11-A COMBINED EXPERIMENTAL AND NUMERICAL APPROACH FOR DESIGN AND OPTIMIZATION OF

收稿日期:1999211219基金项目:国家自然科学基金(59604001)和教育部博士点基金(96014513)资助项目作者简介:杨成祥(1973-),男,安徽芜湖人,东北大学博士研究生;冯夏庭(1964-),男,安徽潜山人,东北大学教授,博士生导师;王泳嘉(1933-),男,上海人,东北大学教授,博士生导师・2000年10月第21卷第5期东北大学学报(自然科学版)Journal of Northeastern University (Natural Science )Oct.2000Vol 121,No.5文章编号:100523026(2000)0520566203材料本构模型的唯一性杨成祥,冯夏庭,王泳嘉(东北大学资源与土木工程学院,辽宁沈阳　110006)摘 要:利用作者最新提出的材料本构模型智能识别的进化学习算法,结合实例分析,从一个新的角度对该问题进行了阐述,证明了刻意追求学习效果的不合理性・指出根据实验数据建立材料本构模型的正确方法应该是使获得的本构模型不仅对学习样本而且对类似条件下的应力分析都能获得很好的效果・并说明了进化学习算法是解决问题的一个好方法,为材料本构模型的研究提供了一个新的有力工具・关　键　词:本构模型;唯一性;进化学习算法中图分类号:TB 124 文献标识码:A采用有限单元法对岩土工程结构进行数值分析时,关键问题就是选择恰当的地质材料本构模型[1]・因此,建立合理的岩土材料本构模型是岩石力学研究的一个重要方面・按传统数学建模方法,建立材料本构模型的基本途径是通过对实测数据的学习分析,在一定的条件下确定出一个数学表达式及一些必要的参数,从而获得材料的本构模型・然而对于复杂的工程材料,如地质材料、复合材料等,受客观上不可避免的数据有限问题的约束,通过不同的分析手段对同样一组数据的学习结果可以有许多个・这就提出了一个本构模型选择的唯一性问题・由于缺乏严整的理论判据,容易形成过于强调学习效果的选择方案,往往造成结果的不合理・本文利用作者最新提出的材料本构模型智能识别的进化学习算法,结合实例分析,从一个新的角度对该问题进行阐述,探索解决问题的新途径・1　进化学习算法原理进化学习算法是本文作者最新提出的一种全新的建模方法,它吸收了多学科交叉,多种算法工具和处理技术相集合的先进思想,借鉴了遗传算法的快速全局寻优的特点[2],结合目前存在的一些先进的应力分析手段(如有限单元法),可以直接从实验室或现场较容易获得的少量宏观数据中学到复杂的非线性应力应变关系・其基本原理是,对于复杂的非线性材料,在简单模型(如线弹性材料本构模型)的基础上根据材料在实验中反映出来的一些宏观特性及影响材料应力应变关系的一些重要因素添加一些任意结构的非线性项,可以充分考虑应力分量之间的非线性耦合对材料的非线性行为的影响,然后利用遗传算法的参数搜索和结构优化功能,与应力分析方法相协作,确定这些添加项的结构和所需的参数,从而最终确定材料的非线性本构模型・该方法克服了传统数学建模方法存在的局限性,在对复杂的非线性材料的建模中显现出较高的性能和较强的生命力・2　实例分析211　原始数据复合材料不仅具有细观的非均质性和宏观的各向异性,还具有明显的物理非线性・由正交各向异性单层板层叠成的复合材料层合板在低应力水平时就表现出明显的非线性[3],是一类典型的非线性材料・本文就以这类材料为例・原始数据来源于美国斯坦福大学Lessard 和Chang 所做的实验[4]・实验如图1所示・实测的是层合板的面内荷载2位移数据・本次计算从中选择了两组实验数据:将对[(±45)6]S 板的实验数据作为学习样本,用于建立复合材料单层板的非线性本构模型;[(±30)6]S 板的实验结果用作检验所建立的本构模型的合理性・图1　试验示意图(Le ssard 和Chang )212　算法实施考虑横向和剪切非线性[5,6],按进化学习算法思想,复合材料单层板的非线性本构关系可以表达如下Δσ1Δσ2Δσ6=S 11S 120S 12S 22+f ij (σt -1,i )S 66+f ij (σt -1,i )-1Δε1Δε2Δε6其中f ij (σt -1,i )=6nk =0a ijk σkt -1,i(i =j =2,6;k =0,1,…,n )为非线性添加项,这里是一个与应力状态有关的多项式,n 为多项式的最高阶次,n ≥1;σt -1,i 表示前一计算步的应力状态,a ijk 为参数,也就是要优化的参变量・一旦对复合材料单层板的非线性本构关系进行了正确的学习,它就可根据同一个叠加原理(如经典层合理论[3])对按不同方式(铺层的角度与顺序)叠合成的复合材料层合板进行应力分析・图2给出了n 分别取为1到5时的学习和预测结果・图中ΔE 为变形・作为对照,图中还给出了Lessard 和Chang 的试验结果・从图中可以看出,随n 的增大,学习效果逐步改善,n =5时的学习效果最好,但他们的预测能力不同,只有n =2时的模型的预测效果最好・这说明预测效果并不是随着学习效果的改善而改善,不能完全根据学习情况来确定最终的本构模型;进化学习算法能够从众多的可能方案中通过模型进化找出最佳的本构模型,为问题的解决提供了一个新方法・为更清楚地说明问题,图3给出了平均意义上的学习误差和预测误差随n 的变化情况,其中平均误差由各测点的计算值与实测值间的差值的平方平均根计算得到・可以看出,学习误差随n 增大而逐步减小,而预测误差变化却无规律可循,比如,这几种计算结果中,n =1时的学习效果最差,它的预测误差却只比n =2和n =3时的结果差,而比n =4和n =5时的预测结果都好・这进一步说明学习结果与预测结果不存在明显的对应关系,好的学习效果只是合理的材料本构模型所必须具备的条件,而不能表示此时的结果就是合理的・为了反映各个测点计算值和实测值间误差随n 变化的情况,对学习和预测结果的计算值和实测值图2　对复合材料层合板的算法执行结果(a )—学习预测结果;(b )—推广预测结果・○—试验结果;n =1;┈┈n =2;n =3; n =4; n =5・765第5期 杨成祥等:材料本构模型的唯一性进行线性回归,则回归直线的斜率越接近于1,说明计算值与实测值吻合得越好・表1列出了所得到的回归直线斜率s ・由表中结果可以看出,5种情况都具有满意的学习效果,但它们的预测效果却相差很大・图3　平均学习误差和预测误差随n 的变化○—学习误差;●—预测误差・表1　每次拟合和计算中计算值与实测值的回归直线斜率sn12345对学习样本的预测1.00540.92940.9674 1.0053 1.0052对非学习样本的预测1.78710.968 1.7721 1.96422.06093　结 论(1)在通过对实测数据的学习分析建立材料的本构模型时,并不是学习效果越好,预测效果就越好,学习效果好的结果其预测效果反而可能更差・片面强调学习结果是不合理的・(2)学习结果与预测结果之间不存在明显的对应关系,相近的学习效果,其预测效果却可以千差万别・学习效果只能作为判别材料本构模型合理与否的一条依据,在确定结果时不能过多依赖于学习效果・因此,根据实验数据建立材料本构模型的正确方法应该是使获得的本构模型不仅对学习样本而且对类似条件下的应力分析都能获得很好的效果・(3)进化学习算法能够从众多的可能结果中找出最佳的,为本构模型唯一性问题的解决提供了一个新方法,是岩石材料本构模型研究的一个新的有力工具・参考文献:[1]章根德,朱维耀・岩土介质横观各向同性的模拟[J ]・力学进展,1998,28(4):499-508・(Zhang G D ,Zhu W Y.Simulation of transverse isotropy of rcok and soil [J ].Mechanics Advances ,1998,28(4):499-508.)[2]刘勇,康立山,陈毓屏・非数值并行算法(第二册)—遗传算法[M ]・北京:科学出版社,1997.1-137・(Liu Y ,Kang L S ,Chen Y P.G enetic algorithm of non 2numerical value concurrent.Vol 2[M ].Beijing :Science Press ,1997.1-137.)[3]沈观林・复合材料力学[M ]・北京:清华大学出版社,1995.1-184・(Shen G posite material mechanics [M ].Beijing :Tsinghua University Press ,1995.1-184.)[4]Lessard L ,Chang F 2K.Damage tolerance of laminated composites containing an open hole and subjected to compressive loadings :part Ⅱ2experiment [J ].J Composite Mater ,1991,25:44-64.[5]Hahn H T ,Tsai S W.Nonlinear elastic behavior ofunidirectional composite lamina [J ].J Composite Mater ,1973,7:102-108.[6]陈浩然・复合材料非线性效应对层合板承载能力的影响[J ]・大连工学院学报,1987,26(1):15-20・(Chen H R.Nonlinear effect of composite material on the load tolerance of lamina[J ].Journal of Dalian Institute of T echnology ,1987,26(1):15-20.)Uniqueness of Material Constitutive ModelYA N G Cheng 2xiang ,FEN G Xia 2ting ,W A N G Yong 2jia(School of Resources and Civil Engineering ,Northeastern University ,Shenyang 110006,China )Abstract :The material constitutive model is usually obtained by fitting analysis on experimental data.G enerally ,there areseveral fitting results ,thus ,the uniqueness problem occurred.It brings difficulties in selecting the result ,and it often led to the misunderstanding that the more accurate the fitting result is ,the better the obtained model will ing the evolving learning algorithm (ELA ),proposed by the author recently ,which can be used to perform the intellective identification of material constitutive model ,the paper stated the uniqueness from a different point.The result shows that there is no direct mapping relationship between fitted result and predicted result ,and it is unreasonable to pursue the fitting result excessively.Pointed out that the correct model obtained form experimental data should works well in the numeric simulation on both the ex periment sample and other similar problem.It is showed that the ELA can find the global best answer ,it is a good method to solve the uniqueness problem ,and provides a new theory for the study of constitutive model.K ey w ords :constitutive model ;uniqueness ;evolving learning algorithm(Received November 19,1999)865东北大学学报(自然科学版) 第21卷。

Package‘minimaxApprox’October13,2023Type PackageTitle Implementation of Remez Algorithm for Polynomial and RationalFunction ApproximationVersion0.2.2Date2023-10-12Description Implements the algorithm of Remez(1962)for polynomial minimaxapproximation and of Cody et al.(1968)<doi:10.1007/BF02162506>forrational minimax approximation.License MPL-2.0URL https:///aadler/MiniMaxApproxBugReports https:///aadler/MiniMaxApprox/issuesImports stats,graphicsSuggests tinytest,covrByteCompile yesNeedsCompilation yesEncoding UTF-8UseLTO yesAuthor Avraham Adler[aut,cre,cph](<https:///0000-0002-3039-0703>) Maintainer Avraham Adler<***********************>Repository CRANDate/Publication2023-10-1321:10:02UTCR topics documented:minimaxApprox-package (2)coef.minimaxApprox (3)minimaxApprox (4)minimaxErr (7)minimaxEval (8)plot.minimaxApprox (9)print.minimaxApprox (10)12minimaxApprox-packageIndex11minimaxApprox-package Implementation of Remez Algorithm for Polynomial and RationalFunction ApproximationDescriptionImplements the algorithm of Remez(1962)for polynomial minimax approximation and of Cody etal.(1968)<doi:10.1007/BF02162506>for rational minimax approximation.DetailsThe DESCRIPTIONfile:Package:minimaxApproxType:PackageTitle:Implementation of Remez Algorithm for Polynomial and Rational Function ApproximationVersion:0.2.2Date:2023-10-12Authors@R:person(given="Avraham",family="Adler",role=c("aut","cre","cph"),email="********************* Description:Implements the algorithm of Remez(1962)for polynomial minimax approximation and of Cody et al.(1 License:MPL-2.0URL:https:///aadler/MiniMaxApproxBugReports:https:///aadler/MiniMaxApprox/issuesImports:stats,graphicsSuggests:tinytest,covrByteCompile:yesNeedsCompilation:yesEncoding:UTF-8UseLTO:yesAuthor:Avraham Adler[aut,cre,cph](<https:///0000-0002-3039-0703>)Maintainer:Avraham Adler<***********************>Archs:x64Index of help topics:coef.minimaxApprox Extract coefficients from a "minimaxApprox"objectminimaxApprox Minimax Approximation of FunctionsminimaxApprox-package Implementation of Remez Algorithm forPolynomial and Rational Function ApproximationminimaxErr Evaluate the Minimax Approximation ErrorminimaxEval Evaluate Minimax Approximationplot.minimaxApprox Plot errors from a "minimaxApprox" objectprint.minimaxApprox Print method for a "minimaxApprox object"coef.minimaxApprox3Author(s)Avraham Adler[aut,cre,cph](<https:///0000-0002-3039-0703>)Maintainer:Avraham Adler<***********************>coef.minimaxApprox Extract coefficients from a"minimaxApprox"objectDescriptionExtracts the numerator and denominator vectors from a"minimaxApprox"object.Usage##S3method for class minimaxApproxcoef(object,...)Argumentsobject An object inheriting from class"minimaxApprox"....Other arguments.ValueCoefficients extracted from the"minimaxApprox"object.A list containing:a The polynomial coefficients or the rational numerator coefficients.b The rational denominator coefficients.Missing for polynomial approximation. Author(s)Avraham Adler<***********************>See AlsominimaxApproxExamplesPP<-minimaxApprox(exp,0,1,5)coef(PP)identical(unlist(coef(PP),s=FALSE),PP$a)RR<-minimaxApprox(exp,0,1,c(2,3))coef(RR)identical(coef(RR),list(a=RR$a,b=RR$b))minimaxApprox Minimax Approximation of FunctionsDescriptionCalculates minimax approximations to functions.Polynomial approximation uses the Remez (1962)algorithm.Rational approximation uses the Cody-Fraser-Hart (Cody et al.,1968)version of the al-gorithm.Polynomial evaluation uses the Compensated Horner Scheme of Langlois et al.(2006).UsageminimaxApprox(fn,lower,upper,degree,relErr =FALSE,xi =NULL,opts =list())Argumentsfnfunction;A vectorized univariate function having x as its first argument.This could be a built-in R function,a predefined function,or an anonymous function defined in the call;see Examples .lower numeric;The lower bound of the approximation interval.upper numeric;The upper bound of the approximation interval.degreeinteger;Either a single value representing the requested degree for polynomial approximation or a vector of length 2representing the requested degrees of the numerator and denominator for rational approximation.relErr logical;If TRUE ,calculate the minimax approximation using relative error.The default is FALSE which uses absolute error.xinumeric;For rational approximation,a vector of initial points of the correct length— (degree )+2.If missing,the approximation will use the appropriate Chebyshev nodes.Polynomial approximation always uses Chebyshev nodes and will ignore xi with a message.optslist ;Configuration options including:•maxiter :integer;The maximum number of iterations to attempt conver-gence.Defaults to 100.•miniter :integer;The minimum number of iterations before allowing con-vergence.Defaults to 10.•conviter :integer;The number of successive iterations with the same re-sults allowed before assuming no further convergence is possible.Defaults to 10.Will overwrite maxiter if conviter is explicitly passed and is larger than maxiter .•showProgress :logical;If TRUE will print error values at each iteration.•convRatio :numeric;The convergence ratio tolerance.Defaults to 1+1×10−9.See Details .•tol :numeric;The absolute difference tolerance.Defaults to 1×10−14.See Details .•tailtol :numeric;The tolerance of the coefficient of the largest power of x to be ignored when performing the polynomial approximation a secondtime.Defaults to the smaller of 1×10−10or upper −lower106.Set to NULL to skip the degree +1check completely.See Details .•ztol :numeric;The tolerance for each polynomial or rational numerator or denominator coefficient’s contribution to not to be set to 0.Similar to polynomial tailtol but applied at each step of the algorithm.Defaults to NULL which leaves all coefficients as they are regardless of magnitude.DetailsConvergence:The function implements the Remez algorithm using linear approximation,chiefly as described by Cody et al.(1968).Convergence is considered achieved when all three of the fol-lowing criteria are met:1.The observed error magnitudes are within tolerance of the expected error—the Distance Test .2.The observed error magnitudes are within tolerance of each other—the Magnitude Test .3.The observed error signs oscillate—the Oscillation Test .“Within tolerance”can be met in one of two ways:1.The difference between the absolute magnitudes is less than or equal to tol .2.The ratio between the absolute magnitudes of the larger and smaller is less than or equal to convRatio .For efficiency,the Distance Test is taken between the absolute value of the largest observed error and the absolute value of the expected error.Similarly,the Magnitude Test is taken between the absolute value of the largest observed error and the absolute value of the smallest observed error.Both tests can be passed by either being within tol or convRatio as described above.Polynomial Evaluation:The polynomials are evaluated using the Compensated Horner Scheme of Langlois et al.(2006)to enhance both stability and precision.Polynomial Algorithm “Singular Error”Response:When too high of a degree is requested for the tolerance of the algorithm,it often fails with a singular matrix error.In this case,for the polynomial version,the algorithm will try looking for an approximation of degree n +1.If it finds one,and the contribution of that coefficient to the approximation is ≤tailtol ,it will ignore that coefficient and return the resulting degree n polynomial,as the largest coefficient is effectively 0.The contribution is measured by multiplying that coefficient by the endpoint with the larger absolute magnitude raised to the n +1power.This is done to prevent errors in cases where a very small coefficient is found on a range with very large absolute values and the resulting contribution to the approximation is not de minimis .Setting tailtol to NULL will skip the n +1test completely.Close-to-Zero Tolerance:For each step of the algorithms’iterations,the contribution of the found coefficient to the total sum (as measured in the above section)is compared to the ztol option.When less than or equal to ztol ,that coefficient is set to 0.Setting ztol to NULL skips the test completely.For intervals near or containing zero,setting this option to anything other than NULL may result in either non-convergence or poorer results.ValueminimaxApprox returns an object of class"minimaxApprox"which inherits from the class list.The generic accessor function coef will extract the numerator and denominator vectors.There are also default print and plot methods.An object of class"minimaxApprox"is a list containing the following components:a The polynomial coefficients or the rational numerator coefficients.b The rational denominator coefficients.Missing for polynomial approximation.EE The absolute value of the expected error as calculated by the Remez algorithms.OE The absolute value of largest observed error between the function and the ap-proximation at the extremal basis points.iterations The number of iterations of the algorithm.This does not include any iterations required to converge the error value in rational approximation.x The basis points at which the minimax error was achieved.Warning A logicalflag indicating if any warnings were thrown.NoteAt present,the algorithms are implemented using machine double precision,which means that the approximations are at best slightly worse.Research proceeds on more precise,stable,and efficient implementations.So long as the package remains in an experimental state—noted by a0major version—the API may change at any time.Author(s)Avraham Adler<***********************>ReferencesRemez,E.I.(1962)General computational methods of Chebyshev approximation:The problems with linear real Atomic Energy Commission,Division of Technical Information.AEC-tr-4491Fraser W.and Hart J.F.(1962)“On the computation of rational approximations to continuous functions”,Communications of the ACM,5(7),401–403,doi:10.1145/368273.368578Cody,W.J.and Fraser W.and Hart J.F.(1968)“Rational Chebyshev approximation using linear equations”,Numerische Mathematik,12,242–251,doi:10.1007/BF02162506Langlois,P.and Graillat,S.and Louvet,N.(2006)“Compensated Horner Scheme”,in Algebraic and Numerical Algorithms and Computer-assisted Proofs.Dagstuhl Seminar Proceedings,5391, doi:10.4230/DagSemProc.05391.3See AlsominimaxEval,minimaxErrminimaxErr7ExamplesminimaxApprox(exp,0,1,5)#Built-in&polynomialfn<-function(x)sin(x)^2+cosh(x)#Pre-definedminimaxApprox(fn,0,1,c(2,3))#RationalminimaxApprox(function(x)x^3/sin(x),0.7,1.6,6L)#Anonymousfn<-function(x)besselJ(x,nu=0)#More than one inputb0<-0.893576966279167522#Zero of besselYminimaxApprox(fn,0,b0,c(3L,3L))#Cf.DLMF3.11.19 minimaxErr Evaluate the Minimax Approximation ErrorDescriptionEvaluates the difference between the function and the minimax approximation at x.UsageminimaxErr(x,mmA)Argumentsx a numeric vectormmA a"minimaxApprox"return objectDetailsThis is a convenience function to evaluate the approximation error at x.ValueA vector of the same length as x containing the approximation error values.Author(s)Avraham Adler<***********************>See AlsominimaxApprox,minimaxEval8minimaxEval Examples#Show resultsx<-seq(0,0.5,length.out=11L)mmA<-minimaxApprox(exp,0,0.5,5L)err<-minimaxEval(x,mmA)-exp(x)all.equal(err,minimaxErr(x,mmA))#Plot resultsx<-seq(0,0.5,length.out=1001L)plot(x,minimaxErr(x,mmA),type="l")minimaxEval Evaluate Minimax ApproximationDescriptionEvaluates the rational or polynomial approximation stored in mmA at x.UsageminimaxEval(x,mmA)Argumentsx a numeric vectormmA a"minimaxApprox"return objectDetailsThis is a convenience function to evaluate the approximation at x.ValueA vector of the same length as x containing the approximated values.Author(s)Avraham Adler<***********************>See AlsominimaxApprox,minimaxErrExamples#Show resultsx<-seq(0,0.5,length.out=11L)mmA<-minimaxApprox(exp,0,0.5,5L)apErr<-abs(exp(x)-minimaxEval(x,mmA))all.equal(max(apErr),mmA$EE)#Plot resultscurve(exp,0.0,0.5)curve(minimaxEval(x,mmA),0.0,0.5,add=TRUE,col="red",lty=2L)plot.minimaxApprox Plot errors from a"minimaxApprox"objectDescriptionProduces a plot of the error of the"minimaxApprox"object,highlighting the basis points and the error bounds.Usage##S3method for class minimaxApproxplot(x,y,...)Argumentsx An object inheriting from class"minimaxApprox".y Ignored.In call as required by R in Writing R Extensions:chapter7....Further arguments to plot.Specifically to pass ylim to allow for zooming in or out.ValueNo return value;called for side effects.Author(s)Avraham Adler<***********************>See AlsominimaxApproxExamplesPP<-minimaxApprox(exp,0,1,5)plot(PP)print.minimaxApprox Print method for a"minimaxApprox object"DescriptionProvides a more human-readable output of a"minimaxApprox"object.Usage##S3method for class minimaxApproxprint(x,digits=6L,...)Argumentsx An object inheriting from class"minimaxApprox".digits integer;Number of digits to which to round the ratio....Further arguments to print.DetailsTo print the raw"minimaxApprox"object use print.default.ValueNo return value;called for side effects.Author(s)Avraham Adler<***********************>See AlsominimaxApproxExamplesPP<-minimaxApprox(exp,0,1,5)PPprint(PP,digits=2L)print.default(PP)Index∗NumericalMathematicscoef.minimaxApprox,3minimaxApprox,4minimaxErr,7minimaxEval,8plot.minimaxApprox,9print.minimaxApprox,10∗hplotplot.minimaxApprox,9∗methodscoef.minimaxApprox,3plot.minimaxApprox,9print.minimaxApprox,10∗optimizeminimaxApprox,4∗packageminimaxApprox-package,2∗printprint.minimaxApprox,10class,3,6,9,10coef.minimaxApprox,3list,3,4,6minimaxApprox,3,4,7–10minimaxApprox-package,2minimaxErr,6,7,8minimaxEval,6,7,8plot.minimaxApprox,9print.minimaxApprox,1011。

目　录2012年北京邮电大学211翻译硕士英语考研真题及详解2013年北京邮电大学211翻译硕士英语考研真题及详解2015年北京邮电大学211翻译硕士英语考研真题及详解2016年北京邮电大学211翻译硕士英语考研真题及详解2012年北京邮电大学211翻译硕士英语考研真题及详解Part 1 Multiple Choice(20 points)Directions: Thereare20 blanks in the following passage. For each blank there are four choice marked A, B, C. and D. Y ou should choose the ONE that best fits into the passage. Then mark the corresponding letter on the Answer Sheet with a single line through the center.From childhood to old age, we all use language as a means of broadening our knowledge of ourselves and the world about us. When humans first 1　,they were like newborn children, unable to use this 2 tool. Y et once language developed, the possibilities for humankind’s future 3 and cultural growth increased.Many linguists believe that evolution is 4 for our ability to produce and use language. They 5 that our highly evolved brain provides us 6 animate language ability not found in lower 7　. Proponents of this innateness theory say that our 8 for language is inborn, but that language itself develops gradually 9 a function of the growth of the brain during childhood. Therefore there are critical 10 times for language development.Current 11 of innateness theory are mixed, however, evidence supporting the existence of some innate abilities is undeniable. 12　, more and more schools are discovering that foreign languages are best taught in 13　grades. Y oung children often can learn several languages by being 14 to them, while adults have a much harder time learning another language once the 15 of their first language have firmly fixed.　16　some aspects of language are undeniably innate, language does not develop automatically in a vacuum. Children who have been 17 from other human beings do not possess language. This demonstrates that 18 with other human beings is necessary for proper language development. Some linguists believe that this is even more basic to human language　19　than any innate capacities. These theorists view language as imitative, learned behavior. 20　,children learn language from their parents by imitating them. Parents gradually shape their child’s language skills by positively reinforcing precise imitations and negatively reinforcing imprecise ones.1．A. generatedB. evolvedC. bornD. originated2．A. valuableB. appropriateC. convenientD. favorite 3．A. attainmentsB. feasibilityC. entertainmentsD. evolution 4．A. essentialB. availableC. reliableD. responsible 5．A. confirmB. informC. claimD. convince 6．A. forB. fromC. ofD. with7．A. organizationsB. organismsC. humansD. children 8．A. potentialB. performanceC. preferenceD. passion 9．A. asB. just asC. likeD. unlike 10．A. ideologicalB. biologicalC. socialD. psychological 11．A. reviewsB. referenceC. reaction　D. recommendation 12．A. In a wordB. In a senseC. IndeedD. In other words 13．A. variousB. differentC. the higherD. the lower 14．A. revealedB. exposed　C. engaged　15．A. regulationsB. formationsC. rulesD. constitutions 16．A. AlthoughB. WhetherC. SinceD. When17．A. distinguishedB. differentC. protectedD. isolated 18．A. expositionB. comparisonC. contrastD. interaction 19．A. acquisitionB. appreciationC. requirementD. alternative 20．A. As a resultB. After allC. In other words【答案与解析】1．B 此为动词词义辨析题。

Development of PLC-based Tension Control SystemAbstractFiber winding tension is an important factor in the molding techniques of composite material which influences the quality of winding product directly, and the tension control is a key technique in fiber winding techniques. This paper introduces a closed—loop tension control system with the programmable logic controller (PLC）with function modules as its control kernel, the alternating current (AC) servo motor as execute element and the radius-following device to accomplish the real-time radius compensation. The mechanism of the tension control system is analyzed and the numerical model is set up。

The compensation technique of the radius of the scroll is analyzed。

Experimental results show that the system is well qualified with high control precision and high reaction speed.The components of composite material fiber winding possess such advantages as low weight，high strength, and high corrosion resistance，and they are widely applied in aviation and aerospace industry。

高中英语科技论文翻译单选题40题答案解析版1.The term “artificial intelligence” is often abbreviated as _____.A.AIB.IAC.AIID.IIA答案：A。

“artificial intelligence”的常见缩写是“AI”。

B 选项“IA”并非此词组的缩写。

C 和D 选项都是错误的组合。

2.In a scientific research paper, “data analysis” can be translated as _____.A.数据分析B.数据研究C.数据调查D.数据理论答案：A。

“data analysis”的正确翻译是“数据分析”。

B 选项“数据研究”应为“data research”。

C 选项“数据调查”是“data survey”。

D 选项“数据理论”是“data theory”。

3.The phrase “experimental results” is best translated as _____.A.实验结论B.实验数据C.实验结果D.实验过程答案：C。

“experimental results”的准确翻译是“实验结果”。

A 选项“实验结论”是“experimental conclusion”。

B 选项“实验数据”是“experimental data”。

D 选项“实验过程”是“experimental process”。

4.“Quantum mechanics” is translated as _____.A.量子物理B.量子力学C.量子化学D.量子技术答案：B。

“Quantum mechanics”是“量子力学”。

A 选项“量子物理”是“quantum physics”。

C 选项“量子化学”是“quantum chemistry”。

D 选项“量子技术”是“quantum technology”。

Proceedings of the Combustion Institute (2000-2001) 1.甲烷燃烧相关Da Cruz A P et al.[1] studied the laminar flame speed of stratified methane flames by using a modified version of the Lawrence Livermore National Laboratory HCT code in spatially stratified equivalence ratio conditions at atmospheric pressure. Results showed that the laminar flame speed was strongly affected by the equivalence ratio gradient and by the burned gas composition and temperature. High burned gas temperature behind the flame controls lean stratified flames traveling from stoichiometric to lean conditions and these flames are faster than their equivalent homogeneous ones. The propagation of rich stratified flames is controlled by production and consumption of molecular hydrogen in the flame front and in the burned gases. If the fuel decomposition leads to high H2 production that is not consumed because of insufficient oxygen, then the flame tends to accelerate if oxygen is available in the fresh gases. This causes the stoichiometric to rich flames to slow down and the rich to stoichiometric flames to accelerate compared with homogeneous propagation (as fig1 shows). The importance of heat and mass transfer on the observed results implies that their extrapolation to high pressure and to turbulent systems must be made with care.(a) stoichiometric to rich(b) rich to stoichiometricparison between the evolution of the laminar flame speed and the laminar flame speed of steady state flames at fixed equivalence ratio.Da Cruz A P等人[1]通过使用劳伦斯利弗莫尔国家实验室HCT编码的修改版本在大气压下的空间分层当量比条件下研究了分层甲烷火焰的层流火焰速度。

⼀些英⽂词的标准缩写有些词可能共⽤⼀些缩写。

带星号的缩写或词来源于PeopleSoft标准。

The following standard word abbreviations should be used in naming records, fields, and SQRs:Word(s)Abbreviation DescriptionAbbreviateABRVAbbreviationAcademic ACADAcceptACPTAcceptanceAcceptedAccess ACCSAccident ACDNTAccomplishACMPAccomplishmentAccomplishmentsAccount*ACCT*Accounting*ACCTG*Accounts PayableAPAdvanced PlacementAccounts Receivable ARAccredited ACRDAccrual ACRLAccumulated*ACCUM*AccumulationACUMAccumulativeAchieveACHVAchievementAcquisition*ACQ*ActActiveACTActivityAmerican College TestAction*ACTN*Actual ACTLAddADDAddedAdditional*ADDL*Address*ADDR*Narrative data which describes a person, place or thing's location Ad hoc ADHCAdjudicateADJDAdjudicatedAdjudicationAdjusted Gross Income AGIAdjustment*ADJ*AdministeredAdministratedADMAdministrationAdmissibleAdmission ADMSAdmittanceADMTAdmittedAdvanced PlacementAPAccounts PayableAdvice ADVCAffiliation AFFLAfter AFTAge AGEAgency AGCYAgent AGNTAid AIDAlien ALNAll ALLAllocateALLOC*Allocation*ALPHALTALMNAM"Ante Meridiem" (morning)ACTAMT*Monetary value(s)ANLSANNL*ANONANSAPTAPELAPP*APPL*APPTAPRVAREAARAYARRSASCASGNASSCASMPATHLATCHATNDATTNATTRADTAUTHAUXAVLAVG The mean of two or more numbers ACGAWRDBAL*The net value (balance) of an account BNKBARGBASBTCHBEFBEGNBOTBENBIDBILLBRSBRTHBRDBRKBUDBBABLDBUSBU*BUYCALC*CAL*CALLCMPNCMPSCANCAPCPLZCRDCARCRIRCARTCSECSHCTLGCATG*CENSCTRCERTCERTCHGCHAPCRGCHARTFCHKCTZNCTYCLASCLRCLEPCLOCLBCBR*CD*Data which represents encoded values (translate or code table)CLCTCOLGCLMNCOMBCMDCMT An explanatory, illustrative or critical note, remark or observation CMMTTEECO*COMPA*CPTRCMPLCMPT When the meaning is "part", use abbreviation "PRT".COMPCONDCNFDCONF*CNSTData which is unchanging or invariableCSTCTCTCONTCNTRCNTL*CONVR*CNV*CRSPCOSTA number of people or things that have been "counted", such as inventory cycle CNTCNT A number of people or things that have been "counted", such as inventory cycle countCTRY CNTY CRSE* COVRG* CRE CRDLCR* CRDT Use "CR" for field names relating to financial data Use "CRDT" for field names relating to academic workCREFCRSXLSTXREFCUMCURR*CUR*CRSRCSTNCUST*DLYDATADPDT* A calendar day, month, and year (including century) DTTMDD*DY*A day of the week (Sunday, Monday, etc.)DEADDR*DED*DFLT*DFCTDEFN*DEGDELDLVRDMODNTLDEPT*DMVDEP*DPSTDEPR*DESCR* DSC Narrative data which translates a code or number. When a suffix, use "_DSC" (see Standard Field Name Suffix table).DSGN DEST* DETL*DETL* DEV DIFFDGT DIR DISA DSBDISC* DSPL DISP DSPDIST*DSTR DIV DCE DOC DONR DNDRVDUE DUP*EA ERLYEARN* EIC EDU EFF*EFFDT* EFFSEQ* EFRTELCTEDIEFTEM ELIG*EMRG EMPH EE* EMPL EMPLID*EMPLID* ER* EMPLMTENCB END EOT ENDR ENDR ENDW ENGNENGL ENRCH ENRLENTR ENTL EQEEOEQP ERR ESTB ETHNEVALEVNT EXM EXCPEXCL EXEC EXMT EXPCEFC XPDTEXP EXPM EXPR EXP EXTEXTR FCLT FAC FMLYFERPAFST FATH FED FLSA FEEFTFICAFLD FILE FNL FIN*FA FINE FRST FISC FY FYTDFIXFLG SW Data which functions as a flag or indicator. Used with only two possible states/conditions. Data should normally be "Y" or "N".FSA FLR FOR FGN FK FRM FMT FORMR FREEFAFSAFOBFRZFREQ*FRSHFRFULFFT FTEFCN FUNDFUNDFUTGARN*GENLGEDGLGEOGGFTGLBLGOVTGDEGRD A value assigned to reflect performance or position on a scale GPAGRADGRNTGROSGRPGUARGSLGSTHANDHEADHDR*HLTHHLDHLPHIERH Normally used in conjunction with another word (i.e., High School abbreviated as "HS").HSHSSHEDHWAYHIREHSTHMHONRHSCHOSPHH A duration of time expressed in hoursHRLYHRS*HSEHOWHRHRSID*Alphanumeric data which identifies a person, place, or thing IMGIMGIMUNIMPC IMPL IMP IMPEXP IN INCL INCMINCRINDXIDIND INDV ISIR INFOINITINJ* INOC INPT INQ ISRT INSTISTRINAS INSIU*INT INTFC* INTR INTL INVLINTVINVN INV INVEST*INVTINVC ISSITM JOB JRNL* JRJSKEY LBL LBR LABLABLNGLSTLATELATLAYFLVLCTRLED*LGLLNDRLEN*LTRLVLLISNLBDLIBLICLIC_PLTE_NBR LIFELIM*LN*LNKLIQLSTLTRLLOADLNLOC*LKLKRLOGLOGON LONGLTCLTDLONLOTLOWMAILMAINT*MJRMKMGRMAPMRTLMASMASMSKMARSMTCHMTHMTRCMAX*MEDMTMBRMSHPMMOMEMRMERCHNDSMERCHMERTMSG*MTRMETHMFILMMIDMILMIN*MINRMNTA duration of time expressed in minutesMMMISCMDEMODMONYMM*A calendar month in numeric form (e.g., 01=January)MN*MTD*MOREMOTHMOVEMULTNMWord(s) by which a person, place or thing is commonly known NMENATLNACUBONSLDS Commonly known as the "Perkins Loan"NAVNEWNXTNOKNCNCNOCRNPRTNOMNONNPSNOTNANOTENBR*Numeric data which identifies a person, place, or thing OBJOCPOCCOFFROFFCOFCROFCLOLDONLNOPNOPR*OPTORDRORGORNTORIGOTHROUTOVROHOVRDOTOWNOWNRPACKPAIDPPRPARM*PARPRTYPRKPRTPTPTPRTPPASSPASTPTRNPAYPYRLPEDPELPENDPENSPCT*Part of a whole expressed in hundredthsPD*PTD*NSLDS Common name for National Student Loan Direct System PERMPRMTPERSPSNLPINPANPHNPHYSPLCEPLNPLTEPLDGPM"Post Meridiem" (afternoon)PNTPLCYPOSN*POSTPSTLPOTNPREDPREFPRFXPREMPREQPSCRPRSTPRESPREVPRCPLPRIMPKPRINPIPRNPREVPRTYPROBPROCPRFSPRFCPROF*PROGPROJPRMSPROMPRPSPRSPPRVNPURPOPRGPURPQALQTY* A number of things other than moneyQTD*QTRQSTNRACERNGRNK Relative standing or positionRT*Numeric value expressing amount per some unit of coverage READREALRSN*RCLRCPTRECV*RCVRRCHGRECGRCMDRECON* REC*RECR RCRT RED* REF*RFND RGNL REGR REGRJCT RLAT RLSE RELGRMNG RMDR RNWLREPTREPLRPLY RPT*REQ*RQMT* RESRSRV ROTC RSDTRSGN RSRC RESP RST RSTKRSTRRSLT RET*RET*RETRRTNREVRVWREVSREVKRLRLUPRMROUTROWRSVP French abbreviation meaning "please reply" RUNRUNCTLSAL*SALESLTNSMSAVESCALSCHED*SCHLRSCHLSATSCISCR A number that expresses merit or performance SCRNSRCHSCND SS Use "SCND" for field names relating to number two in a countable series Use "SS" for field names relating to a duration of time expressed in secondsSCTN SEC* SEGSEL*SEM SEMFSENSND SR SNT SEPR SEQ* SERL SERV SESSN* SEXSHR SHET SHLT SHFT SHIP SHRT SGN SIM SITE SZ SKL SKPSOCSSN SFT SLID SOPH SRTSRC SPCL SPECSPONSPRT SPSE SQ STCK STF STG STMP STD STDVSTRTST STMT STC STAT* STS STP STPD STK STOP STR STRG STRC STU SAR SCH STDY SCMPSCMP SUBJ SUB SUBS SFXSUM* SUP* SUPL*SRVY SUSP SUSPNFLG SW Data which functions as a flag or indicator. Used with only two possible states/conditions. Data should normally be "Y" or "N".SYSTBLTKNTAPETRGTTGHTTXTINTEAMTEMPTMPL*TMPTENRTRMTRMLTRMTTSTTXT Narrative informational data such as a message or error text THERM13th MonthTIAATKTTM Hours and minutes. May include seconds, hundredths of seconds. TMKPTS A system generated Time-stampTITLTDYTOT*TOURCTYTRKTRADTRN*TRANS*TSCPXFER*XFER*XLT Meaning "Crosswalk Table" XMITTRVLTUIT*TYPUGRDUNEMPLUNITUOM*UNVRSLUNIVUNPDUNSECMAXUPDTUPRUSDEUSEUSRVACN*VLDCVLDVALVARVEH*VENDVRBLVERFVETVPVIOVISAVSTVCHRW2W4W9WVEDWKWIDW Normally used as part of a compound word (i.e., Withdrawl abbreviated as "WDRL").WDRL WHLDWHLDWMN WKSTWRT YR*YTD* ZIP ZN。

Probing the Relationship between Anisotropic Magnetoresistanceand Magnetization of ferromagnetic filmsWanli Zhang,Jing Chen,and Wenxu Zhang aState Key Laboratory of Electronic Thin Films and Integrated Devices,University of Electronic Science and Technology of China,Chengdu,610054,P.R.China (Dated:December 27,2018)Abstract The anisotropic magnetoresistance (AMR)in thin permalloy strips was calculated at each steps during magnetization by the finite element method.The magnetization at equilibrium under differ-ent external fields was obtained by micromagnetic simulations,while the resistance with different magnetization was obtained by solving the Poisson equations iteratively until self-consistence.We find that the relation between magnetization and AMR deviates from the Stoner-Wohlfarth predic-tion when the magnetization is reduced from saturation.The reason is that the demagnetization is not necessarily from coherent rotation of the magnetic moment.We conclude that it is necessary to use numeric simulations to optimize the responses of AMR sensors.a Corresponding author.E-mail address:*****************.cna r X i v :1812.10294v 1 [c o n d -m a t .m t r l -s c i ] 26 D e c 2018I.INTRODUCTIONSince its discovery by William Thomson in1857,the anisotropic magnetoresistance (AMR)effect,where the longitudinal resistance of ferromagnetic metals changes when the magneticfield is changed,has been one of the key methods to sense the magneticfield ranges from10−5Oe to several Oe[1].Due to the process compatibility of silicon,it can be easily integrated onto silicon chips[2]so that the applications can be found in varies areas, including magneticfield sensing,current sensing and position or angle sensing.They are widely used in modern Internet of Things(IoT).In order to design and optimize the performance of the sensing elements in real devices, besides the analytical expressions for Stoner-Wohlfarth(SW)models[1],it is unavoidable to use numeric methods which can couple at least micromagnetics and Maxwell equations.Dy-namic effect was investigated by using this strategy to model the transfer effect in magnetic heads[3].A multiscale modeling strategy based on phenomenological empirical equations is proposed to describe the performance of the magneticfield sensors[4].It can be used to study the behavior of an AMR thinfilm sensor with material composition,crystallographic texture,andfilm thickness taken into account.The magnetoresistance change is found to increase significantly as the width of the wire is decreased[5].Combination of micromag-netic modeling of magnetic moment distributions and the SW AMR model,exchange biased MR head was investigated by Koehler et al.[6,7].In the SW model the change of the re-sistance∆R/R is proportional to cos2θwhereθis the angle between the magnetic moment and current density.Multiphysics program package Comsol and micromagnetic simulations MuMax3were used to calculate the AMR effect.The results of numerical simulations with allowance for inhomogeneous magnetization distribution showed that the proposed shape-coupled structures exhibit a significant increase in sensitivity as compared to that of classical barber-pole structures[8].However,the simulations above calculate the AMR with the assumption that the current is parallel to the externalfield,therefore do not treat the current and the AMR in a self-consistent way:Atfixed moment,the resistance and the current are independent upon each other.In their calculations,the resistance wasfixed to the values corresponding to the current parallel to the magneticfield.Self-consistent calculations were recently done by Fangohr et al.[9]and Abert et el.[10],where the micromagnetic problem was coupled withthe electrostatic problem and the two sets of equations were solved by thefinite element method[9].The work shows that it is important to take into account the spatial variation of the current density when computing AMR.Based on the SW model and general arguments of the symmetry,the AMR is proportional to cos2θ,whereθis the angle between the magnetic moment of the samples and the current. However,in real materials,the magnetization are different in directions which is dependent on positions.Domain walls will generally appear when the sample dimensions exceed the single domain criteria.How will the AMR deviate from the cos2θrelations?The question can be answered by numeric simulations base on the micromagnetics.In this work,finite element based micromagnetic simulations were used to studied the magnetic reversal pro-cesses of nano element.Our simulationsfind that there is are noticeable differences between the AMR calculated numerically and approximated by proportional to magnetization.This is the result of complex magnetic moment distribution.Regarding to this results,in order to optimization of the performances of AMR sensors,it is crucial to use numeric simulations rather than the simple coherent moment rotation models.PUTATION MODELS AND EXPERIMENTAL DETAILSWe use a nano thin plate elements withfixed length(L),width(W)and thickness(t).The element was meshed into tetrahedrons with the maximum edge length of1.0nm.Magnetic moment distributions at different magneticfields were obtained with Nmag which provides a systematic approach to multiphysics simulations withfinite-element method[11].The dynamics of the magnetic moment under externalfield is governed by the Landau-Lifschitz-Gilbert(LLG)equation:d M dt =−γ1+α2M× Heff+αMM×( M× Heff),(1)whereγis the gyromagnetic ratio,αis the damping coefficient and the auxiliary effective field H eff includes the contributions from various effects of different nature:Heff= H ext+ H anis+ H exch+ H demag+ (2)The problem offinding the resistance(R)of the sample can be solved by using the Poisson equations∇( σ( r, m)∇U( r))=0,(3)FIG.1.Schematic drawing of samples for micromagnetic electrostatic simulations,with voltage V measured at the two faced surface of the orthogonal block with specified length(L),width(W) and thickness(t).where σ( r, m)is the position dependent electron conductivity matrix depending on the local magnetic moment( m( r)),and U( r)is the electric potentials.In more details,the electric field E is computed viaE=−∇U( r),(4)and the current densityJ( r)= σ( r) E=− σ( r)∇U( r)(5)with suitable boundary conditions.In the electrostatic problem,the divergence of the current density must vanish∇· J( r)=0.(6) When combined Equ.(4),(5)and(6),the Poisson equation for the potential is obtained as in Equ.(3).Using the same mesh as in micromagnetics,Equ.(3)was solved by FEniCS [12].The resistivityρ=σ−1at different vertexes were set to beρ(θ)=ρ0(1+αcos2θ), whereρ0is the resistivity of the material in the absence of AMR andαis the AMR ratio. In our simulations,we usedσ0=5.99×107S/m andα=0.5%.These two parameters do not influence the discussions of the AMR effects in our work due to the fact that the voltage and its variation scale with them.The Poisson equation was solved iteratively until the current density distributions converge to10−8.The resistance between two electrodes was calculated by R=V/I where I is the integration of current normal to the electrodes,and V is the voltages set between the electrodes as the boundary condition for the problem.A schematic drawing of our samples with the FEM net are shown in Fig. 1.The geometric parameters are set to L=210nm,W=60nm and t=10nm.The electrodes are defined at the opposite sides of the sample.FIG.2.The hysteresis loop of the rectangle element used in this simulation and the magnetic moment distributions at different external fields (a)23.0kA/m,(b)-24.6kA/m,(c)-25.0kA/m and (d)-100kA/m.III.RESULTS AND DISCUSSIONSFor the typical square plate shaped elements,the demagnetization field will cause a small misaligned moment at both ends forming a “flower”-state when the magnetic field is decreased from the initial positive one as shown in Fig.2where the hysteresis loop is obtained by micromagnetic simulations.Decrease the field leads to the gradual reversal of the moment as required to minimize the free energy of the systems as from (a)to (b).The reversal regions expands.When the field reaches the critical value,here,is about 25kA/m antiparallel to the initial field,a first order transition of the magnetic state occurs.This leads to the flip of the magnetic moment to the negative value as in (b)and (c).The magnetization rapidly saturates in the negative direction and in (d),when the negative field increases.Then the field is decreased and then reversed.During this magnetic field variation,the AMR of the sample calculated are shown in Fig.3.We can see that during the process of when the magnetization decrease,the AMR decreases with it.It reaches the minimum at the critical point and shoots up when the magnetic moment switched to the opposite direction.In order to investigate the relationship between the AMR and variation of magnetization,we plot the (M x M s )2 ,where · is theaverage over the finite element cells,as the function of AMR shown in the inset of Fig.3.In the ideal SW model they should be on a straight linear because of the relationship of AMR ∝ cos 2θ defined above.In the initial stage of decrease of the moment,whenFIG.3.The calculated AMR of the rectangle element.Relation between the AMR and(M xM s)2is shown in the inset.The data are shown by thefilled circles,while the solid lines are guide for eyes.the magnetic moment is more than80%of the initial values,the linearity is reasonable. However,the deviation from linearity is obvious as in the inset when the magnetic moment is further reduced.It gives a positive contribution to the AMR value,which can be as large as50%.The reason for this nonlinearity comes from the noncollinearity of the magnetic moment distribution,which causes noncollinearity of the current density in the cells with respect to the magnetic moment.The distributions of the current density are shown in Fig.4.In the region where the magnetic moment is deviated from the magneticfield,the resistance on the path through which the current pass is also different from the homogenous region.However,the distribution of the current density does not take a copy of the magnetic moment.At the same time,when the decrease of the magnetization does not lead to a change of the magnetic moment direction with respect to the current density,they do not contribute to the AMR effect.For example,during the Bloch wall displacement,the magnetization varies while the AMR retains.In this case,there is no hope to get a linear response of the magnetoresistance with respect to the square of the magnetization.With regarding to these results,it is crucial to form a homogenous magnetized samples to achieved good linearity in the magnetic sensors.At the same time,it is necessary to use numeric simulations to optimize the performances of magneticfield sensor,so that the linearity can be optimized by proper design of barber poles.FIG.4.The position dependent magnetic moment m x(a),m y(b)and the current density j x(c) j y(d)in the x-y plane of the sample.IV.CONCLUSIONSTo summarize,we have shown in this work,the magnetization and the AMR are not proportional as suggested by the coherent moment rotation model.The proportionality is only good when the magnetization variation is less than80%of its saturation value.It is deviated from the analytical model prediction when the magnetic moment is far from saturation.Wefind that it is due to the formation of inhomogeneous magnetization region. Our work points to the conclusion that the joint self-consistent solution of LLG equations in micromagnetics and Poisson equations in electrostatics is necessary to understand and optimization the performances of AMR sensors.V.ACKNOWLEDGMENTSDiscussions with Fangohr were acknowledged.This work is supported by National Key R&D Program of China(No.2017YFB0406403)from MOST.[1]S.Tumanski.Thin Film Magnetoresistive Sensor.IOP Publishing Ltd,2001.[2]Radivoje S.Popovic,Predrag M.Drljaca,and Pavel Kejik.CMOS magnetic sensors withintegrated ferromagnetic parts.Sensors and Actuators A:Physical,129(1-2):94–99,may2006.[3]Florian Bruckner,Christoph Vogler,Bernhard Bergmair,Thomas Huber,Markus Fuger,Di-eter Suess,Michael Feischl,Thomas Fuehrer,Marcus Page,and Dirk bining micromagnetism and magnetostatic maxwell equations for multiscale magnetic simulations.Journal of Magnetism and Magnetic Materials,343:163–168,oct2013.[4]Andr´a s Bart´o k,Laurent Daniel,and Adel Razek.A multiscale model for thinfilm AMRsensors.Journal of Magnetism and Magnetic Materials,326:116–122,jan2013.[5] A.O.Adeyeye,J.A.C.Bland,C.Daboo,D.G.Hasko,and H.Ahmed.Optimized process forthe fabrication of mesoscopic magnetic structures.Journal of Applied Physics,82(1):469–473, jul1997.[6]T.R.Koehler,Bo Yang,Wenjie Chen,and D.R.Fredkin.Simulation of magnetoresistiveresponse in a small permalloy strip.Journal of Applied Physics,73(10):6504–6506,may1993.[7]T.R.Koehler and M.L.Williams.Micromagnetic modeling of a single element MR head.IEEE Transactions on Magnetics,31(6):2639–2641,1995.[8]N.A.Dyuzhev,A.S.Yurov,R.Yu.Preobrazhenskii,N.S.Mazurkin,and M.Yu.Chinenkov.Shape-coupled magnetoresistive structures:a new approach to higher sensitivity.Technical Physics Letters,42(5):546–549,may2016.[9]Giuliano Bordignon,Thomas Fischbacher,Matteo Franchin,Jurgen P.Zimmermann,Alexan-der A.Zhukov,Vitali V.Metlushko,Peter A.J.de Groot,and Hans Fangohr.Analysis of magnetoresistance in arrays of connected nano-rings.IEEE Transactions on Magnetics, 43(6):2881–2883,jun2007.[10]Claas Abert,Lukas Exl,Florian Bruckner,Andr´e Drews,and Dieter Suess.magnum.fe:Amicromagneticfinite-element simulation code based on fenics.Journal of Magnetism and Magnetic Materials,345:29–35,nov2013.[11]Thomas Fischbacher,Matteo Franchin,Giuliano Bordignon,and Hans Fangohr.A system-atic approach to multiphysics extensions offinite-element-based micromagnetic simulations: Nmag.IEEE Transactions on Magnetics,43(6):2896–2898,jun2007.[12]Anders Logg,Kent-Andre Mardal,and Garth Wells,editors.Automated Solution of Differen-tial Equations by the Finite Element Method.Springer Berlin Heidelberg,2012.。

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Antique Airplane Association 古老飞机协会( 美）AAA Association of African Airways 非洲航空公司协会AGNCY Agency 代理机构AGNIS Aircraft Guidance Nose—In System 引导飞机停靠登机桥滑行系统AGNIS Azimuth Guidance Nose—In Stand 方位引导机头向内停机位AGNST Against 反对,抵付AGNT Agent 代理人，代理机构AGP Aircraft Grounded for Lack of Parts 缺件停飞AGP Aircraft Grounded For Lack of Parts 因缺乏零件停飞的飞机AGR Agree 同意AGR Arresting Gear 停止索装置AGRD Agreed 已同意AGREE Advisory Group on Reliablility of Electronic Equipment 电子设备可靠性咨询组AGRMT Agreement 协议AGRT Automatic Ground Reciever Terminal 自动地面接收机终端AGRT Automatic Guard Reciever Terminals 自动值班接收机终端AGS Abort Guidance Susyem 应急制导系统AGS Advanced Graphic System 高级图形系统AGS Advanced Guidance Susyem 高级制导系统AGS Aircraft General Stores 飞机通用( 器材）仓库AGS Airport Ground Service 机场地面服务AGS Automatic Gain Stabilization 自动增益稳定AGSD Advanced Ground Segment Design 先进地面段设计AGST Against 反对AGT Agent 代理人,代理机构AGT Agreement 协议AGT Aviation Gas Turbine 航空燃气涡轮AGTA Airline Ground Transportation Association （US) 航空公司地面运输协会AGTA Airline Ground Transportation Association Ins 民航地面交通协会（美)AGTC Airport Ground Traffic Control 机场地面交通管制AGW actual Gross Weight 实际全重AGW Actual Gross Weight 实际总重AGW Actual Gross Weight 实际总重量AGW Allowable Gross Weight 容许起飞总重AH AIR ALGERIE 阿尔及利亚航空公司AH Alert Height 警戒高度AH Ampere Hour 安培小时AH Ampere/Hour 安培/ 小时AH Antihunt 阻尼稳定器AH Artificial Horizon 航空地平仪，人工地平, 地平线AHC AIR HAW AII 夏威夷航空公司AHC ANCHORAGE 安克雷季（美国阿拉斯加)AHCS Automatic Hovering Control System 自动悬停控制系统AHD Ahead 在前面，提前AHD AIR HOLLAND B。