Abstract Visualization of Scalar Topology for Structural Enhancement

Visualization of Scalar Topology for Structural Enhancement

C.L.Bajaj V.Pascucci

Department of Computer Sciences and TICAM

University of Texas,Austin,TX78733

D.R.Schikore

Center for Applied Scienti?c Computing

Lawrence Livermore National Laboratory,Livermore,CA94550

Abstract

Scalar?elds arise in every scienti?c application.Existing scalar visualization techniques require that the user infer the global scalar structure from what is frequently an insuf?cient display of information.We present a visualization technique which nu-merically detects the structure at all scales,removing from the user the responsibility of extracting information implicit in the data,and presenting the structure explicitly for analysis.We further demonstrate how scalar topology detection proves use-ful for correct visualization and image processing applications such as image co-registration,isocontouring,and mesh com-pression.

Keywords:Scienti?c Visualization,Scalar Fields,Curves and Surfaces,V ector Topology

1Introduction

Visualization of scalar?elds is common across all scienti?c dis-ciplines,including geographic data such as altitude and temper-ature,medical applications with CT and MRI values,and pres-sure and vorticity magnitude in computational?uid dynamics. The purpose of the visualization is to aid the user in understand-ing the structure of the data[29].

Common methods for visualizing scalar ?elds can be grouped into two broad classes.First are methods whose aim is to detect structure and present a display to the user which communicates this structure.Critical to these methods is the de?nition of structure,and how well the de?nition matches the visualization users’need.Second are those methods which attempt to display the entire scalar?eld simultaneously,leav-ing interpretation of the display to the https://www.wendangku.net/doc/0f10852026.html,binations of the two methods serve to reinforce the information provided by each visualization.We will use for comparison one technique from each of these categories,isocontouring and colormapping. Isocontours,or constant valued curves and surfaces from continuous2D and3D scalar?elds,are a common visualiza-tion technique for displaying scalar?eld structure[21].By their de?nition,isocontours represent the data only at discrete lev-els,and as such are an effective technique for determining the

“shape”of objects in the scalar?eld.Shape extraction as de-?ned by isocontoursis well understood and appreciated in many applications,such as Medical Imaging,as isocontours in a den-sity?eld may result in realistic models of skeletal structure,skin surface,or various organs[22].Also implicit in their de?nition is the fact that isocontours are an incomplete representation of the scalar?eld,as one can only infer from an isocontour that the data to one side is above the isovalue,and the data to the other side is below the isovalue.With multiple isocontours,the scalar?eld effectively becomes segmented into a?nite number of ranges,within which the structure remains unknown.The same claim of incompleteness can be made of any technique which only displays a portion of the?eld.Moreover it is not obvious which isovalues one should select and how namy of them[4].

Colormapping of scalar data de?nes a discrete or continuous range of colors onto which the scalar values are https://www.wendangku.net/doc/0f10852026.html,e of color,though proven to be useful in many visualization tech-niques,introduces complications due of perceptual issues,such as colorblindness.Colormaps may also mislead the user,for ex-ample when small-scale structure in the data is washed out due to the large range of values taken on by the variable.

Scienti?c data which is time-varying in nature intensi?es the problems with the methods described above.In the typical case,

a scalar variable may take on a wide range of values over the

course of a simulation,however at certain times during the sim-ulation the range may be much smaller.With both isocontours and colormapped display,it is desirable to use the same isoval-ues and colormap for each time-step being displayed in order to reduce the possibility of introducing artifacts which may be misinterpreted as features.This requirement complicates the task of choosing a good colormap or selection of isovalues for

a time-varying visualization.

In this paper we present a complementary scalar structure visualization technique which does not depend on the user to determine structure from the graphical display,but instead de-?nes,computes,and displays the structure of a scalar?eld di-rectly.Through detection of all critical points(saddles,max-ima,and minima),we construct an embedded graph by com-puting integral curves in the gradient?eld from saddle points to an attached critical point,as illustrated in?gure1.Curves in 1

Figure1:Isocontours(dotted)of part of a scalar?eld along with the critical points and integral curves

this topological graph are always perpendicular to isocontours of the scalar?eld[23],and we will demonstrate that these curves contain complementary information to that provided by display of isocontours or colormapped scalar?elds,providing a method which is both useful in its own right and which also enhances the commonly used techniques for visualizing scalar?elds.We further indicate that the de?nition of structure which is provided by the scalar topology proves useful in several additional visu-alization and image processing applications.

2Related Work

Much of the work in enhancing colormapped visualization of scalar?elds has dealt with determining“good”colormaps which effectively display the data.Bergman,et.al.,de?ne rules based on perception,user goals,and data characteristics to automatically select a colormap which will meet the user requirements[6].Histogram equalization is a technique which spreads the data evenly over the range of colors,using the avail-able color space to it’s fullest[28].The result is that each color in the colormap is used an equal number of times.Gershon[14] uses“Generalized Animation”to display otherwise static scalar data in a dynamic way,taking advantage of the ability of the visual system to detect dynamic changes.Animation draws at-tention to fuzzy details in the data which may not be detected in the static representation.

There has been several papers in detecting isocontours in2d and3d scalar data[21,30].Additional work concentrates on handling problems in regions containing saddle points which cause dif?culty in determining the topological structure of the surface contained in the region[25,31,26].The problem of de-tecting ridges and valleys in digital terrain has been treated in several papers[12].McCormack,et.al.consider the problem of detecting drainage patterns in geographic terrain[24].Inter-rante,et.al.have used ridge and valley detection on3d surfaces to enhance the shape of transparently rendered surfaces[19]. Extrema graphs were used by Itoh and Koyamada to speed iso-contour extraction[20].A graph containing extreme points and boundary points of a scalar?eld can be guaranteed to intersect every isocontour at least once,allowing seed points to be gener-ated by searching only the cells contained in the extrema graph. Helman and Hesselink detect vector?eld topology by clas-sifying the zeros of a vector?eld and performing particle trac-ing from saddle points[17].The resulting partitioning consists of regions which are topologically equivalent to uniform?ow. Globus,et.al.describe a software system for3d vector topol-ogy and brie?y note that the technique may also be applied to the gradient of a scalar?eld in order to identify maxima and minima[15].Bader et.al.and Collard et.al.examine the gra-dient?eld of the charge density in a molecular system[2,1,10]. The topology of this scalar?eld represents the bonds linking to-gether the atoms of the molecule.Bader goes on to show how features higher level structures in the topology represent chains, rings,an cages in the molecule.Bader’s example is a de?n-ing motivation for developing the automatic extraction and vi-sualization of topology from a scalar?eld.In many situations, topology provides a more intuitive and physically meaningful visualization.Grosse[16]also presents methods of approxi-mating the scalar topology of the electron density function of proteins.One of his methods uses tensor product B-spline?ts while the other scales Fourier coef?cients of the electron den-sity function.

3Scalar Topology

Previous techniques for enhancing scalar?eld visualization at-tempt to address the inability of colormapping and isocontour-ing to capture and directly represent features in the data.We ad-dress this problem not through feature enhancement using ex-isting visualization techniques,but through direct feature detec-tion and display.For our purpose of detection and display,we de?ne the topology of a scalar?eld de?ned with domain

to consist of the following:

1.The local maxima of

2.The local minima of

3.The saddle points of

4.Selected integral curves joining each of the above Integral curves are de?ned as curves which are everywhere tangent to the gradient?eld of.Intuitively,these curves rep-resent the path followed by a heat-seeking particle in a temper-ature?eld,or the path followed by a ball rolling down a hill in a ?eld of elevation values.In vector?eld topology,the curves ad-vected in the?ow?eld segment the?eld into regions which are topologically equivalent to uniform?ow.In the case of scalar topology,integral curves segment the?eld into regions in which the gradient?ow is uniform,or in other words,the scalar func-tion is monotonic.Such a segmentation of the scalar?eld into regions of simple behavior reveals the structure of the scalar ?eld for the visualization user.

We outline the procedure for visualization of scalar topology as follows:

1.Detect stationary(critical)points in.

2.Classify stationary points.

3.Integrate selected integral curves in gradient?eld.

In the following subsections,we will de?ne our model of a continuous scalar?eld and look at each of the steps de?ned above.

3.1Scalar Field Model

In typical scienti?c applications,data is represented at the nodes of a mesh of elements and interpolated linearly across the inte-rior of the elements.Such a data model is continuous and has a discontinuous gradient?eld,making it unsuitable for our purpose of tracing integral curves in the gradient?eld.We seek to construct a data model such that:

1.The original nodal data is interpolated.

2.The gradient at the boundaries is continuous.

3.Critical points in the scalar?eld are not removed,and the

number introduced is kept

small.

Figure2:Arti?cial extreme points introduced by central differ-encing

We could satisfy the?rst two properties by computing derivatives by a method such as central differencing,which would uniquely de?ne a continuous bi-cubic scalar inter-polant[3].However,such a choice of interpolant is likely to violate our third requirement by introducing critical points,as illustrated for the1-D case in?gure2.

To address this problem,we use a“damped”central differ-encing scheme as described in the following sections.The re-sulting scalar?eld will remain a piecewise continuous bi-cubic function,which we represent in Bernstein-B′e zier form as:

where

As a result,the derivatives of the scalar?eld can be repre-sented as:

Figure3:Damped central differences maintain critical points Otherwise,the point data at,,and are monotonic,

and we dampen the central difference as follows:

Original vertex weight Weight determined by ?st order partial derivatives

Weight determined by second order partial derivatives in two variables Weight determined by third order partial derivative in three variables

===Figure 6:Constraints on the mixed partial derivatives for 3D

ever,due to the special construction of our interpolant,we have knowledge about where the critical points will occur,and can compute them quite ef?ciently.

Critical points which occur at the vertices of the mesh will be preserved,and can be computed from the bilinear or trilin-ear ?eld respectively,with the guarantee that they exist as well in the higher order shape preserving interpolant.Critical points interior to a cell will occur in locations at which the monotonic-ity constraint could not be met.In smooth parts of the ?eld,there will be no problem computing a monotone ?eld,which will guarantee the absence of critical points.In cells at which constraints were violated,we perform subdivision of the cell in order to locate the critical points,followed by Newton-Rhapson iteration to re?ne the positions of the zeroes.Saddles from the initial bilinear or trilinear mesh can be approximated by com-puting the position of the bilinear or trilinear saddle analyti-cally,followed by iteration in the bi-cubic or tri-cubic ?eld,re-spectively.

3.3Classi?cation of Critical Points

Qualitative information about the behavior of the gradient ?eld near a critical point is obtained by analysis of the Hessian of ,given for 2D:

The eigenvalues and eigenvectors of the above matrix de-termine the behavior of the gradient ?eld and hence the scalar ?eld near the critical point,much the same as for the behav-ior of a general vector ?eld[7,17].One difference to note is that for a gradient ?eld,the matrix of derivatives is symmetric (),and therefore the eigenvalues will all be real.This is intuitively expected,as imaginary eigenval-ues indicate rotation about the critical point,and a gradient ?eld is an irrotational vector ?eld.This observation allows us to sim-plify the classi?cation of critical points as depicted in ?gure 7.A positive eigenvalue corresponds to gradient ?ow away from the critical point,while a negative eigenvalue indicates

Maxima

Minima

Regular Saddle

Constant

Degenerate Saddle

Figure 7:Some of the scalar critical points

gradient ?ow toward the critical point.In the case of a sad-dle point,there is gradient ?ow toward and away from the crit-ical point,distinguishing it from the ?eld behavior near other critical points.In this case,the eigenvectors corresponding to the positive and negative eigenvalues de?ne the principal direc-tions of the ?ow toward and away from the saddle,respectively.It is this property that will be used in the next section to compute critical curves in the gradient ?eld.

3.4Tracing Integral Curves

Having computed and classi?ed the critical points,the ?nal step for computing the scalar topology is the tracing of selected crit-ical curves between the detected points.Even for three and higher dimensional scalar ?elds we restrict our focus to only computing critical curves,and ignore critical surfaces and hy-persurfaces and other degeneracies in the ?eld,

Saddle points have the property that the eigenvectors of the Hessian are the separatrices of the saddle.A particle following the gradient ?eld along the these directions will come to rest at the saddle point,while particles slightlyto either side of the sep-aratrices will diverge rapidly near the point.It is for this reason that saddle points and the critical curves associated with their separatrices are useful in determining the structure of a scalar ?eld.The number of critical curves emanating from saddles along separatrices is twice the ?eld dimension.In 2D,four crit-ical curves are computed for each saddle point,two in the di-rection corresponding to the positive eigenvalue,and two in the direction corresponding to the negative eigenvalue.In 3D,the number is six,and so on.

Integral curves are computed using the following 4th order adaptive step Runge Kutta integration in the gradient ?eld[27],where is the time step which adapts per iteration,and is a ?eld point :

1.2.

4.

5.

The initial position for the iterative stepping is placed a small distance from the saddle point along the appropriate eigenvec-tor.The steps are bounded such that we take no less than5steps per cell,maintaining a high level of https://www.wendangku.net/doc/0f10852026.html,putation of the critical curve ends when we reach the vicinity of another critical point within a certain,in which case the curve termi-nates at that point.Other curves may end at the boundaries of the mesh.

4Quality Comparison

Here we compare the qualities of scalar topology visualization with those of isocontours and colormapping.

Integral curves are everywhere orthogonal to isocontours. The two techniques arise from an orthogonal de?nition of “structure”for a scalar variable.Contours are an attempt to compute and display the exact shape of an object in a scalar ?eld,while the topology graph attempts to show the relations among all such objects in the?eld,without giving the details of shapes of particular objects.Note that scalar?eld topology is invariant under translation and uniform scaling.This quality is very similar to colormapping of scalar variables,in which the entire range of variables is mapped into a color space.Transla-tion and scaling of the scalar variables changes only the map-ping function,not the result.

5Examples

Figures8,9,10and the top two pictures of the Color Plate, demonstrate the use of scalar topology along with both isocon-tours and colormapped visualizations of density in an off-axis pion collision.Figure8uses a simple greyscale colormap,and it is clear that much of the area of interest in the center is washed out.Figure9uses a hue-based colormap and adds isocontours of three isovalues to reveal more of the structure and aid the per-ception.In?gure10,we show the scalar topology of density. This image clearly brings out the detail of the structure of the variable.The top?gures of the Color Plate show a closeup of the interesting topological regions,as well as shows a combi-nation of all three visualization techniques.

While small scale structure is important in many scienti?c applications,in some circumstances the visualization user is in-terested only in large scale structure.For this situation,we ap-ply a?lter to smooth the data before applying the topology de-tection algorithm.Figures11,12show two visualizations of topology in a scalar?eld representing wind speed.In?gure 11,the un?ltered scalar?eld topology reveals some noise in the data.Figure12shows the topology for the same data after a Gaussian?lter has been applied.

The middle?gures of the color plate shows an example of scalar topology applied to a mathematically de?ned surface.In the left?gure the scalar topology is displayed.In the right?g-ure both topology and four isocontours are displayed.Notice that even with four isolevels displayed,there are critical points within contour regions which are not revealed like the two max-ima on the bottom left that are not separated by any isocontour. The bottom?gures of the color plate show an example of scalar topology applied to a3D scalar?elds(the wave function computed for a high potential iron protein).

6Other Applications

Computation of scalar topology has the potential to serve many other visualization and image processing applications.We mention only a few here:

Data Correlation-Due in part to the invariance under trans-lation and scaling,scalar topology is useful in visually de-termining linear correlation between multiple scalar vari-ables.

Image Co-registration-Scalar topology in adjacent planes provides a“1D skeleton”which may be used to align the planes.

Warping/Morphing-Editing of the scalar backbone may be used to apply a warping effect to an image,or to warp be-tween the backbones of two similar images.

Mesh Reduction-The scalar topology may serve as a guide to aid in computation of reduced resolution meshes. Surface Triangulation-Adaptive triangulation of arbitrary mathematical surfaces by decomposition into monotonic patches which may be subdivided to an arbitrary precision.

7Conclusions

Existing scalar visualization techniques lack the ability to ex-plicitly present the structure of a scalar?eld to the user.We have presented a de?nition of scalar structure and a straight-forward algorithm for computing and displaying the structure. For typical scienti?c data,the scalar data model remains true to the original linear data,minimizing introduction of false critical points,and also simplifying the detection of critical points. The resulting topology visualization serves to both provide information which is not available in commonly used scalar visualization techniques,as well as reinforcing or enhancing the information provided by common visualization techniques. Furthermore,computation of scalar topology offers promise to-ward improving several visualization and image processing ap-plications.

Acknowledgements

We are grateful to Lawrence Livermore National Lab for ac-cess to the pion collision data set.The Earth Science dataset is

courtesy the Space Science and Engineering Center at the Uni-versity of Wisconsin.The Wave function data set is courtesy the Visualization lab,SUNY-Stony Brook.This research was supported in part by AFOSR grant F49620-97-1-0278and ONR grant N00014-97-1-0398.

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常用介词的用法

分考点1 表示时间的介词 Point 1 at, in, on 的用法 （1）at 的用法 At 表示时间点，用于具体的时刻（几点，正午，午夜，黎明，拂晓，日出，日落等），或把某一时间看作某一时刻的词之前以及某些节假日的词之前。 at 6：00 在6点钟 At noon 在中午 At daybreak 在拂晓 At down 在黎明 At Christmas 在圣诞节 【特别注意】在以下的时间短语中，at 表示时间段。 At dinner time 在（吃）晚饭时 At weekends/ the weekend 在周末 （2）in 的用法 ①表示时间段，与表示较长一段时间的词搭配，如年份，月份，季节，世纪，朝代，还可以用于泛指的上午、下午、傍晚等时间段的词前。 In 2009 在2009年 In April 在四月 In the 1990s 在20世纪90年代 In Tang Dynasty 在唐朝 In the morning在上午 ②后接时间段，用于将来时，表示“在一段时间之后”。 The film will begin in an hour. 电影将于一个小时之后开始。 【特别注意】当时间名词前有this，that，last，next，every，each，some等词修饰时，通常不用任何介词。 This morning 今天上午last year 去年 （3）on 的用法 ①表示在特定的日子、具体的日期、星期几、具体的某一天或某些日子。 On September the first 在9月1号 On National Day 在国庆节 We left the dock on a beautiful afternoon. 我们在一个明媚的下午离开了码头。 ②表示在具体的某一天的上午、下午或晚上（常有前置定语或后置定语修饰）。 On Sunday morning 在星期日的早上 On the night of October 1 在10月1号的晚上 【特别注意】“on +名词或动名词”表示“一...就...”. On my arrival home/ arriving home, I discovered they had gone. 我一到家就发现他们已经离开了。 Point 2 in，after 的用法 In 和after都可以接时间段，表示“在...之后”，但in 常与将来时连用，after 常与过去时连用。 We will meet again in two weeks.

英语介词用法大全

英语介词用法大全 TTA standardization office【TTA 5AB- TTAK 08- TTA 2C】

介词（The Preposition）又叫做前置词，通常置于名词之前。它是一种虚词，不需要重读，在句中不单独作任何句子成分，只表示其后的名词或相当于名词的词语与其他句子成分的关系。中国学生在使用英语进行书面或口头表达时，往往会出现遗漏介词或误用介词的错误，因此各类考试语法的结构部分均有这方面的测试内容。 1. 介词的种类 英语中最常用的介词，按照不同的分类标准可分为以下几类： (1). 简单介词、复合介词和短语介词 ①.简单介词是指单一介词。如： at , in ,of ,by , about , for, from , except , since, near, with 等。②. 复合介词是指由两个简单介词组成的介词。如： Inside, outside , onto, into , throughout, without , as to as for , unpon, except for 等。 ③. 短语介词是指由短语构成的介词。如： In front of , by means o f, on behalf of, in spite of , by way of , in favor of , in regard to 等。 (2). 按词义分类 {1} 表地点（包括动向）的介词。如： About ,above, across, after, along , among, around , at, before, behind, below, beneath, beside, between , beyond ,by, down, from, in, into , near, off, on, over, through, throught, to, towards,, under, up, unpon, with, within , without 等。 {2} 表时间的介词。如： About, after, around , as , at, before , behind , between , by, during, for, from, in, into, of, on, over, past, since, through, throughout, till(until) , to, towards , within 等。 {3} 表除去的介词。如： beside , but, except等。 {4} 表比较的介词。如： As, like, above, over等。 {5} 表反对的介词。如： againt ,with 等。 {6} 表原因、目的的介词。如： for, with, from 等。 {7} 表结果的介词。如： to, with , without 等。 {8} 表手段、方式的介词。如： by, in ,with 等。 {9} 表所属的介词。如： of , with 等。 {10} 表条件的介词。如：

流热仿真课后作业

第一章 1、计算流体动力学的基本任务是什么？ 答：计算流体动力学，简称CFD，是通过计算机数值计算和图像显示，对包含流体流动和热传导等相关物理现象的系统所做的分析。CFD可以看作是在流动基本方程（质量守恒方程、动量守恒方程、能量守恒方程）控制下对流动的数值模拟。通过这种模拟我们可以得到极其复杂问题的流场内各个位置上的基本物理量（如速度、压力、温度、浓度）的分布，以及这些物理量随时间的变化，确定漩涡分布的特性、空化特性及脱流区等。 2、什么叫控制方程？常用的控制方程有哪几个？各用在什么场合？ 答：（1）流体流动要受物理守恒定律的支配，基本的守恒定律包括：质量守恒定律、动量守恒定律、能量守恒定律。如果流动包含了不同组分的混合成相互作用系统，还要遵守组分守恒定律，而控制方程是这些守恒组分守恒定律，而控制方程是这些守恒定律的数学描述。 （2）①质量守恒方程：任何流动问题都必须满足；②动量守恒方程：任何流动系统都必须满足；③能量守恒方程：包含有热交换的流动系统必须满足。 3、试写出变径圆管内液体流动的控制方程及其边界条件（假定没有热交换），并写出用CFD来分析时的求解过程。注意说明控制方程如何使用。 第二章 1、什么叫离散化？意义是什么？ 2、常用的离散化方法有哪些？各有何特点？ 3、简述有限体积法的基本思想，说明其使用的网格有何特点？ 4、简述瞬态问题与稳态问题之控制方程的区别，说明在时间域上离散控制方程的基本思想及方法？

5、分析比较中心差分格式、一阶迎风格式、混合格式、指数格式、二阶迎风格式、QUICK格式各自的特点及使用场合？ 第四章 1、湍流流动的特征是什么？ 答：Reynolds数值大于临界值，流动呈现无序的混乱状态。这时，即使边界条件保持不变，流动也是不稳定的，速度等流动特性都随机变化。 2、三维湍流数值模拟的方法分类？ 答：直接数值模拟方法、非直接数值模拟方法。 3、标准k—ε模型方程的解法及适用性？ 4、Realizable K—ε模型的适用模型？ 答：Realizable K—ε模型已被有效地用于各种不同类型的流动模拟，包括旋转均匀剪切流、包含有射流、混合流的自由流动、管道内流动、边界层流动、以及带有分离的流动等。 5、LES方法的基本思想如何？它与DNS方法有怎样的联系和区别？它的控制方程组与时均化方法的控制方程有什么异同？ 答：（1）LES方法的主要思想是：用瞬时的N-S方程直接模拟湍流中的大尺度涡，不直接模拟小尺度涡，而小涡对大涡的影响通过近似的模型来考虑。 （2）LES和DNS是湍流数值模拟常用的方法，DNS是直接用瞬时的N-S方程对湍流进行计算，最大好处是无需对湍流流动作任何简化或近似，理论上可以得到相对精确的计算结果，是直接数值模拟方法，而LES是非直接数值模拟方法，同时，DNS对内存空间及计算速度的要求高于LES。 （3）LES方法的控制方程组不考虑脉动对湍流运用的影响，将湍流运动看作是时间上的平均流动而DNS考察脉动的影响，把湍流运动看作是时间平均流动和

英语介词用法详解

英语常用介词用法与辨析 ■表示方位的介词：in, to, on 1. in 表示在某地范围之内。如： Shanghai is/lies in the east of China. 上海在中国的东部。 2. to 表示在某地范围之外。如： Japan is/lies to the east of China. 日本位于中国的东面。 3. on 表示与某地相邻或接壤。如： Mongolia is/lies on the north of China. 蒙古国位于中国北边。 ■表示计量的介词：at, for, by 1. at表示“以……速度”“以……价格”。如： It flies at about 900 kilometers a hour. 它以每小时900公里的速度飞行。 I sold my car at a high price. 我以高价出售了我的汽车。 2. for表示“用……交换，以……为代价”。如： He sold his car for 500 dollars. 他以五百元把车卖了。 注意：at表示单价(price) ，for表示总钱数。 3. by表示“以……计”，后跟度量单位。如： They paid him by the month. 他们按月给他计酬。 Here eggs are sold by weight. 在这里鸡蛋是按重量卖的。 ■表示材料的介词：of, from, in 1. of成品仍可看出原料。如： This box is made of paper. 这个盒子是纸做的。 2. from成品已看不出原料。如： Wine is made from grapes. 葡萄酒是葡萄酿成的。 3. in表示用某种材料或语言。如： Please fill in the form in pencil first. 请先用铅笔填写这个表格。 They talk in English. 他们用英语交谈(from 。 注意：in指用材料，不用冠词；而with指用工具，要用冠词。请比较：draw in penc il/draw with a pencil。 ■表示工具或手段的介词：by, with, on 1. by用某种方式，多用于交通。如by bus乘公共汽车，by e-mail. 通过电子邮件。

with的用法大全

with的用法大全----四级专项训练with结构是许多英语复合结构中最常用的一种。学好它对学好复合宾语结构、不定式复合结构、动名词复合结构和独立主格结构均能起很重要的作用。本文就此的构成、特点及用法等作一较全面阐述，以帮助同学们掌握这一重要的语法知识。 一、 with结构的构成 它是由介词with或without+复合结构构成，复合结构作介词with或without的复合宾语，复合宾语中第一部分宾语由名词或代词充当，第二部分补足语由形容词、副词、介词短语、动词不定式或分词充当，分词可以是现在分词，也可以是过去分词。With结构构成方式如下： 1. with或without-名词/代词+形容词; 2. with或without-名词/代词+副词; 3. with或without-名词/代词+介词短语; 4. with或without-名词/代词+动词不定式; 5. with或without-名词/代词+分词。 下面分别举例：

1、 She came into the room，with her nose red because of cold.(with+名词+形容词，作伴随状语) 2、 With the meal over ， we all went home.(with+名词+副词，作时间状语) 3、The master was walking up and down with the ruler under his arm。(with+名词+介词短语，作伴随状语。) The teacher entered the classroom with a book in his hand. 4、He lay in the dark empty house，with not a man ，woman or child to say he was kind to me.(with+名词+不定式，作伴随状语) He could not finish it without me to help him.(without+代词 +不定式，作条件状语) 5、She fell asleep with the light burning.(with+名词+现在分词，作伴随状语) 6、Without anything left in the cupboard， she went out to get something to eat.(without+代词+过去分词，作为原因状语) 二、with结构的用法 在句子中with结构多数充当状语，表示行为方式，伴随情况、时间、原因或条件(详见上述例句)。

第三章,湍流模型

第三章，湍流模型 第一节， 前言 湍流流动模型很多，但大致可以归纳为以下三类： 第一类是湍流输运系数模型，是Boussinesq 于1877年针对二维流动提出的，将速度脉动的二阶关联量表示成平均速度梯度与湍流粘性系数的乘积。即： 2 1 21 x u u u t ??=-μρ 3－1 推广到三维问题，若用笛卡儿张量表示，即有： ij i j j i t j i k x u x u u u δρμρ32 -??? ? ????+ ??=''- 3－2 模型的任务就是给出计算湍流粘性系数t μ的方法。根据建立模型所需要的微分方程的数目，可以分为零方程模型（代数方程模型），单方程模型和双方程模型。 第二类是抛弃了湍流输运系数的概念，直接建立湍流应力和其它二阶关联量的输运方程。 第三类是大涡模拟。前两类是以湍流的统计结构为基础，对所有涡旋进行统计平均。大涡模拟把湍流分成大尺度湍流和小尺度湍流，通过求解三维经过修正的Navier-Stokes 方程，得到大涡旋的运动特性，而对小涡旋运动还采用上述的模型。 实际求解中，选用什么模型要根据具体问题的特点来决定。选择的一般原则是精度要高，应用简单，节省计算时间，同时也具有通用性。 FLUENT 提供的湍流模型包括：单方程（Spalart-Allmaras ）模型、双方程模型（标准κ-ε模型、重整化群κ-ε模型、可实现(Realizable)κ-ε模型）及雷诺应力模型和大涡模拟。 湍流模型种类示意图 第二节，平均量输运方程 包含更多 物理机理 每次迭代 计算量增加 提的模型选 RANS-based models

雷诺平均就是把Navier-Stokes 方程中的瞬时变量分解成平均量和脉动量两部分。对于速度，有： i i i u u u '+= 3－3 其中，i u 和i u '分别是平均速度和脉动速度（i=1,2,3） 类似地，对于压力等其它标量，我们也有： φφφ'+= 3－4 其中，φ表示标量，如压力、能量、组分浓度等。 把上面的表达式代入瞬时的连续与动量方程，并取平均（去掉平均速度i u 上的横线），我们可以把连续与动量方程写成如下的笛卡儿坐标系下的张量形式： 0)(=?? +??i i u x t ρρ 3－5 () j i j l l ij i j j i j i i u u x x u x u x u x x p Dt Du -?? +???????????? ????-??+????+??-=ρδμρ32 3－6 上面两个方程称为雷诺平均的Navier-Stokes （RANS ）方程。他们和瞬时Navier-Stokes 方程有相同的形式，只是速度或其它求解变量变成了时间平均量。额外多出来的项j i u u ''-ρ是雷诺应力，表示湍流的影响。如果要求解该方程，必须模拟该项以封闭方程。 如果密度是变化的流动过程如燃烧问题，我们可以用法夫雷（Favre ）平均。这样才可以求解有密度变化的流动问题。法夫雷平均就是出了压力和密度本身以外，所有变量都用密度加权平均。变量的密度加权平均定义为： ρρ/~ Φ=Φ 3－7 符号～表示密度加权平均；对应于密度加权平均值的脉动值用Φ''表示，即有： Φ''+Φ=Φ~ 。很显然，这种脉动值的简单平均值不为零，但它的密度加权平均值等于零，即： 0≠Φ''， 0=Φ''ρ Boussinesq 近似与雷诺应力输运模型 为了封闭方程，必须对额外项雷诺应力j i u u -ρ进行模拟。一个通常的方法是应用Boussinesq 假设，认为雷诺应力与平均速度梯度成正比，即： ij i i t i j j i t j i x u k x u x u u u δμρμρ)(32 ??+-??? ? ????+??=''- 3－8 Boussinesq 假设被用于Spalart-Allmaras 单方程模型和ε-k 双方程模型。Boussinesq 近似 的好处是与求解湍流粘性系数有关的计算时间比较少，例如在Spalart-Allmaras 单方程模型中，只多求解一个表示湍流粘性的输运方程；在ε-k 双方程模型中，只需多求解湍动能k 和耗散率ε两个方程，湍流粘性系数用湍动能k 和耗散率ε的函数。Boussinesq 假设的缺点是认为湍流粘性系数t μ是各向同性标量，对一些复杂流动该条件并不是严格成立，所以具有其应用限制性。

昆腾Quantum Scalar i40-i80维护手册

第1章昆腾Quantum Scalar i40/i80维护 手册 1.1.1关机 操作面板选择Actions > Shutdown > Shutdown Library Web客户端选择Operations > System Shutdown. 当操作面板出现关机提示，如下图： 按下前面电源键 1.1.2重启带库 操作面板选择Actions > Shutdown >Restart Library Web客户端选择Operations > System Shutdown> Restart 1.1.3解锁I/E槽 操作面板选择Actions > I/E > Unlock I/E Station Web客户端选择Operations > I/E Station Unlock 1.1.4释放磁带抽屉

操作面板选择Actions >Magazine > Release Web客户端选择Operations >Release Magazine 1.1.5导入磁带 通过操作面板： 通过前面板只能一次导入一盘磁带 1 选择 Actions > Import Tape. 2 选择要将磁带导入的分区 3 用上、下按钮选择一盘磁带导入 4 选择 Import. 磁带将会被导入到分区的第一个空槽位中 1.1.6批量导入磁带 1 通过web客户端选择Reports > Library Configuration查看带库的槽位分配 2 操作面板选择Actions >Magazine > Release Web客户端选择Operations >Release Magazine 释放磁带抽屉 3 将磁带放在存储槽位中 1.1.7移动磁带 移动磁带只能通过web客户端 1 选择 Operations > Media > Move. 2 如果多于一个分区存在，请选择需要移动磁带的分区

高中英语45个介词的基本用法

——45个基本介词的用法 1、about 【原始含义】 a-b-out “A在B外面” 【引申含义】 [prep] （1）在…到处，在…各处here and there eg: We wandered about the town for an hour or so. He looked about the room. （2）在…附近next to a place eg. She lives about the office. （3）关于in connection with eg: a book about English study I don’t know what you are talking about. [adv] （1）大约close to eg: We left there about 10 o’clock. It costs about 500 dollars. （2）到处，各处 eg: The children were rushing about in the garden. （3）在附近 eg : There is no food about. 【常见搭配】 作介词时的搭配: 一.动词+(about+名词) （1）arrange (about sth) 安排关于某事（2）argue (about sth) 讨论某事 （3）ask (about sth) 询问关于某事（4）boast (about sb/sth) 吹嘘... （5）care (about sb/sth)关心…,对…感兴趣（6）chat(about sth) 谈论某事（7）complain(about sb/sth) 抱怨… （8）dream (about sb/sth) 梦见某人/某物（9）go (about sth) 着手做...；从事...

with用法归纳

with用法归纳 （1）“用……”表示使用工具，手段等。例如： ①We can walk with our legs and feet. 我们用腿脚行走。 ②He writes with a pencil. 他用铅笔写。 （2）“和……在一起”，表示伴随。例如： ①Can you go to a movie with me? 你能和我一起去看电影'>电影吗？ ②He often goes to the library with Jenny. 他常和詹妮一起去图书馆。 （3）“与……”。例如： I’d like to have a talk with you. 我很想和你说句话。 （4）“关于，对于”，表示一种关系或适应范围。例如： What’s wrong with your watch? 你的手表怎么了？ （5）“带有，具有”。例如： ①He’s a tall kid with short hair. 他是个长着一头短发的高个子小孩。 ②They have no money with them. 他们没带钱。 （6）“在……方面”。例如： Kate helps me with my English. 凯特帮我学英语。 （7）“随着，与……同时”。例如： With these words, he left the room. 说完这些话，他离开了房间。 [解题过程] with结构也称为with复合结构。是由with+复合宾语组成。常在句中做状语，表示谓语动作发生的伴随情况、时间、原因、方式等。其构成有下列几种情形： 1.with+名词(或代词)+现在分词 此时，现在分词和前面的名词或代词是逻辑上的主谓关系。 例如:1)With prices going up so fast, we can't afford luxuries. 由于物价上涨很快，我们买不起高档商品。（原因状语） 2)With the crowds cheering, they drove to the palace. 在人群的欢呼声中，他们驱车来到皇宫。（伴随情况） 2.with+名词(或代词)+过去分词 此时，过去分词和前面的名词或代词是逻辑上的动宾关系。

湍流流动的近壁处理详解

壁面对湍流有明显影响。在很靠近壁面的地方，粘性阻尼减少了切向速度脉动，壁面也阻止了法向的速度脉动。离开壁面稍微远点的地方，由于平均速度梯度的增加，湍动能产生迅速变大，因而湍流增强。因此近壁的处理明显影响数值模拟的结果，因为壁面是涡量和湍流的主要来源。 实验研究表明，近壁区域可以分为三层，最近壁面的地方被称为粘性底层，流动是层流状态，分子粘性对于动量、热量和质量输运起到决定作用。外区域成为完全湍流层，湍流起决定作用。在完全湍流与层流底层之间底区域为混合区域（Blending region），该区域内分子粘性与湍流都起着相当的作用。近壁区域划分见图4－1。 图4－1，边界层结构 第一节，壁面函数与近壁模型 近壁处理方法有两类：第一类是不求解层流底层和混合区，采用半经验公式（壁面函数）来求解层流底层与完全湍流之间的区域。采用壁面函数的方法可以避免改进模型就可以直接模拟壁面存在对湍流的影响。第二类是改进湍流模型，粘性影响的近壁区域，包括层流底层都可以求解。 对于多数高雷诺数流动问题，采用壁面函数的方法可以节约计算资源。这是因为在近壁区域，求解的变量变化梯度较大，改进模型的方法计算量比较大。由于可以减少计算量并具有一定的精度，壁面函数得到了比较多的应用。对于许多的工程实际流动问题，采用壁面函数处理近壁区域是很好的选择。 如果我们研究的问题是低雷诺数的流动问题，那么采用壁面函数方法处理近壁区域就不合适了，而且壁面函数处理的前提假设条件也不满足。这就需要一个合适的模型，可以一直求解到壁面。FLUENT提供了壁面函数和近壁模型两种方法，以便供用户根据自己的计算问题选择。

4.1.1壁面函数 FLUENT 提供的壁面函数包括:1，标准壁面函数；2，非平衡壁面函数两类。标准壁面函数是采用Launder and Spalding [L93]的近壁处理方法。该方法在很多工程实际流动中有较好的模拟效果。 4.1.1.1 标准壁面函数 根据平均速度壁面法则，有： **1 ln()U Ey k = 4－1 其中，1/41/2 * /p p w U C k U μτρ ≡ ，1/41/2 * p p C k y y μρμ≡，并且 k ＝0.42，是V on Karman 常数；E ＝9.81，是实验常数；p U 是P 点的流体平均速度；p k 是P 点的湍动能；p y 是P 点到壁面的距离；μ是流体的动力粘性系数。 通常，在*30~60y >区域，平均速度满足对数率分布。在FLUENT 程序中，这一条件改变为*11.225y >。 当网格出来*11.225y <的区域时候，FLUENT 中采用层流应力应变关系，即：**U y =。这里需要指出的是FLUENT 中采用针对平均速度和温度的壁面法则中，采用了*y ，而不是y +（/u y τρμ≡）。对于平衡湍流边界层流动问题，这两个量几乎相等。 根据雷诺相似，我们可以根据平均速度的对数分布，同样给出平均温度的类似分布。FLUENT 提供的平均温度壁面法则有两种：1，导热占据主要地位的热导子层的线性率分布；2，湍流影响超过导热影响的湍流区域的对数分布。 温度边界层中的热导子层厚度与动量边界层中的层流底层厚度通常都不相同，并且随流体介质种类变化而变化。例如，高普朗特数流体（油）的热导子层厚度比其粘性底层厚度小很多；对于低普朗特数的流体（液态金属）相反，热导子层厚度比粘性底层厚度大很多。 1/41/2 * ()w p p P T T c C k T q μρ-≡ '' 4－2 ＝()1/41/2 *2*1/41/222 1Pr Pr 21Pr ln()1Pr Pr Pr 2p p t p t p t c C k y U q Ey P k C k U U q μμρρ?+?''? ????++???? ??????+-??''?? ** **()()T T y y y y <> 4－3

介词with的用法大全

介词with的用法大全 With是个介词，基本的意思是“用”，但它也可以协助构成一个极为多采多姿的句型，在句子中起两种作用；副词与形容词。 with在下列结构中起副词作用： 1.“with+宾语+现在分词或短语”，如： (1) This article deals with common social ills, with particular attention being paid to vandalism. 2.“with+宾语+过去分词或短语”，如： (2) With different techniques used, different results can be obtained. (3) The TV mechanic entered the factory with tools carried in both hands. 3.“with+宾语+形容词或短语”，如： (4) With so much water vapour present in the room, some iron-made utensils have become rusty easily. (5) Every night, Helen sleeps with all the windows open. 4.“with+宾语＋介词短语”，如： (6) With the school badge on his shirt, he looks all the more serious. (7) With the security guard near the gate no bad character could do any thing illegal. 5.“with+宾语＋副词虚词”，如： (8) You cannot leave the machine there with electric power on. (9) How can you lock the door with your guests in? 上面五种“with”结构的副词功能，相当普遍，尤其是在科技英语中。 接着谈“with”结构的形容词功能，有下列五种： 一、“with+宾语+现在分词或短语”，如： (10) The body with a constant force acting on it. moves at constant pace. (11) Can you see the huge box with a long handle attaching to it ? 二、“with+宾语+过去分词或短语” (12) Throw away the container with its cover sealed. (13) Atoms with the outer layer filled with electrons do not form compounds. 三、“with+宾语+形容词或短语”，如： (14) Put the documents in the filing container with all the drawers open.

粘性流体力学一些概念

无量纲参数 2 02 00Re L V L V L V μρμρ= = ) (/)(00003 000020T T C L V L V T T C V Ec w p w p - =-= ρρ 热传递中流体压缩性的影响，也就是推进功与对流热之比。00 0Pr K C p μ= 表示流体的物性的影响，表征温度场和速度场的相似程度。边界层特征厚度dy u u h e e ?- =0 * )1(ρρδ 边界层的存在而使自由流流线向外推移的距离。 θ δ* =H 能够反映速度剖面的形状，H 值越小， 剖面越饱满。动量积分方程：不可压流二维 f e w e e C u dx du u H dt d ==++2)2(ρτθθ /2 普朗特方程的导出，相似解的概念，布拉休斯解的主要结论 ?????????????+??+??-=??+??+????+??+??-=??+??+??=??+ ??)(1)(1022222222y v x v y p y v v x v u t v y u x u x p y u v x u u t u y v x u νρνρ 将方程无量纲化： ./,/,/,/*2***L tU t u p p U u u L x x ====ρ ν/Re UL =，Re /1*≈δ ,/,/,,**L L y U u v L y u v δδ=?==?= 分析：当Re 趋于很大时，**y p ??是大量，则**y p ??＝0，根据量纲分析，去掉小量化为有量纲形式则可得到普朗特边界层方程： ???? ?? ??? =????+??-=??+??+??=??+??01022y p y u x p y u v x u u t u y v x u υρ 相似解的概念：对不同x 截面上的速度剖面u(x,y)都可以通过调整速度u 和坐标y 的尺度因子,使他们重合在一起。外部势流速度Ue(x)作为u 的尺度因子，g(x)作为坐标y 的尺度因子。则无量纲坐标)(x g y ，无量纲速度)(x u u e ，则 对所有不同的x 截面其速度剖面的形状将会相 同。即= )(])(,[111x u x g y x u e ) (] ) (,[222x u x g y x u e 布拉修斯解（零攻角沿平板流动的解）的主要结论： x x Re 721.1* =δx x Re 664.0=θ 591.2/*==θδH 壁面切应力为： x y w U y u Re 1332.0)(2 0∞ ==??=ρμτ 壁面摩擦系数为：x w f u C Re 1664.022 ==∞ρτ 平均为：l l f Df dx C l C Re 1328.110? == 湍流的基本概念及主要特征，湍流脉动与分子随机运动之间的差别湍流是随机的，非定常的，三维的有旋流动，随机背后还存在拟序结构。特征：随机脉动耗散性，有涡性（大涡套小涡）。 湍流脉动：不断成长、分裂和消失的湍流微团；漩涡的裂变造成能量的传递；漩涡运动与边界条件有密切关系，漩涡的最小尺度必大于分子的自由程。分子随机运动：是稳定的个体；碰撞时发生能量交换；平均自由程λ与平均速度 和边界条件无关。层流稳定性的基本思想：在临界雷诺数以下时，流动本身使得流体质点在外力的作用下具有一定的稳定性，能抵抗微弱的扰动并使之消失，因而能保持层流；当雷诺数超过临界值后，流动无法保持稳定，只要存在微弱的扰动便会迅速发展，并逐渐过渡到湍流。平板边界层稳定性研究得到的主要结果：1.雷诺数达到临界雷诺数时流动开始不稳定，成为不稳定点，而转捩点则对应与更高的雷诺数。2.导致不稳定扰动最小波长 δ δλ65.17min ≈=*，可见不稳定波是一种 波长很长的扰动波，约为边界层厚度的6倍。3. 不稳定扰动波传播速度远小于边界层外部势流速度，其最大的扰动波传播速度 4.0/=∞U c r 。当雷诺数相当大时，中性稳定线的上下两股趋于水平轴。判别转捩的试验方法： 升华法（主要依据：湍流的剪切应力大小）热膜法（主要依据：层流和湍流边界层内 气流脉动和换热能力的差别）液晶法（主要依 据：湍流传热和层流传热能力之间的差异）湍流的两种统计理论：1. 湍流平均量的半经验分 析（做法：主要研究各个参数的平均量以及它们之间的相互关系，如平均速度，压力，附面层厚度等。2. 湍流相关函数的统计理论分析（做法；将流体视为连续介质，将各物理量如：流速，压力，温度等脉动值视为连续的随机函数， 并通过各脉动值的相关函数和谱函数来描述湍流结构。）耗散涡、含能涡的尺度耗散涡为小尺 度涡，它的尺度受粘性限制，但必大于分子自由行程。控制小尺度运动的参数包括单位质量的能量消耗量ε和运动粘性系数ν。因此，由 量纲分析，小涡各项尺度为：长度尺度 4/13)(ενη=时间尺度2/1)(εντ=速度尺度4/1)(νε=v 耗散雷诺数 1Re →=νη v d 可知：小尺度涡体的湍流 脉动是粘性主宰的耗散流动，因此这一尺度的 涡叫耗散涡。含能涡为大尺度涡，在各向同性湍流中，可以认为大尺度涡体由它所包含的湍动总能量k ，以及向小尺度传递的能量ε决定。 长度尺度ε2/3k l =时间尺度εk t =速度尺度k u =积分尺度雷诺数1Re →>>=ν ul d 可知在含能尺度范围 内，惯性主宰湍流运动，因此含能尺度范围又 称惯性区。均匀湍流：统计上任何湍流的性质与空间位置无关，或者说，任何湍动量的平均 值及它们的空间导数，在坐标做任何位移下不 变。特征：不论哪个区域，湍流的随机特性是相同的，理论上说，这种湍流在无界的流场中 才可能存在。各向同性湍流：任何统计平均量与方向无关，或者说，任何湍动量在各个方向 都一样，不存在任何特殊地位的方向。任何统计平均湍动量与参考坐标轴的位移、旋转和反 射无关。特征：各向同性湍流，必然是均匀湍 流，因为湍流的任何不均匀性都会带来特殊的方向性。在实际中，只存在局部各向同性湍流 和近似各向同性湍流。各向同性下，雷诺应力 由9个量减为3个量。 了解时均动能方程、湍动能方程中各项的物理意义和特点，及能量平衡时均动能方程： 流体微团内平均动能变化率；外力的作功；平均压 力梯度所作的功； 雷诺应力所作功的扩散；雷诺应力所作的变形功；时均流粘性应力所作功 的扩散；时均流动粘性的耗散，即粘性应力的 变形功。 湍动能方程：

Scalar i2000安装维护指南

Scalar i2000磁带库系统日常维护管理指南 美国先进数字信息公司 二零零六年

目录 1. 简介 (3) 2. Scalar i2000磁带库安装 (6) 2.1 安装环境准备 (6) 2.2 磁带库安装步骤及基本设置 (6) 3. Scalar i2000磁带库驱动程序安装及检测 (9) 3.1 Scalar i2000磁带库驱动程序安装 (9) 3.2 Scalar i2000磁带库运行检测 (9) 4. Scalar i2000磁带库系统操作管理 (11) 4.1 控制面板 (11) 4.2 基于面板的管理操作 (12) 4.2.1 系统信息查询 (12) 4.2.2 磁带移动操作 (16) 5. 磁带库系统日常维护管理 (19) 5.1 Scalar i2000磁带库系统加断电步骤 (19) 5.2 磁带库系统链接调试 (20) 5.3 磁带介质的保护 (20) 5.4 磁带库系统日常维护方法 (21) 5.4.1 磁带库系统维护原则 (21) 5.4.2 磁带库系统巡检维护服务 (22)

1. 简介 Scalar i2000磁带库系统是美国先进数字信息公司基于iPlatform技术实现的新一代磁带技术存储产品。 iPlatform是一种全新的控制和管理系统，基于iPlatform技术实现的磁带库系统中拥有一个智能计算核心引擎，这个智能引擎允许磁带库集成前代产品通过外部服务器或其它组件才能提供的大多数功能，并进一步扩展了磁带库的功能，增加了诸如更加全面的工作报告、主动就绪性检查、连续系统监控和面向服务的操作咨询等等。 维护人员可从一个单点管理磁带库系统提供的所有功能。 下图为一个控制模块Scalar i2000磁带库系统配置 下图为一个控制模块，一个扩展模块配置的配置。

介词at的基本用法

介词at的基本用法： 一、at引导的时间短语通常可表示： 1.在几点几分，例如：at one o’clock(在一点钟) I usually make the bed at one o’clock.. 2.在用餐时间，例如：at lunchtime（在午餐时间） 3.在某个节日，例如：at Christmas 在圣诞节的时候 4.在某个年龄的时候，例如：at the age of 12。在12岁的时候 5.一天中的某段较短的时间，例如：at noon在中午at night在夜里 二、at也可引导地点短语，常用于小地点之前，例如： at the bus stop在汽车站at the butcher’s 在肉店里at school在学校里at home在家里 介词on的基本用法： 一、on可引导地点短语，表示“在…上面”，例如：on the table在桌子上 二、on也可引导时间短语，通常有以下用法： 1.用于“星期”和“月份”中的任何一天之前，例如：On Monday在星期一on April 1st. 2.用于某个“星期几”当天的某段时间，例如：on Monday morning在星期一上午 3.用于具体某一天之前，例如：on that day在那一天On my birthday在我的生日那天 On Christmas day在圣诞节那天 介词in的基本用法： 一、in可引导地点短语，常表示“在…里面”，例如：in the bag在袋子里 二、in引导的时间短于通常有以下用法： 1.在某个世纪，例如：in the 21st century在21世纪 2.在某一年，例如：in 1995在1995年 3.在某一个季节，例如：in spring在春季 4.在某一个月份，例如：in March在三月里 5.在某段时期，例如：in the holidays在假期里 6.在某个持续几天的节日里，例如：in Easter Week在复活周 7.在一天中的某段时间，例如：in the morning在上午（早晨）

初中 英语 介词“with”的用法

介词“with”的用法 1、同, 与, 和, 跟 talk with a friend 与朋友谈话 learn farming with an old peasant 跟老农学习种田 fight [quarrel, argue] with sb. 跟某人打架 [争吵, 辩论] [说明表示动作的词, 表示伴随]随着, 和...同时 change with the temperature 随着温度而变化 increase with years 逐年增加 be up with the dawn 黎明即起 W-these words he left the room. 他说完这些话便离开了房间。2 2、表示使用的工具, 手段 defend the motherland with one s life 用生命保卫祖国 dig with a pick 用镐挖掘 cut meat with a knife 用刀割肉3

3、说明名词, 表示事物的附属部分或所具有的性质]具有; 带有; 加上; 包括...在内 tea with sugar 加糖的茶水 a country with a long history 历史悠久的国家4 4、表示一致]在...一边, 与...一致; 拥护, 有利于 vote with sb. 投票赞成某人 with的复合结构作独立主格,表示伴随情况时，既可用分词的独立结构，也可用with的复合结构： with +名词(代词)+现在分词/过去分词/形容词/副词/不定式/介词短语。例如： He stood there, his hand raised. = He stood there, with his hand raise.他举手着站在那儿。 典型例题 The murderer was brought in, with his hands ___ behind his back A. being tied B. having tied C. to be tied D. tied 答案D. with +名词(代词)+分词+介词短语结构。当分词表示伴随状况时，其主语常常用