidad de Guadalajara,M´e xico Jos´e Miguel Rocha P...............Freescale Semiconductor,Motorola Puebla,M´e xico Jose Rosario Gallardo Lopez.........................................CICESE,M´e xico Juan Humberto Sossa Azuela.......................................CIC-IPN,M´e xico Juan Manuel Hern´a ndez Cid..........................................ITESO,M´e xico Luis Gerardo de la Fraga...................................CINVESTAV-IPN,M´e xico Manuel Duarte-Mermoud.................................Universidad de Chile,Chile Maria De La Luz Olvera Amador..........................CINVESTAV-IPN,M´e xico Mariano Aceves Mijares......................................INAOE,Puebla,M´e xico Mario Alfredo Reyes Barranca.............................CINVESTAV-IPN,M´e xico Mauricio Lara.............................................CINVESTAV-IPN,M´e xico Mauricio Ortega L´o pez....................................CINVESTAV-IPN,M´e xico M´a ximo L´o pez-L´o pez......................................CINVESTAV-IPN,M´e xico MengChu Zhou...........................................................NJIT,USA Miguel´Angel Le´o n Ch´a vez....................................BUAP,Puebla,M´e xico Miguel Garc´ıa-Rocha......................................CINVESTAV-IPN,M´e xico Mohamed Moustafa Abd-El Aziz Moustafa.......The Cabinet-Information&DecisionSupport.Egypt Oscar Castillo...............................Instituto Tecnol´o gico de Tijuana,M´e xico Oscar D´ıaz...................................University of the Basque Country,Spain Pablo Rogelio Hern´a ndez Rodr´ıguez........................CINVESTAV-IPN,M´e xico Rafael Castro-Linares......................................CINVESTAV-IPN,M´e xico Ram´o n Mart´ın Rodr´ıguez Dagnino...............ITESM,Campus Monterrey,M´e xico Ram´o n Parra Michel............................ITESM Campus Guadalajara,M´e xico Ram´o n Pe˜n a Sierra........................................CINVESTAV-IPN,M´e xico Ricardo G´o mez Villanueva.................................CINVESTAV-IPN,M´e xico Roberto Mu˜n oz Guerrero..................................CINVESTAV-IPN,M´e xico Rodolfo Quintero Romo....................................CINVESTAV-IPN,M´e xico Rogelio Alc´a ntara Silva.......................Facultad de Ingenier´ıa,UNAM,M´e xico Valeri Kontorovich Mazover................................CINVESTAV-IPN,M´e xico Vicente Parra Vega........................................CINVESTAV-IPN,M´e xico Xiaoou Li..................................................CINVESTAV-IPN,M´e xico Yasuhiro Matsumoto.......................................CINVESTAV-IPN,M´e xicoFinal ProgramWednesday7,September2005Auditory Room1Room2 8:309:30Registration9:309:50Opening Ceremony10:0011:00PLE1EP11SSE1111:0011:30Break Break Break11:3012:30CS1EP12SSE1212:3013:30CS1MEC11BIO1113:3015:00Lunch Lunch Lunch15:0016:00CS2MEC12BIO1216:0017:00CS2COM1BIO217:0018:00-COM1BIO218:00-Welcome cocktailThrusday8,September2005Auditory Room1Room2 9:0010:00COM2SSE2BIO3 10:0011:00PLE2SSE2BIO3 11:0011:30Break Break Break 11:3012:30PLE3COM3EP2 12:3013:30Round-T1COM3EP2 13:3015:00Lunch Lunch Lunch 15:0017:00CS31MEC21EP3 17:0017:30Break Break–17:3018:10CS32MEC22–Friday9,September2005Auditory Room1Room2 9:0010:00–EC1SEM1 10:0011:00PLE4EC1SEM1 11:0011:30Break Break Break 11:3012:30PLE5EC2SEM2 12:3014:00Round-T2EC2SEM2 14:00-Closing CeremonySymbol list:PLE PlenaryBIO Bioengineering and Medical ElectronicsCOM Communication SystemsCS Computer ScienceSSE Solid-State Electronics and VLSIMEC Mechatronics and Automatic ControlEC Electronic CircuitsSEM Semiconductor MaterialsEP Electrical PowerRound-T Round Table1CS1Computer ScienceWednesday11:30-13:30AuditoryChair:Dr.Luis Gerardo de la Fraga..................1.111:30-11:50.An Algorithm for Reduct of Boolean Functions Basedon Primes (27)1.211:50-12:10.A Virtual Machine for the Ambient Calculus (27)1.312:10-12:30.Algorithms for Robust Graph Coloring on Paths (27)1.412:30-12:50.Animation of Deformable Objects Built with SimplexMeshes (27)1.512:50-13:10.Mathematical Tools for Speeding Up the Determina-tion of Configurations of the n-Dimensional Orthogonal Pseudo-Polytopes (28)1.613:10-13:30.Non-Linear Filters for colour imaging implemented byDSP (28)2CS2Computer ScienceWednesday15:00-17:00AuditoryChair:Dra.Xiaoou Li...........................2.115:00-15:20.Environmental Sounds Recognition System Using theSpeech Recognition System Techniques (28)2.215:20-15:40.Analysis of Audio Watermarking Schemes (29)2.315:40-16:00.Wavelet Domain Statistical Order Filter using the Tri-State Median Filter Algorithm (29)2.416:00-16:20.Analysis of a DFT-Based Watermarking Algorithm..292.516:20-16:40.Implementation of Artificial Neural Networks for Recog-nition of Target and Clutter Images (30)2.616:40-17:00.SIMD Architecture for Image Segmentation using So-bel Operators Implemented in FPGA Technology (30)3CS31Computer ScienceThursday15:00-17:00AuditoryChair:Dr.Arturo D´ıaz P´e rez.......................3.115:00-15:20.Mobile RFID Reader with Database Wireless Synchro-nization (30)3.215:20-15:40.Experimental Analysis of Wireless Propagation Modelswith Mobile Computing Applications (31)3.315:40-16:00.Performance Analysis of the Confidentiality SecurityService in the IEEE802.11using WEP,AES-CCM,and ECC (31)3.416:00-16:20.A Tool for Analysis of Internet Metrics (31)3.516:20-16:40.A Library Framework for the POSIX Application-Defined Scheduling Proposal (31)3.616:40-17:00.Dynamic invocation of Web services by using aspect-oriented programming (32)4CS32Computer ScienceThursday17:30-18:10AuditoryChair:Dr.Arturo D´ıaz P´e rez.......................4.117:30-17:50.LIDA/REC Visual Language for Databases interfacePostgreSQL (32)4.217:50-18:10.Aspect-Oriented Web Services Orchestration (33)5COM1Communication SystemsWednesday16:00-18:00Room1Chair:Dr.Aldo Gustavo Orozco Lugo.................5.116:00-16:20.Adaptive Echo Canceller Using a Modified LMS Algo-rithm (33)5.216:20-16:40.The Universality of the Prolate Spheroidal Wave Func-tions for Channel Orthogonalization and its Modeling (33)5.316:40-17:00.On the generalized and modified Suzuki model(GMSM):approximations and level crossing statistics (34)5.417:00-17:20.On MIMO Space-Time Coded Systems:Unleashingthe Spatial Domain (34)5.517:20-17:40.On the design of an FPGA-Based OFDM modulatorfor IEEE802.11a (34)5.617:40-18:00.DSP Digital Modulation Software Implementation andRF Impairments Analysis (35)6COM2Communication SystemsThursday9:00-10:00AuditoryChair:Dr.Javier Gonz´a lez........................6.19:00-9:20.State of the Art in Ultra-Wideband Antennas (35)6.29:20-9:40.Design and Simulation of a1to14GHz BroadbandElectromagnetic Compatibility DRGH Antenna (35)6.39:40-10:00.RF System Concepts Applied to Digital Wireless Re-ceivers Design Based on wireless standards (36)7COM3Communication SystemsThursday11:30-13:30Room1Chair:Dra.Giselle Galv´a n Tejada...................7.111:30-11:50.Design of a Backup Wireless Network for the Depart-ment of Electrical Engineering of CINVESTAV-IPN (36)7.211:50-12:10.Cell Planning Based on the WiMax Standard for HomeAccess:A Practical Case (36)7.312:10-12:30.Performance Analysis of an All-Optical WavelengthConverter Using a Semiconductor Optical Amplifier Simulator (37)7.412:30-12:50.Quasi Mobile IP-based Architecture for Seamless In-terworking between WLAN and GPRS Networks (37)7.512:50-13:10.Design and Verification Based on Assertions:SomeStatistics (37)7.613:10-13:30.Traffic Analysis for IP Telephony (38)8BIO11Bioengineering and Medical ElectronicsWednesday12:30-13:30Room2Chair:Dr.Pablo Rogelio Hern´a ndez Rodr´ıguez...........8.112:30-12:50.A Microprocessor-Based System for Pulse-Echo Over-lap Measurement of Ultrasonic Velocity (38)8.212:50-13:10.Rotation Effects of an Axicon Ultrasonic Transducerwhen Measuring a Blood Flow Rate (38)8.313:10-13:30.Experimental Estimation of Acoustic Attenuation andDispersion (38)9BIO12Bioengineering and Medical ElectronicsWednesday15:00-16:00Room2Chair:Dr.Pablo Rogelio Hern´a ndez Rodr´ıguez...........9.115:00-15:20.New X-wave Solutions of Isotropic/Homogenous ScalarWave Equation (39)9.215:20-15:40.Feasibility study of using ultrasonic transducer borderwaves for centering hydrophones in ultrasonicfield characterization399.315:40-16:00.ELF magneticfields generator,variable in intensityand frequency for biological applications (39)10BIO2Bioengineering and Medical ElectronicsWednesday16:00-18:00Room2Chair:Dr.Roberto Mu˜n oz Guerrero..................10.116:00-16:20.Automatic Detection of ECG Ventricular ActivityWaves using Continuous Spline Wavelet Transform (40)10.216:20-16:40.Crayfish Brain States Characterization with WaveletTransform (40)10.316:40-17:00.Measurement of Skin-Electrode Impedance for a12-lead Electrocardiogram (41)10.417:00-17:20.Cancer Model Identification Via Sliding Mode andDifferential Neural Networks (41)10.517:20-17:40.Experimental Seat for the Study of the Effects of Ran-dom Pneumatic Stimulation for the Prevention of Pressure Ulcers.41 11BIO3Bioengineering and Medical ElectronicsThursday9:00-11:00Room2Chair:Dr.Arturo Vera Hern´a ndez...................11.19:00-9:20.Foveal model of artificial retina with phototransistors inDarlington configuration in the high-resolution region (42)11.29:20-9:40.Distributed Retinal Stimulation Model Based on Adap-tive System (42)11.39:40-10:00.Chromatic Pupillary Response in Diabetic Patients (42)11.410:00-10:20.Neuro Tracking Control for Glucose-Insulin InteractionModel (43)11.510:20-10:40.PVDF Strength Sensor for Biomechanical Analysis inMice (43)11.610:40-11:00.Conception and Realization of a3D Dynamic Sensoras a Tool in Human Walking Study (43)12MEC11Mechatronics and Automatic ControlWednesday12:30-13:30Room1Chair:Dr.Gerardo Silva Navarro....................12.112:30-12:50.New Results on the Energy-Based Control of SeriesResonant Inverters (44)12.212:50-13:10.Modeling and Controller Design of a Magnetic Levita-tion System (44)12.313:10-13:30.Global observability and detectability analysis for aclass of nonlinear models of biological processes with bad inputs..44 13MEC12Mechatronics and Automatic ControlWednesday15:00-16:00Room1Chair:Dr.Gerardo Silva Navarro....................13.115:00-15:20.On New Passivity Property:Review and Extension toMechanical Rotational Systems (44)13.215:20-15:40.Fault Detection Using Dynamic Principal ComponentAnalysis by Average Estimation (45)14MEC21Mechatronics and Automatic ControlThursday15:20-17:00Room1Chair:ardo Aranda Bricaire..................14.115:20-15:40.Stability of a diamond-type quasipolynomial family..4514.215:40-16:00.Lyapunov Matrices for Time Delay Systems (45)14.316:00-16:20.Lyapunov Matrices for Neutral Type Time Delay Sys-tems (45)14.416:20-16:40.Solving the Coupled Riccati Equation for the N-PlayersLQ Differential Game (46)14.516:40-17:00.Improving Stability and Performance in a GeneralizedMinimum Variance Controller using Dynamic Pole Assignment (46)15MEC22Mechatronics and Automatic ControlThursday17:30-18:50Room1Chair:Dr.Vicente Parra Vega......................15.117:30-17:50.Stable Task Space Neurocontroller for Robot Manipu-lators without Jacobian Matrix (46)15.217:50-18:10.New Position Controllers for Robot Manipulators (46)15.318:10-18:30.A design strategy of discrete event controllers for au-tomated manufacturing systems (47)15.418:30-18:plexity and Path Planning for a car-like robot..47 16SSE11Solid-State Electronics and VLSIWednesday10:00-11:00Room2Chair:Dr.Alfredo Reyes Barranca...................16.110:00-10:20.Morphological effects and their relation with the elec-trical resistivity measured during the initial stages of growth ofAu/glas (47)16.210:20-10:40.Charging/discharging effects in nc-Si/SiO2superlat-tice prepared by LPCVD (48)16.310:40-11:00.Effect of Nitrogen in the Photoluminescence of SiliconRich Oxidefilms prepared by LPCVD (48)17SSE12Solid-State Electronics and VLSIWednesday11:30-12:30Room2Chair:Dr.Alfredo Reyes Barranca...................17.111:30-11:50.SnO2,SnO2/Ag and Ag/SnO2Thin Films used asPropane Sensors (48)17.211:50-12:10.Two-Dimensional Nonlinear Spin-Dipole Waves in theMillimeter Wave Range (48)18SSE2Solid-State Electronics and VLSIThursday9:00-11:00Room1Chair:Dr.Jos´e A.Moreno Cadenas..................18.19:00-9:20.Polyimide Passivation Approaches on Double-Mesa Thyris-tors (49)18.29:20-9:40.A Low-Power Bootstrapped CMOS Full Adder (49)18.39:40-10:00.An Improved EKV Model for Partially Depleted SOIDevices (49)18.410:00-10:20.Macromodel for CMOS Photogate-Type Active PixelSensors (50)18.510:20-10:40.Linear theory of the thermoelectric cooling based onthe Peltier effect (50)18.610:40-11:00.Fuzzy Equalizer in VLSI (50)18.711:00-11:20.1-D BJT Parameter Extraction for Cuasi-3D Simula-tion of Four-Layer Devices (50)19EP11Electrical PowerWednesday10:00-11:00Room1Chair:Ing.Jos´e A.Urbano Castel´a n..................19.110:00-10:20.Modeling of the Circuit Parameters of an Induction De-vice for Heating of a Non-Magnetic Conducting Cylinder by Meansof a Travel (51)19.210:20-10:ing Edsa on Radial Primary Feeder Capacitor Sizeand Location Simulation (51)19.310:40-11:00.A Complex Fault-Tolerant Power System Simulation.51 20EP12Electrical PowerWednesday11:30-12:30Room1Chair:Ing.Jos´e A.Urbano Castel´a n..................20.111:30-11:50.Internal Winding Faults in Three-Phase Five-LimbTransformer (52)20.211:50-12:10.Analysis of the generator-transformer interaction inthe abc reference (52)21EP2Electrical PowerThursday11:30-13:30Room2Chair:Dr.Francisco Ru´ız S´a nchez...................21.111:30-11:50.Dinamics of Solar-Powerwd Fractional Horse PowerMotor (52)21.211:50-12:10.Sliding Mode Observer-Based Control for a Series Ac-tive Filter (53)21.312:10-12:30.Fuzzy Logic Enhanced Speed Control System of a VSI-Fed Three Phase Induction motor (53)21.412:30-12:50.Intelligent Control of the Regenerative Braking in anInduction Motor Drive (53)21.512:50-13:10.Analysis of Propulsion Systems in Electric Vehicles..54 22EP3Electrical PowerThursday15:20-17:00Room2Chair:To be defined............................22.115:20-15:40.Electrical Network Simulation for Increasing Quality.5422.215:40-16:00.A trust-region algorithm based on global SQP for re-active power optimization (54)22.316:00-16:20.Stability Analysis of Power Market with Bounded Ra-tionality Cournot Game (54)22.416:20-16:40.A RBFN Hierarchical Clustering Based Network Parti-tioning Method for Zonal Pricing (55)23EC1Electronic CircuitsFriday9:40-11:00Room1Chair:Dr.Hildeberto Jard´o n Aguilar.................23.19:40-10:00.MMIC Differential Amplifier Implementation Based onRF&MW Analytical Tools (55)23.210:00-10:20.900MHz band class E PA using high voltage n-channeltransistors in standard CMOS technology (56)23.310:20-10:40.Efficient Design Approach for a SiGe HBT OscillatorIncorporating Reflection Sapphire Loaded Cavity Resonator (56)。

专利名称：Displacement control system for variable displacement hydraulic pump发明人：Yosuke Oda,Kiyoshi Shirai申请号：US08/416757申请日：19950413公开号：US05697764A公开日：19971216专利内容由知识产权出版社提供摘要：There is provided a displacement control system for a variable displacement hydraulic pump which has a displacement control piston assembly (6) having a large diameter chamber (7) for operating a displacement control member (5) of the variable displacement hydraulic pump selectively in a direction of smaller displacement and in a direction of larger displacement, first control valve (8) and second control valve (9) for selectively communicating the large diameter chamber of the displacement control piston assembly with a pump discharge line and a tank, the first control valve being placed at a supply position by the pump discharge pressure, and at a drain position by a spring associated with the displacement control piston assembly via a feedback lever, and the second control valve being placed at a first position by the pump discharge pressure for communicating the pump port and the large diameter chamber and at a second position by a load pressure for communicating the pump port and the large diameter chamber and at a second position by a load pressure for communicating the large diameter chamber to the first control valve, the flow path area is varied at the intermediate position of a fluid passage from the large diameter chamber to the pump discharge passage or to a tank. With the construction set forth above, supply speed anddrain speed of the pump discharge pressure to and from the large diameter chamber of the displacement control piston assembly is varied by variation of cross- sectional flow area at the intermediate position of the fluid passage. By this, response characteristics in displacement control of the variable displacement hydraulic valve can be adjusted to improve operability of a work implement.申请人：KABUSHIKI KAISHA KOMATSU SEISAKUSHO代理人：Ronald P. Kananen更多信息请下载全文后查看。

A 高分子化学和高分子物理UNIT 1 What are Polymer?第一单元什么是高聚物？What are polymers? For one thing, they are complex and giant molecules and are different from low molecular weight compounds like, say, common salt. To contrast the difference, the molecular weight of common salt is only 58.5, while that of a polymer can be as high as several hundred thousand, even more than thousand thousands. These big molecules or ‘macro-molecules’ are made up of much smaller molecules, can be of one or more chemical compounds. To illustrate, imagine that a set of rings has the same size and is made of the same material. When these things are interlinked, the chain formed can be considered as representing a polymer from molecules of the same compound. Alternatively, individual rings could be of different sizes and materials, and interlinked to represent a polymer from molecules of different compounds.什么是高聚物？首先，他们是合成物和大分子，而且不同于低分子化合物，譬如说普通的盐。

2021年第40卷第3期传感器与微系统（Transducer and MicrosystemTechnologies)93D O I:10.13873/J.1000-9787(2021)03-0093-02新型大位移非对称微夹钳设计+陈晓东，胡思雅，邓子龙，高兴军(辽宁石油化工大学机械工程学院，辽宁抚顺113001)摘要：针对传统对称微夹钳输出位移大，但很容易因左右钳指受力不均匀破坏微组件或零件;传统非对称微夹钳输出位移小，但钳指输出力稳定的问题，设计一种大位移非对称微夹钳。

首先通过几何关系计算出理论输人位移与理论输出位移之间的关系；其次进行建模;最后对模型进行仿真分析得出微夹钳的性會旨。

设计的微夹钳理论放大比为12.34,仿真放大比为11. 56,仿真结果与理论计算数值相比,误差为6.32 %，证实了理论计算的正确性以及设计的有效性。

关键词：微夹钳；非对称；设计；仿真分析中图分类号：T H12文献标识码：A文章编号：1000-9787(2021)03-0093-02D e s i g n o f n o v e l l a r g e d i s p l a c e m e n t a s y m m e t r i c m i c r o g r i p p e r*C H E N Xiao d o n g,H U Siya,DE N G Zilong,G A O X i n g u n(School of M echanical E ngineering,Liaoning Shihua U niversity，Fushun 113001,C hina)A bstract ：Aiming at the problems that output displacement of traditional symmetrical microgripper i si s easy t o destroy the micro-components or parts because of the uneven force on the l e f t and right jaws,and outputdisplacement of traditional asymmetrical microgripper i s small，but the output force of the grasping jaw i s stable，alarge displacement asymmetric microgripper i s designed.Firstly, relationship between theoretical inputdisplacement and theoretical output d i splacement i s calculated by geometric relationship；secondly, modeling i scarried out.Finally, the performance of the micro-clamp i s obtained by simulation analysis on the model.Thetheoretical amplification ratio o f the designed microgripper i s12. 34 and the simulation amplification rat i o i s11.56. Compared with t he theoretical calculation, the error of simulation results i s 6. 32 %, which proves thecorrectness of the theoretical calculation and the validity of the design.K eyw ords：microgripper；asymmetry；design；simulation analysis〇引言近年来，随着微机电系统（micro-electro-mechanical system,M E M S)等高新科技的快速发展，微操作的研究取得了巨大进步[1]。

GGALVANIC DISTORTIONThe electrical conductivity of Earth materials affects two physical processes:electromagnetic induction which is utilized with magneto-tellurics(MT)(q.v.),and electrical conduction.If electromagnetic induction in media which are heterogeneous with respect to their elec-trical conductivity is considered,then both processes take place simul-taneously:Due to Faraday’s law,a variational electric field is induced in the Earth,and due to the conductivity of the subsoil an electric cur-rent flows as a consequence of the electric field.The current compo-nent normal to boundaries within the heterogeneous structure passes these boundaries continously according tos1E1¼s2E2where the subscripts1and2indicate the boundary values of conductiv-ity and electric field in regions1and2,respectively.Therefore the amplitude and the direction of the electric field are changed in the vicinity of the boundaries(Figure G1).In electromagnetic induction studies,the totality of these changes in comparison with the electric field distribution in homogeneous media is referred to as galvanic distortion. The electrical conductivity of Earth materials spans13orders of mag-nitude(e.g.,dry crystalline rocks can have conductivities of less than 10–6S mÀ1,while ores can have conductivities exceeding106S mÀ1). Therefore,MT has a potential for producing well constrained mod-els of the Earth’s electrical conductivity structure,but almost all field studies are affected by the phenomenon of galvanic distortion, and sophisticated techniques have been developed for dealing with it(Simpson and Bahr,2005).Electric field amplitude changes and static shiftA change in an electric field amplitude causes a frequency-indepen-dent offset in apparent resistivity curves so that they plot parallel to their true level,but are scaled by a real factor.Because this shift can be regarded as spatial undersampling or“aliasing,”the scaling factor or static shift factor cannot be determined directly from MT data recorded at a single site.If MT data are interpreted via one-dimensional modeling without correcting for static shift,the depth to a conductive body will be shifted by the square root of the factor by which the apparent resistivities are shifted.Static shift corrections may be classified into three broad groups: 1.Short period corrections relying on active near-surface measurementssuch as transient electromagnetic sounding(TEM)(e.g.,Meju,1996).2.Averaging(statistical)techniques.As an example,electromagneticarray profiling is an adaptation of the magnetotelluric technique that involves sampling lateral variations in the electric field con-tinuously,and spatial low pass filtering can be used to suppress sta-tic shift effects(Torres-Verdin and Bostick,1992).3.Long period corrections relying on assumed deep structure(e.g.,a resistivity drop at the mid-mantle transition zones)or long-periodmagnetic transfer functions(Schmucker,1973).An equivalence relationship exists between the magnetotelluric impedance Z and Schmucker’s C-response:C¼Zi om0;which can be determined from the magnetic fields alone,thereby providing an inductive scale length that is independent of the dis-torted electric field.Magnetic transfer functions can,for example, be derived from the magnetic daily variation.The appropriate method for correcting static shift often depends on the target depth,because there can be a continuum of distortion at all scales.As an example,in complex three-dimensional environments near-surface correction techniques may be inadequate if the conductiv-ity of the mantle is considered,because electrical heterogeneity in the deep crust creates additional galvanic distortion at a larger-scale, which is not resolved with near-surface measurements(e.g.,Simpson and Bahr,2005).Changes in the direction of electric fields and mixing of polarizationsIn some target areas of the MT method the conductivity distribution is two-dimensional(e.g.,in the case of electrical anisotropy(q.v.))and the induction process can be described by two decoupled polarizations of the electromagnetic field(e.g.,Simpson and Bahr,2005).Then,the changes in the direction of electric fields that are associated with galvanic distortion can result in mixing of these two polarizations. The recovery of the undistorted electromagnetic field is referred to as magnetotelluric tensor decomposition(e.g.,Bahr,1988,Groom and Bailey,1989).Current channeling and the“magnetic”distortionIn the case of extreme conductivity contrasts the electrical current can be channeled in such way that it is surrounded by a magneticvariational field that has,opposite to the assumptions made in the geo-magnetic deep sounding(q.v.)method,no phase lag with respect to the electric field.The occurrence of such magnetic fields in field data has been shown by Zhang et al.(1993)and Ritter and Banks(1998).An example of a magnetotelluric tensor decomposition that includes mag-netic distortion has been presented by Chave and Smith(1994).Karsten BahrBibliographyBahr,K.,1988.Interpretation of the magnetotelluric impedance tensor: regional induction and local telluric distortion.Journal of Geophy-sics,62:119–127.Chave,A.D.,and Smith,J.T.,1994.On electric and magnetic galvanic distortion tensor decompositions.Journal of Geophysical Research,99:4669–4682.Groom,R.W.,and Bailey,R.C.,1989.Decomposition of the magneto-telluric impedance tensor in the presence of local three-dimensional galvanic distortion.Journal of Geophysical Research,94: 1913–1925.Meju,M.A.,1996.Joint inversion of TEM and distorted MT sound-ings:some effective practical considerations.Geophysics,61: 56–65.Ritter,P.,and Banks,R.J.,1998.Separation of local and regional information in distorted GDS response functions by hypothetical event analysis.Geophysical Journal International,135:923–942. Schmucker,U.,1973.Regional induction studies:a review of methods and results.Physics of the Earth and Planetary Interiors,7: 365–378.Simpson,F.,and Bahr,K.,2005.Practical Magnetotellurics.Cam-bridge:Cambridge University Press.Torres-Verdin,C.,and Bostick,F.X.,1992.Principles of special sur-face electric field filtering in magnetotellurics:electromagnetic array profiling(EMAP).Geophysics,57:603–622.Zhang,P.,Pedersen,L.B.,Mareschal,M.,and Chouteau,M.,1993.Channelling contribution to tipper vectors:a magnetic equivalent to electrical distortion.Geophysical Journal International,113: 693–700.Cross-referencesAnisotropy,ElectricalGeomagnetic Deep SoundingMagnetotelluricsMantle,Electrical Conductivity,Mineralogy GAUSS’DETERMINATION OF ABSOLUTE INTENSITYThe concept of magnetic intensity was known as early as1600in De Magnete(see Gilbert,William).The relative intensity of the geomag-netic field in different locations could be measured with some preci-sion from the rate of oscillation of a dip needle—a method used by Humboldt,Alexander von(q.v.)in South America in1798.But it was not until Gauss became interested in a universal system of units that the idea of measuring absolute intensity,in terms of units of mass, length,and time,was considered.It is now difficult to imagine how revolutionary was the idea that something as subtle as magnetism could be measured in such mundane units.On18February1832,Gauss,Carl Friedrich(q.v.)wrote to the German astronomer Olbers:“I occupy myself now with the Earth’s magnetism,particularly with an absolute determination of its intensity.Friend Weber”(Wilhelm Weber,Professor of Physics at the University of Göttingen)“conducts the experiments on my instructions.As, for example,a clear concept of velocity can be given only through statements on time and space,so in my opinion,the complete determination of the intensity of the Earth’s magnetism requires to specify(1)a weight¼p,(2)a length¼r,and then the Earth’s magnetism can be expressed byffiffiffiffiffiffiffip=rp.”After minor adjustment to the units,the experiment was completed in May1832,when the horizontal intensity(H)at Göttingen was found to be1.7820mg1/2mm–1/2s–1(17820nT).The experimentThe experiment was in two parts.In the vibration experiment(Figure G2) magnet A was set oscillating in a horizontal plane by deflecting it from magnetic north.The period of oscillations was determined at different small amplitudes,and from these the period t0of infinite-simal oscillations was deduced.This gave a measure of MH,where M denotes the magnetic moment of magnet A:MH¼4p2I=t20The moment of inertia,I,of the oscillating part is difficult to deter-mine directly,so Gauss used the ingenious idea of conductingtheFigure G2The vibration experiment.Magnet A is suspended from a silk fiber F It is set swinging horizontally and the period of an oscillation is obtained by timing an integral number of swings with clock C,using telescope T to observe the scale S reflected in mirror M.The moment of inertia of the oscillating part can be changed by a known amount by hanging weights W from the rodR. 278GAUSS’DETERMINATION OF ABSOLUTE INTENSITYexperiment for I and then I þD I ,where D I is a known increment obtained by hanging weights at a known distance from the suspension.From several measures of t 0with different values of D I ,I was deter-mined by the method of least squares (another of Gauss ’s original methods).In the deflection experiment,magnet A was removed from the suspension and replaced with magnet B.The ratio M /H was measured by the deflection of magnet B from magnetic north,y ,produced by magnet A when placed in the same horizontal plane as B at distance d magnetic east (or west)of the suspension (Figure G3).This required knowledge of the magnetic intensity due to a bar magnet.Gauss deduced that the intensity at distance d on the axis of a dipole is inversely proportional to d 3,but that just one additional term is required to allow for the finite length of the magnet,giving 2M (1þk/d 2)/d 3,where k denotes a small constant.ThenM =H ¼1=2d 3ð1Àk =d 2Þtan y :The value of k was determined,again by the method of least squares,from the results of a number of measures of y at different d .From MH and M /H both M and,as required by Gauss,H could readily be deduced.Present methodsWith remarkably little modification,Gauss ’s experiment was devel-oped into the Kew magnetometer,which remained the standard means of determining absolute H until electrical methods were introduced in the 1920s.At some observatories,Kew magnetometers were still in use in the 1980s.Nowadays absolute intensity can be measured in sec-onds with a proton magnetometer and without the considerable time and experimental skill required by Gauss ’s method.Stuart R.C.MalinBibliographyGauss,C.F.,1833.Intensitas vis magneticae terrestris ad mensuram absolutam revocata.Göttingen,Germany.Malin,S.R.C.,1982.Sesquicentenary of Gauss ’s first measurement of the absolute value of magnetic intensity.Philosophical Transac-tions of the Royal Society of London ,A 306:5–8.Malin,S.R.C.,and Barraclough,D.R.,1982.150th anniversary of Gauss ’s first absolute magnetic measurement.Nature ,297:285.Cross-referencesGauss,Carl Friedrich (1777–1855)Geomagnetism,History of Gilbert,William (1544–1603)Humboldt,Alexander von (1759–1859)Instrumentation,History ofGAUSS,CARL FRIEDRICH (1777–1855)Amongst the 19th century scientists working in the field of geomag-netism,Carl Friedrich Gauss was certainly one of the most outstanding contributors,who also made very fundamental contributions to the fields of mathematics,astronomy,and geodetics.Born in April 30,1777in Braunschweig (Germany)as the son of a gardener,street butcher,and mason Johann Friderich Carl,as he was named in the certificate of baptism,already in primary school at the age of nine perplexed his teacher J.G.Büttner by his innovative way to sum up the numbers from 1to ter Gauss used to claim that he learned manipulating numbers earlier than being able to speak.In 1788,Gauss became a pupil at the Catharineum in Braunschweig,where M.C.Bartels (1769–1836)recognized his outstanding mathematical abilities and introduced Gauss to more advanced problems of mathe-matics.Gauss proved to be an exceptional pupil catching the attention of Duke Carl Wilhelm Ferdinand of Braunschweig who provided Gauss with the necessary financial support to attend the Collegium Carolinum (now the Technical University of Braunschweig)from 1792to 1795.From 1795to 1798Gauss studied at the University of Göttingen,where his number theoretical studies allowed him to prove in 1796,that the regular 17-gon can be constructed using a pair of compasses and a ruler only.In 1799,he received his doctors degree from the University of Helmstedt (close to Braunschweig;closed 1809by Napoleon)without any oral examination and in absentia .His mentor in Helmstedt was J.F.Pfaff (1765–1825).The thesis submitted was a complete proof of the fundamental theorem of algebra.His studies on number theory published in Latin language as Disquitiones arithi-meticae in 1801made Carl Friedrich Gauss immediately one of the leading mathematicians in Europe.Gauss also made further pioneering contributions to complex number theory,elliptical functions,function theory,and noneuclidian geometry.Many of his thoughts have not been published in regular books but can be read in his more than 7000letters to friends and colleagues.But Gauss was not only interested in mathematics.On January 1,1801the Italian astronomer G.Piazzi (1746–1820)for the first time detected the asteroid Ceres,but lost him again a couple of weeks later.Based on completely new numerical methods,Gauss determined the orbit of Ceres in November 1801,which allowed F.X.von Zach (1754–1832)to redetect Ceres on December 7,1801.This prediction made Gauss famous next to his mathematical findings.In 1805,Gauss got married to Johanna Osthoff (1780–1809),who gave birth to two sons,Joseph and Louis,and a daughter,Wilhelmina.In 1810,Gauss married his second wife,Minna Waldeck (1788–1815).They had three more children together,Eugen,Wilhelm,and Therese.Eugen Gauss later became the founder and first president of the First National Bank of St.Charles,Missouri.Carl Friedrich Gauss ’interest in the Earth magnetic field is evident in a letter to his friend Wilhelm Olbers (1781–1862)as early as 1803,when he told Olbers that geomagnetism is a field where still many mathematical studies can be done.He became more engaged in geo-magnetism after a meeting with A.von Humboldt (1769–1859)and W.E.Weber (1804–1891)in Berlin in 1828where von Humboldt pointed out to Gauss the large number of unsolved problems in geo-magnetism.When Weber became a professor of physics at the Univer-sity of Göttingen in 1831,one of the most productive periods intheFigure G3The deflection experiment.Suspended magnet B is deflected from magnetic north by placing magnet A east or west (magnetic)of it at a known distance d .The angle of deflection y is measured by using telescope T to observe the scale S reflected in mirror M.GAUSS,CARL FRIEDRICH (1777–1855)279field of geomagnetism started.In1832,Gauss and Weber introduced the well-known Gauss system according to which the magnetic field unit was based on the centimeter,the gram,and the second.The Mag-netic Observatory of Göttingen was finished in1833and its construc-tion became the prototype for many other observatories all over Europe.Gauss and Weber furthermore developed and improved instru-ments to measure the magnetic field,such as the unifilar and bifilar magnetometer.Inspired by A.von Humboldt,Gauss and Weber realized that mag-netic field measurements need to be done globally with standardized instruments and at agreed times.This led to the foundation of the Göttinger Magnetische Verein in1836,an organization without any for-mal structure,only devoted to organize magnetic field measurements all over the world.The results of this organization have been published in six volumes as the Resultate aus den Beobachtungen des Magnetischen Vereins.The issue of1838contains the pioneering work Allgemeine Theorie des Erdmagnetismus where Gauss introduced the concept of the spherical harmonic analysis and applied this new tool to magnetic field measurements.His general theory of geomagnetism also allowed to separate the magnetic field into its externally and its internally caused parts.As the external contributions are nowadays interpreted as current systems in the ionosphere and magnetosphere Gauss can also be named the founder of magnetospheric research.Publication of the Resultate ceased in1843.W.E.Weber together with such eminent professors of the University of Göttingen as Jacob Grimm(1785–1863)and Wilhelm Grimm(1786–1859)had formed the political group Göttingen Seven protesting against constitutional violations of King Ernst August of Hannover.As a consequence of these political activities,Weber and his colleagues were dismissed. Though Gauss tried everything to bring back Weber in his position he did not succeed and Weber finally decided to accept a chair at the University of Leipzig in1843.This finished a most fruitful and remarkable cooperation between two of the most outstanding contribu-tors to geomagnetism in the19th century.Their heritage was not only the invention of the first telegraph station in1833,but especially the network of36globally operating magnetic observatories.In his later years Gauss considered to either enter the field of bota-nics or to learn another language.He decided for the language and started to study Russian,already being in his seventies.At that time he was the only person in Göttingen speaking that language fluently. Furthermore,he was asked by the Senate of the University of Göttingen to reorganize their widow’s pension system.This work made him one of the founders of insurance mathematics.In his final years Gauss became fascinated by the newly built railway lines and supported their development using the telegraph idea invented by Weber and himself.Carl Friedrich Gauss died on February23,1855as a most respected citizen of his town Göttingen.He was a real genius who was named Princeps mathematicorum already during his life time,but was also praised for his practical abilities.Karl-Heinz GlaßmeierBibliographyBiegel,G.,and K.Reich,Carl Friedrich Gauss,Braunschweig,2005. Bühler,W.,Gauss:A Biographical study,Berlin,1981.Hall,T.,Carl Friedrich Gauss:A Biography,Cambridge,MA,1970. Lamont,J.,Astronomie und Erdmagnetismus,Stuttgart,1851. Cross-referencesHumboldt,Alexander von(1759–1859)Magnetosphere of the Earth GELLIBRAND,HENRY(1597–1636)Henry Gellibrand was the eldest son of a physician,also Henry,and was born on17November1597in the parish of St.Botolph,Aldersgate,London.In1615,he became a commoner at Trinity Col-lege,Oxford,and obtained a BA in1619and an MA in1621.Aftertaking Holy Orders he became curate at Chiddingstone,Kent,butthe lectures of Sir Henry Savile inspired him to become a full-timemathematician.He settled in Oxford,where he became friends withHenry Briggs,famed for introducing logarithms to the base10.Itwas on Briggs’recommendation that,on the death of Edmund Gunter,Gellibrand succeeded him as Gresham Professor of Astronomy in1627—a post he held until his death from a fever on16February1636.He was buried at St.Peter the Poor,Broad Street,London(now demolished).Gellibrand’s principal publications were concerned with mathe-matics(notably the completion of Briggs’Trigonometrica Britannicaafter Briggs died in1630)and navigation.But he is included herebecause he is credited with the discovery of geomagnetic secular var-iation.The events leading to this discovery are as follows(for furtherdetails see Malin and Bullard,1981).The sequence starts with an observation of magnetic declinationmade by William Borough,a merchant seaman who rose to“captaingeneral”on the Russian trade route before becoming comptroller ofthe Queen’s Navy.The magnetic observation(Borough,1581,1596)was made on16October1580at Limehouse,London,where heobserved the magnetic azimuth of the sun as it rose through sevenfixed altitudes in the morning and as it descended through the samealtitudes in the afternoon.The mean of the two azimuths for each alti-tude gives a measure of magnetic declination,D,the mean of which is11 190EÆ50rms.Despite the small scatter,the value could have beenbiased by site or compass errors.Some40years later,Edmund Gunter,distinguished mathematician,Gresham Professor of Astronomy and inventor of the slide rule,foundD to be“only6gr15m”(6 150E)“as I have sometimes found it oflate”(Gunter,1624,66).The exact date(ca.1622)and location(prob-ably Deptford)of the observation are not stated,but it alerted Gunterto the discrepancy with Borough’s measurement.To investigatefurther,Gunter“enquired after the place where Mr.Borough observed,and went to Limehouse with...a quadrant of three foot Semidiameter,and two Needles,the one above6inches,and the other10inches long ...towards the night the13of June1622,I made observation in sev-eral parts of the ground”(Gunter,1624,66).These observations,witha mean of5 560EÆ120rms,confirmed that D in1622was signifi-cantly less than had been measured by Borough in1580.But was thisan error in the earlier measure,or,unlikely as it then seemed,was Dchanging?Unfortunately Gunter died in1626,before making anyfurther measurements.When Gellibrand succeeded Gunter as Gresham Professor,allhe required to do to confirm a major scientific discovery was towait a few years and then repeat the Limehouse observation.Buthe chose instead to go to the site of Gunter’s earlier observationin Deptford,where,in June1633,Gellibrand found D to be“muchless than5 ”(Gellibrand,1635,16).He made a further measurement of D on the same site on June12,1634and“found it not much to exceed4 ”(Gellibrand,1635,7),the published data giving4 50 EÆ40rms.His observation of D at Paul’s Cray on July4,1634adds little,because it is a new site.On the strength of these observations,he announced his discovery of secular variation(Gellibrand,1635,7and 19),but the reader may decide how much of the credit should go to Gunter.Stuart R.C.Malin280GELLIBRAND,HENRY(1597–1636)BibliographyBorough,W.,1581.A Discourse of the Variation of the Compass,or Magnetical Needle.(Appendix to R.Norman The newe Attractive).London:Jhon Kyngston for Richard Ballard.Borough,W.,1596.A Discourse of the Variation of the Compass,or Magnetical Needle.(Appendix to R.Norman The newe Attractive).London:E Allde for Hugh Astley.Gellibrand,H.,1635.A Discourse Mathematical on the Variation of the Magneticall Needle.Together with its admirable Diminution lately discovered.London:William Jones.Gunter,E.,1624.The description and use of the sector,the crosse-staffe and other Instruments.First booke of the crosse-staffe.London:William Jones.Malin,S.R.C.,and Bullard,Sir Edward,1981.The direction of the Earth’s magnetic field at London,1570–1975.Philosophical Transactions of the Royal Society of London,A299:357–423. Smith,G.,Stephen,L.,and Lee,S.,1967.The Dictionary of National Biography.Oxford:University Press.Cross-referencesCompassGeomagnetic Secular VariationGeomagnetism,History ofGEOCENTRIC AXIAL DIPOLE HYPOTHESISThe time-averaged paleomagnetic fieldPaleomagnetic studies provide measurements of the direction of the ancient geomagnetic field on the geological timescale.Samples are generally collected at a number of sites,where each site is defined as a single point in time.In most cases the time relationship between the sites is not known,moreover when samples are collected from a stratigraphic sequence the time interval between the levels is also not known.In order to deal with such data,the concept of the time-averaged paleomagnetic field is used.Hospers(1954)first introduced the geocentric axial dipole hypothesis(GAD)as a means of defining this time-averaged field and as a method for the analysis of paleomag-netic results.The hypothesis states that the paleomagnetic field,when averaged over a sufficient time interval,will conform with the field expected from a geocentric axial dipole.Hospers presumed that a time interval of several thousand years would be sufficient for the purpose of averaging,but many studies now suggest that tens or hundreds of thousand years are generally required to produce a good time-average. The GAD model is a simple one(Figure G4)in which the geomag-netic and geographic axes and equators coincide.Thus at any point on the surface of the Earth,the time-averaged paleomagnetic latitude l is equal to the geographic latitude.If m is the magnetic moment of this time-averaged geocentric axial dipole and a is the radius of the Earth, the horizontal(H)and vertical(Z)components of the magnetic field at latitude l are given byH¼m0m cos l;Z¼2m0m sin l;(Eq.1)and the total field F is given byF¼ðH2þZ2Þ1=2¼m0m4p a2ð1þ3sin2lÞ1=2:(Eq.2)Since the tangent of the magnetic inclination I is Z/H,thentan I¼2tan l;(Eq.3)and by definition,the declination D is given byD¼0 :(Eq.4)The colatitude p(90 minus the latitude)can be obtained fromtan I¼2cot pð0p180 Þ:(Eq.5)The relationship given in Eq. (3) is fundamental to paleomagnetismand is a direct consequence of the GAD hypothesis.When applied toresults from different geologic periods,it enables the paleomagneticlatitude to be derived from the mean inclination.This relationshipbetween latitude and inclination is shown in Figure G5.Figure G5Variation of inclination with latitude for a geocentricdipole.GEOCENTRIC AXIAL DIPOLE HYPOTHESIS281Paleom a gnetic polesThe positio n where the time-averaged dipole axis cuts the surface of the Earth is called the paleomagnetic pole and is defined on the present latitude-longitude grid. Paleomagnetic poles make it possible to com-pare results from different observing localities, since such poles should represent the best estimate of the position of the geographic pole.These poles are the most useful parameter derived from the GAD hypothesis. If the paleomagnetic mean direction (D m , I m ) is known at some sampling locality S, with latitude and longitude (l s , f s ), the coordinates of the paleomagnetic pole P (l p , f p ) can be calculated from the following equations by reference to Figure G6.sin l p ¼ sin l s cos p þ cos l s sin p cos D m ðÀ90 l p þ90 Þ(Eq. 6)f p ¼ f s þ b ; when cos p sin l s sin l porf p ¼ f s þ 180 À b ; when cos p sin l s sin l p (Eq. 7)wheresin b ¼ sin p sin D m = cos l p : (Eq. 8)The paleocolatitude p is determined from Eq. (5). The paleomagnetic pole ( l p , f p ) calculated in this way implies that “sufficient ” time aver-aging has been carried out. What “sufficient ” time is defined as is a subject of much debate and it is always difficult to estimate the time covered by the rocks being sampled. Any instantaneous paleofield direction (representing only a single point in time) may also be con-verted to a pole position using Eqs. (7) and (8). In this case the pole is termed a virtual geomagnetic pole (VGP). A VGP can be regarded as the paleomagnetic analog of the geomagnetic poles of the present field. The paleomagnetic pole may then also be calculated by finding the average of many VGPs, corresponding to many paleodirections.Of course, given a paleomagnetic pole position with coordinates (l p , f p ), the expected mean direction of magnetization (D m , I m )at any site location (l s , f s ) may be also calculated (Figure G6). The paleocolatitude p is given bycos p ¼ sin l s sin l p þ cos l s cos l p cos ðf p À f s Þ; (Eq. 9)and the inclination I m may then be calculated from Eq. (5). The corre-sponding declination D m is given bycos D m ¼sin l p À sin l s cos pcos l s sin p; (Eq. 10)where0 D m 180 for 0 (f p – f s ) 180and180 < D m <360for 180 < (f p –f s ) < 360 .The declination is indeterminate (that is any value may be chosen)if the site and the pole position coincide. If l s ¼Æ90then D m is defined as being equal to f p , the longitude of the paleomagnetic pole.Te s ting the GAD hy p othesis Tim e scale 0– 5 MaOn the timescale 0 –5 Ma, little or no continental drift will have occurred, so it was originally thought that the observation that world-wide paleomagnetic poles for this time span plotted around the present geographic indicated support for the GAD hypothesis (Cox and Doell,1960; Irving, 1964; McElhinny, 1973). However, any set of axial mul-tipoles (g 01; g 02 ; g 03 , etc.) will also produce paleomagnetic poles that cen-ter around the geographic pole. Indeed, careful analysis of the paleomagnetic data in this time interval has enabled the determination of any second-order multipole terms in the time-averaged field (see below for more detailed discussion of these departures from the GAD hypothesis).The first important test of the GAD hypothesis for the interval 0 –5Ma was carried out by Opdyke and Henry (1969),who plotted the mean inclinations observed in deep-sea sediment cores as a function of latitude,showing that these observations conformed with the GAD hypothesis as predicted by Eq. (3) and plotted in Figure G5.Testing the axial nature of the time-averaged fieldOn the geological timescale it is observed that paleomagnetic poles for any geological period from a single continent or block are closely grouped indicating the dipole hypothesis is true at least to first-order.However,this observation by itself does not prove the axial nature of the dipole field.This can be tested through the use of paleoclimatic indicators (see McElhinny and McFadden,2000for a general discus-sion).Paleoclimatologists use a simple model based on the fact that the net solar flux reaching the surface of the Earth has a maximum at the equator and a minimum at the poles.The global temperature may thus be expected to have the same variation.The density distribu-tion of many climatic indicators (climatically sensitive sediments)at the present time shows a maximum at the equator and either a mini-mum at the poles or a high-latitude zone from which the indicator is absent (e.g.,coral reefs,evaporates,and carbonates).A less common distribution is that of glacial deposits and some deciduous trees,which have a maximum in polar and intermediate latitudes.It has been shown that the distributions of paleoclimatic indicators can be related to the present-day climatic zones that are roughly parallel with latitude.Irving (1956)first suggested that comparisons between paleomag-netic results and geological evidence of past climates could provide a test for the GAD hypothesis over geological time.The essential point regarding such a test is that both paleomagnetic and paleoclimatic data provide independent evidence of past latitudes,since the factors con-trolling climate are quite independent of the Earth ’s magnetic field.The most useful approach is to compile the paleolatitude values for a particular occurrence in the form of equal angle or equalareaFigure G6Calculation of the position P (l p ,f p )of thepaleomagnetic pole relative to the sampling site S (l s ,f s )with mean magnetic direction (D m ,I m ).282GEOCENTRIC AXIAL DIPOLE HYPOTHESIS。

INTERNATIONAL JOURNAL OF NUMERICAL MODELLING:ELECTRONIC NETWORKS,DEVICES AND FIELDS Int.J.Numer.Model.2010;23:1–19Published online6July2009in Wiley InterScience().DOI:10.1002/jnm.720 Advanced models for transient analysis of lossy and dispersiveanisotropic planar layersGiulio AntoniniÃ,yUAq EMC Laboratory,Dipartimento di Ingegneria Elettrica e dell’Informazione,Universita`degli Studi dell’Aquila,Monteluco di Roio,67040L’Aquila,ItalySUMMARYA new model is proposed for the transient analysis of the electromagneticfield propagation through anisotropic lossy and dispersive layers.The propagation equations of the electromagneticfields are solved as a Sturm–Liouville problem leading to identify its dyadic Green’s function in a series rational form. Then,the corresponding poles and residues are obtained and a reduced order macromodel is generated, which can be easily embedded within existing three dimensional solvers.The model is applied to lossy and dispersive anisotropic layers with differently polarized plane–waves.Copyright r2009John Wiley& Sons,Ltd.Received1November2008;Revised23January2009;Accepted3June2009KEY WORDS:planar anisotropic layers;lossy and dispersive media;dyadic Green’s function;transient analysis1.INTRODUCTIONComposite materials have received an increasing interest in industrial and military applications and have been suggested as substitutes for metals in modern aircrafts systems by virtue of their superior mechanical properties in strength-to-weight and modulus-to-weight ratios.They are generally laminated,anisotropic and lossy.A pioneering investigation of the electromagnetic properties of advanced composite materials is reported in[1].More recently,the characteriza-tion of the reflection,transmission and shielding properties of such materials have been presented in several studies in the frequency domain[2–4].Transient analysis of anisotropic lossy slabs can be performed using an equivalent-transmission-line-circuit[5,6].This approach*Correspondence to:Giulio Antonini,UAq EMC Laboratory,Dipartimento di Ingegneria Elettrica e dell’Informazione, Universita degli Studi dell’Aquila,Monteluco di Roio,67040,L’Aquila,Italy.y E-mail:giulio.antonini@univaq.itContract/grant sponsor:Italian Ministry of University(MIUR)under a Program for the Development of Research of National Interest;contract/grant number:2006095890Copyright r2009John Wiley&Sons,Ltd.relies on the analogy between the field equations and the coupled transmission line equations [7]and,as a consequence,the standard halt-T ladder network (HTLN)is used.On the other hand,it is known that the HTLN model contains much more information than needed [8]and a reduced order model may be more suitable for a computer implementation.Such a limitation has been overcome in [9]by adopting the vector fitting technique [10],which allows the extraction of a reduced order rational macromodel,which is interfaced to a finite difference time domain solver.In this way,thin composite structures are modeled through the use of convolution integrals avoiding their spatial discretization,which is typically a cpu-time consuming process.In [11]a new methodology for the transient analysis of plane waves obliquely incident on a planar lossy and dispersive layer has been presented.The proposed model is based on the Sturm–Liouville problem associated with the propagation equations.The Green’s function is calculated in a rational series form and the open-end impedance matrix is obtained as the sum of infinite rational functions.The rational form permits an easy identification of poles and residues.The pole–residue representation is converted into a state-space model,which can be easily interfaced with ordinary differential equation solvers.The aim of this paper is to extend the previous approach to the transient analysis of plane waves impinging on planar anisotropic lossy and dispersive layers.The TM z –TE z mode coupling generated by the anisotropy leads to a multidimensional wave propagation problem.The propagation equation within the layer is solved as a Sturm–Liouville problem where tangential electric fields are considered as unknowns and tangential magnetic fields as sources.This allows one to write the dyadic Green’s function of the problem in a rational series form from which poles and residues can be easily identified.Hence,an arbitrary large rational macromodel can be generated and used to obtain a finite state-space representation,which is well suited for computer implementation.The paper is organized as follows.In Section 2,the propagation equations of electromagnetic fields through lossy and dispersive anisotropic layers are derived and re-cast as a Sturm–Liouville problem.Then,in Section 3,the dyadic Green’s function is obtained as solution of the corresponding Sturm–Liouville problem and the impedance matrix computed.The knowledge of the rational form of the impedance matrix pawns the way to the computation of a reduced order macromodel and,finally,to a state-space realization.Sections 4presents the numerical results validating the proposed method and Section 5draws the conclusions.2.PROPAGATION OF TANGENTIAL FIELDSLet us assume that the incident electromagnetic fields is described as a uniform plane wave with angle of incidence and polarization with respect to a spherical coordinate system as illustrated in Figure 1.Free space is assumed as the background medium.The propagation vector k of the wave is incident at angles y p from the x axis and /p from the projection onto the y –z plane from the y axis,as shown in Figure 1(a).The polarization of the electric field vector is described in terms of the unit vectors in the spherical coordinate system,a y and a f ,as illustrated in Figure 1(b).The general expression for the electric field vector in the Laplace domain is:E i ¼E 0e x a x þe y a y þe z a z ÀÁe Àk x x Àk y y Àk z z ð1ÞG.ANTONINI2Copyright r 2009John Wiley &Sons,Ltd.Int.J.Numer.Model.2010;23:1–19DOI:10.1002/jnmwhere the components of the incident electric field vector (e x ,e y ,e z )can be expressed in terms of the polarization angles y E ;y p ;f p [12].The propagation vector k ¼ðkx ;ky ;kz Þhas an amplitude k ¼s =c 0¼s ffiffiffiffiffiffiffiffiffim 0e 0p ,being s the complex frequency variable.Let us consider the propagation of a obliquely impinging plane wave through an anisotropic planar layer,as shown in Figure 2.Curl Maxwell’s equations,in the Laplace domain,read:H ÂE ðr ;s Þ¼Às m ðs ÞH ðr ;s Þð2a ÞH ÂH ðr ;s Þ¼s ðs ÞE ðr ;s Þþs e ðs ÞE ðr ;s Þð2b Þwhere m ðs Þ;e ðs Þ;s ðs Þare frequency dependent tensors of the magnetic permeability,electric permittivity and electric conductivity of the layer,respectively.Assuming that the anisotropyis Figure 1.Definitions of the parameters characterizing the incident field as a uniform plane wave.Figure 2.Global coordinates and principal coordinates for an anisotropic planar layer.ADVANCED MODELS FOR TRANSIENT ANALYSIS 3Copyright r 2009John Wiley &Sons,Ltd.Int.J.Numer.Model.2010;23:1–19DOI:10.1002/jnmin the transverse plane x–y only,they are given by:m sðÞ¼m xx m xy0m yx m yy000m zz26643775ð3Þe sðÞ¼e xx e xy0e yx e yy000e zz264375ð4Þs sðÞ¼s xx s xy0s yx s yy000s zz2435ð5Þwheree xx¼e0x cos f2þe0y sin f2ð6aÞe xy¼e yx¼ðe0x Àe0yÞcos f sin fð6bÞe yy¼e0x sin f2þe0ycos f2ð6cÞe zz¼e0zð6dÞThe dependence on the Laplace variable has been omitted for the sake of clarity.Here,ðe0x ;e0y;e0zÞare the permittivities with respect to the principal axis and f is the angle between the global and the principal axis of the layer.Similar expressions are used for the conductivities s xx;s xy;ð¼s yxÞ;s yy;s zz and permeabilities m xx;m xy;ð¼m yxÞ;m yy;m zz.Since we want to obtain impedance boundary conditions which connect tangential components on the interfaces,it is convenient to separate the tangentialfield components (E t(r,s),H t(r,s))from the normal ones(E n(r,s),H n(r,s)).Hence,we can write:E¼E tþE n n H¼H tþH n nð7ÞwhereE tÁn¼0H tÁn¼0ð8ÞAnalogously,the nabla operator H and the tensors of magnetic permeability,electric permittivity and conductivity can be split into their tangential and normal components[13].In the following,a standard approach is adopted[13]by equating separately the normal components of(2),eliminating the normal components and cross multiplying by n.Finally,a first-order state equation governing the electromagneticfields in the slab can be derived asd d zE xðzÞÀE yðzÞH yðzÞH xðzÞ26666643777775¼AÁE xðzÞÀE yðzÞH yðzÞH xðzÞ26666643777775ð9ÞG.ANTONINI4Copyright r2009John Wiley&Sons,Ltd.Int.J.Numer.Model.2010;23:1–19DOI:10.1002/jnmwhere the matrix A is as follows:A¼00Às m yyÀk2xs zzþs e zzÀs m xyþk x k ys zzþs e zz00Às m yxþk y k xs zzþs e zzÀs m xxÀk2ys zzþs e zz!Às xxþs e xxÀk2ys m zz!ÀÀs xyÀs e xyÀk x k ys m zz00ÀÀs yxÀs e yxÀk x k ys m zzÀs yyþs e yyÀk2xs m zz002 66 66 66 66 66 66 643 77 77 77 77 77 77 75ð10ÞHence,it is possible identifying the per-unit-length impedance and admittance matrices,respectively,as:Z0ðsÞ¼s m yyÀk2xs zzþs e zzs m xyþk x k ys zzþs e zzs m yxþk y k xs zzþs e zzs m xxÀk2ys zzþs e zz26643775ð11aÞY0ðsÞ¼s xxþs e xxÀk2ys m zzÀs xyÀs e xyÀk x k ys m zzÀs yxÀs e yxÀk x k ys m zzs yyþs e yyÀk2xs m zz26643775ð11bÞThe second-order wave equation for the transverse electricfield component~E t¼ðE x;ÀE yÞimmediately follows from the transmission line equations(9),after elimination of the magnetic field and it takes the form;@2 @z2~EtÀGðsÞ~E t¼0ð12Þwhere CðsÞ¼Z0ðsÞY0ðsÞ.It is to be pointed out that thefield pairs(E x,H y)and(ÀE x,H y) corresponds to TM z and TE z polarizations.Both the polarizations exhibit a Poynting vector along the z axis;a perfect analogy with coupled transmission lines can be established,as it is presented in[5–14].It is also clearly recognized that the model presented in those papers is a special case of the methodology proposed in this work.2.1.Boundary conditionsThe system of global coordinates x,y and z can always be chosen such that k y50,as in Figure3.In this case,the component k x of the propagation vector can be related to the Laplace variable ask x¼ssin y ið13Þwhere c0is the speed of light in the background homogenous medium and y i is the incidence angle of the incident plane wave.The incidence angle y i can be expressed in terms of the polarization angle y p as:y i¼pÀy pð14ÞADVANCED MODELS FOR TRANSIENT ANALYSIS5 Copyright r2009John Wiley&Sons,Ltd.Int.J.Numer.Model.2010;23:1–19DOI:10.1002/jnmHence,boundary conditions need to be enforced at the two interfaces z ¼0;z ¼d ;they read:ÀE y ð0;s Þ¼À2E i y ðs ÞÀZ 0cos y iH x ð0;s Þð15a ÞÀE y ðd ;s Þ¼Z 0cos y i H x ðd ;s Þð15b Þfor the TE z polarization andE x ð0;s Þ¼2E i x ðs ÞÀZ 0cos y i H y ð0;s Þð16a ÞE x ðd ;s Þ¼Z 0cos y i H y ðd ;s Þð16b Þfor the TM z polarization.2.2.Incorporation of interface magnetic fields as sourcesMagnetic (or electric)fields at abscissa z 50and z 5d can be regarded as external sources and described in terms of distributed sourcesH ys ðz ;s Þ¼H y ð0;s Þd ðz ÞþH y ðd ;s Þd ðz Àd Þð17a ÞH xs ðz ;s Þ¼H x ð0;s Þd ðz ÞþH x ðd ;s Þd ðz Àd Þð17b Þwhere d ðz Þrepresents the Dirac delta function.The sources can be written in a vector form asH s ðz ;s Þ¼H 0ðs Þd ðz ÞþH d ðs Þd ðz Àd Þð18Þwhere H 0ðs Þ¼½H y ð0;s Þ;H x ð0;s Þ T and H d ðs Þ¼½H y ðd ;s Þ;H x ðd ;s Þ T .Following the same approach described in [11],the incorporation of such distributed source in Telegrapher’s equations (12)permits to obtain@2~E t ÀG ðs Þ~E t ¼ÀZ 0ðs ÞH s ðz ;s Þð19ÞFrom (10)it is seen that the TM z and TE z modes are coupled by both the wave vector components k x and k y ,which depend on the system of coordinates,and the anisotropy,described by the off-diagonal terms oftensors.Figure 3.Incident plane wave to the planar structure:(a)TE z polarization mode and (b)TM z polarization mode.G.ANTONINI6Copyright r 2009John Wiley &Sons,Ltd.Int.J.Numer.Model.2010;23:1–19DOI:10.1002/jnm3.DYADIC GREEN’S FUNCTION FOR A PLANAR ANISOTROPIC LAYER Equation(19)can be regarded as a vector Sturm–Liouville problem,which,in general,can be written as½Lþl rðzÞ yðzÞ¼fðzÞð20Þwhere0z d,L is the Sturm–Liouville operator,l is a z-independent matrix,r(z)is a diagonal z-dependent matrix and f(z)is the vector of distributed sources.The boundary conditions can be either of Dirichlet or Neumann or mixed type and,in general,we can writea1yðzÞþa2dd zyðzÞz¼0j¼0ð21aÞb1yðzÞþb2dd zyðzÞz¼dj¼0ð21bÞIn the specific case of oblique incidence of plane waves on anisotropic layers,it is easy to recognize that:L¼U d2d zð22aÞl¼ÀZ0ðsÞY0ðsÞð22bÞrðzÞ¼Uð22cÞfðzÞ¼ÀZ0ðsÞH sðz;sÞð22dÞwhere U represents the identity matrix.Furthermore,since the magneticfield at the interface is already modeled through the source vector(18),boundary conditions of the Neumann type can be adopted:d d z ~Et z¼0j¼dd z~Et z¼dj¼0ð23aÞSince both TE z and TM z modes can be excited separately,two vector Green’s functions,one for each mode,are ing a dyadic notation[15]yields:G jðz;z0Þ¼X2i¼1G ij z;z0ÀÁu i j¼1;2ð24ÞThe two Green’s functions G jðz;z0Þare the solution of the equations:A G jðz;z0Þ¼½Lþl rðzÞ G jðz;z0Þ¼dðz;z0Þu j j¼1;2ð25Þwhere dðz;z0Þis the one-dimensional Dirac delta function.The dyadic Green’s function G z;z0ðÞis given by:Gðz;z0Þ¼X2j¼1G jðz;z0Þu j¼X2j¼1X2i¼1G ijðz;z0Þu i u jð26ÞADVANCED MODELS FOR TRANSIENT ANALYSIS7 Copyright r2009John Wiley&Sons,Ltd.Int.J.Numer.Model.2010;23:1–19DOI:10.1002/jnmwhich,with a matrix notation,can be written as:G ðz ;z 0Þ¼G 11G 12G 21G 22"#ð27ÞSince the Sturm–Liouville problem (22),along with the boundary conditions (23)is self-adjoint[16],it is possible to expand the vector Green’s function in terms of a set of basis functionsf n ðz Þas:G j ðz ;z 0Þ¼X 1n ¼0a nj ðz 0Þf n ðz Þð28Þwhere a nj is the amplitude coefficient vector.Eigenfunctions f n ðx Þsatisfy the corresponding eigenvalue problem d 2d x þk 2n !f n ðx Þ¼0ð29Þwhere the eigenvalues are all positive k 2n ¼l n 40since the Sturm–Liouville problem is self-adjoint.Furthermore,the boundary conditions are of the Neumann type:d f n ðx Þz ¼0j ¼d f nðz Þz ¼d j ¼0ð30ÞEigenvalues k n and eigenfunctions f n ðz Þ;n ¼0;1;ÁÁÁ1can be easily found as [17]:k n ¼n p d n ¼0;1;ÁÁÁ;1ð31a Þf 0ðz Þ¼ffiffiffi1dr n ¼0ð31b Þf n ðz Þ¼ffiffiffi2d r cos n p dz n ¼1;ÁÁÁ;1ð31c Þwhere the magnitude of the eigenfunctions has been computed enforcing their orthonormality Z df m ðz Þf n ðz Þd z ¼d mn ð32ÞForcing the vector Green’s function G j ðz ;z 0Þto be the solution of (25)and using the orthonormality conditions of the eigenfunctions (32),the coefficient vector a nj z 0ðÞis obtained a nj z 0ÀÁ¼l Àl n ðÞÀ1f n ðz 0Þu j j ¼1;2ð33ÞApplying the right dyadic product [15]to (33),multiplying it by u j ,and taking the sum over index j ,yields:X2j ¼1a mj z 0ÀÁu j ¼a n ðz 0Þ¼l Àl n ðÞÀ1f n ðz 0ÞX 2j ¼1u j u j¼l Àl n ðÞÀ1U f n ðz 0Þ¼l Àl n ðÞÀ1f n ðz 0ÞHence,the dyadic Green’s function (27)can be written as:G z ;z 0ÀÁ¼X 1n ¼0a n ðz 0Þf n ðz Þ¼X 1n ¼0l Àl n ðÞÀ1f n ðz 0Þf n ðz ÞG.ANTONINI8Copyright r 2009John Wiley &Sons,Ltd.Int.J.Numer.Model.2010;23:1–19DOI:10.1002/jnm3.1.Rational macromodel of the Z impedanceThe knowledge of the dyadic Green’s function G z ;z 0ðÞin the rational form (34)pawns the way to the development of a rational macromodel of the layer.In fact,the electric field vector ~E t ¼ðE x ;ÀE y Þcan be computed as:~E t ðz ;s Þ¼Z d 0G ðz ;z 0Þf ðz 0Þd z 0ð34ÞEvaluating ~E t ðz ;s Þin correspondence to the interfaces z 50and z 5d yields ~E t ð0;s Þ~Et ðd ;s Þ2435¼Z 11Z 12Z 21Z 222435ÁH ð0;s ÞH ðd ;s Þ2435ð35Þwhere the impedance matrix Z (s )entries are:Z 11¼Z 22¼X 1n ¼0G 2ðs Þþn p d 2U !À1ÁA 2n Z 0ðs Þð36a ÞZ 21¼Z 12¼X 1n ¼0G 2ðs Þþn p d 2U !À1ÁA 2n Z 0ðs ÞÀ1ðÞn ð36b ÞIf dispersive media are considered,we assume that the physical properties of the layer are known as tabulated data,at discrete frequencies.A rational model of the per-unit-length impedance Z 0(s )and admittance Y 0(s )can be obtained by using the vector fitting algorithm [10]:Z 0ðs Þ¼s ~lþX P Z q ¼1R Z s Àp q ;Z ¼B p ðs ÞA p ðs Þ¼b 1s P Z þ1þb 2s P Z s þÁÁÁþb P Z s þb P Z þ11Z 2Z P Z À1P Zð37a ÞE x (0,s -E y (0,s )E x (d ,s )-E y (d,s )Figure 4.Planar layer macromodel.ADVANCED MODELS FOR TRANSIENT ANALYSIS 9Copyright r 2009John Wiley &Sons,Ltd.Int.J.Numer.Model.2010;23:1–19DOI:10.1002/jnmY 0s ðÞ¼~sþs ~e þX P Y q ¼1R Y s Àp q ;Y ¼D p ðs ÞC p ðs Þ¼d 1s P Y þ1þd 2s P Y s þÁÁÁþd P Y s þd P Y þ1c 1s Y þc 2s Y þÁÁÁþc P Y À1s þc P Yð37b Þ02468x 1013Real(poles)Order 20 model Reduced order model 00.51 1.5024681012141618x 1013x 1011Frequency [GHz]I m a g (p o l e s )M a g n i t u d e o f r e s i d u e s Order 20 model Reduced order modelx 104Figure 5.Location of poles in the complex plane (top)and magnitude spectrum of residues of impedance Z 14(bottom)(Section 4.1).The circle refer to the poles of the order 20model,the stars refers to the polesselected as dominant.G.ANTONINI10Copyright r 2009John Wiley &Sons,Ltd.Int.J.Numer.Model.2010;23:1–19DOI:10.1002/jnmwhere P z and P Y represent the number of poles used in the rational approximation,B p (s )and D p (s )are polynomial matrices and A p (s )and C p (s )can be made strictly Hurwitz polynomials by enforcing their zeros to be on the left complex plane,when using the vector fitting algorithm.Impedance matrix Z(s )can be recast as Z ðs Þ¼X 1n ¼0B p ðs ÞA p ðs ÞD p ðs ÞC p ðs Þþn p d 2U !À1ÁA 2n B p ðs ÞA p ðs Þ1À1ðÞn À1ðÞn 12435¼X1n ¼0B p ðs ÞD p ðs ÞþA p ðs ÞC p ðs Þn p d 2U !À1ÁA 2n B p ðs ÞC p ðs Þ1À1ðÞn À1ðÞn 12435¼X1n ¼0E p s ðÞÀ1A 2n B p ðs ÞC p ðs Þ1À1ðÞn À1ðÞn 12435ð38Þwhere E p ðs Þ¼B p ðs ÞD p ðs ÞþA p ðs ÞC p ðs Þn p d ÀÁ2U .The entries of impedance matrix Z (s )are strictlyproper rational functions and share the same poles,which can be evaluated as the zeros of the characteristic polynomial Q n (s):Q n ðs Þ¼det B p ðs ÞD p ðs ÞþA p ðs ÞC p ðs Þn p d2U !¼0ð39Þfor n ¼0;...;1.Each mode n generates a number of poles depending on the order of the rational approximations (37a)and (37b):~n poles ;n ¼order conv ðB p ;D p ÞÂÃÁ2¼P Z þP Y þ2ðÞÁ2ð40Þ05101520100Frequency [GHz]|G 14|Figure 6.Magnitude spectrum of the Green’s function G 14(Section 4.1).The solid line refers to the result obtained considering all the poles (GF),the dashed line refers to the reduced order model (GF-mor).Copyright r 2009John Wiley &Sons,Ltd.Int.J.Numer.Model.2010;23:1–19DOI:10.1002/jnmwhere conv denotes the product of polynomials in argument and order is the order of the polynomial in argument.The corresponding residues can be computed,using standard techniques [18],asR k ¼adj E ðs ÞðÞA 2n B p ðs ÞC p ðs Þs ¼p n ðk ÞQ n 1Q poles l ¼1ð77Þl ¼k p n ðk ÞÀp n ðl Þ½Á1À1ðÞn À1ðÞn 1"#ð41Þ202530354045500.20.40.60.81Time [ns]E i [V /m ]Figure 8.Incident electric field (Section 4.1).05101520101.895101.896Frequency [GHz]|Z 14| []Figure 7.Magnitude spectrum of impedance Z 14(Section 4.1).The solid line corresponds to the result obtained with use of the plane waves theory (PWT),the dashed line refers to the results obtained by using the proposed methodology (GF),the dashdot line refers to the proposed methodology considering only thedominant poles (GF-mor).Copyright r 2009John Wiley &Sons,Ltd.Int.J.Numer.Model.2010;23:1–19DOI:10.1002/jnmfor k ¼0;...;n poles ,where adj ðÁÞrepresents the adjoint operator of the matrix in argument,p n (k )is the k -th pole generated by the n -th mode and Q n 1denotes the coefficient of the highest power in s in polynomial matrix E p (s ).Once poles and residues of the rational representation of matrix Z(s )are obtained,a pole pruning can be performed and the n d poles dominant poles identified,following the criteria illustrated in [8].The impedance matrix Z(s )can be re-written in a pole/residue form asZ ðs Þ¼Xn d polesk ¼1R k s Àp k ð42Þ0.020.040.060.08Time [ns]E [V /m ]0.020.04Time [ns]E [V /m ]Figure 9.Transmitted electric field for the TE z (top)and TM z (bottom)polarizations (Section 4.1).The solid line corresponds to the result obtained with use of the PWT via IFFT,the dashdot line refers to theresults obtained using the proposed methodology in the time domain (GF-TD).Copyright r 2009John Wiley &Sons,Ltd.Int.J.Numer.Model.2010;23:1–19DOI:10.1002/jnmwhich is suited for both circuit synthesis [19]and state-space realization [20,21].The equivalent circuit can be analyzed by means of SPICE-like solvers [22];the state-space equations can be written as_x ðt Þ¼Ax ðt ÞþBH ðt Þð43a Þ~Et ðt Þ¼Cx ðt ÞþDH ðt Þð43b Þwhere A 2<n d poles Ân d poles ,B 2<n d poles Â4,C 2<4Ân d poles ,D 2<4Â4,n d poles being the number of theselected dominant poles (Figure 4).4.NUMERICAL RESULTS4.1.Anisotropic lossy layer-TE polarizationIn the first example,a TE z polarized plane wave is assumed impinging with incidence angle y i ¼p =3on a planar composite layer exhibiting anisotropy due to the presence of conducting fibers (see Figure 2).The planar layer is 0.5mils thick and characterized by electrical conductivity s x 54Â104S/m and s y 5s z 550S/m and permittivity e x ¼e y ¼e z ¼5e 0,in the local system of coordinates.The orientation of fibers,with respect to the global system of coordinates,is defined by f ¼p =4.The magnetic permeability is assumed equal to that of vacuum.A rational model of order 21has been generated;the computation has been carried out on a AMD Athlon 2GHz processor,equipped with 1.5Gb RAM and took 2.5s,leading to 84poles among which only 29have been selected as dominant.Figure 5(top)shows the location of poles in the complex plane.The selection of the dominant poles has been accomplished on the base of their resonance frequency and the magnitude of the corresponding residues,as shown in Figure 5(bottom).0246810103104105106Frequency [GHz]|Z 13| []PWTGFFigure 10.Magnitude spectrum of impedance Z 13(Section 4.2).The solid line corresponds to the result obtained with use of the PWT,the dashed line refers to the results obtained by using the proposedmethodology (GF).Copyright r 2009John Wiley &Sons,Ltd.Int.J.Numer.Model.2010;23:1–19DOI:10.1002/jnmFigure 6shows the comparison of the magnitude spectrum of the Green’s function G 14as evaluated considering all the poles and only the dominant ones.Figure 7shows a sample of the magnitude spectrum of impedance Z 14as evaluated by the plane wave theory (PWT)and the proposed Green’s function-based methodology.A satisfactory agreement is obtained over the entire frequency bandwidth of interest.The layer is excited by a TE z polarized plane wave whose time behavior is shown in Figure 8.Due to the anisotropy,transmitted electric field is characterized by both TE z and TM z modes,shown in Figure 9.The results have been computed by using the PWT via IFFT4550550.10.20.30.40.5Time [ns]E [V /m]45505512345Time [ns]E [V /m]Figure 11.Transmitted electric field for the TM z (top)and TE z (bottom)polarizations (Section 4.2).The solid line corresponds to the result obtained with use of the PWT via IFFT,the dashdot line refers to theresults obtained using the proposed methodology in the time domain (GF-TD).Copyright r 2009John Wiley &Sons,Ltd.Int.J.Numer.Model.2010;23:1–19DOI:10.1002/jnm。