Electromagnetic Form Factors of the SU(3) Octet Baryons in the semibosonized SU(3) Nambu-Jo

光的衍射英文作文Light DiffractionLight is a fundamental aspect of our physical world, and its behavior has been the subject of intense study and fascination for centuries. One of the most intriguing and complex phenomena associated with light is diffraction, which refers to the bending and spreading of light waves as they encounter obstacles or apertures. This phenomenon has profound implications in various fields, from optics and quantum mechanics to biology and technology.At its core, diffraction is a wave-like property of light, where the interaction between light and the physical structures it encounters leads to the interference and redistribution of the light waves. This process is governed by the principles of wave interference, where the constructive and destructive interference of light waves result in patterns of light and dark regions, known as diffraction patterns.The fundamental principles of diffraction can be understood by considering the wave nature of light. Light, like other forms of electromagnetic radiation, can be described as a wave, with a specific wavelength and frequency. When light encounters an obstacle or anaperture, the waves are forced to bend and spread out, creating a diffraction pattern. The specific characteristics of this pattern are determined by factors such as the size and shape of the obstacle or aperture, as well as the wavelength of the light.One of the most well-known examples of diffraction is the phenomenon of single-slit diffraction. When light passes through a narrow slit, the resulting diffraction pattern consists of a central bright region, known as the central maximum, surrounded by alternating bright and dark regions, known as diffraction fringes. The spacing and intensity of these fringes are directly related to the wavelength of the light and the width of the slit.Another important aspect of diffraction is the concept of the Fraunhofer diffraction, which describes the diffraction pattern observed at large distances from the aperture or obstacle. In this case, the diffraction pattern is characterized by a series of bright and dark spots, known as the Fraunhofer diffraction pattern. This pattern is particularly useful in applications such as optical imaging, spectroscopy, and the design of diffraction-based optical devices.Diffraction also plays a crucial role in the behavior of light in various natural and man-made systems. For example, the diffraction of light through small apertures or slits is responsible for the characteristic patterns observed in the interference of light, such as those seen inYoung's double-slit experiment. Additionally, the diffraction of light around the edges of objects or through small openings is responsible for the phenomena of diffraction fringes, which can be observed in various optical devices and natural phenomena, such as the colorful patterns seen in the wings of some insects or the halos and glories observed around the Sun or Moon.The study of diffraction has also led to the development of numerous applications in science and technology. In optics, diffraction is used in the design of various optical devices, such as diffraction gratings, which are used in spectroscopy and other analytical techniques. In the field of quantum mechanics, the wave-like nature of particles, as described by the de Broglie hypothesis, has led to the observation of diffraction patterns in the behavior of subatomic particles, such as electrons and neutrons.Furthermore, the understanding of diffraction has been instrumental in the development of modern imaging techniques, such as X-ray crystallography, where the diffraction of X-rays by the atoms in a crystal is used to determine the arrangement and structure of the atoms within the crystal. Similarly, the diffraction of light by various biological structures, such as the compound eyes of insects or the structures found in the wings of some butterflies, has inspired the development of biomimetic materials and devices.In conclusion, the phenomenon of light diffraction is a fundamental and fascinating aspect of our physical world. It is a testament to the wave-like nature of light and the complex interplay between light and the physical structures it encounters. The study of diffraction has led to numerous insights and advancements in various fields, and its continued exploration promises to yield further discoveries and innovations that will shape our understanding of the universe and the technology we use to interact with it.。

ElectromagneticsRichard H.Selfridge,David V.Arnold,and Karl F.Warnick Department of Electrical and Computer Engineering459Clyde BuildingBrigham Young UniversityProvo,UT84602July30,2001We would appreciate your suggestions and corrections to this draft.Send email to warnick@. Website:/ee/forms/(c)1999Chapter1ELECTROSTATICS1.1Introduction1.1.1OverviewMany applications of electrical engineering require a knowledge of the behavior of voltages and currents in electronic devices and within conductors.In many other situations it is not enough to understand the behavior the voltages and currents in just the conductors and other components,but also the influence of the voltage and current on surrounding materials.In physics classes we learn that electric and magneticfields extend beyond the electrical carriers within a device.In electrical and computer engineering the extension of thefields beyond electronic devices and wires can have both beneficial and deleterious effects.Withoutfields we would not have such modern conveniences as cellFigure1.1:Crosstalk between two telephone transmission lines.phones,television,or even the simplest computer memory chip.On the other hand,unwantedfield interactions can cause reversible and irreversible degradation in almost all types of electrical engineering systems.A common example of this type of degradation is evident when a telephone signal on one line leaks over to an adjacent line.This annoying phenomenon is known as cross talk.The diagram in Fig.1.1shows that thefield from one line extends into the other.In this chapter we examine some of the behavior of electricfields and electricflux.We use theflat panel display as a motivating example for this study.We have chosen theflat panel display as an illustrative example because it shows the ubiquitous nature of electromagnetics in current technology.Flat panel displays are expected to be the video display technology of the future for replacing the current bulky screens on laptop,television,and other applications.The most commonflat panel displays are based on liquid crystal display(LCD)technology.Fig.1.2shows a representative cell of aflat panel LCD.Each cell or pixel has a liquid crystal material sandwiched between two transparent conducting plates as shown in Fig.1.2.The LCD either passes light or blocks light depending on the voltage difference between the two plates.The difference in voltage affects the liquid crystal material by means of the electricfield generated between the two plates.Each of the liquid crystal cells represents one of the more than 50,000individual picture elements or pixels on the screen.Each cell is similar to the parallel plate capacitor studied in fundamental physics courses.The parallel plate structure is used throughout this section as a basis for our description of electricfields and electricfluxes.34CHAPTER1.ELECTROSTATICSCel lFigure1.2:A cell in aflat panel LCD display.Traditionally electrical engineers describe electricfields in terms of vectors.Although vector descriptions of electromagnetic principles are valuable because most engineering students are already familiar with them and because they provide insights into some of the physical properties offields,vector descriptions offields are somewhat limited in presenting a complete visual description offields.This chapter introduces differential forms as a powerful tool for describing and analyzing electricfields.Given that this is likely the reader’sfirst exposure to differential forms,the principles of differential forms are discussed in detail as they are introduced.For both comparison and completeness electromagneticfields are represented in terms of vectors also.We introduce differential forms because they provide a powerful and concise mathematical framework for electro-magnetics.Differential forms make a clear distinction between electricflux and electricfield.They make it simpler to derive theorems and to make coordinate transformations in electromagnetics.However,probably the most important advantage of differential forms at the undergraduate level is that they offer a unique and clear geometric description of electromagnetics not possible using vectors alone.The visual representations that accompany forms are likely to re-main in the minds of students whether or not they go on to specialize in electromagnetics or one of its sub-disciplines. These advantages make the additional effort in learning forms worthwhile.Also,students usuallyfind it fun to learn differential forms because forms are elegant and simple to manipulate.1.1.2Parallel conducting platesIn this section we focus our attention on the electricfields associated with parallel conducting plates.In the other chapters we shall see that parallel plate transmission lines are often used to describe a variety of important waveguide types.Figure1.3shows a general description of parallel conducting plates,the parallel plate capacitor.VFigure1.3:A parallel plate capacitorIn this representation we usually consider the separation distance of the plates to be less than one-tenth the length of the conductors.This means that thefields between the plates will not be very different from how they would appear if the plates were infinite in extent.We assume that a potential of5volts is applied to the top conducting plate,that the1.1.INTRODUCTION5Figure1.4:The potential between plates of a parallel plate capacitorlower plate is grounded and that the two plates are separated by1mm.For now we assume the material between the two plates is uniform.We notice that the voltage(electric potential)changes with position from the top to the bottom plate.Ourfirst important question is:“What is the potential distribution between the two plates?”It is reasonable to assume that the potential varies from5volts at the top plate to0volts at the bottom plate in a linear fashion because the material between the plates is the same throughout.We can think of planes of constant voltage between the plates as shown in Fig.1.4.These planes represent the change in potential from the top plate to the bottom plate.If one follows a path from the top plate to the bottom plate,counting the planes crossed along the way,the number of planes pierced by the path is proportional to the voltage difference between the two conducting plates.The constant of proportionality is the electricfield strength in volts per plane.We can express this sum in terms of an integral astopbottomThe quantity under the integral sign is a differential form.It is called a1-form because it has a single variableof integration.The differential form is called the electricfield1-form.In this expression,is a measure of howmuch the potential changes per unit distance and has units of V/m.In this case V/m.The planes inFig.1.4are a convenient geometrical representation of the electricfield1-form.The spacing of the planes indicates the strength of thefield;the higher thefield the more closely spaced the planes.In three dimensional space four degrees of forms exist,0,1,2,and3-forms.Each of these forms has several important examples in electromagnetics.These forms are used and explained in detail as needed in later sections and chapters.For the parallel plate configuration the electricfield only has surfaces perpendicular to the direction.Similarly,the1-form surfaces could be perpendicular to the-axis or-axis and would then be written in terms of dyor dz,respectively.In the general case a1-form is a linear combination of these differentials,so the surfaces may be skew to the coordinate axes and curved as shown in Fig.1.5.In the differential forms model of parallel conducting plates,not only does a voltage exist on the plates,but an electricfield,represented by forms,exists between the plates.This is the equipotential representation of thefield,or the energy picture.Understanding offields is also enhanced if one looks at the electricfield between the plates from the point of view of what happens to small charged body placed in between the two plates.Consider the potential difference created between the parallel plates as connected to the voltage source.The voltage source draws electrons away from the top conducting plate leaving excess positive charges on its surface. Likewise the bottom conducting plate has negative charges on its surface.A positive test charge placed between the plates is attracted to the negative plate as shown in Fig.1.6.This force of attraction is proportional to the strength of the electricfield between the plates,is in the direction of the electricfield,and is known as the Lorentz force.When using the force picture of electricfields it is usually most convenient to use vectors in place of forms.The electricfield vector is shown in thefigure.Its length represents the strength of the electricfield and its direction is indicated by the ing vector notation the Lorentz force law is expressed as(Lorentz force law,no magneticfields)where is the charge,is the force vector,and is the electricfield vector.6CHAPTER1.ELECTROSTATICSyzxFigure1.5:A general1-form with surfaces that curve in space.-VFigure1.6:A test charge experiences a force due to an electricfield.Electric charge plays an important role in the description offields using differential forms.From physics we know that with every positive charge there is an associated negative charge.We can view this association as a tube that links or connects a positive charge to a negative charge through intervening material.For the parallel plate example these tubes are shown connecting positive charges on the top plate to negativecharges on the bottom plate.ThetubesshowninFig.1.7are the geometrical representation of a2-form.The2-forms shown can be expressed as.This is a2-form because it has two differential elements.Notice that each tube contains a specified amount of charge.The charge that exists on the plates of the capacitor can be found by counting theflux tubes joining the top and bottom plates.Mathematicallythiscounting is equivalenttointegratingthe2-formtubesover the surface area between the plates ofthecapacitor:areaInthis representation we see that is the charge per tube,so that represents the concentration of charge per unit area.From the discussion ofthe graphical representation of1-forms it isapparent that the2-form is composed of a 1-form perpendicular to the-direction and another perpendicular to the–direction.The connection between charges represented by tubes is called the electricflux density.Flux meansflow,and although no physical particlesflow from one plate to the other we can think of a stream of influenceflowing from one plate to the other as one charge connects through space to its equal and opposite counterpart.The coefficients of a2-form give the spacing of the tubes,the larger the coefficients are,the more densely packed the tubes become.An arbitrary2-form has coefficients that are functions of position and the associated tubes may curve and diverge and converge at various points in space.From the example of the parallel conducting plates it is clear that there is a physical connection between the1.1.INTRODUCTION 7Figure 1.7:Tubes of flux in a parallel plate capacitorelectric field and the electric flux density.We can make geometric and algebraic connections between field and flux using differential forms.Examination of the geometry of electric fields and fluxes shows that the 1-form planesare composed of the planes that are mutually perpendicular to both of the planes that comprise the 2-form tubes asshown in Fig.1.7.In terms of the algebra of forms we require an operator that creates a 1-form from a 2-form and vice versa.This operator is discussed in Sec.1.5.Figure 1.8:Energy density boxes formed by intersection of electric field intensity surfaces and flux density tubes.To now,we have shown that the electric field may be represent as 1-form planes and that the flux is represented by 2-form tubes.Now let us see what if anything can be made of the boxes formed by combining the field planes and the flux tubes as shown in Fig.1.8.To find out what those boxes represent we express the combination algebraically asvolThe combination of the 1-form electric field and the 2-form magnetic flux creates an 3-form entity under the integral sign.Multiplying the dimensional units of and givesCm V m J mHence the volume integral of the field multiplied by the flux is the total energy stored in a region of space by the fields present in the region.The 3-form quantity under the integral sign is the energy contained in a cube.This description of energy density helps us understand why the refresh rate on a flat panel display is limited.Recall that the individual picture elements (pixels)of a flat panel display are illuminated or not depending on the voltage that is applied to them.To switch from one view to another requires that the pixels be changed about 30times8CHAPTER 1.ELECTROSTATICS each second to prevent the eye from seeing a flicker.This means that time is required to move energy to and from the region between the plates to switch from the off state to the on state and any energy stored between the plates must be removed during the process of switching from the on state to the off state.Energy transfer in time is de fined as power.Therefore,switching states in a finite amount of time requires power and takes time.In another view of this we can consider the capacitance of the system and calculate the time required to change states by using the RC time constant of the circuit.It is interesting to note that we can calculate the capacitance from the electric field and the electric flux.The fundamental de finition of capacitance is the amount of charge stored given a separation voltage.The capacitance of a single cube de fined by the intersection of the tubes of with the planes ofis simply the quotient,C/V or Farads.The examples given in this section have introduced physical descriptions of both electric field and electric flux.Although these examples are simple they present a useful foundation upon which systems with greater mathematical and physical complexity can be built.The following sections of this chapter show how to use these concepts in a more general setting.1.21-formsThe graphical representations described in the introduction are useful in gaining intuitive understanding of the behavior of electromagnetic fields.In order to work analytically with the laws which govern the fields,we must develop a mathematical structure to accompany the graphical representations of the previous section.As we saw in the previous section,electric field intensity represents potential change with distance.In order to find the total potential difference between two points,we need to integrate the electric field along a path between the points.Graphically,this means that we count electric field intensity surfaces.Mathematically,we must perform a path integral.Quantities which are integrated over paths are called 1-forms.In the introduction,we discussed the example of a 1-form which represented variation of a field in the –direction.In general,a 1-form can represent variation in any direction,and can be a combination of differentials of all of the coordinates.An arbitrary 1-form can be written(1.1)The three quantities ,,and are the components of the 1-form.Two 1-forms and can be added,so that(1.2)1-forms can be integrated over paths.As shown in the introduction,we graphically represent a 1-form as surfaces.The 1-form has surfaces perpendicular to the –axis spaced a unit distance apart.These surfaces are in finite in theand directions.The integral of over a path from the point to isThis matches the graphical representation in Fig.1.9a,since the path shown in the figure crosses four surfaces.If the path were not of integer length,we would have to imagine fractional surfaces in between the unit spaced surfaces.A path from to ,for example,crosses surfaces.We can also think of as a 1-form in the plane.In this case,the picture becomes a series of lines perpendicularto the –axis spaced a unit distance apart,as shown in Fig.1.9b.Graphically,integrals in the plane are similar tointegrals in three dimensions:the value of a path integral is the number of lines pierced by the path.In order to graphically integrate a 1-form properly,we also have to think of the surfaces as having an orientation.The integral of the 1-form over a path from to is .Thus,when we count surfaces piercedby a path,we have to compare the sign of the 1-form with the direction of the path in order to determine whether the surface contributes positively or negatively.The orientation of surfaces can be indicated using an arrowhead on each surface,but since the orientation is usually clear from context,to reduce clutter we do not indicate it in figures.A more complicated 1-form,such as ,has surfaces that are oblique to the coordinate axes.This 1-formis shown in Fig.1.10.The greater the magnitude of the components of a 1-form,the closer the surfaces are spaced.For 1-forms with components that are not constant,these surfaces can be curved,as shown in Fig.1.5.The surfaces can also originate along a line or curve and extend away to in finity,or the surfaces may be finite.In this case,the1.2.1-FORMS9xy(a)(b)yxFigure1.9:(a)The1-form integrated overa path from the pointto.(b)The1-form in the plane.yxFigure1.10:The1-form.integral over a path is still the number of surfaces or fractional surfaces pierced by the path.Some1-forms are too complicated to be drawn as surfaces in three dimensions(we will give a condition for this later),but any1-form can be drawn in the plane.A1-form represents a quantity which is integrated over a path.A vector represents a quantity with a magnitude and direction,such as displacement or velocity.Despite this difference,both types of quantities have three independent components,and can be used interchangeably in describing electromagneticfield quantities.Mathematically,vectors and differential forms are closely related.In euclidean coordinates,wecan makeacorrespondence betweenvectorsand forms.The1-formandthevector areequivalentifthey have thesamecomponents:(1.3) We say that the1-form and the vector are dual.Since it is easy to convert between the differential form and vector representations,one can choose the quantity which best suits a particular problem.We will see in the next section that in coordinate systems other then euclidean,the duality relationship between forms and vectors changes.1.2.1Curvilinear CoordinatesMany electromagnetics problems have some type of inherent symmetry.In solving problems,it isconvenient tochoose acoordinatesystem whichreflects that symmetry.Forexample,the equation which defines acylinder in rectangularcoordinates,,becomes in the cylindrical coordinate system,where is the radial distance from the–axis.10CHAPTER 1.ELECTROSTATICS In general,in three dimensions a coordinate system consists of threefunctions,,and which assign numbers to each point of space.For convenience,we assume that the directions in which each of the coordinates is changing are perpendicular,so that the coordinate system is orthonormal.In such a coordinate system,the unit differentials are writtenas,,and .The the threefunctions,,and are such that the integral over any one of the unit differentials over a path of unit euclidean length in the direction of the particular coordinate is equal to one.For example,if the length of the pathfromto has unit length,thenThese unit differentials correspond to basis vectors according to therelationshipsIn this section,we give thefunctions,,and for two of the most common curvilinear coordinate systems.yzxFigure 1.11:The surfaces of unit differentials in general orthonormal curvilinear coordinates are always a unit distance apart.Cylindrical CoordinatesIn the cylindrical coordinate system,a point in space is speci fied by theradial distanceofitscoordinates,anglefromthe axisin the–plane ,and height in the direction (Fig.1.12).Thus,a point iswritten(1.4)in cylindrical coordinates.The differentials of thecylindricalcoordinate systemare,and .To convert forms into unit vectors,the angular differential must be made intoaunit differential .1-forms correspond tovectorsby therulesFigure 1.13shows the pictures of the differentials of the cylindrical coordinate system.The 2-forms can be obtained by superimposingthesesurfaces.Tubesof ,for example,are square donut–shaped andpoint in the direction.Spherical CoordinatesIn the spherical coordinate system,a point in space is speci fied by the radialdistancefromtheorigin,angle from theaxis inthe–plane ,andangle fromthe axis ,as shown in Fig.1.15.A point iswritten(1.5)1.2.1-FORMS11Figure 1.12:The cylindrical coordinate system.(a)z yx (c)(b)zyx xyz Figure1.13:Surfacesof,scaled byand.inthese coordinates.Thedifferentials ofthe spherical coordinate system are,and .To convertformsintounit vectors,theangular differentials mustbe madeinto unit differentialsand.1-formscorrespondto vectorsbytherules Fig.1.16shows the pictures of the differentials of the spherical coordinate system.1.2.2Integrating 1-forms over pathsThe laws of electromagnetics are expressed in terms of integrals of fields represented by differential forms.In order to apply the laws of electromagnetics,we must therefore be able to compute the values of integrals of differential forms.Since 1-forms are by de finition mathematical quantities which are integrated over paths,the process of evaluating an integral of a 1-formis very natural.The key ideaisthat wecan replacethe coordinates ,,and (or ,,in curvilinear coordinates),with an equation for a path in terms of a parameter.The parameter of a path is often denoted by .12CHAPTER 1.ELECTROSTATICSFigure 1.14:Unit differentials in cylindrical coordinates represented as faces of a differential volume.Figure 1.15:The spherical coordinate system.In general,a path is written in the form (f(t),g(t),h(t)),so that thefunctions,,and give the coordinates of a point on the path for each value of .We replace the coordinates in a 1-form by these functions,and then the integral can be evaluated.For a differential,when the coordinate is replaced by a function de fining the path,we then take the derivative by to produce a new differential in the variable .Forexample,becomes ,where the prime denotes the derivative of thefunction by (this operation is a special case of the exterior derivative ,which will be discussed in a later chapter).The differential form now has a singledifferential,,and the integral can be performed using standard rules of calculus.Example 1.1.Integrating a 1-form over a path in rectangular coordinatesConsider the1-formand apath which lies along thecurve from thepointto .We wish to find (1.6)We parameterize the path in the variable ,so that the pathbecomes ,withranging from zero to one.We then substitute these valuesforand into theintegral,1.2.1-FORMS13yzx(a)(b)zyx(c)yxzFigure1.16:Surfacesof,scaled by and scaledby.Figure1.17:Unitdifferentialsin sphericalcoordinates represented as faces of adifferentialvolume.Example1.2.Integrating a1-form over apath incylindrical coordinatesSuppose we want to integrate the1-form over the unit circle in the-plane.Wewant tochange variables fromto,so that we parameterize the unitcircleas.The integralis14CHAPTER 1.ELECTROSTATICSWe could have guessed the result by noting that each surface of pierced by the path in the positive direction(such that the orientation of the surface is the same as the counterclockwise direction of integration along the path)is canceled when the path pierces the same surface in the negative direction.1.32-forms,3-forms,and the Exterior ProductAs we showed in the introduction to this chapter,a 2-form is a quantity which is integrated over a two–dimensional surface.The quantity representing flow of a fluid,for example,has units of flow rate per area,and would be integrated over a surface to find the total flow rate through the surface.Similarly,the integral of electric flux density over a surface is the total flux through the surface,which has units of charge.A general 2-form is written as(1.7)The wedge between differentials is known as the exterior product .This product allows one to combine 1-forms to produce differential forms of higher degree.The 2-form ,for example,is the exterior product of the 1-formsand .The exterior product has the important property that if two differentials are interchanged,the sign of theproduct changes.In other words,the exterior product of 1-forms is antisymmetric.For example,.Using this property,it is easily seen that the wedge product of two like differentials is zero:.Forconvenience,we usually use the antisymmetry of the exterior product to put differentials of 2-forms into right cyclic order,as in Eq.(1.7).Two 1-forms and can be added,so that if and are 2-forms,their sum is(1.8)Like 1-forms,2-forms have three independent components,and a correspondence between 2-forms and vectors can be made.A 2-form with differentials in right cyclic order can be converted in euclidean coordinates to a vector as follows:(1.9)The 2-form is said to be dual to the vector .Example 1.3.Exterior product of 1-forms.Let and .ThenThis 2-form is dual to the cross product .Example 1.4.Exterior product of a 1-form and a 2-form.Let and .ThenThe result is a 3-form.The coef ficient of this 3-form is equal to the dot product.We will discuss 3-forms in greater detail below.1.3.2-FORMS,3-FORMS,AND THE EXTERIOR PRODUCT 15(a)x zyFigure 1.18:The2-form integrated over a squareinthe –plane of side2-forms are integrated over areas,or two–dimensional regions of space.When a 2-form appears under an integral,we often drop the wedgesforconciseness:(1.10)2-forms are graphically represented as tubes.Thepictureof consists ofthesurfaces of superimposed withthesurfaces of .The sets of surfaces intersect to form tubesin the direction.The integral of a 2-form over an area is the number of tubes crossingthearea.For ,the integral over asquare inthe –plane of side is 4,and as shown in in Fig.1.18,nine tubes cross this square.The greater the components of a 2-form are in magnitude,the smaller and more dense are the tubes of the 2-form.As with 1-forms,the tubes of a 2-form have an orientation.Thetubesof ,for example,areorientedin the direction,whereasthetubesof are orientedin the direction.Areas of integration also have an orientation,since their are two possible normal directions for any area.The limits of a double integral specify a direction around the perimeter,and the right–hand rule applied to this direction speci fies the orientation of the area.When integrating graphically,we compare the orientation of each tube with the orientation of the area of integration,and the tube counts positively if the orientations are the same,and negatively otherwise.1.3.12-forms in Curvilinear CoordinatesIn general curvilinear coordinates,the unit differentialfor 2-formsare,,and .If the2-form is integrated over a surface whichlies inthe -plane,thenthefactor is such that the value of the integral is equal to the area of the surface.The unit differentials are dual to theunitvectors ,,and .In the cylindrical coordinate system,2-forms and vectorsarerelatedbyThe2-form ,for example,is dual tothevector .In the spherical coordinate system,2-forms and vectorsarerelatedby The2-form ,for example,is dual tothevector .Example 1.5.Integrating a 2-form using spherical coordinates。

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A choice of flow primary linings affords further protection against coating and high sediment flows, with users able to choose from a variety of materials, including ceramic linings for particularly abrasive flows.The ability of electromagnetic flowmeters to better handle distorted velocity profiles also reduces the amount of piping upstream and downstream of the meter.Modern electromagnetic flowmeters are also capable of being buried, eliminating the need for the construction of costly installation chambers.Available in sizes from 10 to 2400 mm (3/8 to 96 in), ABB’s WaterMaster electromagnetic flowmeter is ideally suited to wastewater flow measurement applications.A key feature is the WaterMaster’s revolutionary octagonal sensor design. By improving the flow profile, the octagonal design minimizes the upstream and downstream pipe lengths required from the point of installation, greatly reducing the cost of fitting the meters into new or existingpipelines.3 ACCU R ATE WA S TE WATE R F LOW M E A S U R E M E NT | WATER M A S TER| A D/FLOW/006–EN R E V. AABB’s WaterMaster electromagnetic flowmeter enables operators to gain an enhanced overview of their wastewater flows.The WaterMaster also features on-board verification capability. Called VeriMaster, it assures operators of the performance of the meter through constant self-checking. When coupled with ABB’s VeriMaster software tool, it enables operators to produce a printed verification certificate for regulatory compliance.The effects of signal noise are also minimized by the WaterMaster’s use of advanced Digital Signal Processing (DSP) technology. This enables the WaterMaster’s transmitter to separate the real signal from the noise, thereby providing high quality outputs especially in harsh environments involving vibration, hydraulic noise and temperature fluctuation.All WaterMaster sensors have a rugged, robust construction to ensure a long, maintenance-free life even under the most difficult conditions experienced in water and waste water applications. The sensors are inherently submersible (IP68, NEMA 6P) as standard, ensuring suitability for installation in chambers and metering pits which are liable to flooding.All sizes of the WaterMaster are buriable and are straightforward to install, with installation merely involving excavating to the underground pipe, installing the sensor and wiring the factory pre-potted cabling to the transmitter and then backfilling the hole. Operation has been simplified by the use of ABB’s universal Human Machine Interface (HMI), which has now been extended across its range of instrumentation products. Based on Windows™ technology, the HMI simplifies operation, maintenance and training, reducing cost of ownership and providing a consistent user experience. Data can also be accessed remotely via HART™, Profibus DP™ and Modbus™ communications.Installation is further simplified by the WaterMaster’s ‘Fit and Flow’ data storage feature. On initial installation, the selfconfiguration sequence automatically replicates into the transmitter all calibration factors, meter size and serial numbers as well as customer site-specific settings. This eliminates the opportunity for errors and leads to increased speed of start-up.Measurement integrity is ensured by redundant storage of data in both the sensor and transmitter memory, which is continually updated during all operations. The on-board sensor memory eliminates the possible problems associated with pluggable data memory modules.WaterMaster is proven to be robust and reliable, with unmatched diagnostic capabilities providing the right information to keep the process up and running. Alarms and warnings are classified in accordance with NAMUR NE107.The meter is also verified to OIML R49 type ‘P’ requirements to ensure the highest accuracy and long term performance of the system by continuously self-checking the sensor and transmitter in the field.All ABB flow meters are designed and manufactured in accordance with international quality procedures (ISO 9001) and are calibrated on nationally-traceable calibration rigs to provide the end-user with complete assurance of both quality and performance. Acknowledgments• HART is a registered trademark of the FieldComm Group • Modbus is a registered trademark of Schneider Electric USA Inc.• PROFIBUS is a registered trademark of PROFIBUSorganization.A D /F L O W /006-E N R e v . A 02.2019—ABB LimitedMeasurement & Analytics Oldends Lane StonehouseGloucestershire GL10 3TA UKTel: +44 (0)1453 826 661Fax: +44 (0)1453 829 671Email: **********************.com ABB Inc.Measurement & Analytics 125 E. County Line Road Warminster PA 18974USATel: +1 215 674 6000Fax: +1 215 674 7183ABB Engineering (Shanghai) Ltd.Measurement & Analytics No. 4528, Kangxin Highway Pudong New District Shanghai, 201319,P.R. ChinaPhone: +86 (0)21 6105 6666Fax: +86 (0)21 6105 6677Email:****************************.com /measurement—We reserve the right to make technical changes or modify the contents of this document without prior notice. With regard to purchase orders, the agreed particulars shall prevail. ABB does not accept any responsibility whatsoever for potential errors or possible lack of information in this document.We reserve all rights in this document and in the subject matter and illustrations contained therein. Any reproduction, disclosure to third parties or utilization of its contents – in whole or in parts – is forbidden without prior written consent of ABB.©ABB 2019All rights reserved.。

光不能穿过物体英语作文Title: The Phenomenon of Light Not Passing Through Objects。

Introduction:The phenomenon of light being unable to pass through certain objects is a fascinating aspect of physics that has intrigued scientists and thinkers for centuries. Whilelight is often considered as an omnipresent force capable of penetrating through various mediums, there exist materials that can block or obstruct its passage. In this essay, we will explore the science behind this phenomenon, its practical implications, and its significance in our understanding of the natural world.Understanding Light and Matter:Light, as we know it, travels in the form of electromagnetic waves. These waves propagate through spaceuntil they encounter an obstacle or a medium with different optical properties. When light interacts with matter, several processes can occur, including reflection, refraction, absorption, and transmission. The ability of a material to allow light to pass through it depends on its molecular structure and the energy levels of itsconstituent particles.Factors Affecting Light Transmission:The transmission of light through a material depends on various factors, including the wavelength of light, the density of the material, and its chemical composition. Materials such as glass, air, and water are transparent to visible light because their molecular structures allow photons to pass through relatively unhindered. On the other hand, opaque materials like metals and dense ceramicsabsorb or reflect light, preventing it from passing through. Mechanisms of Light Blocking:The inability of certain materials to transmit lightcan be attributed to different mechanisms. In some cases, the atoms or molecules in the material absorb the photons, converting their energy into internal vibrations or electronic transitions. This absorption process effectively prevents the light from propagating through the material. In other cases, the material may scatter or reflect light due to irregularities in its structure, further inhibiting its transmission.Applications and Implications:The phenomenon of light blocking has numerous practical applications across various fields. In architecture and design, opaque materials are used to create privacy and control the amount of light entering a space. In photography and imaging, the manipulation of light-blocking materials allows for the creation of shadows, contrasts, and artistic effects. Moreover, in industries such asoptics and telecommunications, the development of materials with specific light-blocking properties is crucial for the fabrication of lenses, filters, and optical fibers.Scientific Significance:The study of materials that block light not only has practical applications but also contributes to our understanding of fundamental physical principles. By investigating the interaction between light and matter at the atomic and molecular levels, scientists gain insights into the behavior of photons and the electronic structure of materials. This knowledge is essential for advancing fields such as quantum mechanics, photonics, and materials science.Conclusion:In conclusion, the phenomenon of light being unable to pass through certain objects is a complex yet intriguing aspect of physics. Through the study of light-blocking materials, scientists have gained valuable insights into the nature of electromagnetic waves and the behavior of matter at the atomic scale. Moreover, the practical applications of this phenomenon underscore its significance in everyday life, from architecture and design totelecommunications and scientific research. As our understanding of light and matter continues to deepen, so too will our ability to harness and manipulate these phenomena for the benefit of society.。

发电机线圈匝数与电压公式物理1.发电机线圈的匝数与电压之间存在着直接的关系。

The number of turns of the generator coil is directly related to the voltage.2.发电机线圈的匝数增加，所产生的电压也随之增加。

As the number of turns of the generator coil increases, the generated voltage also increases.3.发电机线圈的匝数减少，则所产生的电压也相应地减少。

If the number of turns of the generator coil decreases, the generated voltage will also decrease accordingly.4.电压与线圈匝数的关系可用数学公式表示。

The relationship between voltage and coil turns can be expressed by a mathematical formula.5.发电机线圈的匝数是影响电压大小的重要因素之一。

The number of turns of the generator coil is one of the important factors affecting the voltage.6.通过改变发电机线圈的匝数，可以调节所产生的电压大小。

By changing the number of turns of the generator coil,the generated voltage can be adjusted.7.发电机线圈的匝数与磁场的变化也会影响到所产生的电压。

The number of turns of the generator coil and the changein the magnetic field also affect the generated voltage.8.在设计发电机时，需要考虑线圈的匝数对电压的影响。

Standard R1Environmental Design &Testing of Electronic & Electrical ComponentsTable of Contents 目錄1. SCOPE AND DEFININTIONS范圍與述語定義2. APPLICATION 應用3. ENVIRONMENTAL FACTORS, TEST METHODS AND GENERAL GUIDELINES環境及測試方法的指導4. DEVIATIONS 偏差5. TESTING AND INSTRUMENTATION ACCURACY 測試和儀器精確度6. ELECTRICAL REQUIREMENTS 電子要求6.1 LOAD DUMP 甩負荷測試6.2 ELECTROSTATIC DISCHARGE (ESD) 抗ESD干擾測試(ASA做< JONNY19.12.07復> )6.3 DC VOLTAGE OVERSTRESS DC電壓負荷測試6.4 REVERSE BATTERY 電池反接測試6.5 INDUCTIVE LOAD SWITCHING TRANSIENT VOLTAGE 感應負載切換瞬時電壓測試(ASA做<JONNY19.12.07復> )6.6 MUTUAL COUPLING TRANSIENT VOLTAGE 互耦瞬時電壓測試 (ASA做< JONNY19.12.07復> )6.7 SHORTED I/O 短接I/O測試6.8 POWER SUPPLY/ALTERNATOR RIPPLE REJECTION 拒絕電源紋波測試(ASA做< JONNY19.12.07復> )6.9 SIMULATED CRANK-START VOLTAGE 模擬曲柄啟動電壓(ASA做< JONNY19.12.07復> )7.1 LOW OPERATING VOLTAGE 低電壓操作。

高频电磁场环境对电子器件的影响研究IntroductionWith the development of modern technology, electronic devices have become an indispensable part of our daily life. However, the increasing use of electronic devices in our life has led to the emergence of a new challenge - electromagnetic radiation interference. High-frequency electromagnetic fields are generated by a wide range of sources, such as communication systems, power lines, and electronic devices. These high-frequency electromagnetic fields can interfere with the normal operation of electronic devices, affecting their performance and reliability. Therefore, it is essential to research the impact of high-frequency electromagnetic fields on electronic devices.Effect of High-Frequency Electromagnetic Fields on Electronic Devices1. Electromagnetic InterferenceThe electromagnetic interference (EMI) phenomenon is a significant challenge for electronic devices that operate in a high-frequency electromagnetic environment. This interference can significantly affect the performance of electronic devices, leading to malfunction or even failure. EMI can be induced by external sources of electromagnetic fields or generated internally within devices.External EMI can be caused by devices such as broadcast transmitters, cell phones, and radios. On the other hand, internal EMI can arise from the circuitry within the electronic device itself, such as clock signals, switching transistors, or inductive loads.2. Radiation EffectsRadiation effects are associated with the impact of high-energy particles, including electromagnetic radiation, on electronic devices. These effects can cause single-event upsets (SEUs), which are essentially errors that occur when high-energy particles strike a sensitive region of a device, such as a transistor or memory cell.SEUs are critical concerns for electronic devices that operate in high-altitude environments, such as satellites or aircraft. These electronic devices must be designed with special protective measures to avoid SEUs.3. Signal IntegritySignal integrity refers to the ability of electronic devices to maintain the correct signal quality within their operating environment. Signal integrity issues can result from a variety of factors, including noise, distortion, and crosstalk. High-frequency electromagnetic fields can often cause signal integrity issues by creating noise or crosstalk and degrading the signal quality.Methods to Evaluate the Impact of High-Frequency Electromagnetic Fields on Electronic Devices1. Experimental ApproachesExperimental techniques are commonly used to evaluate the impact of high-frequency electromagnetic fields on electronic devices. In the laboratory, devices are subjected to a range of electromagnetic fields, and their performance is evaluated. The effectiveness of this approach depends on the ability to accurately replicate the real operating conditions of the device.2. Modeling and SimulationModeling and simulation techniques allow for the evaluation of the impact of high-frequency electromagnetic fields on electronic devices in a virtual environment. These techniques are particularly useful for complex devices or systems that are challenging to analyze experimentally.Modeling and simulation can help to identify the most significant sources of EMI and suggest possible solutions. It is possible to use different types of simulation techniques, such as finite element method (FEM), finite-difference time-domain (FDTD), or integral equation methods.3. Design ConsiderationsDesign considerations play a significant role in mitigating the impact of high-frequency electromagnetic fields on electronic devices. One of the primary design considerations is the selection of appropriate components. Components with high noise immunity, such as shieldedcables or filters, may be used to minimize the impact of high-frequency electromagnetic fields.Another design consideration is the implementation of electromagnetic shielding, which is intended to minimize the penetration of electromagnetic fields into the device. Shielding can be achieved using conductive materials, such as copper or aluminum foil.ConclusionThe impact of high-frequency electromagnetic fields on electronic devices is a significant concern that must be taken seriously in modern technology. The effects of EMI, radiation, and signal integrity issues can cause severe problems, including device failure or malfunction. Experimental techniques, modeling, and simulation, and design considerations are all essential tools for evaluating these effects and developing solutions. By taking these factors into consideration, electronic devices can be designed and operated with greater reliability in high-frequency electromagnetic fields.。

外星人和地球人的不同英语作文Humanity has long been fascinated by the prospect of extraterrestrial life. From science fiction stories to serious scientific speculation, the idea of intelligent beings from other worlds has captured our collective imagination. As we continue to explore the cosmos and search for signs of life beyond our planet, it is natural to wonder about the potential differences between extraterrestrials and the inhabitants of Earth. While we can only speculate about the nature of alien civilizations, there are several key areas where we might expect to find significant contrasts between extraterrestrials and earthlings.One of the most fundamental differences would likely be in the area of biology and physiology. Depending on the conditions of their home planet, extraterrestrials could have vastly different physical characteristics compared to humans. Their biochemistry, anatomy, and even sensory capabilities might be radically different from our own. For example, an alien species might possess additional limbs, organs, or sensory organs that we cannot even conceive of. Their means of locomotion could be completely foreign to us, perhapsinvolving levitation, flight, or a mode of movement that is entirely alien to terrestrial life.The way extraterrestrials perceive and interact with their environment could also be profoundly different from human experience. Their senses might operate on wavelengths of the electromagnetic spectrum that are invisible to us, allowing them to detect phenomena that are imperceptible to human eyes, ears, and other senses. They may have sensory capabilities that we cannot even imagine, giving them an entirely different understanding of their surroundings. Additionally, the cognitive processes and decision-making strategies of extraterrestrials could be radically different from our own, shaped by the unique evolutionary pressures and environmental conditions of their home world.Another key area of potential difference is in the realm of language and communication. The development of language on Earth has been shaped by the specific biological and cultural characteristics of human societies. Extraterrestrial civilizations, however, may have evolved radically different systems of communication, perhaps involving non-verbal modes of expression or even forms of communication that transcend the limitations of our own spoken and written languages. Their "languages" could be based on entirely different principles, utilizing novel modes of information transmission that are foreign to us. This could present significantchallenges in terms of mutual understanding and interspecies communication.The social and cultural structures of extraterrestrial civilizations are also likely to be quite different from those found on Earth. The specific environmental, technological, and historical factors that have shaped human societies may not apply to alien worlds, leading to the development of social organizations, political systems, and cultural practices that are vastly different from our own. Extraterrestrials may have radically different value systems, modes of conflict resolution, and approaches to decision-making and resource allocation. Their concepts of individuality, community, and the role of the individual within society could be fundamentally alien to us.Furthermore, the technological capabilities of extraterrestrial civilizations could be far beyond our current understanding and level of development. While we often envision aliens as possessing advanced technologies that are indistinguishable from magic, the reality may be even more profound. Extraterrestrials may have mastered forms of energy, matter manipulation, and information processing that are completely foreign to human experience. Their technological prowess could allow them to transcend the limitations of their physical form, perhaps even achieving a level of post-biological existence that is difficult for us to comprehend. The ways in which they harness and apply technology could be so radicallydifferent from our own that meaningful comparisons become nearly impossible.Finally, the worldviews and belief systems of extraterrestrial civilizations may be radically different from those found on Earth. Their philosophical and spiritual perspectives could be shaped by entirely different cosmological understandings, with vastly different conceptions of the nature of reality, the origins of the universe, and the place of intelligent life within it. Their approaches to questions of ethics, morality, and the meaning of existence could be profoundly alien to human thought, perhaps even challenging our most fundamental assumptions about the nature of consciousness and the human condition.In conclusion, the potential differences between extraterrestrials and earthlings are vast and multifaceted. From the realm of biology and physiology to the domains of language, social structures, technology, and worldviews, the contrasts between alien civilizations and human society could be staggering. As we continue to explore the cosmos and search for signs of life beyond our planet, it is important to maintain an open and flexible mindset, recognizing that the diversity of intelligent life in the universe may be far greater than we can currently imagine. Embracing this potential for radical difference will be crucial as we navigate the challenges and opportunities presented by future encounters with extraterrestrial civilizations.。