Low-lying Dirac eigenmodes and monopoles in 3+1D compact QED

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物探专业术语中英文对照

物探专业术语中英文对照lunar tide 太阴潮solar tide 太阳潮turbulence 湍流spectrum of turbulence 湍流谱turbulent diffusion 湍流扩散turbulent dissipation 湍流耗散turbulent exchange 湍流交换turbulent mixing 湍流混合twilight 曙暮光wind shear 风切变yield function 产额函数zonal circulation 纬向环流zonal wind 纬向风airglow 气辉MST radar MST雷达，对流层、平流层、中层大气探测雷达。

aeronomy 高空大气学deviative absorption 偏移吸收non-deviative absorption 非偏移吸收after-effect of [magnetic] storm 磁暴后效Chapman layer 查普曼层Appleton anomaly 阿普尔顿异常equatorial anomaly 赤道异常winter anomaly 冬季异常magneto-ionic theory 磁离子理论buoyancy frequency 浮力频率D - region Ｄ区E - region Ｅ区F - region Ｆ区F1 layer Ｆ1层F1 ledge Ｆ1缘F2 layer Ｆ2层Chapman production function 查普曼生成函数Cowling conductivity 柯林电导率Pedersen conductivity 彼得森电导率Hall conductivity 霍尔电导率direct conductivity 直接电导率cosmic radio noise 宇宙射电噪声riometer 宇宙噪声吸收仪critical frequency 临界频率dissociative recombination 离解性复合dynamo region 发电机区evanescent wave 消散波fade 衰落fadeout, blackout [短波通讯]中断ordinary wave 寻常波extraordinary wave 非寻常波Faraday rotation 法拉第旋转field-aligned irregularity 场向不规则结构Harang discontinuity 哈朗间断impedance probe 阻抗探针incoherent scattering radar 非相干散射雷达ionospheric storm 电离层暴ionosonde 电离层测高仪virtual height 虚高true height 真高digisonde 数字式测高仪ionogram 电离图polar cap absorption, PCA 极盖吸收sudden ionospheric disturbance, SID 突发电离层骚扰spread F 扩展 Fsporadic E 散见 E 层top-side sounder 顶视探测仪bottom-side sounder 底视探测仪travelling ionospheric disturbance, TID 电离层行扰short wave fadeout, SWF 短波突然衰落sudden frequency deviation, SFD [短波]频率急偏sudden phase anomaly, SPA 突发相位异常characteristic wave 特征波cross-modulation 交叉调制total electron content, TEC 电子总含量ambipolar diffusion 双极扩散eclipse effect [日]食效应skip distance 跳距outer space 外层空间interplanetary space 行星际空间interstellar space [恒]星际空间deep space 深空solar-terrestrial space 日地空间solar-terrestrial physics 日地物理学one-hop propagation 一跳传播quasi-transverse propagation 准横传播quasi-longitudinal propagation 准纵传播maximum usable frequency, MUF 最大可用频率geomagnetism 地磁[学] main field 主磁场inclination, dip angle 磁倾角declination 磁偏角agonic line 零偏线aclinic line 零倾线magnetic isoclinic line 等磁倾线magnetic chart 磁图isomagnetic chart 等磁图isomagnetic line 等磁强线isoporic line, isopore 等年变线magnetic isoanomalous line 等磁异常线geomagnetic pole 地磁极dip pole 磁倾极magnetic local time 磁地方时magnetic dipole time 磁偶极时central dipole 中心偶极子dipole coordinate 偶极子坐标corrected geomagnetic coordinate 修正地磁坐标north magnetic pole 磁北极south magnetic pole 磁南极invariant latitude 不变纬度dip equator 倾角赤道eccentric dipole 偏心偶极子magnetogram 磁照图magnetically quiet day, q 磁静日magnetically disturbed day, d 磁扰日secular variation 长期变化solar daily variation, S 太阳日变化disturbed daily variation, Sd 扰日日变化storm-time variation, Dst 暴时变化magnetic disturbance 磁扰magnetic bay 磁湾扰magnetic crochet 磁钩扰magnetic storm 磁暴gradual commencement [magnetic] storm 缓始磁暴sudden commencement [magnetic] storm 急始磁暴sudden commencement 急始initial phase 初相main phase 主相recovery phase 恢复相magnetic substorm 磁亚暴expansive phase 膨胀相equivalent current system 等效电流系internal field 内源场external field 外源场aurora 极光aurora australis 南极光aurora borealis 北极光auroral oval 极光卵形环auroral belt 极光带subauroral zone 亚极光带Alfvēen layer 阿尔文层cleft, cusp 极隙pseudo-trapped particle 假捕获粒子radiation belt, Van Allen belt 辐射带又称“范艾伦带”。

用密度函数理论和杜比宁方程研究活性炭纤维多段充填机理

密度函数理论和杜比宁方程可以用来研究活性炭纤维在多段充填过程中的吸附行为。

密度函数理论是一种分子统计力学理论，它建立在分子统计学和热力学的基础上，用来研究一种系统中分子的分布。

杜比宁方程是一种描述分子吸附行为的方程，它可以用来计算吸附层的厚度、吸附速率和吸附能量等参数。

在研究活性炭纤维多段充填过程中，可以使用密度函数理论和杜比宁方程来研究纤维表面的分子结构和吸附行为。

通过分析密度函数和杜比宁方程的解，可以得出纤维表面的分子结构以及纤维吸附的分子的种类、数量和能量。

这些信息有助于更好地理解活性炭纤维的多段充填机理。

在研究活性炭纤维的多段充填机理时，还可以使用其他理论和方法来帮助我们更好地了解这一过程。

例如，可以使用扫描电子显微镜(SEM)和透射电子显微镜(TEM)等技术来观察纤维表面的形貌和结构。

可以使用X射线衍射(XRD)和傅里叶变换红外光谱(FTIR)等技术来确定纤维表面的化学成分和结构。

还可以使用氮气吸附(BET)和旋转氧吸附(BJH)等技术来测量纤维表面的比表面积和孔结构。

通过综合运用密度函数理论、杜比宁方程和其他理论和方法，可以更全面地了解活性炭纤维的多段充填机理，从而更好地控制和优化多段充填的过程。

在研究活性炭纤维多段充填机理时，还可以使用温度敏感性测试方法来研究充填过程中纤维表面的动力学性质。

例如，可以使用动态氧吸附(DAC)或旋转杆氧吸附(ROTA)等技术来测量温度对纤维表面吸附性能的影响。

通过对比不同温度下纤维表面的吸附性能，可以更好地了解充填过程中纤维表面的动力学性质。

此外，还可以使用分子动力学模拟方法来研究纤维表面的吸附行为。

例如，可以使用拉曼光谱或红外光谱等技术来测量纤维表面的分子吸附构型。

然后，使用分子动力学模拟方法来模拟不同分子吸附构型下的纤维表面的动力学性质，帮助我们更好地了解活性炭纤维的多段充填机理。

检测两种蛋白质之间相互作用之欧阳音创编

检测两种蛋白质之间相互作用的实验方法比较1. 生化方法●免疫共沉淀免疫共沉淀是以抗体和抗原之间的专一性作用为基础的用于研究蛋白质相互作用的经典方法。

改法的优点是蛋白处于天然状态，蛋白的相互作用可以在天然状态下进行，可以避免认为影响；可以分离得到天然状态下相互作用的蛋白复合体。

缺点：免疫共沉淀同样不能保证沉淀的蛋白复合物时候为直接相互作用的两种蛋白。

另外灵敏度不如亲和色谱高。

●Far-Western又叫做亲和印记。

将PAGE胶上分离好的凡百样品转移到硝酸纤维膜上，然后检测哪种蛋白能与标记了同位素的诱饵蛋白发生作用，最后显影。

缺点是转膜前需要将蛋白复性。

2. 等离子表面共振技术（Surface plasmonresonance）该技术是将诱饵蛋白结合于葡聚糖表面，葡聚糖层固定于几十纳米厚的技术膜表面。

当有蛋白质混合物经过时，如果有蛋白质同“诱饵”蛋白发生相互作用，那么两者的结合将使金属膜表面的折射率上升，从而导致共振角度的改变。

而共振角度的改变与该处的蛋白质浓度成线性关系，由此可以检测蛋白质之间的相互作用。

该技术不需要标记物和染料，安全灵敏快速，还可定量分析。

缺点：需要专门的等离子表面共振检测仪器。

3. 双杂交技术原理基于真核细胞转录因子的结构特殊性，这些转录因子通常需要两个或以上相互独立的结构域组成。

分别使结合域和激活域同诱饵蛋白和猎物蛋白形成融合蛋白，在真核细胞中表达，如果两种蛋白可以发生相互作用，则可使结合域和激活域在空间上充分接近，从而激活报告基因。

缺点：自身有转录功能的蛋白会造成假阳性。

融合蛋白会影响蛋白的真实结构和功能。

不利于核外蛋白研究，会导致假隐性。

5. 荧光共振能量转移技术指两个荧光法色基团在足够近（<100埃）时，它们之间可发生能量转移的现象。

荧光共振能量转移技术可以研究分子内部对某些刺激发生的构象变化，也能研究分子间的相互作用。

它可以在活体中检测，非常灵敏，分辩率高，能够检测大分子的构象变化，能够定性定量的检测相互作用的强度。

低In组分量子阱垒层AlGaN对GaN基双蓝光波长发光二极管性能的影响

关键词：Ａ１ＧａＮ垒层；ＧａＮ垒层；双蓝光波长；发光二极管中图分类号：０４８２．７文献标志码：Ａｄｏｉ：１０．６０５４／ｊ．ｊｓｃｎｕｎ．２０１３．０４．０１２
电致发光（ＥＬ）光谱影响不大，但在混合多量子阱的双波长ＬＥＤ中电子空穴分布不均匀对ＥＬ光谱产生严重影响．本文采用数值模拟方法，通过在ＩｎＧａＮ／
ＧａＮ混合多量子阱中的低Ｉｎ组分Ａ１ＧａＮ垒层来优
绝大部分白光ＬＥＤ是通过蓝光芯片发射的部分蓝
光激发ＹＡＧ：Ｃｅ黄色荧光粉产生黄光与部分未被吸
收的蓝光耦合成白光 ¨ Ｊ，在高色温情况下能满足较高的光效和显色性，但是在低色温情况下，显色指数
蓝光波长芯片激发ＹＡＧ：Ｃｅ黄色荧光粉实现了白光
１模拟参数与器件结构
１．１模拟参数
ＬＥＤ，显色性达到了８８，但其发光光谱随着驱动电流
的改变而变化．
在ＧａＮ基材料中，由于电子的有效质量（０．２
般不高于７０．ＭＩＲＨＯＳＳＥＩＮＩ等通过模拟结果
显示基于双蓝光波长芯片激发ＹＡＧ：Ｃｅ荧光粉，能
在保持流明效率的同时得到高显色指数的白光ＬＥＤ．本研究组采用混合多量子阱结构的ＧａＮ基双

卡尔曼滤波的安瓿针剂杂质检测算法研究

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第３１卷第１期
文章编号：１００６ — ９３４８（２０１４）０１一Ｏ２２ｏ一０４
计
算
机
仿
真
２０１４年１月
卡尔曼滤波的安瓿针剂杂质检测算法研究
邱新华，谢云
（广东工业大学自动化学院，广东广曼滤波；背景估计；运动目标检测
中图分类号：ＴＰ３９１．４１文献标识码：Ｂ
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ＤｅｔｅｃｔｉｏｎＡｌｇｏｒｉｔｈｍＢａｓｅｄｏｎＫａｌｍａｎＦｉｌｔｅｒ
ＱＩＵｘｉｎ — ｈｕａ．ＸＩＥＹｕｎ
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半导体一些术语的中英文对照

半导体一些术语的中英文对照离子注入机ion implanterLSS理论Lindhand Scharff and Schiott theory 又称“林汉德-斯卡夫-斯高特理论”。

沟道效应channeling effect射程分布range distribution深度分布depth distribution投影射程projected range阻止距离stopping distance阻止本领stopping power标准阻止截面standard stopping cross section 退火annealing激活能activation energy等温退火isothermal annealing激光退火laser annealing应力感生缺陷stress-induced defect择优取向preferred orientation制版工艺mask-making technology图形畸变pattern distortion初缩first minification精缩final minification母版master mask铬版chromium plate干版dry plate乳胶版emulsion plate透明版see-through plate高分辨率版high resolution plate, HRP超微粒干版plate for ultra-microminiaturization 掩模mask掩模对准mask alignment对准精度alignment precision光刻胶photoresist又称“光致抗蚀剂”。

负性光刻胶negative photoresist正性光刻胶positive photoresist无机光刻胶inorganic resist多层光刻胶multilevel resist电子束光刻胶electron beam resistX射线光刻胶X-ray resist刷洗scrubbing甩胶spinning涂胶photoresist coating后烘postbaking光刻photolithographyX射线光刻X-ray lithography电子束光刻electron beam lithography离子束光刻ion beam lithography深紫外光刻deep-UV lithography光刻机mask aligner投影光刻机projection mask aligner曝光exposure接触式曝光法contact exposure method接近式曝光法proximity exposure method光学投影曝光法optical projection exposure method 电子束曝光系统electron beam exposure system分步重复系统step-and-repeat system显影development线宽linewidth去胶stripping of photoresist氧化去胶removing of photoresist by oxidation等离子［体］去胶removing of photoresist by plasma 刻蚀etching干法刻蚀dry etching反应离子刻蚀reactive ion etching, RIE各向同性刻蚀isotropic etching各向异性刻蚀anisotropic etching反应溅射刻蚀reactive sputter etching离子铣ion beam milling又称“离子磨削”。

匹配场处理检测因子

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文档下载后可定制随意修改，请根据实际需要进行相应的调整和使用，谢谢!并且，本店铺为大家提供各种各样类型的实用资料，如教育随笔、日记赏析、句子摘抄、古诗大全、经典美文、话题作文、工作总结、词语解析、文案摘录、其他资料等等，如想了解不同资料格式和写法，敬请关注!Download tips: This document is carefully compiled by the editor. I hope that after you download them, they can help yousolve practical problems. The document can be customized and modified after downloading, please adjust and use it according to actual needs, thank you!In addition, our shop provides you with various types of practical materials, such as educational essays, diary appreciation, sentence excerpts, ancient poems, classic articles, topic composition, work summary, word parsing, copy excerpts,other materials and so on, want to know different data formats and writing methods, please pay attention!匹配场处理检测因子在现代科学研究中扮演着重要角色，通过匹配场处理检测因子的测定，可以更准确地分析样品中的成分和含量。

Chirality Correlation within Dirac Eigenvectors from Domain Wall Fermions

a r X i v :h e p -l a t /0105006v 1 7 M a y 2001CU-TP-1014,BNL-HET-01/10,RBRC-185Chirality Correlation within Dirac Eigenvectors from DomainWall FermionsT.Blum a ,N.Christ b ,C.Cristian b ,C.Dawson c ,X.Liao b ,G.Liu b ,R.Mawhinney b ,L.Wu b ,Y.Zhestkov ba RIKEN-BNL Research Center,Brookhaven National Laboratory,Upton,NY 11973b Physics Department,Columbia University,New York,NY 10027c Physics Department,Brookhaven National Laboratory,Upton,NY 11973(May 6,2001)Abstract In the dilute instanton gas model of the QCD vacuum,one expects a strong spatial correlation between chirality and the maxima of the Dirac eigenvectors with small eigenvalues.Following Horvath,et al.we examine this question using lattice gauge theory within the quenched approximation.We extend the work of those authors by using weaker coupling,β=6.0,larger lattices,164,and an improved fermion formulation,domain wall fermions.In contrast with this earlier work,we ﬁnd a striking correlation between the magnitude of the chirality density,|ψ†(x )γ5ψ(x )|,and the normal density,ψ†(x )ψ(x ),for the low-lying Dirac eigenvectors.Typeset using REVT E XI.INTRODUCTIONIn a recent paper,Horvath,Isgur,McCune and Thacker[1]suggest that an important test of various theoretical models of the QCD vacuum can be made by examining the degree to which the space-time localization of a low-lying eigenmode of the Dirac operator is correlated with non-zero chirality.Such correlations are expected in the dilute instanton gas model of the QCD vacuum.In this model,gauge conﬁgurations composed of widely separated instantons and anti-instantons support low-lying Dirac eigenvectors which are near superpositions of the zero modes that these(anti-)instantons would posses if in isolation.These near zero modes are proposed[2]to provide the non-zero density of Dirac eigenvalues,ρ(λ)for vanishing eigenvalueλ,required by the Banks-Casher formula[3]and the non-zero QCD chiral con-densate,πρ(0)=−12 qq obtained in a recent quenched calculation[4]and the factor of12comes from our particular normalization conventions.Since the isolated zero modes associated with an(anti-)instanton are entirely (left-)right-handed,one should expect a strong correlation of handedness with the locations at whichψ†nψn(x)is large.Thus,this class of instanton-based models of the QCD vacuum can be tested by search-ing for such strong correlations between the chiral densityψ†nγ5ψn(x)and normal den-sityψ†nψn(x)for the low-lying eigenmodes of the Dirac operator on a conﬁguration-by-conﬁguration basis within a lattice QCD calculation.As emphasized by Horvath,et al. earlier arguments of Witten[5,6]suggest that the large N c behavior of theη′mass may be inconsistent with the predictions of such an instanton model,providing additional motivation for such qualitative tests of the instanton picture.In the above cited work of Horvath,et al.,the authors search for such correlations using 30gauge conﬁgurations obtained in the quenched approximation on a123×24lattice volume with Wilson fermions and the Wilson gauge action withβ=5.7.In this paper,we extend their study to smaller lattice spacing,a−1=1.922GeV,using a164lattice volume which has a similar physical size of≈1.6Fermi.Making use of conﬁgurations that we had already analyzed,we discuss here results from two diﬀerent gauge actions.Theﬁrst is the standard Wilson action withβ=6.0for which we have32conﬁgurations and the second uses the Iwasaki action withβ=2.6,a value tuned to achieve the same lattice spacing.The latter ensemble contains55conﬁgurations.Finally we employ an improved fermionic action,using the domain wall formalism of Shamir[7].Further references to this method,our implementation of this lattice fermion action and a complete description of the notation used in this paper can be found in Ref.[4].As is detailed below,using thisﬁner lattice spacing and improved fermion formulation, weﬁnd a very diﬀerent result from that seen in the earlier work of Horvath,et al.The chirality of the n th eigenmode,|ψ†n(x)γ5ψn(x)|is surprisingly close to maximum at those lattice sites x where the eigenmode is large.In Section II we brieﬂy review the properties of the spectrum of the continuum Dirac operator and the closely related hermitian Dirac operator that we study.Section III explains the diagonalization procedure.In Section IV we present our results and analysis of the domain wall fermion eigenvectors.Finally,Section V contains a brief conclusion.II.PROPERTIES OF THE CONTINUUM DIRAC OPERATOR In the continuum,the Euclidean Dirac operator is usually written as a non-hermitian sum of an anti-hermitian operator/D=γµDµwhere Dµis the usual gauge covariant derivative and a real mass term.The combined operator,/D+m,is easy to analyze being the sum of commuting hermitian and anti-hermitian pieces.However,the standard Wilson and domain wall lattice Dirac operators are more complex because the so-called Wilson mass term also contains derivatives causing the hermitian and anti-hermitian parts of these lattice Dirac operators to fail to commute.For the Wilson operator,D W,this is easily remedied by working with the productγ5D W which is readily seen to be hermitian.A similar construction is possible for domain wall fermions[8]where the productγ5R5D is hermitian.Here D is the domain wall Dirac operator,given for example in Eq.1of Ref.[4],and R5the reﬂection in the midplane in theﬁfth dimension,s→L s−1−s.Our treatment diﬀers from that of Horvath,et al.in that we work with the hermitian operator,ﬁnding real eigenvalues and their corresponding eigenvectors while the authors of Ref.[1]determine the complex eigenvalues of the non-hermitian Wilson operator and their corresponding eigenvectors.In order to compare our two results,we now review the relation between the eigenvectors of corresponding continuum operators:/D+m andγ5(/D+m).We begin by recalling the basic properties of the eigenmodes of the Dirac operator/D and the hermitian operatorγ5/D in the continuum and then discuss properties of the local chiral density which is the focus of this paper.Since{γ5,/D}=0and/D†=−/D,the spectrum of/D consists of pairs of eigenvectorsψλ(x)andψ−λ(x)=γ5ψλ(x)with imaginary eigenvalues±iλ.Forλ=0the zero modes,{ψ0,i}1≤i≤N,can also be chosen eigenstates of γ5,γ5ψ0,i=±ψ0,i since[γ5,/D]ψ0,i=0.Here we have added the extra subscript i to the zero modes to allow for the possibility that more than one eigenvector with zero eigenvalue exists.The Atiyah-Singer index theorem requires that the number of zero modes,N satisfy, N≥|ν|whereνis the integer winding number of the gaugeﬁeld(ν=...−2,−1,0,1,2,...).Clearly,zero modes of/D are also zero modes ofγ5/D.The remaining eigenvectors of γ5(/D+m)can be easily related to those of/D+m by diagonalizing the former on thetwo-dimensional subspace spanned by the basis{ψλ,ψ−λ}:γ5(/D+m) a b = 0m−iλm+iλ0 a b (1)=λH a b .The eigenvalues are easily seen to beλH=± λ2+m2 1√4 (m−iλ)12ψ−λ .(3)Next we compare the chiral density as determined by these two sets of eigenvectors.For zero modes:ψ†0,i(x)γ5ψ0,i(x)=±ψ†0,i(x)ψ0,i(x),(4) the largest value possible,for both the hermitian and non-hermitian operators.For the other,paired eigenvectors and the non-hermitian operator,the identityψ−λ(x)=γ5ψλ(x)implies that productψ†λ(x)γ5ψλ(x)=ψ†−λ(x)γ5ψ−λ(x)=χ(x)(5) is the same for each eigenvectorψ±λin the pair.Similarly,the norm of the wave function at each point in space-time is the same for each pair of eigenvectorsψ†λ(x)ψλ(x)=ψ†−λ(x)ψ−λ(x)=ω(x)(6) This is not true for the paired eigenvectors of the hermitian operator,where using Eq.3 weﬁnd:ψ†H,λH (x)ψH,λH(x)=w(x)±ǫχ(x)=ωH(x),(7)ψH,λH (x)γ5ψH,λH(x)=χ(x)±ǫω(x)=χH(x),whereǫ=mλ2+m2(8)andλ=±|λ|.In the chiral limitǫvanishes,and the local chiral densities of the anti-hermitian and hermitian Dirac operators coincide.The above analysis should describe the properties of the low-lying eigenstates of the non-hermitian Wilson operator in the continuum limit.Thus,we conclude that the diﬀerencebetween the evaluation of the chiral density for the eigenvectors of the non-hermitian Wilson Dirac operator and those of the hermitian domain wall Dirac operator should agree in the continuum limit for those eigenvectors for which the parameterǫis small.Thus,the resultspresented in this paper and those of Horvath,et al.address the same continuum question and can be compared.Since in our calculation the explicit fermion mass is very small(m f=0for the Wilson action and m f=5·10−4for the Iwasaki action)we expect that for most modes the parameterǫwill also be very small making the normal and chiral densities the same for both operators.The only exception to this conclusion arises for the very smallesteigenvalues,λ≈10−3whereǫmay be of order one due to the residual mass coming from mixing between the walls,m res≈10−3for the Wilson action[4,9]and m res≈10−4for the Iwasaki action[9,10].)III.DIAGONALIZATION METHODUsing the conjugate-gradient method proposed by Kalkreuter and Simma[11],we cal-culate the19lowest eigenvalues and eigenvectors of D H.This corresponds to the range 0<∼λ<∼200(MeV).In this section we describe our implementation of their method1.Following Kalkreuter and Simma,we use the conjugate gradient method to minimize the Ritz functional,µ(Ψ)= Ψ|(D H)2|ΨWe compute the diagonal elements of this matrix equation in our basis of eigenvectors of D H:Λn Ψn|Γ5|Ψn = Ψn| m f Q(w)+Q(mp) |Ψn .(11) If for one or more eigenvectors the fractional diﬀerence of the left-and right-hand sides of Eq.11is larger than0.12we discard the eigenvector producing the largest diﬀerence.If all eigenvectors give diﬀerences lying below this value,we discard the largest eigenvalue.The fraction0.12is a somewhat arbitrary dividing point that separates the few large discrepancies from the majority with a much smaller diﬀerence.Comparison of these two criteria shows disagreement on4of the32Wilson and6of the55 Iwasaki conﬁgurations.However,in each of those cases one method discards the nineteenth eigenvalue while the other identiﬁes either the seventeenth or eighteenth as spurious.Since the eigenvectors of these largest eigenvalues are likely the least well determined,we view this as satisfactory and expect that the diﬃculties from this imprecise identiﬁcation of“spurious”eigenvectors enter our sample of eigenvectors on the level of a few percent or less.IV.ANALYSIS AND RESULTSIn this section we examine some of the properties of the18lowest eigenvalues,ΛH,i and the corresponding eigenvectors|ΛH,i determined by the procedure described above,D H|ΛH,i =ΛH,i|ΛH,i (0≤i<18).(12) The connection between these eigenvectors and eigenvalues and those of the usual4-dimensional Dirac operator was discussed in detail in[4].The5-dimensional wave functions,ΨH,i(x,s)are expected to represent the wave functions of4-dimensional Dirac eigenfunctions with an added exponential dependence on theﬁfth coordinate s,causing|ΨH,i(x,s)|2to fall rapidly as s moves away from the4-dimensional planes s=0and s=L s−1,as shown,for example in Figs.29and30of Ref[4].Likewise the eigenvaluesΛH,i should correspond to 4-dimensional Dirac eigenvalues.For our conventions the components bound to the s=0wall are predominately left-handed while those concentrated on the s=L s−1wall are right-handed.It is important to recall that for a lattice withﬁnite L s,a left-handed mode can propagate with a very small probability to the right-handed wall,and visa-versa,giving a small breaking of chiral symmetry which,for low energy phenomena,can be described by a residual quark mass, m res.Our analysis is based primarily on55quenched gauge conﬁgurations generated with the Iwasaki gauge action[12]atβ=2.6and4-dimensional lattice volume164.We also examine 32conﬁgurations generated with the standard Wilson action atβ=6.0and the same volume.These two gauge actions have been choosen to correspond to approximately the same lattice spacing:a−1≈2GeV.The gauge conﬁgurations that we analyze are separated by2000sweeps of our updating algorithm,a simple two-subgroup heat-bath update of each link.The number of sites in theﬁfth dimension for the domain wall Dirac operator is L s=16,and the domain wall height is M5=1.8.For input quark mass we take m f=0for the Wilson action and m f=5·10−4for the Iwasaki case.This small,non-zero value of m f is used in the Iwasaki case to avoid the very slow convergence of the Kalkreuter Simma method that we found when using m f=0for that action.Finally,the residual quark mass for these couplings is quite small,m res≈0.0001for Iwasaki[9,10],and m res≈0.001for Wilson[9,4]which correspond to0.4and4MeV,respectively.To begin,let us examine the integrated or global chiral structure of D H.We plot the magnitude of ΛH,i|Γ5|ΛH,j in Figs.1and2for a typical“simple”and“complex”con-ﬁguration.The matrixΓ5represents the physicalγ5matrix in the domain wall fermion formalism[8]:ΛH,i|Γ5|ΛH,j = x∈V L s−1 s=0Ψ†ΛH,i(x,s)sign(s−(L s−1)/2)ΨΛH,j(x,s),(13)where V is the4-dimensional space-time volume.The pattern seen in Fig.1for the simple conﬁguration is precisely the chiral structure expected in the continuum.The single,diagonal element corresponding to|ΛH,0 represents a zero mode which is an eigenstate ofγ5with eigenvalue+1.(We will refer to such modes as“near zero modes”since for our choice of parameters,their eigenvalues are not precisely zero.)In our entire sample of Iwasaki and Wilson conﬁgurations,all such near zero modes have very small eigenvalues,Λ≈10−3−10−4,and all are either right-handed or left-handed within a given gauge conﬁguration.Note this behavior is a natural consequence of the Atiyah-Singer theorem which requires an excess of right-handed to left-handed zero modes equal to the winding number of the background gauge conﬁguration.This determines a minimum number of zero modes,all with the same chirality.The presence of additional zero modes would imply added constraints on the gauge background,corresponding to a set of zero measure if our near zero modes had a precisely zero eigenvalue.The remaining eigenvectors are grouped into pairs connected byγ5precisely as expected for the continuum Dirac operator in the limit of vanishing mass.These simple continuum expectations are not satisﬁed by the complex conﬁgurations, such as that shown in Fig.2.Of course,such conﬁgurations must be present forﬁnite L s andﬁnite lattice spacing.As the gauge conﬁgurations change continuously from one winding number to another,a plot of the sort shown in theseﬁgures must also change continuously and hence cannot always have the simple structure of Fig.1.While for the Wilson gauge action somewhat more than half of the conﬁgurations show the complex pattern of Fig.2,for the better-behaved Iwasaki case,this fraction has dropped to10%.It should be emphasized that all the low-lying eigenvectors studied,both complex and simple ones,fall oﬀrapidly away from the walls with the minimum magnitude of the wave function between the walls falling at least a factor thirty below its value on the two physical boundaries.Such gauge conﬁgurations in which the winding number is changing can be associated with zero modes of the4-dimensional Wilson Dirac operator with mass equal to−M5[13,14]. Numerical simulations[15]suggest that the density of such4-dimensional Dirac operator zero modes decreases exponentially with the exponential of the coupling,ρ∼e−c/√expects that localized,rapidly changing gaugeﬁelds will appear and small dislocations,on the scale of a very few lattice spacings will appear or disappear.It is natural to speculatethat such conﬁgurations produce the complexΓ5matrix elements of Fig.2and the non-zero density of4-dimensional Dirac zero modes described above.The comparison of Iwasaki andWilson results suggests that while such conﬁgurations are quite common for the Wilson gauge action when a−1≈2GeV,they are dramatically suppressed under similar circum-stances by the form of the action proposed by Iwasaki.This general topic is the subject ofmuch current research[17–20].If we are to systematically evaluate the domain wall fermion,QCD path integral,we must include all conﬁgurations in our analysis.Although we are explicitly examining the small eigenmodes of the Dirac operator,the eigenvalues and eigenfunctions represent a complex mixture of both long-distance and short-distance physics.While we are able to explicitly focus on small Dirac eigenvalues,the background gaugeﬁelds contain the full spectrum of short-and long-distanceﬂuctuations.This is immediately demonstrated by the potential importance of small,very short-distance dislocations in the gauge conﬁguration on quantities we are examining.However,we should also expect the more conventional short distance eﬀects of wave function and mass renormalization,including short-distance contributions to the residual mass,to inﬂuence the low lying eigenvalues and eigenvectors analyzed here.A brief discussion of these eﬀects on the eigenvalue spectrum can be found in Section VI C of Ref.[4].We speculate that these complex conﬁgurations,which do not behave as is expected for smooth,continuum gaugeﬁelds,represent such short-distance eﬀects.However, we should look carefully to see if conﬁgurations of the complex type introduce further chiral symmetry breaking at low energy beyond the simple residual mass described above.To date we have not recognized such eﬀects.The global chirality of our eigenvectors is summarized in Fig.3.The distribution showsa large narrow peak around zero corresponding to the non-zero modes and two smaller,but also narrow,peaks at±1corresponding to near zero modes.From theseﬁgures it is clear that we can easily distinguish near zero modes from non-zero modes,except for the handful of outliers with chirality neither close to zero nor±1.Next we examine the distribution of local chirality,X H(x)/ΩH(x),which is shown in Figs.4and5for near zero modes and non-zero modes,respectively.Here the quantities X H(x)andΩH(x)are the generalizations of the continuum quantitiesχH(x)andωH(x) deﬁned in Eq.8,to the case of domain wall fermions:ΩH(x)= 0≤s<L sΨΛH,i(x,s)†ΨΛH,i(x,s)X H(x)= 0≤s<L s sign(s−(L s−1)/2)ΨΛH,i(x,s)†ΨΛH,i(x,s)(14)The six histograms superimposed in Figs.4and5correspond to histograms of the quantity X H(x)/ΩH(x)evaluated only at those sites where the normal densityΩH(x)lies above a speciﬁed cut,for each of the eighteen eigenvectors that we have determined.The six cuts displayed correspond to the conditions:ΩH(x)·105>3,4,5,6,7and8which include8.6, 4.3,2.4,1.51.0and0.7%of the sites in the space-time lattice,respectively.These cuts correspond to sampling the local chirality,on average,from sites that account for28,19,13,10,8,and6%,respectively,of the total probability density of each eigenvector.In Table I we give these numbers with more precision for both the Iwasaki and Wilson cases.The near zero mode distributions are sharply peaked at±1for all cuts,as expected. The non-zero mode distributions are also clearly double-peaked,with peaks centered ap-proximately around±.95→±.8,depending on the size of the cut.The distributionsﬁll in between the peaks as more sites are sampled.Thus,our data show that deﬁnite chirality is strongly correlated with local maxima of both near zero and non-zero eigenmodes.The latter is certainly consistent with an instanton-dominated vacuum picture and is in disagreement with the recent work of Horvath,et al..We also note that the strong correlation between chiral and normal density for our non-zero mode eigenvectors is also evident if we use the deﬁnition of local chirality in[1]instead of the ratio X H(x)/ΩH(x).In Fig.6we show a similar set of histograms for the Wilson gauge action.Clearly the same strong correlation between chiral and normal density is seen for this case as well.We now discuss two important consistency checks on this potentially interesting result. First we determine the distribution of“global”chirality of each eigenvector when computed by including only those lattice sites selected by our cuts onΩH(x).We expect this distribu-tion to be similar to that found when summing over all sites in the lattice,with each non-zero mode showing approximately zero total chirality.The results are shown in Fig.7.While considerably broader than the distribution seen for the global chirality,it is still strongly peaked around zero with the sharpness of the peak decreasing as the cut onΩH(x)is made more stringent.This broadening is easily understood as the statistical eﬀect of examining the sum over a smaller number of space-time points.Over-all,Fig.7is quite consistent with the expectation that chirality of the non-zero mode eigenvectors is quite evenly split between left-and right-handed lumps.As a second consistency check,we investigate the extent to which the lowest lying18 eigenmodes which we examine actually play an important role in the low energy physics described by the gauge conﬁgurations being studied.An easy way to address this question is to compute the contribution of the modes which we have isolated to the chiral condensate and to compare that contribution to the total chiral condensate determined independently[4]. In Table II and Fig.8we present such a comparison.As can be seen,these lowest18 eigenvectors provide a large fraction of the actual value ofqq .However,for non-zero quark mass,the quadratically divergent contribution of high mass states∝m f/a2should make an increasingly important contribution.We can easily include these eﬀects,by using aﬁt toa−1qq =+a0+a1m f,(15)q qwhere a−1,a0,a1andδmqq by simply adding the term a1·(m f+m res)to−qq for m f in the range between0.0and0.01.This suggests that the18lowest modes thatwe have examined provide the bulk of the physical vacuum expectation valueHasenfratz became available[24].Our analysis and conclusions are quite similar to those of this paper.While both that paper and the present one,use improved fermion Dirac operators,overlap and domain wall respectively,we have used the gauge conﬁgurations directly,without smearing or fattening.This suggests that this strong correlation between spacial localization and chirality is seen even for gauge conﬁgurations whoseﬂuctuations span the full range of distance scales produced by both the Iwasaki and Wilson gauge actions.ACKNOWLEDGMENTSWe thank RIKEN,Brookhaven National Laboratory and the U.S.Department of Energy for providing the facilities essential for the completion of this work.We also thank Robert Edwards for providing us with his Ritz diagonalization program.The numerical calculations were done on the400Gﬂops QCDSP computer[25]at Columbia University and the600Gﬂops QCDSP computer[26]at the RIKEN BNL Research Center.This research was supported in part by the DOE under grant DE-FG02-92ER40699 (Columbia),in part by the DOE under grant DE-AC02-98CH10886(Dawson),and in part by the RIKEN-BNL Research Center(Blum).REFERENCES[1]I.Horvath,N.Isgur,J.McCune,and H.B.Thacker(2001),hep-lat/0102003.[2]T.Schafer and E.V.Shuryak,Rev.Mod.Phys.70,323(1998),hep-ph/9610451.[3]T.Banks and A.Casher,Nucl.Phys.B169,103(1980).[4]T.Blum et al.(2000),hep-lat/0007038.[5]E.Witten,Nucl.Phys.B149,285(1979).[6]E.Witten,Nucl.Phys.B156,269(1979).[7]Y.Shamir,Nucl.Phys.B406,90(1993),hep-lat/9303005.[8]V.Furman and Y.Shamir,Nucl.Phys.B439,54(1995),hep-lat/9405004.[9]A.A.Khan et al.(CP-PACS)(2000),hep-lat/0007014.[10]We(RBC collaboration)have repeated the calculation of m res in[9]forβ=2.6andL s=16andﬁnd the same result.[11]T.Kalkreuter and H.Simma,mun.93,33(1996),hep-lat/9507023.[12]Y.Iwasaki UTHEP-118.[13]R.Narayanan and H.Neuberger,Nucl.Phys.B443,305(1995),hep-th/9411108.[14]R.G.Edwards,U.M.Heller,and R.Narayanan,Nucl.Phys.B535,403(1998),hep-lat/9802016.[15]R.G.Edwards,U.M.Heller,and R.Narayanan,Phys.Rev.D60,034502(1999),hep-lat/9901015.[16]M.Luscher,Commun.Math.Phys.85,39(1982).[17]F.Berruto,R.Narayanan,and H.Neuberger,Phys.Lett.B489,243(2000),hep-lat/0006030.[18]R.G.Edwards and U.M.Heller(2000),hep-lat/0005002.[19]P.Hernandez,K.Jansen,and M.Luscher(2000),hep-lat/0007015.[20]Y.Shamir,Phys.Rev.D62,054513(2000),hep-lat/0003024.[21]G.T.Fleming et al.,Nucl.Phys.Proc.Suppl.73,207(1999),hep-lat/9811013.[22]S.J.Dong,F.X.Lee,K.F.Liu,and J.B.Zhang,Phys.Rev.Lett.85,5051(2000),hep-lat/0006004.[23]T.DeGrand and A.Hasenfratz(2000),hep-lat/0012021.[24]T.DeGrand and A.Hasenfratz(2001),hep-lat/0103002.[25]D.Chen et al.,Nucl.Phys.Proc.Suppl.73,898(1999),hep-lat/9810004.[26]R.D.Mawhinney,Parallel Comput.25,1281(1999),hep-lat/0001033.TABLE I.Fractions of lattice sites and eigenvector normalization included for the six cuts,ΩH(x)>Ωmin,used in this paper.Iwasaki Action Wilson Action30.0860.2850.0800.31940.0430.1860.0420.23550.0240.1320.0260.18660.0150.1000.0170.15670.0100.0790.0120.13680.0070.0640.0090.121TABLE II.Contributions to the chiral condensate from the18lowest eigenvectors examined in this paper,qq found in that paper.This comparison is done in the case of the Wilson action atβ=6.0where the detailed results forqq 18− qqFIG.1.The magnitude of the matrix elements ΛH,i|Γ5|ΛH,j evaluated on a“simple”conﬁg-uration.The pattern seen is close to that expected for matrix elements ofγ5in the continuum theory:The single near zero mode is an an approximate eigenstate ofΓ5while the non-zero modescome in±ΛH pairs related byΓ5ΨΛH =−ΨΛH.FIG.2.The magnitude of the matrix elements ΛH,i|Γ5|ΛH,j evaluated on a“complex”con-ﬁguration.For the Wilson gauge action more than one-half of the32conﬁgurations look like this while for the Iwasaki action only one in ten has this complex structure with the remaining90%appearing similar to Fig.1.−1−0.500.51Χglobal100200300400N u m b erFIG.3.The distribution of global chirality of the eigenvectors of D H evaluated at zero input quark mass,m f =0.−1−0.500.51ΧH (x)/ΩH (x)1e+052e+053e+054e+05N u m b erFIG.4.The distribution of local chirality X H (x )/ΩH (x )of near zero mode eigenvectors of D H on the Iwasaki ensemble of gauge ﬁelds for sites where Ψ†(x )Ψ(x )is greater than an arbitrary imposed cut.The diﬀerent cuts correspond to keeping between 1and 8%of the total sites in the space-time lattice.−1−0.500.51ΧH (x)/ΩH (x)500001e+05N u m b erFIG.5.The same quantities as in Fig.4,but for non-zero mode eigenvectors and again for the Iwasaki action.The double-peak structure is a feature expected in instanton-dominated models of the QCD vacuum.−1−0.500.51ΧH (x)/ΩH (x)200004000060000N u m b erFIG.6.The same quantities as in Fig.5,except now the Wilson gauge conﬁgurations are examined.The double-peak structure is very similar to that found in the Iwasaki case.−1−0.500.51(Χglobal )cut100200300400N u m b erFIG.7.The distribution of chiral density for non-zero mode eigenvectors of D H summed over those lattice sites obeying the cuts imposed on ΩH (x )as described in the text.As the cut is increased,the width of the distribution becomes more narrow.The distributions indicate that on average,chirality for a single eigenvector is evenly split into left-and right-handed lumps.m f -q q >FIG.8.qq presented in Ref.[4],and the ﬁt of the form given in Eq.15,we also plot the values obtained from the 18eigenvectors studied here (ﬁlled triangles)and the sum of those values with the contribution from far oﬀ-shell states,a 1(m f +m res )(ﬁlled diamonds).。

POSS文献

Progress in Polymer Science 36(2011)1649–1696Contents lists available at ScienceDirectProgress in PolymerSciencej o u r n a l h o m e p a g e :w w w.e l s e v i e r.c o m /l o c a t e /p p o l y s ciPOSS related polymer nanocompositesShiao-Wei Kuo a ,∗,Feng-Chih Chang b ,1a Department of Materials and Optoelectronic Science,Center for Nanoscience and Nanotechnology,National Sun Yat-Sen University,Kaohsiung 804,Taiwan bInstitute of Applied Chemistry,National Chiao-Tung University,Hsin-Chu 30050,Taiwana r t i c l e i n f o Article history:Received 22June 2010Received in revised form 5May 2011Accepted 6May 2011Available online 25May 2011Keywords:POSSNanocompositesStructure–property relationshipa b s t r a c tThis review describes the syntheses of polyhedral oligomeric silsesquioxane (T 8-POSS)compounds,the miscibility of POSS derivatives and polymers,the preparation of both multifunctional and monofunctional monomers and polymers containing POSS including styryl-POSS,methacrylate-POSS,norbornyl–POSS,vinyl-POSS,epoxy–POSS,phenolic–POSS,benzoxazine–POSS,amine-POSS,and hydroxyl-POSS.The thermal,dynamic mechanical,electrical,and surface properties of POSS-related polymeric nanocom-posites prepared from both monofunctional and multifunctional POSS monomers are discussed.In addition,we describe the applications of several high-performance POSS nanocomposites in such systems as light emitting diodes,liquid crystals,photo-resist materials,low-dielectric constant materials,self-assembled block copolymers,and nanoparticles.©2011Elsevier Ltd.All rights reserved.Contents 1.Introduction (1651)2.General approaches in the syntheses of polyhedral oligomeric silsesquioxanes................................................16512.1.Monofunctional POSS.....................................................................................................16522.2.Multifunctional POSS .....................................................................................................16523.Hydrogen bonding and miscibility behavior of polymer/POSS nanocomposites................................................16523.1.Hydrogen bonding interactions between polymers and POSS...........................................................16523.2.Miscibility between polymers and POSS derivatives.....................................................................16544.POSS-containing polymers and copolymers .....................................................................................16574.1.Polyoleﬁn/POSS and norbornyl/POSS copolymers .......................................................................16574.1.1.Polyethylene and norbornyl/POSS copolymers.................................................................16574.1.2.Polypropylene/POSS nanocomposites..........................................................................16594.1.3.Other polyoleﬁn POSS nanocomposites ........................................................................16604.2.Polystyrene/POSS nanocomposites.......................................................................................16604.3.Poly(acrylate)/POSS copolymers..........................................................................................16624.4.Poly(ethylene oxide)/POSS nancomposites...............................................................................16644.5.Polyester/POSS nanocomposites..........................................................................................16654.5.1.PCL/POSS nanocomposites......................................................................................16654.5.2.Other polyester/POSS nanocomposites.........................................................................1666∗Corresponding author.Tel.:+88675252000x4079;fax:+88675254099.E-mail addresses:kuosw@.tw (S.-W.Kuo),changfc@.tw (F.-C.Chang).1Fax:+88635131512.0079-6700/$–see front matter ©2011Elsevier Ltd.All rights reserved.doi:10.1016/j.progpolymsci.2011.05.0021650S.-W.Kuo,F.-C.Chang/Progress in Polymer Science36(2011)1649–16964.6.Polyamide/POSS nanocomposites (1667)4.6.1.Nylon/POSS nanocomposites (1667)4.6.2.PNIPAM/POSS nanocomposites (1667)4.6.3.PVP/POSS nanocomposites (1667)4.6.4.Other polyamide/POSS nanocomposites (1668)4.7.Polyimide/POSS nanocomposites (1670)4.8.Polyurethane/POSS nanocomposites (1672)4.9.Phenolic/POSS nanocomposites (1673)4.10.Epoxy/POSS nanocomposites (1674)4.10.1.Multifunctional epoxy–POSS nanocomposites (1674)4.10.2.Multifunctional NH2-POSS and OH-POSS nanocomposites (1676)4.10.3.Monofunctional epoxy–POSS and NH2-POSS nanocomposites (1677)4.10.4.Other epoxy/POSS systems (1678)4.11.Polybenzoxazine/POSS nanocomposites (1679)5.POSS-containing functional materials (1680)5.1.Polymer light emitting diodes(PLEDs)incorporating POSS hybrid polymers (1680)5.2.Liquid crystal polymers(LCPs)incorporating POSS hybrid polymers (1681)5.3.Lithographic applications of POSS-containing photoresists (1681)5.4.Low-k applications of POSS-containing materials (1683)5.5.Self-assembly behavior of POSS-containing block copolymer materials (1684)5.6.Nanoparticle with POSS-containing materials (1686)5.6.1.POSS modiﬁed clay nanocomposites (1686)5.6.2.POSS modiﬁed gold nanoparticles (1687)6.Conclusions (1689)Acknowledgments (1689)References (1689)NomenclatureAFM atomic force microscopyAM-POSS aminopropylisobutyl POSSATRP atom transfer radical polymerizationiBu-POSS isobutyl-POSSCD cyclodextrinsCp-POSS cyclopentyl-POSSCy-POSS cyclohexyl-POSSDDM4,4 -diaminodiphenyl methaneDDS4,4 -diaminodiphenyl sulfoneDMA dynamic mechanic analysisDSC differential scanning calorimetryDOP dioctyl phthalateDGEBA diglycidyl ether bisphenol AIR infrared spectroscopyLiClO4lithium perchlorateMAiBu-POSS methacrylo isobutyl-POSSNMR nuclear magnetic resonanceMALDI-TOF matrix-assisted laser desorption ionization-time ofﬂightOA-POSS octakis[dimethyl(4-acetoxyphenethyl)siloxy]-POSSOAM-POSS octa(aminopropyl)-POSSOAP-POSS octakis(aminophenyl)-POSSOiBu-POSS octaisobutyl-POSSODA4,4 -diaminodiphenyl etherODADS4,4 -diaminodiphenyl ether-2,2 -disulfonic acidOEC-POSS octaepoxycyclohexyldimethylsilyl-POSS OF-POSS octakis(dimethylsiloxyhexaﬂuoropropyl ether)-POSS OG-POSS octaglycidyl dimethylsilyl-POSSOH-POSS octakis(3-hydroxypropyldimethylsilyl)-POSSOMA-POSS octamethacryl-POSSOM-POSS octa-methyl-POSSOP-POSS octakis[dimethyl(4-hydroxyphenethyl)siloxy]-POSSOV-POSS octa-vinyl POSSOPE-POSS octa-phenethyl-POSSOS-POS octakis[dimethyl(phenethyl)siloxy]-POSS PA polyamidePAA poly(amic acid)PAMAM poly(amidoamine)PAS poly(acetoxystyrene)PBD poly(butadiene)PBLG poly(␥-benzyl-l-glutamate)PBT poly(butylene terephathlate)PC poly(carbonate)PCL poly(␧-caprolactone)PDIB-POSS1,2-propanediolisobutyl-POSSPE poly(ethylene)PEEK poly(ether ether ketone)PEI poly(ethyelene-imine)PET poly(ethylene terephthalate)PLGA poly(lactide-co-glycolide)POSS polyhedral oligomeric silsesquioxanePP poly(propylene)PPO poly(dimethyl phenylene oxide)PP-g-MA PP-grafted maleic anhydridePS poly(styrene)PSMA poly(styrene-co-maleic anhydride)S.-W.Kuo,F.-C.Chang/Progress in Polymer Science36(2011)1649–16961651PU polyurethanePVC poly(vinyl chloride)PVP poly(vinyl pyrrolidone)P4VP poly(4-vinyl pyridine)PVPh poly(vinyl phenol)Q8M8H octakis(dimethylsiloxy)silsesquioxaneSAXS small-angel X-ray scatteringSEM scanning electron microscopySH-POSS mercaptopropyl-isobutyl-POSSTEM transmission electron microscopyTGA thermal gravity analysisWAXD wide-angle X-ray diffraction1.IntroductionRelative to metals and ceramics,polymeric materials generally have lower moduli and strength.One way to effectively improve the mechanical properties of polymers is to reinforce them with nano-sized inorganic parti-cles(deﬁned herein as having at least one dimension in the range1–100nm).Using this approach,the polymer properties can be efﬁciently improved while maintaining its inherently low density and high ductility.Improve-ments in mechanical properties are often found even at relatively lowﬁller content.The nanoﬁllers may have spherical(metal or semi-conductive nanoparticles(NPs)), layered(clay),orﬁbrous(nanoﬁbers and carbon nan-otubes)shapes.Such polymer nanocomposites are diverse and versatile functional materials,with applications in sys-tems ranging from electronic devices to biosensors and catalysts.Theﬁeld of polymer nanocomposite materials has attracted great attention from polymer scientists and engineers in recent years.The simple premise involves using building blocks of nanosize dimensions to create new polymeric materials exhibiting improved physical proper-ties.Silsesquioxanes are nanostructures having the empir-ical formula RSiO1.5,where R is a hydrogen atom or an organic functional group such as an alkyl,alkylene, acrylate,hydroxyl,or epoxide unit.Based on images in theﬁrst review of POSS polymers and resins pub-lished by the Pittman group,Fig.1illustrates that silsesquioxanes can be formed as random,ladder,cage, or partial cage structures[1,2].Scott[3]discovered the ﬁrst oligomeric organosilsesquioxane,(CH3SiO1.5)n,along with other volatile compounds through the thermolysis of polymeric products prepared from co-hydrolysis of methyl trichlorosilane and dimethyl chlorosilane.Although silsequioxane chemistry has been studied for more than half a century,interest in thisﬁeld has increased dramatically in recent years.Baney et al.[4] reviewed the preparation,properties,structures,and appli-cations of silsesquioxanes,especially those of ladder-like polysilsesquioxanes(Fig.1(b)).More recently,attention has been concentrated on silsesquioxanes possessing the speciﬁc cage structures displayed in Figs.1(c)–(f). These polyhedral oligomeric silsesquioxanes are com-monly referred to by the acronym“POSS”.Derivatives of POSS are true hybrid inorganic/organic chemical compos-ites that possess an inner inorganic silicon and oxygen core(SiO1.5)n and external organic substituents that can feature a range of polar or nonpolar functional groups. POSS nanostructures having diameters ranging from1to 3nm can be considered as the smallest possible parti-cles of silica,i.e.,molecular silica.Unlike most silicones orﬁllers,POSS molecules contain organic substituents on their outer surfaces,making them compatible or mis-cible with most polymers.In addition,these functional groups can be speciﬁcally designed as either non-reactive (e.g.,for polymer blending)or reactive(for copolymer-ization).POSS derivatives can be prepared with one or more covalently bonded reactive functionalities suitable for polymerization,grafting,blending,or other trans-formations.Unlike traditional organic compounds,POSS derivatives are nonvolatile,odorless and environmentally friendly materials.The incorporation of POSS moieties into a polymeric material can dramatically improve its mechanical properties(e.g.,strength,modulus,rigidity)as well as reduce itsﬂammability,heat evolution,and vis-cosity during processing.These enhancements apply to a wide range of commercial thermoplastic polymers,high-performance thermoplastic polymers,and thermosetting polymers[1,2].It is especially convenient to incorporate POSS moieties into polymers through simple blending or copolymerization.In addition,when POSS monomers are soluble in monomer mixtures,they can be incorporated as true molecular dispersions in the resulting polymer matrix. The macrophase separation that usually occurs through the aggregation of POSS units can be avoided through copoly-merization(i.e.,covalent bond formation between the POSS units and the polymers)-a signiﬁcant advantage over the traditionalﬁller technologies.POSS nanostructures also have signiﬁcant promise for use in catalyst supports and biomedical applications,such as scaffolds for drug delivery, imaging reagents,and combinatorial drug development [5,6].In this review,we describe methods for synthesizing POSS compounds and preparing monomers and polymers containing POSS derivatives.We discuss both mono-and multifunctional POSS monomers that have been used to develop thermoplastic and thermosetting polymers.In addition,we compare the miscibility,phase behavior,ther-mal,dynamic mechanical,electrical,and surface properties of polymers containing POSS units.2.General approaches in the syntheses ofpolyhedral oligomeric silsesquioxanesPOSS derivatives featuring Si–O linkages in the form of a cage present a silicon atom at each vertex,with substituents coordinating around the tetrahedral silicon vertices.The nature of the exo cage substituents in such compounds determines the mechanical,thermal,and other physical properties.The number of RSiO3units determines the shape of the frame,which is uniquely unstrained for 6–12units.Voronkov et al.[7]have reviewed the known methods of synthesizing POSS compounds.Many sub-stituents appended to the silicon/oxygen cages(RSiO1.5)n, (where R is an organic or inorganic group)allow the poly-1652S.-W.Kuo,F.-C.Chang /Progress in Polymer Science 36(2011)1649–1696Fig.1.Structures of silsesquioxanes.merization of POSS units or the copolymerization of speciﬁc POSS derivatives with other monomers.2.1.Monofunctional POSSMonofunctional POSS derivatives are among the most useful compounds for polymerization or copolymerization with other monomers.Fig.2summarizes the three general approaches to synthesize monofunctional POSS derivatives of the form R R 7Si 8O 12[10].Route I.Cohydrolysis of trifunctional organo-or hydrosi-lanes:Polycondensation of monomers is the classical method of synthesizing silsesquioxanes [8–10].When this reaction is performed in the presence of monomers pos-sessing various R groups,mixtures of heterosubstituted compounds are obtained,including the desired monosub-stituted products (ca.48%overall yield).Route II.Substitution reactions with retention of the silox-ane cage :Fig.2presents a selection of substitution reactions using octahydro-silsesquioxanes as the starting materi-als (IIa–c)that have been applied successfully to prepare monosubstituted silsesquioxanes [11–13].By adjusting the ratio of the reactants,it is possible to obtain a considerable yield (18.6–43.6%)of the desired monosubstituted product.Route III.Corner-capping reactions :Feher and coworkers [14–17]developed this approach starting from incom-pletely condensed R 7Si 7O 9(OH)3molecules (T 7).The three silanol groups are very reactive toward R SiCl 3,giving the fully condensed products.Variation of the R group on the silane enables the syntheses of a variety of monofunction-alized siloxane cages [18].Subsequent transformations can be performed until the desired functionality is obtained.Moreover,incompletely condensed silsesquioxanes offer a route for the generation of hetero-and metalla-siloxanes,in which a hetero main group or a transition metal element is introduced into the Si–O framework [19–21].2.2.Multifunctional POSSPOSS (R SiO 1.5)n derivatives have values of n of 4,6,8,10,or 12,with the R groups being hydrogen,alkyl,aryl,or inorganic units.Unique POSS structures (R =H)can be formed through the hydrolysis and con-densation of trialkoxysilanes [HSi(OR)3]or trichlorosilanes (HSiCl 3)[7].The hydrolysis of trimethoxysilane in a cyclohexane/acetic acid mixtures in the presence of con-centrated hydrochloric acid provides the octamer in low yield (13%)[22].Another synthetic approach to generate multifunctional POSS derivatives is the functionaliza-tion of preformed POSS cages;e.g.,through Pt-catalyzed hydrosilylation of alkenes or alkynes with (HSiO 1.5)8and octakis(dimethylsiloxy)silsesquioxane ((HMe 2SiOSiO 1.5)8,Q 8M 8H )cages (Fig.3)[23–25].3.Hydrogen bonding and miscibility behavior of polymer/POSS nanocomposites3.1.Hydrogen bonding interactions between polymers and POSSMost inorganic silicas or ceramics are immiscible in most organic polymer systems because of poor speciﬁc interactions within these organic/inorganic hybrids and the negligibly small combined entropy contribution to the free energy of mixing.Speciﬁc intermolecular inter-actions are generally required to enhance the miscibility of polymers and inorganic particles.Such interactions include hydrogen bonding,dipole–dipole interactions and acid/base complexation [26].Determining the types and strengths of the interactions between the POSS derivatives and polymers is an important challenge.For convenience,our group has prepared a phenolic/POSS hybrid from a mixture of phenolic resin and an ocatisobutyl-POSSS.-W.Kuo,F.-C.Chang/Progress in Polymer Science36(2011)1649–16961653Fig.2.Three general ways to synthesize monosubstituted octasilasesquioxane.(OiBu-POSS)to investigate the miscibility,speciﬁc interac-tions,and microstructural behavior[27].The nature of the hydrogen bonding sites in the phenolic/POSS hybrid was investigated,using2D-IR correlation spectroscopy[28,29]. Fig.4presents the synchronous and asynchronous2D correlation maps in the range from1000to1250cm−1 [27].The absorption bands of the OiBu-POSS derivative at 1100and1223cm−1correspond to siloxane Si–O–Si and Si–C stretching vibrations,respectively,and the peak at 1223cm−1is due to the phenyl–OH stretching vibration of the phenolic.Two positive cross-peaks in the synchronous 2D map in Fig.4(a)indicate the existence of hydrogen bonds between the siloxane group of the POSS deriva-tive(1100cm−1)and the phenyl–OH group(1223cm−1) Fig.3.An example of the synthesis of a multifunctional POSS,(octakis[dimethyl(phenethyl)siloxy]silsesquioxane,OS-POSS).1654S.-W.Kuo,F.-C.Chang /Progress in Polymer Science 36(2011)1649–1696Fig.4.The synchronous version (a)and asynchronous version (b)of 2D correlation map at 1000–1250cm −1region for phenolic/OiBu-POSS blends under compositions pertubation.Reprinted with permission from Ref.[27].Copyright 2004,Wiley-VCH,Germany.of the phenolic.In the asynchronous 2D correlation map in Fig.4(b),the 1100cm −1absorption splits into two sepa-rate bands located at ca.1105and 1160cm −1for the POSS units,suggesting two different types of siloxane (Si–O–Si)sites in the POSS cage.One (at higher wavenumber)under-goes hydrogen bonding with the OH groups of the phenolic,while the other (at lower wavenumber)is free.The positive crosspeaks at 1105and 1220cm −1also reveals the pres-ence of hydrogen bonding between the siloxane (Si–O–Si)groups of the POSS and the phenyl–OH groups of the phe-nolic resin.3.2.Miscibility between polymers and POSS derivatives Painter and Coleman [26]suggested that adding an additional term to the simple Flory–Huggins expression to account for the free energy of hydrogen bond formation upon mixing two polymers,as formulated in Eq.(1): G m RT = A M A ln A + B M B ln B + A B AB + G HRT(1)where G H denotes the free energy change contributed by the hydrogen bonding between the two components.The combinatorial entropy expressed in the ﬁrst two log-arithmic terms contributes a very small,but nonetheless favorable,amount to the free energy of mixing. A and B are the volume fractions of polymers A and B in the blend,respectively,and M A and M B are the corresponding degrees of polymerization.According to the Painter–Coleman asso-ciation model (PCAM)[30,31],the equilibrium constant for the association of a non carbonyl group component with a hydrogen bond-donating component can be calculated using the classical Coggeshall and Saier (C&S)equation (2)[32]:Ka =1−f mOHf mOH(C A −(1−f m OH)C B )(2)where C A and C B are the concentrations (in mol L −1)ofOiBu-POSS and 2,4-dimethylphenol (a model compoundfor phenolic)and f OH mis the fraction of free hydroxyl group of 2,4-dimethylphenol.Fig.5displays the OH group absorption of 2,4-dimethylphenol in cyclohexane solu-tions containing various concentrations ofOiBu-POSS;Fig.5.FT-IR spectra of 2,4-dimethylphenol (xylenol)with various OiBu-POSS concentrations.Reprinted with permission from Ref.[27].Copyright 2004,Wiley-VCH,Germany.S.-W.Kuo,F.-C.Chang /Progress in Polymer Science 36(2011)1649–16961655Fig.6.Chemical Structures of octakis[dimethyl(4-acetoxy phenethyl)siloxy]-POSS (OA-POSS)and octakis[dimethyl(4-hydroxyphenethyl)siloxy]-POSS (OP-POSS).the intensity of the free OH absorption at 3620cm −1decreases upon increasing the OiBu-POSS content.The absolute intensity of the free OH group at 3620cm −1is an indication of the content of free OH groups in the mixture [33,34].The value of K A of 38.67was obtained by using C&S equation.The equilibrium constant for self-association of the Novalic type phenolic resin is 52.3[33].Since the equilibrium constant for the association between phenolic/OiBu-POSS is smaller than that for the self-association of pure phenolic,the phenolic/OiBu-POSS hybrid should be partially miscible or immiscible.For this reason,functionalization of POSS derivatives with pendent hydrogen bond-acceptor groups should improve their mis-cibility with phenolic resin.Functionalization of Q 8M 8H can be achieved through hydrosilylation of its Si–H groups with acetoxystyrene [35]in the presence of a Pt catalyst to form octakis[dimethyl(4-acetoxy phenethyl)siloxy]silsesquiox-ane [OA-POSS;Fig.6(b)].Fig.7presents scaled room temperature IR spectra of pure phenolic and various phenolic/OA-POSS nanocom-posites [35].Fig.7a reveals that the intensity of the free OH absorption (3525cm −1)decreases gradually as the OA-POSS content of the blend is increased from 5to 90wt%.The band for the hydrogen-bonded OH units in the pheno-lic shifted to higher frequency (toward 3465cm −1)upon increasing the OA-POSS content.This change is due to the switch from hydroxyl–hydroxyl interactions to the formation of hydroxyl–carbonyl and/or hydroxyl–siloxane hydrogen bonds.Fig.7b displays the room temperature IR spectra (1680–1820cm −1)of various phenolic/OA-POSS blend composites.The C O stretching frequency is split into bands at 1763and 1735cm −1,corresponding to free and hydrogen-bonded C O groups,respectively [36–39].Fig.8indicates that the experimental values of K A are generally lower than the predicted values when using the value of K A of 64.6obtained from the pheno-lic/PAS blends [34].This result reveals that the OH groups of phenolic interact with the C O groups of the ace-toxystyrene units as well as the siloxane groups of the POSS core.The equilibrium constants K A for the associ-ation of phenolic/OA-POSS and the phenolic/PAS blend blends are 26.0and 64.6.Therefore,the value of K A for the interaction between the OH group of phenolic and the siloxane groups of the POSS derivative is equal to 38.6(i.e.,64.6–26.0=38.6),consistent with the value reported based on the classical C&S methodology [32].Our group also synthesized a new POSS derivative containing eight phe-nol groups (octakis[dimethyl(4-hydroxyphenethyl)siloxy]silsesquioxane,OP-POSS,Fig.6(b))and copolymerized it with phenol and formaldehyde to form covalently linked novolac-type phenolic/OP-POSS nanocomposites that exhibited higher thermal stabilities and lower surface energies [40].Differential scanning calorimetry (DSC)and thermogravimetric analysis (TGA)of the phenolic/OP-POSS nanocomposites at various weight ratios revealed that each of these hybrids possessed essentially a single value of T g ,suggesting that they each featured a single phase [40].The values of T g of these nanocomposites were signiﬁcantly enhanced after incorporation of OP-POSS units,presum-ably because of the restricted motion of the polymer chains caused by physical crosslinking through hydrogen bonds with the evenly distributed POSS units within the phenolic matrix.In addition,our group has synthesized three amor-phous POSS derivatives:OS-POSS (Fig.3),OA-POSS and OP-POSS (Fig.6).Fig.9displays MALDI-TOF mass spec-tra of these compounds.Monodisperse mass distributions of the sodiated molecular ions appear at 1873g/mol for [OS-POSS +Na]+,2337g/mol for [OA-POSS +Na]+,and 2001g/mol for [OP-POSS +Na]+,the good agreement between the experimental and calculated molecular masses conﬁrms the well-deﬁned structures of OS-POSS,1656S.-W.Kuo,F.-C.Chang /Progress in Polymer Science 36(2011)1649–1696Fig.7.IR spectra for phenolic/AS-POSS blends:(a)hydroxyl and (b)carbonyl.Reprinted with permission from Ref.[35].Copyright 2006,Wiley-VCH,Germany.OA-POSS,and OP-POSS [25].Blending OS-POSS,and OP-POSS with polystyrene PS,PAS,or P4VP facilitated investigation of the effects of intermolecular interac-tions on the dispersion of these POSS derivatives in the polymer matrices [hydrophobic interactions between aromatic rings (OS-POSS/PS),dipole–dipole interactions between ester groups (OA-POSS/PAS),and hydrogen bond-ing between phenol and pyridine units (OP-POSS/P4VP)].Fig.10displays transmission electron microscopy (TEM)images and schematic representations of the microstruc-tures of these POSS-based polymer nanocomposites [25].Fig.8.Fraction of hydrogen-bonded carbonyl groups versus phenolic con-tents.Reprinted with permission from Ref.[27].Copyright 2006,Wiley-VCH,Germany.Our octakis-functionalized amorphous POSS derivatives were dispersed through physical intermolecular interac-tions between their outer organic units and the organic polymer matrices.Thus,the size and distribution of the POSS aggregates depend strongly on the type and strength of the intermolecular interactions.Clearly,the weak aro-matic hydrophobic interactions between OS-POSSandFig.9.MALDI-TOF mass spectra of (a)octakis[dimethyl(phenethyl)siloxy]silsesquioxane,(OS-POSS),(b)octakis[dimethyl(4-acetoxy phenethyl)siloxy]-POSS (OA-POSS)and octakis[dimethyl(4-hydroxyphenethyl)siloxy]-POSS (OP-POSS).Reprinted with permission from Ref.[25].Copyright 2008,Elsevier Science Ltd.,UK.S.-W.Kuo,F.-C.Chang/Progress in Polymer Science36(2011)1649–16961657Fig.10.TEM images and schematic microstructures of POSS-based polymer nanocomposites(a–c)OS-POSS/PS,(d–f)OA-POSS/PAS,and(g–i)OP-POSS/P4VP. Reprinted with permission from Ref.[25].Copyright2008,Elsevier Science Ltd.,UK.PS were unable to overcome the attraction force among of the POSS cores,even though premixing did promote uniform dispersion of the POSS derivatives.With their stronger intermolecular dipole–dipole interactions,we do not observe any dark regions representing OA-POSS aggre-gates.The polar P4VP is also miscible in OP-POSS because of hydrogen bonding between hydroxyl and pyridine units.4.POSS-containing polymers and copolymersPOSS feedstocks functionalized with various reactive organic groups can be incorporated into virtually any exist-ing polymer system through grafting,copolymerization or blending.The incorporation of POSS nanocluster cages into a polymeric material can result in dramatic improvements in the polymer’s properties including greater temperature and oxidation resistance,surface hardening,and reduc-tion inﬂammability.Therefore,research in POSS-related polymers and copolymers has accelerated in recent years. Depending on the number of POSS functional groups,vari-ous architectures of polymer/POSS nanocomposites can be obtained(Fig.11)[41].Some representative systems are discussed below.4.1.Polyoleﬁn/POSS and norbornyl/POSS copolymers4.1.1.Polyethylene and norbornyl/POSS copolymersA number of interesting design strategies for the prepa-ration of polyoleﬁn/POSS hybrid materials have evolved over the past decade[42–50].Coughlin and coworkers [42]synthesized PE hybrid containing POSS through ring-opening metathesis copolymerization(Fig.12).From studies of nanostructured PE-POSS copolymers through controlled crystallization and aggregation,they found that two distinctly different crystallizing components were present in these copolymers and theﬁnal structure depended on the respective crystallization kinetics under different crystallization conditions[42].Fig.13presents TEM micrographs of polybutdaine-POSS(PBD-POSS)ran-dom copolymers with POSS contents of12and43wt%[51]. In Fig.13(a),POSS aggregates are clearly observed as short randomly oriented lamellae having lateral dimensions of ca.50nm.The thickness of the lamellae ca.3–5nm,roughly corresponds to twice the diameter of a POSS NP.Increasing the incorporation ratio of POSS to43wt%resulted in the formation of continuous lamellae having lateral lengths on the order of microns(Fig.13(c)).The irregular lamellar spacing observed in this image possibly arose from a combination of both twisting of the POSS lamella and the random nature of the copolymers.The morphology bears similarity to the lamellar morphology formed by precise diblock copolymers[51].Furthermore,Coughlin and coworkers[42,52]and Mather et al.[53]reported polyoleﬁn copolymers containing norbornyl–POSS macromonomers.Polyoleﬁn-POSS copolymers incor-porating norbornylene–POSS macromonomer have been prepared using a metallocene/methyl aluminoxane(MAO) co-catalyst system[52].Using a Pd-diimine catalyst,Ye and。

化工专业英语Unit8

通过改变工艺或者精炼模式它可以用于许多燃料的生产，而通过化学改变可以用于许多纯的化学物质——石油化工产perate continuously. First a tubular
heater（管式加热器） supplies hot oil to an efficient
异构烷烃系列，CnH2n+2 。这些带有支链的烷烃在内燃机中表现的比正构烷烃好因而是（人们）更加渴望得到的。他们也可以通过重整、烷基化、聚合反应或者异构化反应来制备。在原油中只有一小部分是以异构烷烃的形式存在。
• Olefin(石蜡), or Alkene（烯烃） Series, CnH2n.
paraffins and hence are considered more
desirable. They may be formed by catalytic
reforming, alkylation, and polymerization. Only
small amounts exist in crudes.
因为它是一种几千种有机物质的混合物，所以已经证明它可以适应我们（不断）改变的需要。
It has been adapted, through changing patterns of processing or refining, to the manufacture of a variety of fuels and through chemical changes to the manufacture of a host of pure chemical substances, the petrochemicals（石化产品） .
（期间）所采用的处理工艺包括各种个样的裂化单元（使大分子转化为小分子的操作），如聚合、重整、氢化裂解、氢化处理、异构化和更深度的处理——炼焦，（还有）许多其他的设计的工艺用来改变沸点和分子的几何（形状）。

On the Decay Mode $B^- to mu^- bar nu_mu gamma$

a rXiv:h ep-ph/966219v14J un1996BARI-TH/96-235May 1996On the Decay Mode B −→µ−¯νµγP.Colangelo a,1,F.De Fazio a,b ,G.Nardulli a,b 2a Istituto Nazionale di Fisica Nucleare,Sezione di Bari,Italy b Dipartimento di Fisica,Universit´a di Bari,Italy ABSTRACT A QCD relativistic potential model is employed to compute the decay rate and the photon spectrum of the process B −→µ−¯νµγ.The result B (B −→µ−¯νµγ)≃1×10−6conﬁrms the enhancement of this decay channel with respect to the purely leptonic mode,and supports the proposal of using this process to access relevant hadronic quantities such as the B -meson leptonic decay constant and the CKM matrix element V ub .Noticeable theoretical attention has been recently given to the weak radiative decayB−→µ−¯νµγ.(1) The reason is in the peculiar role of this decay mode for the understanding of the dynamicsof the annihilation processes occuring in heavy mesons[1,2,3,4].Moreover,it has beenobserved that(1)can be studied to obtain indications on the value of the B-mesonleptonic constant f B using a decay channel which diﬀers from the purely leptonic modesB−→ℓ−¯νℓ,and is not hampered by the limitations aﬀecting those latter processes.Such diﬃculties mainly consist in low decay rates3(using V ub=3×10−3,f B=200MeV andτB−=1.646±0.063ps[5]one predicts B(B−→e−¯νe)≃6.610−12and B(B−→µ−¯νµ)≃2.810−7)or in reconstruction problems for B−→τ−¯ντ.In ref.[4]heavy quark symmetry and experimental data on D∗0→D0γhave been exploited to study the dependence of B(B−→µ−¯νµγ)on the heavy meson decay constant ˆF/√m b from future experimental data,in this letter we study the decay(1)within a well deﬁned theoretical model in order to have an independent estimate of the decay rate.We employ a relativistic constituent quark model already used to study several aspects of the B-meson phenomenology[7,8,9].Within this model the mesons are represented as bound states of valence quarks and antiquarks interacting via a QCD inspired istantaneous potential with a linear dependence at large distances,to account for conﬁnement,and a modiﬁed coulombic behaviour at short distances to include the asymptotic freedom property of QCD.We adopt the interpolating form between such asymptotic dependencesprovided by the Richardson potential [10]4.Intherestframe,the state describing a B a meson is represented as:|B a >=i αβδαβ3 rs δrs 2 d k 1ψB ( k 1)b †( k 1,r,α)d †a (− k 1,s,β)|0>,(2)where αand βare colour indices,r and s are spin indices,b †and d †a are creation operators of the quark b and the antiquark ¯q a ,carrying momenta k 1and − k 1respectively.The B -meson wave function ψB ( k 1)satisﬁes a wave equation with relativistic kinematics (Salpeter equation)[11]taking the form (in the meson rest frame):k 21+m 2q a −M B a ψB ( k 1)+ d k ′1V ( k 1, k ′1)ψB ( k ′1)=0(3)where V ( k 1, k ′1)is the interaction potential in the momentum space and ψB is covariantlynormalized:1√3e ¯u (0)γνu (0)−14A smearing of the Richardson potential at short distances has also been introduced to take into account the eﬀects of the relativistic kinematics;see ref.[8]for the explicit form of the potential.2pieces in the e.m.current correspond to the coupling to the light quark and to the heavy quark,respectively.The corresponding contributions toΠµνwill be referred to asΠℓµνandΠhµν,depicted inﬁgs.1a,b.Πℓµνcontains the light quark propagator:S u(x,0)= d4ℓℓ2−m2u(ℓ/+m u)(7) whileΠhµνcontains the analogous b quark propagator.The calculation of the time-ordered product appearing in(6)gives:Πℓµν=−2(2π)4e iℓ·x3↔−1 (2π)3 m b m uq2+m2q and u q(v q)are quark(antiquark)spinors.By exploiting anticommutation relations among annihilation and creation operators, we obtain,in the B meson rest frame:Πµν=i e6 rd3k1E b( k1)E u( k1) 1/2(10)¯v u(− k1,r) −2γν[(q/2−q/)+m u]γµ(1−γ5)(q1−q)2−m2b u b( k1,r) where q1=(E u,− k1)and q2=(E b, k1).We recognize in the two factors in the curly brakets the contributions ofΠℓµνandΠhµν,respectively.SinceΠµνonly depends on two vectors,the B meson momentum pµand the photon momentum kµ,it can be written in terms of six independent Lorentz structures:Πµν=αpµpν+βkµkν+ζkµpν+δpµkν+ξgµν+iηǫµνρσpρkσ.(11)3By gauge invariance one hasα=0andξ=−p·kζ;moreover,after saturation byǫ∗νone gets:Πµ=Πµνǫ∗ν=[ζ(kµpν−p·kgµν)+iηǫµνρσpρkσ]ǫ∗ν,(12) i.e.only the terms proportional toηandζsurvive:they are the vector and the axial vector contribution,respectively.It is convenient to compute eq.(12)in the B rest frame p=(M B, 0),with k=(k0,0,0,k0);the result reads:ζ=Π11i M B k0.(13)At this point,it is straightforward to calculate the rate of the decay process(1);one obtains(mµ≃0):Γ(B−→µ−¯νµγ)=G2F|V ub|24√EbE u(E b+m b)(E u+m u) 1/2−2g (M B−k0)[| k1|2−(E b+m b)(E u+m u)]+| k1|2cos2θ(E u+m u−E b−m b)−| k1|k0cosθ(E u+m u−E b−m b)+(E b+m b)(E u+m u)(E u+m b)−(E u−m b)| k1|2andΠ12=e3π 1−1dcosθ| k1|max0| k1|d| k1|u B(| k1|) 1f−1g =m 2u +M 2B −2M B k 0−2M B E u +2E u k 0+2k 0| k 1|cosθ−m 2b ,(18)whereas the S-wave reduced function u is related to ψB :u B (| k 1|)=| k 1|2πψB ( k 1);(19)we plot in ﬁg.2the function u B obtained as a solution of the wave equation (3).Let us now point out that in computing the diagrams in ﬁgs.1a,b and,therefore,in eqs.(15),(16),we have so far imposed 4-momentum conservation for the physical parti-cles B ,µ,νand γin the process (1).On the other hand,energy conservation has to be imposed also at quark level since,otherwise,(15)and (16)would present spurious kine-matical singularities.In order to deal with this problem we follow the approach originally proposed within the ACCMM model [12]for the decay b →u ℓ¯νℓ.One assumes that the spectator quark has a deﬁnite mass,while the active quark has a ”running”mass,deﬁned consistently with the energy conservation:E b +E u =M B .(20)Therefore,as in the case of the ACCMM model,the running mass of the active b quark can be deﬁned by:m 2b ( k 1)=M 2B +m 2u −2M B2M B .(22)Notice that the masses of the light constituent quarks,as obtained by ﬁts to the meson spectrum,are m u =m d =38MeV .The contribution of the two physical processes when the photon couples to the light or to the heavy quark is still recognizable in eqs.(15)-(16),since the quantities f and g come from the light and heavy quark propagators respectively.It turns out that the contribution of the terms proportional to 1f.This is not surprising,since the e.m.coupling of the photon to the quarks corresponds to a magnetic transition,and therefore it is inversely proportional to the quark mass.5Aﬁnal remark concerns the photon energy.In eq.(14)we have allowed k0to vary in the range[0,M B/2];however the integral diverges at the lower limit k0=0.This result is unphysical since it would correspond to a zero energy photon in theﬁnal state. Formally,this divergence would be canceled by radiative corrections to the formulae(15) and(16).On the other hand,one should take into account that at future experiments, e.g.at the SLAC B-factory,the smallest measurable photon energy is of the order of 50MeV;therefore,it is a reasonable assumption to cut oﬀfrom the integral the small photon energies,and,at the same time,to neglect radiative corrections.In our calculation,the eﬀect of the unphysical divergence begins around a photon energy k0≃350MeV,and therefore we use this value as a lower bound for the photon energy.Inﬁg.3we plot the photon spectrum for the decay(1);the diﬀerential distribution has a peak around1.5GeV,which should render it quite accessible to experimental analyses. For the decay width we obtain the resultΓ(B−→µ−¯νµγ)=3.710−19(V ub√2P2F .(24) The parameter P F is related to the heavy quark average square momentum:<p2>=3inclusive decay B→X cℓ¯νℓ[14]with the result:P F=ing(24)with such a value of P F in the previous formulas,one would obtain B(B−→µ−¯νµγ)≃0.8·10−6.This result suggests that the estimate given in eq.(23)is rather accurate;the rate for the weak radiative decay B−→µ−¯νµγis large enough for a measurement at future accelerators.AcknowledgementsWe thank M.Carpinelli,M.Giorgi,A.Palano and N.Paver for interesting discussions.7References[1]G.Burdman,T.Goldman and D.Wyler,Phys.Rev.D51(1995)111.[2]D.Atwood,G.Eilam and A.Soni,preprint TECHNION-PH-94-13,hep-ph/9411367.[3]G.Eilam,I.Halperin and R.R.Mendel,Phys.Lett.B361(1995)137.[4]P.Colangelo,F.De Fazio and G.Nardulli,Phys.Lett.B372(1996)331.[5]T.E.Browder and K.Honscheid,Prog.Part.Nucl.Phys.35(1995)81.[6]CLEO Collaboration,M.Artuso et al.,Phys.Rev.Lett.75(1995)785.[7]P.Cea,P.Colangelo,L.Cosmai and G.Nardulli,Phys.Lett.B206(1988)691.[8]P.Colangelo,G.Nardulli and M.Pietroni,Phys.Rev.D43(1991)3002.[9]P.Colangelo,G.Nardulli and L.Tedesco,Phys.Lett.B271(1991)344;P.Colangelo,F.De Fazio and G.Nardulli,Phys.Lett.B334(1994)175.[10]J.L.Richardson,Phys.Lett.B82(1979)272.[11]E.E.Salpeter,Phys.Rev.87(1952)328.[12]G.Altarelli,N.Cabibbo,G.Corb´o,L.Maiani and G.Martinelli,Nucl.Phys.B208(1982)365.[13]D.S.Hwang,C.S.Kim and W.Namgung,preprint KEK-TH-473,hep-ph/9604225.[14]CLEO Collaboration,B.Barish et al.,Phys.Rev.Lett.76(1996)1570.8Figure CaptionsFigure1Diagrams describing the decay B−→µ−¯νµγ.Figure2The wave function u B(k1)as obtained by the QCD relativistic quark model.Figure3Predicted photon energy spectrum.9?u x ©©6µ u 0¨¨W ¯νµ-b γFig.1b 1000.511.522.533.544.5500.51 1.52 2.53 3.5400.10.20.30.40.50.60.70.80.9100.51 1.522.5。

EHOB褥疮预防及护理研究中英文

褥疮的阶段 Stages of Pressure Wounds
• Understanding of anatomy了解解剖学 • Recognizing layers of the skin识别皮肤层 • Knowledge of staging system分期系统的认识 • Wound classification伤口分类 – Moisture湿度 – Candidiasis念珠菌病 – Neuropathic神经系统疾病 • Uncertainty in accuracy
Sharon Lepper BSN RN WOCN
EHOB产品由上海天呈“医流商城”全国代理，招商加盟热线：021-51083677-869 手机：15900626542 谢秋亭传真：51816400，地址：上海市杨浦区翔殷路128号国家大学科技园1号楼B座310室。
Copyright EHOB, 2010
Copyright Copyright EHOB, EHOB, 2010 2010 6 6
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6
体内平衡
Homeostasis
即使外部环境不断变化，但身体却能够维持相对稳定的内环境。 The body’s ability maintain the relatively stable internal conditions even though the outside world changes continuously.
定量的气体的体积与其绝对压力成反比。 Newton’s Law：牛顿定律
For every action, there is a reaction。每个作用力，都有一个反作用力。
Pascal’s Principle:帕斯卡尔原理

Dipropylene Glycol, Regular Grade Technical Data S

Technical Data SheetPage 1 of 2 ®™Trademark of The Dow Chemical Company (“Dow”) or an affiliated company of DowDipropylene Glycol, Regular Grade Form No. 117-42001-10/16Dow Dipropylene Glycol, Regular GradeGeneral Description Dipropylene Glycol (DPG), Regular Grade, is a co-product from the manufacture of monopropylene glycol, involving the high temperature and high pressure hydrolysis of propylene oxide (PO) with excess water. Dipropylene glycol regular grade is a distilled product of greater than 99% purity (as DPG), and is available from The Dow Chemical Company in drum and bulk quantities.The colorless, practically odorless, water soluble, medium viscosity and hygroscopic liquid with low vapor pressure and low toxicity, is a mixture of structural isomers (oxybispropanol CAS 25265-71-8, EINECS 246-770-3), defined by the manufacturing process, and comprising:1,1'-oxybis-2-propanol (CAS 110-98-5, EINECS 203-821-4)2,2'-oxybis-1-propanol (CAS 108-61-2)2-(2-hydroxypropoxy)-1-propanol (CAS 106-62-7)Typical Component Properties(1) Chemical NameFormulaMolecular Weight (g/mol)CAS NumberEINECS NumberDistillation Range, 101.3 kPa (1 atm)Vapor Pressure, 25°C (77°F)Freezing PointPour PointDensity, 25°C (77°F)60°C (140°F)Refractive Index, 20°C (68°F)Viscosity, 25°C (77°F)60°C (140°F)Specific Heat, 25°C (77°F)Surface Tension, 25°C (77°F)Flash Point, Pensky-Martens Closed CupThermal Conductivity, 25°C (77°F)Electrical Conductivity, 25°C (77°F)Heat of FormationHeat of Vaporization, 25°C (77°F)OxybispropanolC6H14O3134.225265-71-8246-770-3228–236°C (442–457°F)0.0021 kPa (0.016 mm Hg)Super cools-39°C (-38.2°F)1.022 g/cm³0.998 g/cm³1.439–1.44275.0 centipoise (mPa.s)10.9 centipoise (mPa.s)2.18 J/(g°K) (0.52 Btu/lb/°F)35 mN/m (dynes/cm)124°C (255°F)0.1672 W/(m°K) (0.09661 Btu/hr ft°F)< 6 micro S/m-628 kJ/mol (-150 Kcal /g-mol)45.4 kJ/mol (257 Btu/lb/°F)1.These are typical values and should not be construed as specifications.Page 2 of 2 ®™Trademark of The Dow Chemical Company (“Dow”) or an affiliated company of DowDipropylene Glycol, Regular Grade Form No. 117-4200110/16Applications Dipropylene Glycol, Regular Grade, is used as a solvent, coupling agent and chemicalintermediate. Typical applications include:1.Esterification with benzoic acid to make dipropylene glycol dibenzoate forplasticizers.2. A reactant in unsaturated polyester resins to add flexibility and hydrolytic stability tothe finished resin.3.Esterification with acrylic acid to make dipropylene glycol diacrylate for radiationcured resin formulations.4.In dicyclopentadiene-based unsaturated polyester resin systems to add flexibility.5.An initiator for urethane polyol synthesis using epoxides, and for the polyol in rigidpolyurethane foams.Dipropylene Glycol’s excellent solvency for certain oils, low evaporation rate and low toxicitylend its use in brake fluid formulations, cuttings oils, textile lubricants, printing inks, coatings,industrial soaps and as a solvent for agricultural and insecticidal formulations.Dipropylene Glycol, Regular Grade is for technical applications only.Storage and Handling Dipropylene Glycol, Regular Grade is stable for at least one year when stored at ambient temperatures in closed containers and away from sunlight and other sources of UV light.Where product heating is utilized (i.e. for bulk storage and/or transport containers) the product temperature should be controlled to prevent unintentional overheating over extended periods as this may potentially lead to accelerated oxidative degradation of the product. As a general guide Dow recommends heating up to not more than 40° C.For more details about product handling and safety information, please refer to the Dow Material Safety Data Sheet (MSDS).Product Stewardship The Dow Chemical Company and its subsidiaries (“Dow”) has a fundamental concern for all who make, distribute, and use its products, and for the environment in which we live. This concern is the basis for our Product Stewardship philosophy by which we assess the safety, health, and environmental information on our products and then take appropriate steps to protect employee and public health and our environment. The success of our Product Stewardship program rests with each and every individual involved with Dow products ─ from the initial concept and research, to manufacture, use, sale, disposal, and recycle of each product.Safety Considerations Material Safety Data (MSD) sheets are available from The Dow Chemical Company. MSD sheets are provided to help customers satisfy their own handling, safety and disposal needs and those that may be required by locally applicable health and safety regulations. MSD sheets are updated regularly, therefore, please request and review the most current MSD sheet before handling or using any product. These are available from the nearest Dow sales office.Customer Notice Dow encourages its customers to review their application of Dow products from the standpoint ofhuman health and environmental quality. To help ensure that Dow products are not used in ways forwhich they were not intended or tested, Dow personnel will assist customers in dealing with ecologicaland products safety. Your Dow sales representative can arrange the proper contacts.Contact information:For more information about this product please call The Dow Chemical Company. North America: 1-800-447-4369 Latin America: (+55) 11-5184-8722 Europe: (+31) 11-567-2626 Asia/Pacific: (+60) 3-7965-5392 /propyleneglycol/NOTICE: No freedom from infringement of any patent owned by Dow or others is to be inferred. Because use conditions and applicable laws may differ from one location to another and may change with time, Customer is responsible for determining whether products and the information in this document are appropriate for Customer's use and for ensuring that Customer's workplace and disposal practices are in compliance with applicable laws and other government enactments. The product shown in this literature may not be available for sale and/or available in all geographies where Dow is represented. The claims made may not have been approved for use in all countries. Dow assumes no obligation or liability for the information in thi s document. References to “Dow” or the “Company” mean the Dow legal entity selling the products to Customer unless otherwise expressly noted. NO WARRANTIES ARE GIVEN; ALL IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE ARE EXPRESSLY EXCLUDED。

低于再碰撞阈值下强激光场原子非序列双电离(英文)

低于再碰撞阈值下强激光场原子非序列双电离(英文)刘运全;刘杰;龚旗煌;Moshammer R;Ullrich J【期刊名称】《物理学进展》【年(卷),期】2010()4【摘要】在最近的实验和理论研究中,我们探讨了氩原子和氖原子在红外强激光场中低于再碰撞阈值的非序列双电离问题。

在研究中,我们发现在非序列双电离过程中,氖原子的电子关联表现为在激光偏振面内肩并肩出射,而对于氩原子的电子关联行为表现为在激光偏振面内的背对背出射,我们采用三维半经典模型(考虑电子隧道电离)很好地解释了实验结果。

在阈值附近,我们发现电子在激光场中的多次散射以及电子再碰撞激发后电子隧道电离是氩原子反关联行为的主要原因,而电子在激光场作用下的单次碰撞是电子关联行为的主要原因。

通过测量双电离过程中产生电子的横向电子动量分布,观察到了库伦聚焦效应,我们认为这是非经典的关联行为。

最后,我们给出了氩原子和氖原子在激光场中阈值的解析模型,并给出了原子的关联和反关联激光强度区域。

【总页数】11页(P335-345)【关键词】强场;非序列双电离;再碰撞;电离阈值【作者】刘运全;刘杰;龚旗煌;Moshammer R;Ullrich J【作者单位】物理学院和人工微结构和介观物理国家实验室,北京大学,北京100871;马克斯普朗克核物理所,D-69117海德堡,德国;应用物理与技术研究中心,北京大学,北京100084;北京应用物理与计算数学研究所,北京100088【正文语种】中文【中图分类】O43【相关文献】1.碰撞阈值下氩原子非次序双电离 [J], 张东玲;汤清彬;余本海;陈东2.强激光场氦原子非序列双电离过程中光子动量分配 [J], 陶建飞;刘杰;3.红外和极紫外双色激光场中氦原子的非序列双电离动量谱研究 [J], 金发成; 张桐4.红外和极紫外双色激光场中氦原子的非序列双电离动量谱研究 [J], 金发成; 张桐5.北京大学“飞秒光物理与介观光学”研究群体在强场原子非序列双电离研究取得进展 [J],因版权原因，仅展示原文概要，查看原文内容请购买。

Principles of Plasma Discharges and Materials Processing第2章

CHAPTER 2BASIC PLASMA EQUATIONS AND EQUILIBRIUM2.1INTRODUCTIONThe plasma medium is complicated in that the charged particles are both affected by external electric and magnetic ﬁelds and contribute to them.The resulting self-consistent system is nonlinear and very difﬁcult to analyze.Furthermore,the inter-particle collisions,although also electromagnetic in character,occur on space and time scales that are usually much shorter than those of the applied ﬁelds or the ﬁelds due to the average motion of the particles.To make progress with such a complicated system,various simplifying approxi-mations are needed.The interparticle collisions are considered independently of the larger scale ﬁelds to determine an equilibrium distribution of the charged-particle velocities.The velocity distribution is averaged over velocities to obtain the macro-scopic motion.The macroscopic motion takes place in external applied ﬁelds and in the macroscopic ﬁelds generated by the average particle motion.These self-consistent ﬁelds are nonlinear,but may be linearized in some situations,particularly when dealing with waves in plasmas.The effect of spatial variation of the distri-bution function leads to pressure forces in the macroscopic equations.The collisions manifest themselves in particle generation and loss processes,as an average friction force between different particle species,and in energy exchanges among species.In this chapter,we consider the basic equations that govern the plasma medium,con-centrating attention on the macroscopic system.The complete derivation of these 23Principles of Plasma Discharges and Materials Processing ,by M.A.Lieberman and A.J.Lichtenberg.ISBN 0-471-72001-1Copyright #2005John Wiley &Sons,Inc.equations,from fundamental principles,is beyond the scope of the text.We shall make the equations plausible and,in the easier instances,supply some derivations in appendices.For the reader interested in more rigorous treatment,references to the literature will be given.In Section2.2,we introduce the macroscopicﬁeld equations and the current and voltage.In Section2.3,we introduce the fundamental equation of plasma physics, for the evolution of the particle distribution function,in a form most applicable for weakly ionized plasmas.We then deﬁne the macroscopic quantities and indicate how the macroscopic equations are obtained by taking moments of the fundamental equation.References given in the text can be consulted for more details of the aver-aging procedure.Although the macroscopic equations depend on the equilibrium distribution,their form is independent of the equilibrium.To solve the equations for particular problems the equilibrium must be known.In Section2.4,we introduce the equilibrium distribution and obtain some consequences arising from it and from theﬁeld equations.The form of the equilibrium distribution will be shown to be a consequence of the interparticle collisions,in Appendix B.2.2FIELD EQUATIONS,CURRENT,AND VOLTAGEMaxwell’s EquationsThe usual macroscopic form of Maxwell’s equations arerÂE¼Àm0@H@t(2:2:1)rÂH¼e0@E@tþJ(2:2:2)e0rÁE¼r(2:2:3) andmrÁH¼0(2:2:4) where E(r,t)and H(r,t)are the electric and magneticﬁeld vectors and wherem 0¼4pÂ10À7H/m and e0%8:854Â10À12F/m are the permeability and per-mittivity of free space.The sources of theﬁelds,the charge density r(r,t)and the current density J(r,t),are related by the charge continuity equation(Problem2.1):@rþrÁJ¼0(2:2:5) In general,J¼J condþJ polþJ mag24BASIC PLASMA EQUATIONS AND EQUILIBRIUMwhere the conduction current density J cond is due to the motion of the free charges, the polarization current density J pol is due to the motion of bound charges in a dielectric material,and the magnetization current density J mag is due to the magnetic moments in a magnetic material.In a plasma in vacuum,J pol and J mag are zero and J¼J cond.If(2.2.3)is integrated over a volume V,enclosed by a surface S,then we obtain its integral form,Gauss’law:e0þSEÁd A¼q(2:2:6)where q is the total charge inside the volume.Similarly,integrating(2.2.5),we obtaind q d t þþSJÁd A¼0which states that the rate of increase of charge inside V is supplied by the total currentﬂowing across S into V,that is,that charge is conserved.In(2.2.2),theﬁrst term on the RHS is the displacement current densityﬂowing in the vacuum,and the second term is the conduction current density due to the free charges.We can introduce the total current densityJ T¼e0@E@tþJ(2:2:7)and taking the divergence of(2.2.2),we see thatrÁJ T¼0(2:2:8)In one dimension,this reduces to d J T x=d x¼0,such that J T x¼J T x(t),independent of x.Hence,for example,the total currentﬂowing across a spatially nonuniform one-dimensional discharge is independent of x,as illustrated in Figure2.1.A generalization of this result is Kirchhoff’s current law,which states that the sum of the currents entering a node,where many current-carrying conductors meet,is zero.This is also shown in Figure2.1,where I rf¼I TþI1.If the time variation of the magneticﬁeld is negligible,as is often the case in plasmas,then from Maxwell’s equations rÂE%0.Since the curl of a gradient is zero,this implies that the electricﬁeld can be derived from the gradient of a scalar potential,E¼Àr F(2:2:9)2.2FIELD EQUATIONS,CURRENT,AND VOLTAGE25Integrating (2.2.9)around any closed loop C givesþC E Ád ‘¼ÀþC r F Ád ‘¼ÀþC d F ¼0(2:2:10)Hence,we obtain Kirchhoff’s voltage law ,which states that the sum of the voltages around any loop is zero.This is illustrated in Figure 2.1,for which we obtainV rf ¼V 1þV 2þV 3that is,the source voltage V rf is equal to the sum of the voltages V 1and V 3across the two sheaths and the voltage V 2across the bulk plasma.Note that currents and vol-tages can have positive or negative values;the directions for which their values are designated as positive must be speciﬁed,as shown in the ﬁgure.If (2.2.9)is substituted in (2.2.3),we obtainr 2F ¼Àre 0(2:2:11)Equation (2.2.11),Poisson’s equation ,is one of the fundamental equations that we shall use.As an example of its application,consider the potential in the center (x ¼0)of two grounded (F ¼0)plates separated by a distance l ¼10cm and con-taining a uniform ion density n i ¼1010cm 23,without the presence of neutralizing electrons.Integrating Poisson’s equationd 2F d x 2¼Àen i eFIGURE 2.1.Kirchhoff’s circuit laws:The total current J T ﬂowing across a nonuniform one-dimensional discharge is independent of x ;the sum of the currents entering a node is zero (I rf ¼I T þI 1);the sum of voltages around a loop is zero (V rf ¼V 1þV 2þV 3).26BASIC PLASMA EQUATIONS AND EQUILIBRIUMusing the boundary conditions that F ¼0at x ¼+l =2and that d F =d x ¼0at x ¼0(by symmetry),we obtainF ¼12en i e 0l 22Àx 2"#The maximum potential in the center is 2.3Â105V,which is impossibly large for a real discharge.Hence,the ions must be mostly neutralized by electrons,leading to a quasi-neutral plasma.Figure 2.2shows a PIC simulation time history over 10210s of (a )the v x –x phase space,(b )the number N of sheets versus time,and (c )the potential F versus x for 100unneutralized ion sheets (with e /M for argon ions).We see the ion acceleration in (a ),the loss of ions in (b ),and the parabolic potential proﬁle in (c );the maximum potential decreases as ions are lost from the system.We consider quasi-neutrality further in Section 2.4.Electric and magnetic ﬁelds exert forces on charged particles given by the Lorentz force law :F ¼q (E þv ÂB )(2:2:12)FIGURE 2.2.PIC simulation of ion loss in a plasma containing ions only:(a )v x –x ion phase space,showing the ion acceleration trajectories;(b )number N of ion sheets versus t ,with the steps indicating the loss of a single sheet;(c )the potential F versus x during the ﬁrst 10210s of ion loss.2.2FIELD EQUATIONS,CURRENT,AND VOLTAGE 2728BASIC PLASMA EQUATIONS AND EQUILIBRIUMwhere v is the particle velocity and B¼m0H is the magnetic induction vector.The charged particles move under the action of the Lorentz force.The moving charges in turn contribute to both r and J in the plasma.If r and J are linearly related to E and B,then theﬁeld equations are linear.As we shall see,this is not generally the case for a plasma.Nevertheless,linearization may be possible in some cases for which the plasma may be considered to have an effective dielectric constant;that is,the “free charges”play the same role as“bound charges”in a dielectric.We consider this further in Chapter4.2.3THE CONSERVATION EQUATIONSBoltzmann’s EquationFor a given species,we introduce a distribution function f(r,v,t)in the six-dimensional phase space(r,v)of particle positions and velocities,with the interpret-ation thatf(r,v,t)d3r d3v¼number of particles inside a six-dimensional phasespace volume d3r d3v at(r,v)at time tThe six coordinates(r,v)are considered to be independent variables.We illus-trate the deﬁnition of f and its phase space in one dimension in Figure2.3.As particles drift in phase space or move under the action of macroscopic forces, theyﬂow into or out of theﬁxed volume d x d v x.Hence the distribution functionaf should obey a continuity equation which can be derived as follows.InFIGURE2.3.One-dimensional v x–x phase space,illustrating the derivation of the Boltzmann equation and the change in f due to collisions.time d t,f(x,v x,t)d x a x(x,v x,t)d t particlesﬂow into d x d v x across face1f(x,v xþd v x,t)d x a x(x,v xþd v x,t)d t particlesﬂow out of d x d v x across face2 f(x,v x,t)d v x v x d t particlesﬂow into d x d v x across face3f(xþd x,v x,t)d v x v x d t particlesﬂow out of d x d v x across face4where a x v d v x=d t and v x;d x=d t are theﬂow velocities in the v x and x directions, respectively.Hencef(x,v x,tþd t)d x d v xÀf(x,v x,t)d x d v x¼½f(x,v x,t)a x(x,v x,t)Àf(x,v xþd v x,t)a x(x,v xþd v x,t) d x d tþ½f(x,v x,t)v xÀf(xþd x,v x,t)v x d v x d tDividing by d x d v x d t,we obtain@f @t ¼À@@x(f v x)À@@v x(fa x)(2:3:1)Noting that v x is independent of x and assuming that the acceleration a x¼F x=m of the particles does not depend on v x,then(2.3.1)can be rewritten as@f @t þv x@f@xþa x@f@v x¼0The three-dimensional generalization,@f@tþvÁr r fþaÁr v f¼0(2:3:2)with r r¼(^x@=@xþ^y@=@yþ^z@=@z)and r v¼(^x@=@v xþ^y@=@v yþ^z@=@v z)is called the collisionless Boltzmann equation or Vlasov equation.In addition toﬂows into or out of the volume across the faces,particles can “suddenly”appear in or disappear from the volume due to very short time scale interparticle collisions,which are assumed to occur on a timescale shorter than the evolution time of f in(2.3.2).Such collisions can practically instantaneously change the velocity(but not the position)of a particle.Examples of particles sud-denly appearing or disappearing are shown in Figure2.3.We account for this effect,which changes f,by adding a“collision term”to the right-hand side of (2.3.2),thus obtaining the Boltzmann equation:@f @t þvÁr r fþFmÁr v f¼@f@tc(2:3:3)2.3THE CONSERVATION EQUATIONS29The collision term in integral form will be derived in Appendix B.The preceding heuristic derivation of the Boltzmann equation can be made rigorous from various points of view,and the interested reader is referred to texts on plasma theory, such as Holt and Haskel(1965).A kinetic theory of discharges,accounting for non-Maxwellian particle distributions,must be based on solutions of the Boltzmann equation.We give an introduction to this analysis in Chapter18. Macroscopic QuantitiesThe complexity of the dynamical equations is greatly reduced by averaging over the velocity coordinates of the distribution function to obtain equations depending on the spatial coordinates and the time only.The averaged quantities,such as species density,mean velocity,and energy density are called macroscopic quantities,and the equations describing them are the macroscopic conservation equations.To obtain these averaged quantities we take velocity moments of the distribution func-tion,and the equations are obtained from the moments of the Boltzmann equation.The average quantities that we are concerned with are the particle density,n(r,t)¼ðf d3v(2:3:4)the particleﬂuxG(r,t)¼n u¼ðv f d3v(2:3:5)where u(r,t)is the mean velocity,and the particle kinetic energy per unit volumew¼32pþ12mu2n¼12mðv2f d3v(2:3:6)where p(r,t)is the isotropic pressure,which we deﬁne below.In this form,w is sumof the internal energy density32p and theﬂow energy density12mu2n.Particle ConservationThe lowest moment of the Boltzmann equation is obtained by integrating all terms of(2.3.3)over velocity space.The integration yields the macroscopic continuity equation:@n@tþrÁ(n u)¼GÀL(2:3:7)The collision term in(2.3.3),which yields the right-hand side of(2.3.7),is equal to zero when integrated over velocities,except for collisions that create or destroy 30BASIC PLASMA EQUATIONS AND EQUILIBRIUMparticles,designated as G and L ,respectively (e.g.,ionization,recombination).In fact,(2.3.7)is transparent since it physically describes the conservation of particles.If (2.3.7)is integrated over a volume V bounded by a closed surface S ,then (2.3.7)states that the net number of particles generated per second within V ,either ﬂows across the surface S or increases the number of particles within V .For common low-pressure discharges in the steady state,G is usually due to ioniz-ation by electron–neutral collisions:G ¼n iz n ewhere n iz is the ionization frequency.The volume loss rate L ,usually due to recom-bination,is often negligible.Hencer Á(n u )¼n iz n e (2:3:8)in a typical discharge.However,note that the continuity equation is clearly not sufﬁcient to give the evolution of the density n ,since it involves another quantity,the mean particle velocity u .Momentum ConservationTo obtain an equation for u ,a ﬁrst moment is formed by multiplying the Boltzmann equation by v and integrating over velocity.The details are complicated and involve evaluation of tensor elements.The calculation can be found in most plasma theory texts,for example,Krall and Trivelpiece (1973).The result is mn @u @t þu Ár ðÞu !¼qn E þu ÂB ðÞÀr ÁP þf c (2:3:9)The left-hand side is the species mass density times the convective derivative of the mean velocity,representing the mass density times the acceleration.The convective derivative has two terms:the ﬁrst term @u =@t represents an acceleration due to an explicitly time-varying u ;the second “inertial”term (u Ár )u represents an acceleration even for a steady ﬂuid ﬂow (@=@t ;0)having a spatially varying u .For example,if u ¼^xu x (x )increases along x ,then the ﬂuid is accelerating along x (Problem 2.4).This second term is nonlinear in u and can often be neglected in discharge analysis.The mass times acceleration is acted upon,on the right-hand side,by the body forces,with the ﬁrst term being the electric and magnetic force densities.The second term is the force density due to the divergence of the pressure tensor,which arises due to the integration over velocitiesP ij ¼mn k v i Àu ðÞv j Àu ÀÁl v (2:3:10)2.3THE CONSERVATION EQUATIONS 31where the subscripts i,j give the component directions and kÁl v denotes the velocity average of the bracketed quantity over f.ÃFor weakly ionized plasmas it is almost never used in this form,but rather an isotropic version is employed:P¼p000p000p@1A(2:3:11)such thatrÁP¼r p(2:3:12) a pressure gradient,withp¼13mn k(vÀu)2l v(2:3:13)being the scalar pressure.Physically,the pressure gradient force density arises as illustrated in Figure2.4,which shows a small volume acted upon by a pressure that is an increasing function of x.The net force on this volume is p(x)d AÀp(xþd x)d A and the volume is d A d x.Hence the force per unit volume isÀ@p=@x.The third term on the right in(2.3.9)represents the time rate of momentum trans-fer per unit volume due to collisions with other species.For electrons or positive ions the most important transfer is often due to collisions with neutrals.The transfer is usually approximated by a Krook collision operatorf j c¼ÀXbmn n m b(uÀu b):Àm(uÀu G)Gþm(uÀu L)L(2:3:14)where the summation is over all other species,u b is the mean velocity of species b, n m b is the momentum transfer frequency for collisions with species b,and u G and u L are the mean velocities of newly created and lost particles.Generally j u G j(j u j for pair creation by ionization,and u L%u for recombination or charge transfer lossprocesses.We discuss the Krook form of the collision operator further in Chapter 18.The last two terms in(2.3.14)are generally small and give the momentum trans-fer due to the creation or destruction of particles.For example,if ions are created at rest,then they exert a drag force on the moving ionﬂuid because they act to lower the averageﬂuid velocity.A common form of the average force(momentum conservation)equation is obtained from(2.3.9)neglecting the magnetic forces and taking u b¼0in theÃWe assume f is normalized so that k f lv ¼1.32BASIC PLASMA EQUATIONS AND EQUILIBRIUMKrook collision term for collisions with one neutral species.The result is mn @u @t þu Ár u !¼qn E Àr p Àmn n m u (2:3:15)where only the acceleration (@u =@t ),inertial (u Ár u ),electric ﬁeld,pressure gradi-ent,and collision terms appear.For slow time variation,the acceleration term can be neglected.For high pressures,the inertial term is small compared to the collision term and can also be dropped.Equations (2.3.7)and (2.3.9)together still do not form a closed set,since the pressure tensor P (or scalar pressure p )is not determined.The usual procedure to close the equations is to use a thermodynamic equation of state to relate p to n .The isothermal relation for an equilibrium Maxwellian distribution isp ¼nkT(2:3:16)so thatr p ¼kT r n (2:3:17)where T is the temperature in kelvin and k is Boltzmann’s constant (k ¼1.381Â10223J /K).This holds for slow time variations,where temperatures are allowed to equilibrate.In this case,the ﬂuid can exchange energy with its sur-roundings,and we also require an energy conservation equation (see below)to deter-mine p and T .For a room temperature (297K)neutral gas having density n g and pressure p ,(2.3.16)yieldsn g (cm À3)%3:250Â1016p (Torr)(2:3:18)p FIGURE 2.4.The force density due to the pressure gradient.2.3THE CONSERVATION EQUATIONS 33Alternatively,the adiabatic equation of state isp¼Cn g(2:3:19) such thatr p p ¼gr nn(2:3:20)where g is the ratio of speciﬁc heat at constant pressure to that at constant volume.The speciﬁc heats are deﬁned in Section7.2;g¼5/3for a perfect gas; for one-dimensional adiabatic motion,g¼3.The adiabatic relation holds for fast time variations,such as in waves,when theﬂuid does not exchange energy with its surroundings;hence an energy conservation equation is not required. For almost all applications to discharge analysis,we use the isothermal equation of state.Energy ConservationThe energy conservation equation is obtained by multiplying the Boltzmannequation by12m v2and integrating over velocity.The integration and some othermanipulation yield@ @t32pþrÁ32p uðÞþp rÁuþrÁq¼@@t32pc(2:3:21)Here32p is the thermal energy density(J/m3),32p u is the macroscopic thermal energyﬂux(W/m2),representing theﬂow of the thermal energy density at theﬂuid velocityu,p rÁu(W/m3)gives the heating or cooling of theﬂuid due to compression orexpansion of its volume(Problem2.5),q is the heatﬂow vector(W/m2),whichgives the microscopic thermal energyﬂux,and the collisional term includes all col-lisional processes that change the thermal energy density.These include ionization,excitation,elastic scattering,and frictional(ohmic)heating.The equation is usuallyclosed by setting q¼0or by letting q¼Àk T r T,where k T is the thermal conduc-tivity.For most steady-state discharges the macroscopic thermal energyﬂux isbalanced against the collisional processes,giving the simpler equationrÁ32p u¼@32pc(2:3:22)Equation(2.3.22),together with the continuity equation(2.3.8),will often prove suf-ﬁcient for our analysis.34BASIC PLASMA EQUATIONS AND EQUILIBRIUMSummarySummarizing our results for the macroscopic equations describing the electron and ionﬂuids,we have in their most usually used forms the continuity equationrÁ(n u)¼n iz n e(2:3:8) the force equation,mn @u@tþuÁr u!¼qn EÀr pÀmn n m u(2:3:15)the isothermal equation of statep¼nkT(2:3:16) and the energy-conservation equationrÁ32p u¼@@t32pc(2:3:22)These equations hold for each charged species,with the total charges and currents summed in Maxwell’s equations.For example,with electrons and one positive ion species with charge Ze,we haver¼e Zn iÀn eðÞ(2:3:23)J¼e Zn i u iÀn e u eðÞ(2:3:24)These equations are still very difﬁcult to solve without simpliﬁcations.They consist of18unknown quantities n i,n e,p i,p e,T i,T e,u i,u e,E,and B,with the vectors each counting for three.Various simpliﬁcations used to make the solutions to the equations tractable will be employed as the individual problems allow.2.4EQUILIBRIUM PROPERTIESElectrons are generally in near-thermal equilibrium at temperature T e in discharges, whereas positive ions are almost never in thermal equilibrium.Neutral gas mol-ecules may or may not be in thermal equilibrium,depending on the generation and loss processes.For a single species in thermal equilibrium with itself(e.g.,elec-trons),in the absence of time variation,spatial gradients,and accelerations,the2.4EQUILIBRIUM PROPERTIES35Boltzmann equation(2.3.3)reduces to@f @tc¼0(2:4:1)where the subscript c here represents the collisions of a particle species with itself. We show in Appendix B that the solution of(2.4.1)has a Gaussian speed distribution of the formf(v)¼C eÀj2m v2(2:4:2) The two constants C and j can be obtained by using the thermodynamic relationw¼12mn k v2l v¼32nkT(2:4:3)that is,that the average energy of a particle is12kT per translational degree offreedom,and by using a suitable normalization of the distribution.Normalizing f(v)to n,we obtainCð2p0d fðpsin u d uð1expÀj2m v2ÀÁv2d v¼n(2:4:4)and using(2.4.3),we obtain1 2mCð2pd fðpsin u d uð1expÀj2m v2ÀÁv4d v¼32nkT(2:4:5)where we have written the integrals over velocity space in spherical coordinates.The angle integrals yield the factor4p.The v integrals are evaluated using the relationÃð10eÀu2u2i d u¼(2iÀ1)!!2ﬃﬃﬃﬃpp,where i is an integer!1:(2:4:6)Solving for C and j we havef(v)¼nm2p kT3=2expÀm v22kT(2:4:7)which is the Maxwellian distribution.Ã!!denotes the double factorial function;for example,7!!¼7Â5Â3Â1. 36BASIC PLASMA EQUATIONS AND EQUILIBRIUMSimilarly,other averages can be performed.The average speed vis given by v ¼m =2p kT ðÞ3=2ð10v exp Àv 22v 2th !4p v 2d v (2:4:8)where v th ¼(kT =m )1=2is the thermal velocity.We obtainv ¼8kT p m 1=2(2:4:9)The directed ﬂux G z in (say)the þz direction is given by n k v z l v ,where the average is taken over v z .0only.Writing v z ¼v cos u we have in spherical coordinatesG z ¼n m 2p kT 3=2ð2p 0d f ðp =20sin u d u ð10v cos u exp Àv 22v 2th v 2d v Evaluating the integrals,we ﬁndG z ¼14n v (2:4:10)G z is the number of particles per square meter per second crossing the z ¼0surfacein the positive direction.Similarly,the average energy ﬂux S z ¼n k 1m v 2v z l v in theþz direction can be found:S z ¼2kT G z .We see that the average kinetic energy W per particle crossing z ¼0in the positive direction isW ¼2kT (2:4:11)It is sometimes convenient to deﬁne the distribution in terms of other variables.For example,we can deﬁne a distribution of energies W ¼12m v 2by4p g W ðÞd W ¼4p f v ðÞv 2d vEvaluating d v =d W ,we see that g and f are related byg W ðÞ¼v (W )f ½v (W ) m (2:4:12)where v (W )¼(2W =m )1=2.Boltzmann’s RelationA very important relation can be obtained for the density of electrons in thermal equilibrium at varying positions in a plasma under the action of a spatially varying 2.4EQUILIBRIUM PROPERTIES 3738BASIC PLASMA EQUATIONS AND EQUILIBRIUMpotential.In the absence of electron drifts(u e;0),the inertial,magnetic,and fric-tional forces are zero,and the electron force balance is,from(2.3.15)with@=@t;0,en e Eþr p e¼0(2:4:13) Setting E¼Àr F and assuming p e¼n e kT e,(2.4.13)becomesÀen e r FþkT e r n e¼0or,rearranging,r(e FÀkT e ln n e)¼0(2:4:14) Integrating,we havee FÀkT e ln n e¼constorn e(r)¼n0e e F(r)=kT e(2:4:15)which is Boltzmann’s relation for electrons.We see that electrons are“attracted”to regions of positive potential.We shall generally write Boltzmann’s relation in more convenient unitsn e¼n0e F=T e(2:4:16)where T e is now expressed in volts,as is F.For positive ions in thermal equilibrium at temperature T i,a similar analysis shows thatn i¼n0eÀF=T i(2:4:17) Hence positive ions in thermal equilibrium are“repelled”from regions of positive potential.However,positive ions are almost never in thermal equilibrium in low-pressure discharges because the ion drift velocity u i is large,leading to inertial or frictional forces in(2.3.15)that are comparable to the electricﬁeld or pressure gra-dient forces.Debye LengthThe characteristic length scale in a plasma is the electron Debye length l De.As we will show,the Debye length is the distance scale over which signiﬁcant charge densities can spontaneously exist.For example,low-voltage(undriven)sheaths are typically a few Debye lengths wide.To determine the Debye length,let us intro-duce a sheet of negative charge having surface charge density r S,0C/m2into an。

磁梯度张量不变量的目标定位滤波,英文文献

磁梯度张量不变量的目标定位滤波,英文文献Magnetic Gradient Tensor Invariant-Based Target Localization FilteringThe precise localization of targets is a critical task in various applications, such as remote sensing, geophysical exploration, and defense systems. One of the effective approaches to target localization is the utilization of magnetic gradient tensor (MGT) data, which provides valuable information about the spatial distribution of the magnetic field. The MGT is a second-order tensor that describes the rate of change of the magnetic field in different directions, and it can be used to extract useful features for target detection and localization.The use of MGT data for target localization is based on the concept of tensor invariants, which are scalar quantities that are independent of the coordinate system used to represent the tensor. These invariants can be used to characterize the magnetic field and its spatial variations, and they can be employed in the design of target localization filters that are robust to changes in the sensor orientation or the target's position.One of the key advantages of using MGT-based target localization is its ability to provide accurate and reliable results even in the presence of various types of noise and interference, such as sensor errors, environmental disturbances, and target-induced magnetic fields. By exploiting the tensor invariant properties of the MGT, it is possible to develop filtering algorithms that can effectively suppress these unwanted effects and enhance the target detection and localization performance.In the literature, several MGT-based target localization approaches have been proposed, each with its own strengths and limitations. One common approach is to use the MGT eigenvalues, which represent the principal components of the magnetic field gradient, to identify and locate targets. Another approach is to utilize the MGT invariants, such as the trace, determinant, and eigenvalues, to construct target detection and localization filters.For example, one study presented a target localization method based on the MGT invariants, where the authors developed a filter that exploits the fact that the target-induced magnetic field is characterized by a specific pattern in the MGT invariants. The filter was shown to be effective in locating targets even in the presence of strong background magnetic fields and sensor noise.Another study proposed a Bayesian framework for MGT-based targetlocalization, where the authors used the MGT invariants to construct a likelihood function that describes the probability of detecting a target given the observed MGT data. The Bayesian approach allowed for the incorporation of prior information about the target's characteristics and the sensor's capabilities, leading to improved localization accuracy.In addition to these approaches, researchers have also explored the use of machine learning techniques, such as neural networks and support vector machines, to leverage the MGT data for target localization. These data-driven methods have the potential to capture complex relationships between the MGT features and the target's position, potentially leading to even more accurate and robust localization algorithms.Despite the significant progress in MGT-based target localization, there are still several challenges and open research questions that need to be addressed. For example, the sensitivity of the MGT data to environmental factors, such as geological structures and electromagnetic interference, can pose challenges in real-world applications. Additionally, the development of efficient and scalable algorithms for processing large-scale MGT data, particularly in the context of sensor networks or aerial surveys, is an active area of research.In conclusion, the use of magnetic gradient tensor data for target localization is a promising approach that has been extensively studied in the literature. By exploiting the tensor invariant properties of the MGT, researchers have developed a range of effective filtering and detection algorithms that can provide accurate and reliable target localization results, even in the presence of various types of noise and interference. As the field continues to evolve, further advancements in MGT-based target localization are expected to have a significant impact on a wide range of applications, from remote sensing and geophysical exploration to defense and security systems.。

[转载]WARNING

[转载]WARNING in EDDRMM： call to ZHEGV fail 原⽂地址：WARNING in EDDRMM: call to ZHEGV failed, returncode= 6 3 9作者：cyniuthe error is due to a LAPCK call (ZHEGV):ZHEGV computes all the eigenvalues, and optionally, the eigenvectorsof a complex generalized Hermitian-definite eigenproblem .there may be several reasons for that error:1) the RMM-DIIS diagonalisation algorithm is not stable for your specificsetup of the calculation.–> use ALGO = Normal (blocked Davidson) orALGO = Fast (5 steps blocked Davidson, RMM-DIIS)2)a) maybe your input geometry was not reasonable (error occurs at the very first ionicstep, please have a look for the geometry data of your run in OUTCAR ) orb) the last ionic relaxation step lead to an unreasonable geometry (compare the inputand output geometries of the last ionic relaxation steps in XDATCAR).In that case (2b) it can be helpful to–> switch to a different relaxation algorithm (IBRION-tag)–> reduce the step size of the first step by setting POTIM smaller than the defaultvalue3) The installation of the LAPACK on your machine was not done properly:use the LAPACK which is delivered with the code(vasp.4.lib/lapack_double.o)4) If the error persist although you switched to the Davidson algorithm:on some architectures (especially SGI) some LAPACK routines are not workingproperly. However, it is possible to avoid the usage of the ZHEGV subroutineby commenting the line#define USE_ZHEEVXin davidson.F, subrot.F, and wavpre_noio.F and recompiling VASP.。

微生物测试均质拍打法英语

微生物测试均质拍打法英语Microbial Homogenization Tapping Method。

Introduction。

Microbial homogenization tapping method is a technique used to obtain a representative sample of microorganisms from a larger population. It involves the use of tapping or shaking to evenly distribute the microorganisms in a sample, ensuring accurate and reliable test results. This method is commonly used in microbiology laboratories for various applications, including environmental monitoring, food safety testing, and clinical diagnostics. In this article, we will discuss the principles, procedure, and advantages of the microbial homogenization tapping method.Principles。

The microbial homogenization tapping method is based on the principle that microorganisms tend to settle or clump together, leading to uneven distribution in a sample. This uneven distribution can result in biased test results, as some areas of the sample may contain higher or lower concentrations of microorganisms. By tapping or shaking the sample, the microorganisms are dislodged from their settled positions and distributed more evenly, providing a representative sample for testing.Procedure。