Torsion waves in metric-affine field theory

合集下载

聚焦离子束溅射(FIB)

聚
题目：A Review of Focused Ion Beam Sputtering
作者：Mohammad Yeakub Ali, Wayne Hung and Fu Yongqi
期刊：International journal of precision engineering and manufacturing vol. 11, no. 1, pp. 157-170
3FIB溅射模型
尽管FIB溅射能制备高精确度的微元件，控制溅射深度是相当困难的。如果衬底的材料既不是集成电路，也不是晶圆，那么SIMS（二次离子质谱技术）能以20nm的精确度探测并鉴定出过渡层。但是，对于单一组成的材料而言，SIMS技术则无法使用。这样就导致末端点的检测成为FIB溅射的难点。表面粗糙度的估测则是FIB溅射微加工中的另一个关键性问题。在如下几个部分中，若干模型被讨论如何达到期望的溅射深度、几何完整性以及表面抛光处理。
他们较高的质量能诱导溅射效应的发生。加速电压使离子在接地点加速，加速电压越高，离子移动速度越快
2.1仪器
基本的单波束仪器由液态金属离子源、一个离子柱、样品载台、真空腔组成。
典型的离子束显微镜包括液态金属离子源及离子引出极、预聚焦极、聚焦极所用的高压电源、电对中、消像散电子透镜、扫描线圈、二次粒子检测器、可移动的样品基座、真空系统、抗振动和磁场的装置、电路控制板和电脑等硬件设备。
在给定入射角度的溅射产额随有多种因素变化，通道的晶体取向。容易的通道取向，离子只经历非弹性作用，与躺在晶面里样品原子掠射角碰撞，在引起弹性散射前，深入晶体内部，因此只有少数原子从表面被溅射。这好比晶体取向效应对低能电子产额的影响。在垂直晶界的溅射通道效应。溅射剖面图还有赖于在样品表面扫描光栅的方向和序列。例如，环形的溅射轮廓，被快速和重复的扫描切割，与慢扫描逐点切割不同。

Thermal gravitational waves

v12
3kTc . 12
For a core temperature of Tc 10 7 K , the velocity of the particles is of the order of
8 10 5 m / s . For a star of density 200 g / cc 2 10 5 kg / m 3 , the numbeting in these values we get the power of thermal gravitational waves emitted as,
10 9 Watt at a frequency of 1017 Hz . E
2
The flux of thermal gravitational waves from the sun, received at earth is of the order of half a watt. 2. Thermal gravitational waves from compact stars In the case of white dwarfs, the number density is of the order of n1 n2 10 37 m 3 , and the velocity corresponding to the white dwarf temperature of Tc 10 8 K , is of the order of 2 10 6 m / s . The volume of the white dwarf is of the order of 4 1018 m 3 and the frequency corresponding to the temperature Tc 10 8 K is And for a white dwarf,

衰减全反射-傅里叶红外光谱法快速测试干酪根样品

ＲＮｉｇ，ＤＵＧＡＪｎｕ，ＰＮｈｎ —ｉＡＺｏｇｘ
（ｅｇｕＩｓｉｔｆｏｏｙａｄＭｉｒｌｅｏｒｅ，ｅｇｕ６０８，ＣｉａＣｈｎｄｔｕｅｏｎｔＧｅｌｎｎａＲｓｕｃｓＣｈｎｄ１０２ｈｎ）ｇｅ
ＲａｉａｙｉｏｒｇｎｂｔｎａｅｔｌＲｅｅｔｏｐｄＡｎｌｓｓｆｒＫｅｏｅｙＡｔｅｕｔｄＴｏａｆｃｉｎ－ｌＦｏｒｅａｓｏｍｎｒｒｄＳｅｔｏｃｐｕｉｒＴｒｎｆｒＩｆａｅｐｃｒｓｏｙ
衰减全反射一傅里叶红外光谱法快速测试干酪根样品
冉敬，杜谷，潘忠习
６０８）１０２（成都地质矿产研究所，四川成都
摘要：生油母质干酪根是石油地质工作研究的重要对象。文章利用衰减全反射（Ｔ）ＡＲ技术对干酪根样品进行傅里叶变换红外光谱分析，通过与传统压片法谱图进行峰形峰位特征、结构参数比较，明：ＡＲ表 ① Ｔ谱具有与压片法吸收谱类似的谱图特征；与压片法吸收谱相比，Ｔ ② ＡＲ谱的吸收强度较弱；ＡＲ技术 ③ Ｔ和压片法所获得的红外结构参数具有可比性。由于ＡＲ技术具有无需制样、Ｔ可以减少水分干扰等优点，因此可以作为干酪根样品快速测试的方法应用于干酪根样品的类型鉴别、演化程度研究和来源对比。热关键词：里叶变换红外光谱法；衰减全反射；干酪根傅中图分类号：０５．３６７３文献标识码：Ａ

二叠纪-三叠纪灭绝事件

二叠纪-三叠纪灭绝事件二叠纪-三叠纪灭绝事件（Permian–Triassic extinction event）是一个大规模物种灭绝事件，发生于古生代二叠纪与中生代三叠纪之间，距今大约2亿5140万年[1][2]。

若以消失的物种来计算，当时地球上70%的陆生脊椎动物，以及高达96%的海中生物消失[3]；这次灭绝事件也造成昆虫的唯一一次大量灭绝。

计有57%的科与83%的属消失[4][5]。

在灭绝事件之后，陆地与海洋的生态圈花了数百万年才完全恢复，比其他大型灭绝事件的恢复时间更长久[3]。

此次灭绝事件是地质年代的五次大型灭绝事件中，规模最庞大的一次，因此又非正式称为大灭绝（Great Dying）[6]，或是大规模灭绝之母（Mother of all mass extinctions）[7]。

二叠纪-三叠纪灭绝事件的过程与成因仍在争议中[8]。

根据不同的研究，这次灭绝事件可分为一[1]到三[9]个阶段。

第一个小型高峰可能因为环境的逐渐改变，原因可能是海平面改变、海洋缺氧、盘古大陆形成引起的干旱气候；而后来的高峰则是迅速、剧烈的，原因可能是撞击事件、火山爆发[10]、或是海平面骤变，引起甲烷水合物的大量释放[11]。

目录? 1 年代测定? 2 灭绝模式o 2.1 海中生物o 2.2 陆地无脊椎动物o 2.3 陆地植物? 2.3.1 植物生态系统? 2.3.2 煤层缺口o 2.4 陆地脊椎动物o 2.5 灭绝模式的可能解释? 3 生态系统的复原o 3.1 海洋生态系统的改变o 3.2 陆地脊椎动物? 4 灭绝原因o 4.1 撞击事件o 4.2 火山爆发o 4.3 甲烷水合物的气化o 4.4 海平面改变o 4.5 海洋缺氧o 4.6 硫化氢o 4.7 盘古大陆的形成o 4.8 多重原因? 5 注释? 6 延伸阅读? 7 外部链接年代测定在西元二十世纪之前，二叠纪与三叠纪交界的地层很少被发现，因此科学家们很难准确地估算灭绝事件的年代与经历时间，以及影响的地理范围[12]。

Surface wave higher-mode phase velocity measurements using a roller- coaster-type algorithm

Geophys.J.Int.(2003)155,289–307Surface wave higher-mode phase velocity measurements usinga roller-coaster-type algorithm´Eric Beucler,∗´El´e onore Stutzmann and Jean-Paul MontagnerLaboratoire de sismologie globale,IPGP,4place Jussieu,75252Paris Cedex05,France.E-mail:beucler@ipgp.jussieu.frAccepted2003May20.Received2003January6;in original form2002March14S U M M A R YIn order to solve a highly non-linear problem by introducing the smallest a priori information,we present a new inverse technique called the‘roller coaster’technique and apply it to measuresurface wave mode-branch phase velocities.The fundamental mode and theﬁrst six overtoneparameter vectors,deﬁned over their own signiﬁcant frequency ranges,are smoothed averagephase velocity perturbations along the great circle epicentre–station path.These measurementsexplain well both Rayleigh and Love waveforms,within a maximum period range includedbetween40and500s.The main idea of this technique is toﬁrst determine all possibleconﬁgurations of the parameter vector,imposing large-scale correlations over the model space,and secondly to explore each of them locally in order to match the short-wavelength variations.Theﬁnal solution which achieves the minimum misﬁt of all local optimizations,in the least-squares sense,is then hardly inﬂuenced by the reference model.Each mode-branch a posteriorireliability estimate turns out to be a very powerful instrument in assessing the phase velocitymeasurements.Our Rayleigh results for the Vanuatu–California path seem to agree correctlywith previous ones.Key words:inverse problem,seismic tomography,surface waves,waveform analysis.1I N T R O D U C T I O NOver the last two decades,the resolution of global tomographic models has been greatly improved,because of the increase in the amount and the quality of data,and due to more and more sophisticated data processing and inversion schemes(Woodhouse&Dziewonski1984, 1986;Montagner1986;Nataf et al.1986;Giardini et al.1987;Montagner&Tanimoto1990;Tanimoto1990;Zhang&Tanimoto1991; Su et al.1994;Li&Romanowicz1995;Romanowicz1995;Trampert&Woodhouse1995;Laske&Masters1996;Ekstr¨o m et al.1997; Grand et al.1997;van der Hilst et al.1997;Liu&Dziewonski1998;Ekstr¨o m&Dziewonski1998;Laske&Masters1998;M´e gnin& Romanowicz2000;Ritsema&van Heijst2000,among others).These models are derived from surface wave phase velocities and/or body wave traveltimes(or waveforms)and/or free-oscillation splitting measurements.Body wave studies provide high-resolution models but suffer from the inhomogeneous distribution of earthquakes and recording stations,even when considering reﬂected or diffracted phases.On the other hand,the surface wave fundamental mode is mainly sensitive to the physical properties of the upper mantle.So,the investigation of the transition zone on a global scale,which plays a key role in mantle convection,can only be achieved by using higher-mode surface waves.Aﬁrst attempt at providing a global tomographic model using these waves has been proposed by Stutzmann&Montagner(1994),but with a limited amount of data.More recently,van Heijst&Woodhouse(1999)computed degree-12phase velocity maps of the fundamental mode and the fourﬁrst overtones for both Love and Rayleigh waves.These data have been combined with body wave traveltimes measurements and free-oscillation splitting measurements,to provide a global tomographic model with a high and uniform resolution over the whole mantle (Ritsema et al.1999;van Heijst et al.1999).The most recent S H model for the whole mantle was proposed by M´e gnin&Romanowicz (2000).This degree-24model results from waveform inversion of body and surface Love waves,including fundamental and higher modes and introducing cross-branch coupling.Extracting information from higher-mode surface waves is a difﬁcult task.The simultaneous arrivals(Fig.3in Section3)and the interference between the different mode-branches make the problem very underdetermined and non-linear.To remove the non-linearity,Cara &L´e vˆe que(1987)and L´e vˆe que et al.(1991)compute the cross-correlogram between the data and monomode synthetic seismograms and ∗Now at:´Ecole Normale Sup´e rieure,24rue Lhomond,75231Paris Cedex05,France.C 2003RAS289290´E.Beucler,´E.Stutzmann and J.-P.Montagnerinvert the amplitude and the phase of theﬁltered cross-correlogram.On the other hand,Nolet et al.(1986)and Nolet(1990)use an iterative inverse algorithm toﬁt the waveform in the time domain and increase the model complexity within the iterations.These two methods provide directly a1-D model corresponding to an average epicentre–station path.They wereﬁrst used‘manually’,which limited the amount of data that could be processed.The exponential increase in the amount of good-quality broad-band data has made necessary the automation of most parts of the data processing and an automatic version of these methods has been proposed by Debayle(1999)for the waveform inversion technique of Cara&L´e vˆe que(1987)and by Lebedev(2000)and Lebedev&Nolet(2003)for the partition waveform inversion.Stutzmann&Montagner(1993)split the inversion into two steps;at each iteration,a least-squares optimization to measure phase velocities is followed by an inversion to determine the1-D S-wave velocity model,in order to gain insight into the factors that control the depth resolution.They retrieve the phase velocity for a set of several seismograms recorded at a single station and originating from earthquakes located in the same area in order to improve the resolution.Another approach has been followed by van Heijst&Woodhouse(1997)who proposed a mode-branch stripping technique based on monomode cross-correlation functions.Phase velocity and amplitude perturbations are determined for the most energetic mode-branch,the waveform of which is then subtracted from the seismogram in order to determine the second most energetic mode-branch phase velocity and amplitude perturbations,and so on.More recently,Y oshizawa&Kennett(2002)used the neighbourhood algorithm(Sambridge1999a,b)to explore the model space in detail and to obtain directly a1-D velocity model which achieves the minimum misﬁt.It is difﬁcult to compare the efﬁciency of these methods because they all follow different approaches to taking account of the non-linearity of the problem.Up to now,it has only been possible to compare tomographic results obtained using these different techniques.In this paper,we introduce a new semi-automatic inverse procedure,the‘roller coaster’technique(owing to the shape of the misﬁt curve displayed in Fig.6b in Section3.4.1),to measure fundamental and overtone phase velocities both for Rayleigh and Love waves.This method can be applied either to a single seismogram or to a set of seismograms recorded at a single station.To deal with the non-linearity of the problem,the roller coaster technique combines the detection of all possible solutions at a large scale(which means solutions of large-wavelength variations of the parameter vector over the model space),and local least-squares inversions close to each of them,in order to match small variations of the model.The purpose of this article is to present an inverse procedure that introduces as little a priori information as possible in a non-linear scheme.So,even using a straightforward phase perturbation theory,we show how this algorithm detects and converges towards the best global misﬁt model.The roller coaster technique is applied to a path average theory but can be later adapted and used with a more realistic wave propagation theory.One issue of this study is to provide a3-D global model which does not suffer from strong a priori constraints during the inversion and which then can be used in the future as a reference model.We describe hereafter the forward problem and the non-linear inverse approach developed for solving it.An essential asset of this technique is to provide quantitative a posteriori information,in order to assess the accuracy of the phase velocity measurements.Resolution tests on both synthetic and real data are presented for Love and Rayleigh waves.2F O RWA R D P R O B L E MFollowing the normal-mode summation approach,a long-period seismogram can be modelled as the sum of the fundamental mode(n=0) and theﬁrst higher modes(n≥1),hereafter referred to as FM and HM,respectively.Eigenfrequencies and eigenfunctions are computed for both spheroidal and toroidal modes in a1-D reference model,PREM(Dziewonski&Anderson1981)in our case.Stoneley modes are removed,then the radial order n for the spheroidal modes corresponds to Okal’s classiﬁcation(Okal1978).In the following,all possible sorts of coupling between toroidal and spheroidal mode-branches(Woodhouse1980;Lognonn´e&Romanowicz1990;Deuss&Woodhouse2001) and off-great-circle propagation effects(Woodhouse&Wong1986;Laske&Masters1996)are neglected.For a given recorded long-period seismogram,the corresponding synthetic seismogram is computed using the formalism deﬁned by Woodhouse&Girnius(1982).In the most general case,the displacement u,corresponding of theﬁrst surface wave train,in the time domain, can be written asu(r,t)=12π+∞−∞nj=0A j(r,ω)exp[i j(r,ω)]exp(iωt)dω,(1)where r is the source–receiver spatial position,ωis the angular frequency and where A j and j represent the amplitude and the phase of the j th mode-branch,respectively,in the frequency domain.In the following,the recorded and the corresponding synthetic seismogram spectra (computed in PREM)are denoted by(R)and(S),respectively.In the Fourier domain,following Kanamori&Given(1981),a recorded seismogram spectrum can be written asA(R)(r,ω)expi (R)(r,ω)=nj=0B j(r,ω)expij(r,ω)−ωaCj(r,ω),(2)where a is the radius of the Earth, is the epicentral distance(in radians)and C(R)j(r,ω)is the real average phase velocity along the epicentre–station path of the j th mode-branch,which we wish to measure.The term B j(r,ω)includes source amplitude and geometrical spreading, whereas j(r,ω)corresponds to the source phase.The instrumental response is included in both terms and this expression is valid for bothRayleigh and Love waves.The phase shift due to the propagation in the real medium then resides in the term exp[−iωa /C(R)j(r,ω)].C 2003RAS,GJI,155,289–307The roller coaster technique291 Figure1.Illustration of possible2πphase jumps over the whole frequency range(dashed lines)or localized around a given frequency(dotted line).Thereference phase velocity used to compute these three curves is represented as a solid line.Considering that,toﬁrst order,the effect of a phase perturbation dominates over that of the amplitude perturbation(Li&Tanimoto 1993),and writing the real slowness as a perturbation of the synthetic slowness(computed in the1-D reference model),eq.(2)becomesA(R)(r,ω)expi (R)(r,ω)=nj=0A(S)j(r,ω)expij(r,ω)−ωaC(S)j(ω)−χ,(3) whereχ=ωa1C(R)j(r,ω)−1C(S)j(r,ω).(4) Let us now denote by p j(r,ω),the dimensionless parameter vector of the j th mode-branch deﬁned byp j(r,ω)=C(R)j(r,ω)−C(S)j(ω)Cj(ω).(5)Finally,introducing the synthetic phase (S)j(r,ω),as the sum of the source phase and the phase shift due to the propagation in the reference model,the forward problem can be expressed asd=g(p),A(R)(r,ω)expi (R)(r,ω)=nj=0A(S)j(r,ω)expi(S)j(r,ω)+ωaCj(ω)p j(r,ω).(6)For practical reasons,the results presented in this paper are computed following a forward problem expression based on phase velocity perturbation expanded to third order(eq.A5).When considering an absolute perturbation range lower than10per cent,results are,however, identical to those computed following eq.(6)(see Appendix A).Formally,eq.(6)can be summarized as a linear combination of complex cosines and sines and for this reason,a2πundetermination remains for every solution.For a given parameter p j(r,ω),it is obvious that two other solutions can be found by a2πshift such asp+j(r,ω)=p j(r,ω)+2πC(S)j(ω)ωa and p−j(r,ω)=p j(r,ω)−2πC(S)j(ω)ωa.(7) As an example of this feature,all the phase velocity curves presented in Fig.1satisfy eq.(6).This means that2πphase jumps can occur over the whole frequency range but can also be localized around a given frequency.Such an underdetermination as expressed in eq.(6)and such a non-unicity,in most cases due to the2πphase jumps,are often resolved by imposing some a priori constraints in the inversion.A contrario, the roller coaster technique explores a large range of possible solutions,with the smallest a priori as possible,before choosing the model that achieves the minimum misﬁt.3D E S C R I P T I O N O F T H E R O L L E R C O A S T E R T E C H N I Q U EThe method presented in this paper is a hybrid approach,combining detection of all possible large-scale solutions(which means solutions of long-wavelength conﬁgurations of the parameter vector)and local least-squares optimizations starting from each of these solutions,in order to match the short-wavelength variations of the model space.The different stages of the roller coaster technique are presented in Fig.2and described hereafter.Theﬁrst three stages are devoted to the reduction of the problem underdetermination,while the non-linearity and the non-unicity are taken into account in the following steps.C 2003RAS,GJI,155,289–307292´E.Beucler,´E.Stutzmann and J.-P.MontagnerStage1Stage2Stage3Stage4using least-squares2phasejumps?Stage5Stage6Figure2.Schematic diagram of the roller coaster technique.See Section3for details.3.1Selection of events,mode-branches and time windowsEvents with epicentral distances larger than55◦and shorter than135◦are selected.Thus,the FM is well separated in time from the HM(Fig.3), and theﬁrst and the second surface wave trains do not overlap.Since the FM signal amplitude is much larger than the HM amplitude for about 95per cent of earthquakes,each seismogram(real and synthetic)is temporally divided into two different time windows,corresponding to the FM and to the HM parts of the signal.An illustration of this amplitude discrepancy in the time domain is displayed in Fig.3(b)and when focusing on Fig.4(a),the spectrum amplitude of the whole real signal(FM+HM)is largely dominated by the FM one.Eight different pickings deﬁning the four time windows,illustrated in Fig.3(a),are computed using synthetic mode-branch wave trains and are checked manually.For this reason,this method is not completely automated,but this picking step is necessary to assess the data quality and the consistency between recorded and synthetic seismograms.In Appendix B,we show that the phase velocity measurements are not signiﬁcantly affected by a small change in the time window dimensions.An advantage of this temporal truncation is that,whatever the amplitude of the FM,the HM part of the seismograms can always be treated.Hence,the forward problem is now split into two equations,corresponding to the FM and to the HM parts,respectively.A(R) FM (r,ω)expi (R)FM(r,ω)=A(S)0(r,ω)expi(S)0(r,ω)+ωaC(ω)p0(r,ω)(8)andA(R) HM (r,ω)expi (R)HM(r,ω)=6j=1A(S)j(r,ω)expi(S)j(r,ω)+ωaC(S)j(ω)p j(r,ω).(9)Seismograms(real and synthetic)are bandpassﬁltered between40and500s.In this frequency range,only theﬁrst six overtone phase velocities can be efﬁciently retrieved.Tests on synthetic seismograms(up to n=15)with various depths and source parameters have shown that the HM for n≥7have negligible amplitudes in the selected time and frequency windows.C 2003RAS,GJI,155,289–307The roller coaster technique293Figure3.(a)Real vertical seismogram(solid line)and its corresponding synthetic computed in PREM(dotted line).The earthquake underlying this waveform occurred on1993September4in Afghanistan(36◦N,70◦E,depth of190km)and was recorded at the CAN GEOSCOPE station(Australia).The epicentral distance is estimated at around11340km.Both waveforms are divided into two time windows corresponding to the higher modes(T1–T2,T5–T6)and to the fundamental mode(T3–T4,T7–T8).(b)The contribution of each synthetic monomode shows the large-amplitude discrepancy and time delay between the fundamental mode and the overtones.The different symbols refer to the spectra displayed in Fig.4.3.2Clustering the eventsFollowing eq.(8),a single seismogram is sufﬁcient to measure the FM phase velocity,whereas for the HM(eq.9)the problem is still highly underdetermined since the different HM group velocities are very close.This can be avoided by a reduction of the number of independent parameters considering mathematical relations between different mode-branch phase velocities.The consequence of such an approach is to impose a strong a priori knowledge on the model space,which may be physically unjustiﬁed.Another way to reduce this underdetermination is to increase the amount of independent data while keeping the parameter space dimension constant.Therefore,all sufﬁciently close events are clustered into small areas,and each individual ray path belonging to the same box is considered to give equivalent results as a common ray path.This latter approach was followed by Stutzmann&Montagner(1993),but with5×5deg2boxes independently of epicentral distance and azimuth values,due to the limited number of data.Here,in order to prevent any bias induced by the clustering of events too far away from one to another,and to be consistent with the smallest wavelength,boxes are computed with a maximum aperture angle of2◦and4◦in the transverse and longitudinal directions,respectively(Fig.5),with respect to the great circle path.The boxes are computed in order to take into account as many different depths and source mechanisms as possible.The FM phase velocity inversion is performed for each path between a station and a box,whereas the HM phase velocities are only measured for the boxes including three or more events.Since only the sixﬁrst mode-branches spectra are inverted,the maximum number of events per box is set to eight.The use of different events implies average phase velocity measurements along the common ray paths which can be unsuitable for short epicentral distances,but increases the accuracy of the results for the epicentral distances considered.C 2003RAS,GJI,155,289–307294´E.Beucler,´E.Stutzmann and J.-P.MontagnerFigure4.(a)The normalized amplitude spectra of the whole real waveform(solid line)displayed in Fig.3(a).The real FM part of the signal(truncated between T3and T4)is represented as a dotted line and the real HM part(between T1and T2)as a dashed line.(b).The solid line corresponds to the normalized spectrum amplitude of the real signal truncated between T3and T4(Fig.3a).The corresponding synthetic FM is represented as a dotted line and only the frequency range represented by the white circles is selected as being signiﬁcant.(c)Selection of HM inversion frequency ranges using synthetic signiﬁcant amplitudes.The solid line corresponds to the real HM signal,picked between T1and T2(Fig.3a).For each mode-branch(dotted lines),only the frequency ranges deﬁned by the symbols(according to Fig.3b)are retained for the inversion.(d)Close up of the sixth synthetic overtone,in order to visualize the presence of lobes and the weak contribution frequency range in the spectrum amplitude.The stars delimit the selected frequency range.3.3Determination of the model space dimensionReal and synthetic amplitude spectra are normalized in order to minimize the effects due to the imprecision of source parameters and of instrumental response determination.As presented in Fig.4,a synthetic mode-branch spectrum is frequently composed by several lobes due to the source mechanism.Between each lobe and also near the frequency range edges due to the bandpassﬁlter,the amplitude strongly decreases down to zero,and therefore phase velocities are absolutely not constrained at these frequencies.It is around these frequencies that possible local2πphase jumps may occur(Fig.1).Then,we decide to reduce the model space dimension in order to take into account only well-constrained points.For each spectrum,the selection of signiﬁcant amplitudes,with a thresholdﬁxed to10per cent of the mean maximum spectra amplitude,deﬁnes the inverted frequency range.In the case of several lobes in a synthetic mode-branch amplitude spectrum,only the most energetic one is selected as shown in Figs4(c)and(d).For a given mode-branch,the simultaneous use of different earthquakes implies a discrimination criterion based upon a mean amplitude spectrum of all spectra,which tends to increase the dimensions of the signiﬁcant frequency range.The normalization and this selection of each mode-branch signiﬁcant amplitudes is also a way to include surface wave radiation pattern information in the procedure.Changes in source parameters can result in changes in the positions of the lobes in the mode-branch amplitude spectra over the whole frequency range(40–500s).In the future,it will be essential to include these possible biases in the scheme and then to simultaneously invert moment tensor,location and depth.C 2003RAS,GJI,155,289–307The roller coaster technique295Figure5.Geographical distribution of inversion boxes for the SSB GEOSCOPE station case.The enlarged area is deﬁned by the bold square in the inset (South America).Black stars denote epicentres and hatched grey boxes join each inversion group.Each common ray path(grey lines)starts from the barycentre (circles)of all events belonging to the same box.The maximum number of seismograms per box isﬁxed at eight.3.4Exploration of the model space at very large scaleThe main idea of this stage is to test a large number of phase velocity large-scale perturbations with the view of selecting several starting vectors for local inversions(see Section3.5).The high non-linearity of the problem is mainly due to the possible2πphase jumps.And,even though the previous stage(see Section3.3)prevents the shifts inside a given mode-branch phase velocity curve,2πphase jumps over the whole selected frequency range are still possible.For this reason a classical gradient least-squares optimization(Tarantola&Valette1982a)is inadequate.In a highly non-linear problem,a least-squares inversion only converges towards the best misﬁt model that is closest to the starting model and the number of iterations cannot change this feature.On the other hand,a complete exploration of all possible conﬁgurations in the parameter space is still incompatible with a short computation time procedure.Therefore,an exploration of the model space is performed at very large scale,in order to detect all possible models that globally explain the data set well.3.4.1Fundamental mode caseWhen considering a single mode-branch,the number of parameter vector components is rather small.The FM large-scale exploration can then be more detailed than in the HM case.Considering that,at low frequencies,data are correctly explained by the1-D reference model,the C 2003RAS,GJI,155,289–307296´E.Beucler,´E.Stutzmann and J.-P.MontagnerabFigure6.(a)Five examples of the FM parameter vector conﬁgurations during the exploration of the model space at large scale corresponding toαvalues equal to−5,−,0,+2.5and+5per cent.The selected points for which the phase velocity is measured(see Section3.3)are ordered into parameter vector components according to increasing frequency values.Theﬁrst indices then correspond to the low-frequency components(LF)and the last ones to the high-frequency(HF) components.Varying the exploration factorα,different perturbation shapes are then modelled and the misﬁt between data and the image of the corresponding vector is measured(represented in theﬁgure below).(b)The misﬁt in the FM case,symbolized by+,is the expression of the difference between data and the image of the tested model(referred to as pα)through the g function(eq.8).Theαvalues are expressed as a percentage with respect to the PREM.As an example,theﬁve stars correspond to the misﬁt values of theﬁve models represented in theﬁgure above.The circles represent the bestαvalues and the corresponding vectors are then considered as possible starting models for the next stage.dimensionless phase velocity perturbation(referred to as pα)can be modelled as shown in theﬁve examples displayed in Fig.6(a).Basically, the low-frequency component perturbations are smaller than the high-frequency ones.However,if such an assumption cannot be made,the simplest way to explore the model space is then byﬁxing an equalαperturbation value for all the components.The main idea is to impose strong correlations between all the components in order to estimate how high the non-linearity is.Varyingαenables one to compute different parameter vectors and solving eq.(8)to measure the distance between data and the image of a given model through the g function,integrated over the whole selected frequency range.Considering that only small perturbations can be retrieved,the exploration range is limited between−5and+5per cent,using an increment step of0.1per cent.The result of such an exploration is displayed in Fig.6(b)and clearly illustrates the high non-linearity and non-unicity of the problem.In a weakly non-linear problem,the misﬁt curve(referred to as||d−g(pα)||)should exhibit only one minimum.This would indicate that,whatever the value of the starting model,a gradient algorithm always converges towards the sameﬁnal model,the solution is then unique.In our case,Fig.6(b)shows that,when choosing the reference model(i.e.α=0per cent)as the starting model,a gradient least-squares optimization converges to the nearest best-ﬁtting solution(corresponding to the third circle),and could never reach the global best-ﬁtting model(in this example representedC 2003RAS,GJI,155,289–307The roller coaster technique 297by the fourth circle).Therefore,in order not to a priori limit the inversion result around a given model,all minima of the mis ﬁt curve (Fig.6b)are detected and the corresponding vectors are considered as possible starting models for local optimizations (see Section 3.5).3.4.2Higher-mode caseThe introduction of several mode-branches simultaneously is much more dif ﬁcult to treat and it becomes rapidly infeasible to explore the model space as accurately as performed for the FM.However,a similar approach is followed.In order to preserve a low computation time procedure,the increment step of αis ﬁxed at 1per cent.The different parameter vectors are computed as previously explained in Section3.4.1(the shape of each mode-branch subvector is the same as the examples displayed in Fig.6a).In order to take into account any possible in ﬂuence of one mode-branch on another,all combinations are tested systematically.Three different explorations of the model space are performed within three different research ranges:[−4.5to +1.5per cent],[−3to +3per cent]and [−1.5to +4.5per cent].For each of them,76possibilities of the parameter vector are modelled and the mis ﬁt between data and the image of the tested vector through the g function is computed.This approach is almost equivalent to performing a complete exploration in the range [−4.5to +4.5per cent],using a step of 0.5per cent,but less time consuming.Finally,all mis ﬁt curve minima are detected and,according to a state of null information concerning relations between each mode-branch phase velocities,all the corresponding vectors are retained as possible starting models.Thus,any association between each starting model subvectors is allowed.3.5Matching the short-wavelength variations of the modelIn this section,algorithms,notation and comments are identical for both FM and HM.Only the main ideas of the least-squares criterion are outlined.A complete description of this approach is given by Tarantola &Valette (1982a,b)and by Tarantola (1987).Some typical features related to the frequency/period duality are also detailed.3.5.1The gradient least-squares algorithmThe main assumption which leads us to use such an optimization is to consider that starting from the large-scale parameter vector (see Section 3.4),the non-linearity of the problem is largely reduced.Hence,to infer the model space from the data space,a gradient least-squares algorithm is performed (Tarantola &Valette 1982a).The expression of the model (or parameter)at the k th iteration is given by p k =p 0+C p ·G T k −1· C d +G k −1·C p ·G T k −1−1· d −g (p k −1)+G k −1·(p k −1−p 0) ,(10)where C p and C d are the a priori covariance operators on parameters and data,respectively,p 0the starting model,and where G k −1=∂g (p k −1)/∂p k −1is the matrix of partial derivatives of the g function established in eqs (8)and (9).The indices related to p are now expressing the iteration rank and no longer the mode-branch radial order.De ﬁning the k th image of the mis ﬁt function byS (p k )=12[g (p k )−d ]T ·C −1d ·[g (p k )−d ]+(p k −p 0)T ·C −1p ·(p k −p 0) ,(11)the maximum-likelihood point is de ﬁned by the minimum of S (p ).Minimizing the mis ﬁt function is then equivalent to ﬁnding the best compromise between decreasing the distance between the data vector and the image of the parameter vector through the g function,in the data space on one hand (ﬁrst part of eq.11),and not increasing the distance between the starting and the k th model on the other hand (second part of eq.11),following the covariances de ﬁned in the a priori operators on the data and the parameters.3.5.2A priori data covariance operatorThe a priori covariance operator on data,referred to as C d ,includes data errors and also all effects that cannot be modelled by the g function de ﬁned in eq.(8)and (9).The only way to really measure each data error and then to compute realistic covariances in the data space,would be to obtain exactly the corresponding seismogram in which the signal due to the seismic event is removed.Hence,errors over the data space are impossible to determine correctly.In order to introduce as little a priori information as possible,the C d matrix is computed with a constant value of 0.04(including data and theory uncertainties)for the diagonal elements and zero for the off-diagonal elements.In other words,this choice means that the phase velocity perturbations are expected to explain at least 80per cent of the recorded signal.3.5.3A priori parameter covariance operatorIn the model space,the a priori covariance operator on parameters,referred to as C p ,controls possible variations between the model vector components for a given iteration k (eq.10),and also between the starting and the k th model (eq.11).Considering that the phase velocity perturbation between two adjoining components (which are ordered according to increasing frequency values)of a given mode-branch do not vary too rapidly,C p is a non-diagonal matrix.This a priori information reduces the number of independent components and then induces smoothed phase velocity perturbation curves.A typical behaviour of our problem resides in the way the parameter space is discretized.In the matrix domain,the distance between two adjoining components is always the same,whereas,as the model space is not evenly spaced C 2003RAS,GJI ,155,289–307。

Pattern formation in weakly damped Faraday waves

Leabharlann 1. Introduction
The generation of standing waves on the free surface of a ﬂuid layer that is oscillated vertically is known since the work of Faraday (1831). Recently, there has been renewed experimental interest in Faraday waves as an example of a pattern-forming system. Reasons include the ease of experimentation due to short characteristic time scales (of the order of 10−2 seconds), and the ability to reach very large aspect ratios (the ratio of lateral size of the system to the characteristic wavelength of the pattern) of the order of 102 . By varying the form of the driving force and by using ﬂuids of diﬀerent viscosities, a number of interesting phenomena have been observed including the emergence of standing wave patterns of diﬀerent symmetries near onset (Christiansen, Alstrø m & Levinsen 1992; Fauve et al. 1992; Edwards & Fauve 1993, 1994; M¨ uller 1993), secondary instabilities of these patterns when the amplitude of the periodic driving force is increased (Ezerskii, Korotin & Rabinovich 1985; Daudet et al. 1995), and spatiotemporal chaotic states at even larger amplitudes of the driving force (Tuﬁllaro, Ramshankar & Gollub 1989; Gollub & Ramshankar 1991; Bosch & van de Water 1993; Bridger et al. 1993; Kudrolli & Gollub 1996). A numerical linear stability analysis of the Faraday wave problem has been carried out by Kumar & Tuckerman (1994) for a laterally inﬁnite ﬂuid layer of arbitrary viscosity.

全反射红外光谱法英文

全反射红外光谱法英文全反射红外光谱法在英文中被称为 Attenuated Total Reflection Infrared Spectroscopy（ATR-IR Spectroscopy）。

ATR-IR Spectroscopy is a technique used to analyze the molecular composition of samples by measuring the absorption of infrared light. It is based on the principle of total internal reflection, where an infrared beam is passed through a high refractive index material onto the sample surface at a specific angle. This causes a portion of the beam to be reflected back into the material, creating an evanescent wave that interacts with the sample. The attenuated reflection is then measured and analyzed to determine the molecular structure and functional groups present in the sample.ATR-IR Spectroscopy offers several advantages over traditional transmission infrared spectroscopy. It requires minimal sample preparation, as the sample can be analyzed directly without the need for complex sample preparationtechniques. It also allows for analysis of a wide range of sample types, including liquids, solids, and even gases. Additionally, ATR-IR Spectroscopy provides high sensitivity and signal-to-noise ratio, making it suitable for both qualitative and quantitative analysis.This technique finds applications in various fields such as pharmaceuticals, polymers, food and beverage, forensics, and environmental analysis. It can be used to identify unknown compounds, analyze chemical reactions, determine the purity of a substance, and monitor changes in molecular structure.In conclusion, ATR-IR Spectroscopy, or Attenuated Total Reflection Infrared Spectroscopy, is a powerful analytical technique used to investigate the molecular composition of samples. Its advantages include minimal sample preparation, versatility in sample types, and high sensitivity.。

The Influence of the Magnetic Field and Ultraviole

Journal of Electrical Engineering 5 (2017) 349-351doi: 10.17265/2328-2223/2017.06.009The Influence of the Magnetic Field and Ultraviolet Waves to the Liquid Fillers for Liquid LenseLiena Yu. VergunMolecular Physics Department, Faculty of Physics, Taras Shevchenko National University of Kyiv, UkraineAbstract: The question about properties of liquid fillers for liquid lenses under actions of magnetic field and ultraviolet waves are investigated. The liquid model system such as glycerol is used. The coefficients transmission and coefficients of temperatures increasing are experimentally determined. It is shown that the presence of constant magnetic field and UV-waves stabiliz formation of a wall layer. So the vibrational and rotary motions of molecules and its clusters are stabilized in liquid fillers. It is assumed that the chromatic aberration can be associated with the formation and redistribution of particles in the surface layer at the interface between the solid and liquid phases.Key words: Glycerol, magnetic field, ultraviolet waves.1. IntroductionIt is known liquid lenses are used in optoelectronic systems telescopes [1, 2]. The operating conditions of such devices connected with the interaction of UV radiation and constant magnetic field. For increasing of the quality of liquid lenses pay attention to the properties of liquid filler for exclusion of chromatic aberration [3, 4]. The determination of action UV-waves and constant magnetic field in model system is proposed for possible reasons of aberration. It is known glycerol is the simplest composition of liquid filler for liquid lenses [5]. The appearance of feature molecular structure in glycerol under the influence of a magnetic field and UV-radiation is demonstrated in work [6].The nature of the transmission of light waves after constant magnetic field action and action of UV-waves is experimentally determined. Time of action these external factors is corresponded to relaxation time in the system [7]. The transmission coefficients of glycerol after action constant magnetic field and UF-waves are obtained.Corresponding author: Liena Yu. Vergun, Ph.D., research fields: magnetic field, defects in crystal like structures.The value of a magnetic field was 22.4 mT [6]. In view of Ref. [8] it has been suggested that the occurrence of chromatic aberration is due to the relaxation processes in the boundary layer of fluid components. To exclude the impact of these processeson the image quality the author offered to hold preliminary processing liquid fillers under UV-waves and constant magnetic field.2. Materials and MethodThe type of glycerol with GOST technical standards 6259-75 is used. The scheme of laboratory bench is represented in Fig. 1a (where 1—working cell of KFK2MP, 2—glass cuvette, 3—glycerol, 4—UF emitter, 5—Helmholtz coils, 6—electronic scoreboard). The view of working cell of KFK2MP (photoelectric colorimeter) with Helmholtz coils is represented in Fig. 1b.3. Results and DiscussionThe dependences of the transmission coefficient τ(λ) are shown in Fig. 2. In this figure by number “1”—the experimental datas of glyserol without action of the external factors, by number “2”—the experimental data for glyserol after action UV-waves(time of actionAll Rights Reserved.The Influence of the Magnetic Field and Ultraviolet Waves to the Liquid Fillers for Liquid Lense350(a) (b)Fig. 1 The scheme (a) and view (b) of laboratory bench.Fig. 2 The dependence τ(λ).Fig. 3 The dependence()t ϕ.15 minutes), by number “3”—the experimental data of glyserol after action constant magnetic field (time of action 15 minutes), by number “4”—the experimental data after action UV-waves and constant magnetic field (time of action 15 minutes) are indicated.As shown in Fig. 3 the joint action of UV waves and constant magnetic field decreases the differencebetween values of coefficients transmission in the areaof wavelengths from 380 nm (violet color) to 750 nm (red color). The obtained results indicate a decrease in the probability of the appearance of chromatic aberration.According to Ref. [8], the phenomenon of chromatic aberration can be associated with the formation and redistribution of particles in the surface layer at the interface between the solid and liquid phases. The redistribution of particles and their clusters occurs at dissimilarities of velocity of their displacements at change of the action of external factors [9, 10]. An experiment was conducted for this purpose. A cuvette with the substance (glycerol) was placed in the heat-insulating container. The temperature sensor was located in the center of the cuvette. The temperature sensor readings were recorded in increments of minute. Fig. 3 shows the dependence of the dimensionless coefficient φ (the coefficient of temperatures increasing) on time t. The coefficient φ was calculated according to the formulaT T i =ϕ, where 0T is the temperature of themeasurement at the initial moment, i T —the temperature in the following intervals of time.The following symbols are introduced on the graph: In Fig. 3, by number “1”—the experimental data of glycerol without the action of the external factors, by number “2”—the experimental data of glycerol after the action of UV-waves (time of action 15 minutes) by number “3”—the experimental data of glycerol afterAll Rights Reserved.The Influence of the Magnetic Field and Ultraviolet Waves to the Liquid Fillers for Liquid Lense 351the action of the constants, magnetic field (time of action 15 minutes), by number “4”—the experimental data after action of UV-waves and constant magnetic field (time of action 15 minutes). The symbol “*” denotes the experimental data of the standardsubstance (32O Al ).As can be seen from Fig. 3 at treatment of glycerol by constant magnetic field and UV irradiation the smallest increasing of temperature is observed. The experimental data obtained correspond to the experimental results shown in Fig. 2. According to our opinion, the treatment of UV iiradiation with a magnetic field leads to a uniform distribution of molecules both in the surface layer near the wall andin the entire volume.4. ConclusionsExperimental studies of the optical andthermophysical properties of a model system of a liquidcomponent for liquid lenses (glycerin) under theinfluence of UV irradiation and a magnetic field were conducted. It is shown that the presence of constant magnetic field and UV-waves stabiliz formation of awall layer. So the vibrational and rotary motions ofmolecules and its clusters are stabilized in liquid fillers.References[1] Gibson, B. K. 1991. “Liquid Mirror Telescope History.” Journal of the Royal Astronomical Society of Canada 85 (4): 158-71.[2]Berge, B. 2005. “Liquid Lense Technology: Principle of Electrowetting Based Lenses and Applications to Imaging.” IEEE , 227-30.[3]Stallinga, S., Vrehen, J., Wals, J., Stapert, H., and Verstegen, E. 2000. “Liquid Crystal Aberration Compensation Devices.” Proceedings of SPIE 48: 50-9. [4] Vergun, L.Y. 2015. “The Using of Magnetic Field for the Improvement of Properties of Liquid Fillers in a Liquid Lense.” In Abstracts XXII Galyna Puchkovska International School-Seminar Spectroscopy of Molecules and Crystals, 155.[5] Calo, E., and Khutoryanskiy, V. V. 2015. “Biomedical Application of Hydrogels: A Reviews of Patents and Commercial Products.” European Polymer Journal 65： 252-67.[6]Pelizzeti, E., and Schiavello, M. 1991. Photochemical Conversion and Storage of Solar Energy . Springer Science & Business Media.[7]Kaneoke, Y., Furuse, M., and Yoshida, K. 1989.“Transfer Index of MR Relaxation Enhancer: A Quantitative Evaluation of MR Contrast Enhancemen.” AJNR Am J Neuroradiol 10 (2): 329-33.[8] Angell, С. А., and Ngai, K. L. 2000. “Relaxation inGlass-Forming Liquids and Amorphys Solids.” Journal of Applied Physics 88 (6): 3113-57.[9] Root, L. J., and Stillinger, F. H. 1989. “Short-Range Order in Glycerol: A Molecular Dynamics Study.” J.Chern. Phys. 90 (2): 1200-08.[10] Milner, A. A., Korobenko, A., Flo, J., Sh. Averbukh, I.,and Milner, V. 2015. “Magneto-Optical Properties of Paramagnetic Superrotors.” Phys. Rev. Lett. 115 (3): 033005.All Rights Reserved.。

1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。

where R is the Riemann curvature tensor (14). Variation of (1) with respect to the metric g and the connection Γ produces Euler–Lagrange equations which we, for the time being, will write symbolically as ∂SYM /∂g = 0 , (2)
Torsion waves in metric–aﬃne ﬁeld theory
Alastair D King† and Dmif Mathematical Sciences, University of Bath, Bath BA2 7AY, UK
Torsion waves in metric–aﬃne ﬁeld theory
3
It is easy to see that the connections from Theorem 1 are not ﬂat, i.e., R ≡ 0. The non-trivial plane wave solutions of (5) can, of course, be written down explicitly: up to a proper Lorentz transformation they are u(x) = w e−ik·x where wµ = C (0, 1, −αi, 0) , kµ = β (1, 0, 0, 1) , (9) (8)
β = ±1, and C is an arbitrary positive constant (amplitude). Let us now introduce an additional equation into our model: Ric = 0 (10)
where Ric is the Ricci curvature tensor. This is the Einstein equation describing the absence of sources of gravitation. Remark 2 If the connection is that of Levi-Civita then (10) implies (3). In the general case equations (3) and (10) are independent. The question we are about to address is whether there are any spacetimes which simultaneously satisfy the Yang–Mills equation (3), the complementary Yang–Mills equation (2), and the Einstein equation (10). More speciﬁcally, we are interested in spacetimes whose connections are not ﬂat and not Levi-Civita connections. The following theorem provides an aﬃrmative answer to the above question. Theorem 2 A spacetime from Theorem 1 satisﬁes equation (10) if and only if L is proportional to (du)|x=0 , in which case torsion equals contortion up to a natural reordering of indices: Tλµν = Kµλν . (11)
α = ±1; here u is the unknown vector function. In calling (5) the polarized Maxwell equation we are motivated by the fact that any solution of (5) is a solution of (4). We call a solution u of the Maxwell equation (4) non-trivial if du ≡ 0. If the metric is given and the connection is known to be metric compatible then the connection coeﬃcients are uniquely determined by torsion (13) or contortion (16). The choice of torsion or contortion for the purpose of describing a metric compatible connection is purely a matter of convenience as the two are expressed one via the other in accordance with formulae (17). We deﬁne Minkowski space M4 as a real 4-manifold with a global coordinate system (x0 , x1 , x2 , x3 ) and metric gµν = diag(+1, −1, −1, −1) . Our deﬁnition of M4 speciﬁes the manifold M and the metric g , but does not specify the connection Γ. Our ﬁrst result is Theorem 1 Let u be a complex-valued vector function on M4 which is a non-trivial plane wave solution of the polarized Maxwell equation (5), let L = 0 be a constant complex antisymmetric tensor satisfying ∗L=α ˜ iL , α ˜ = ±1, and let Γ be the metric compatible connection corresponding to contortion K λ µν = Re(uµ Lλ ν ) . (7) Then the spacetime {M4 , Γ} is a solution of the system of equations (2), (3). Remark 1 In abstract Yang–Mills theory it is not customary to consider the equation (2) because there is no guarantee that this would lead to physically meaningful results. As an illustration let us examine the Maxwell equation (4) for real-valued vector functions on a Lorentzian manifold, which is the simplest example of a Yang–Mills equation. Straightforward calculations show that it does not have non-trivial solutions which are stationary points of the Maxwell action with respect to the variation of the metric. (6)
Torsion waves in metric–aﬃne ﬁeld theory ∂SYM /∂ Γ = 0 .
2 (3)
Equation (3) is the Yang–Mills equation for the aﬃne connection. Equation (2) does not have an established name; we will call it the complementary Yang–Mills equation. Our initial objective is the study of the combined system (2), (3). This is a system of 74 real non-linear partial diﬀerential equations with 74 real unknowns. In order to state our results we will require the Maxwell equation δ du = 0 as well as the polarized Maxwell equation ∗ du = αidu , (5) (4)
PACS numbers: 04.50.+h, 03.65.Pm
Submitted to: Class. Quantum Grav.
1. Main results We consider spacetime to be a real oriented 4-manifold M equipped with a nondegenerate symmetric metric g and an aﬃne connection Γ. The 10 independent components of the metric tensor gµν and the 64 connection coeﬃcients Γλ µν are the unknowns, as is the manifold M itself. This approach is known as metric–aﬃne ﬁeld ´ Cartan, A S Eddington, theory. Its origins lie in the works of authors such as E A Einstein, T Levi-Civita, E Schr¨ odinger and H Weyl; see, for example, Appendix II in [1], or [2]. Reviews of the more recent work in this area can be found in [3, 4, 5, 6]. The Yang–Mills action for the aﬃne connection is SYM := Rκ λµν Rλ κ µν (1)