Long Phase Coherence Time and Number Squeezing of two Bose-Einstein Condensates on an Atom

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absolute intensityA display or plot mode in which the signal intensity is proportional to theacquisition timeattenuationThe control applied to voltages (including signal from the sample) within the spectrometer. High attenuation gives low-voltage, low-attenuation gives high-voltage.B 0The static magnetic field. The magnetic flux density is expressed in tesla,T, or often, as an equivalent 1H resonance frequency (for example, 300MHz for a 7 T magnet).B 1Magnetic field associated with a radio-frequency (r.f.) pulse. Often expressed as an equivalent value in kHz.bandshapeUsually used when referring to a complex lineshape or a group of overlapping plex bandshapes often arise from quadrupolar nuclei (see figure 2).centrebandThe signal at the isotropic chemical shift. Its position is the same at all spin-rates.channelThe individual frequencies or frequency bands of a spectrometer. For example: H-channel (proton), C-channel (carbon) or broad-band (or X) channel (usually anything except H).chemical shiftNumber used for reporting the position of a line (νi )relative to a reference line (νref ) in a high-resolution spectrum. The chemical shift parameter is denoted δ and quoted in ppm.coherence pathwayDescription of an experiment that allows the excitation of the spins to be followed. Useful for experiments where excitation or selection of signal from one-, two- or multiple-quantum transitions is needed.contact timeTime during which two matched radio-frequency fields are applied simultaneously in a CP experiment.CPCross-polarisation. Any experiment where energy (magnetisation) is transferred from the nuclei of one element (often H) to those of another.dead-time Time between a pulse and the switch on of the receiver. The spectrometercircuitry needs time to settle after transmitting the high voltage associatedwith a pulse before it can detect the very low voltage associated with thesignal from the sample. See figure 1.610×−=ref ref i νννδTerminology Commonly Used in NMR SpectroscopyFigure 2. Bandshape from a single 11B environment.磁共振成像常用技术术语d.c. offset Constant-value offset occurring in the FID (see “Problems”). Results ina central (zero-frequency) “spike” artefact in the spectrum whentransformed.deconvolution Mathematical process used to determine the intensities of overlappinglines.digital resolution This depends on the Fourier number. The bigger the Fourier number thegreater the number of data points per Hz of the spectrum and the higherthe digital resolution. See “Processing”.DP Direct-polarisation. An experiment in which the nuclei to be observedare excited directly.duty cycle A value used to assess whether anexperiment might damage thespectrometer (or the sample). Theduty cycle should never exceed 20 %(see “How to Choose a RecycleDelay”)dwell Spacing between data points in the time-domain. Can depend on theway acquisition is implemented but, commonly, dwell = 1/spectral width. endcap Open rotors have to be closed with endcaps before they can be spun. FID Free Induction Decay (see figure 1).field Magnetic field, with flux density quoted in T (Tesla) for the static magneticfield (B). For the magnetic field associated with an r.f. pulse the fluxdensity is given in mT or, more usually, expressed as a kHz equivalent(see “Matching”).flip-back Experimental procedure for shortening recycle times (see “How to Choosea Recycle”).Fourier number The number of points used in the FT. Always a power of 2.frequency domain Where information is displayed as a function of frequency - the spectrum FT Fourier Transform. Mathematical process to convert time-domain tofrequency-domain. Designed to work with 2n (n = integer) data points. gain Amplification applied to the received signal.Gauss Non-SI unit of magnetic field flux density. The SI equivalent is Tesla (T),1 T = 10,000 Gintensity On its own - the height of a line. Integrated-intensity is the area under theline.linebroadening Spectra can be artificially linebroadened to improve their appearance.This involves multiplying the FID with a decaying function prior to the FT.See “Processing”.lineshape The shape of individual lines in a spectrum. Commonly, Gaussian orLorentzian (figure 3) or a mixture of the two, are encounteredexperimentally.linewidth This is usually the full width at half-height (δν½)r.f. on-timer.f. on-time + r.f. off-timeduty cycle =magic-angle54.7° or 54° 44´magnetisation when described classically (non-quantum mechanically) an ensemble ofspins at equilibrium in an external magnetic field has a net magnetisationprecessing about an axis aligned along that field.magnetogyric ratio Symbol γ . A fundamental physical constant of elements with non-zerospin. For example γH is 2.675x108 rads -1T -1.matchShort for Hartmann-Hahn match (see “Matching”)noisenormalised intensity Signal intensity can be multiplied by an arbitrary factor to give a particularheight to the highest (often) line or the integrated intensity. Opposite ofabsolute intensity.nuclear spin quantum number Symbol I . A fundamental property of a nucleus. Only nuclei with I > 0are said to be NMR “active”.phase (1)The phase of a pulse relates to its position in the xy plane of the rotating frame.phase (2)The phase of a spectral line comes from the way in which the real and imaginary components of a complex FT are combined (see “Processing”).phase cycling The way in which the phase of a pulse (or the receiver) is changed duringsuccessive repetitions of a pulse sequence. Used to suppress artefactsand select specific coherence pathways.ppm Parts per million. Usual way of reporting a chemical shift. A frequencydifference ∆ Hz 610×∆≈n observatio ν ppm precession“Movement of the axis of a spinning body around another axis” (as a gyroscope)probeThe business end of the spectrometer, where the sample goes.pulse angle When described in the rotating frame a pulse rotates the magnetisationthrough an angle θ. A pulse that rotates the magnetisation though 90° iscalled a 90° pulse.pulse duration Time for which a pulse occurs.quadrupole Any nucleus with I > ½.recycle (time)Or pulse delay or relaxation delay. Time between the end of dataacquisition and the start of excitation in successive repetitions of a pulsesequence. (See “How to Choose a Recycle”).referenceThe material giving the signal which defines the zero position in a high-heightresolution spectrum.repetitionsThe number of times a pulse sequence is repeated in an experiment.resolutionThe ability to separate closely spaced lines (see figure 4). As a rule of thumb,a pair of lines will be resolved if their linewidth is less than their separation.resolution enhancementThe opposite of linebroadening. An FID multiplied by an appropriate combination of increasing and decaying functions can yield extra resolution in a spectrum. See “Processing”.rotary echoA feature of an FID that occurs at intervals of 1/spin-rate (see “How to Set the Magic-angle”). They give rise to spinning sidebands in the spectrum.rotating frameA mathematical tool to make the effect of a pulse easy to visualise.Magnetisation precessing at ν Hz in a laboratory-based xyz axis system appears static in an axis system (frame) rotating at ν Hz.rotorThe container that holds the sample. Often referred to in terms of its outside diameter (for example, 5 mm).saturationCondition that arises when there is no population difference between excited and ground states. No signal is observable under such conditions.sidebandsOr spinning sidebands. Under some circumstances sidebands appear in a spectrum. They can occur on both sides of a centreband and separated from it by a frequency equal to the spin-rate. A spectrum may contain a manifold of sidebands and the centreband is not necessarily more intense than all of the sidebands.signalThe FID or one or more of the lines in a spectrum.signal-to-noise ratio (S/N)Ratio of the height of a line or signal (usually the largest) to the noise.Definitions of the measurement of noise vary. Signal increases as n (the number of repetitions) but noise only increases by √n so S/N increases by √n.spectral widthDifference in frequency of the two ends of the full spectrum. Not to be confused with the now largely obsolete term sweep width.spinA property of a nucleus with non-zero nuclear spin-quantum number (I ),as in spin-½. Or, simply, a nucleus with a magnetic moment.spin-lockIf, after a 90°x pulse a second, long-duration (spin-lock) r.f. field is applied along the y-axis the magnetisation is said to be spin-locked.spin-rateThe rate at which the sample is spun.spin-temperature inversionA manipulation carried out within the phase cycling of a CP experiment to remove magnetisation originating directly from the X-channel contact pulse.standard Any sample used to set-up the spectrometer and/or to define the zeroposition in the spectrum.Figure 4. Two lines of constant spacing but different linewidth.T 1Spin-lattice relaxation time-constant. Relates to the time taken for excited spins, in the presence of B 0, to loose energy to their surroundings and return to their equilibrium state.T 1ρSpin-lattice relaxation time-constant in the rotating frame. As for T 1 but this time in the presence of an applied radio-frequency field B 1.T 2Spin-spin relaxation time-constant. Relates to the time for a conserved exchange of energy between spins.T 2*A time-constant sometimes used to describe the decay of the observed time-domain signal (T 2* ≤ T 2). The shorter T 2* the broader the associated signal(s) in the spectrum.time-domainWhere information is recorded or displayed as a function of time (see figure 1).transmitter offsetThis allows fine control of the position of a transmitter (carrier frequency).With an appropriate offset, signals can be put exactly on-resonance or a specific amount off-resonance. Can be applied to any spectrometer channel.truncationIf the acquisition time is shorter than the FID then truncation of the FID is said to have occurred (See “Problems”).zero filling If the number of data points is not a power of two then zeroes are addedto the acquired data so that the total number of points Fourier transformedis 2n . Zero filling adds no signal to the spectrum but it can improveresolution (see “Processing”).。

物理专业英语第6章翻译光波的干涉The light intensity distribution generated when several light waves (member waves) meet does not equal to the sum of the light intensity distribution caused by each member wave alone, and the phenomenon of alternating light and dark appears.For example, in Young's double-hole interference (see Young's interference experiment), the subwave out of each small hole H1 or H2 is a member wave. When the hole is small, the light intensity distribution I1 (x) caused by the member wave from the hole H1 alone is roughly uniform in a considerable range; so is the light intensity distribution I2 (x) caused by the member wave from the hole H2 alone.The sum of the two is still roughly evenly distributed.In the light intensity distribution I (x) caused by the two member waves together, the change of light and shade with position x is very significant, which is obviously not equal to.Each member wave alone causes a roughly uniform distribution of light intensity, which is equivalent to requiring that each member wave itself has no obvious diffraction, because the diffraction alsocauses alternating light and dark stripes (see diffraction of light).Therefore, when a number of member waves meet in a certain region of space and the interference occurs, it should mean that the diffraction of each member wave can not be considered in that region.Note that the aforementioned light intensity is not the instantaneous value of the light field intensity (proportional to the amplitude square), but the average or integral value of the light field intensity within a certain time interval t; t depends on the performance of the detection means or device.For example, during human eye observation, t is the visual retention time; while shooting on film, t is the exposure time. The interference phenomenon usually shows a fairly steady stripe distribution of the light field intensity in space; sometimes, when the certain parameter of the interference device changes with time, the light intensity received at a certain fixed point changes alternately. The discovery of the interference phenomenon of light has historically played an indelible role in the evolution from the particle of light to the fluctuation of light.In 1801, T. Young proposed the principle of interference and first made adouble-slit interference experiment, and also explained the color of the film formation.In 1811, the D.F.J. Arago first studied the interference phenomenon of polarized light.Modern times, light interference has been widely used in precision measurement, astronomical observation, photoelastic stress analysis, automatic control in optical precision machining and many other fields.Generate conditions Only the two columns of light waves of the same frequency, the phase difference is constant, the vibration direction of the same direction of the coherent light source, can produce light interference.The light emitted by two ordinary independent light sources can not have the same frequency, let alone have a fixed difference, so, the interference phenomenon cannot produce. Specific methods In order to stabilize the light intensity distribution of the synthetic wave field over a time interval t, the frequency of each ① member wave v (and hence the wavelength) is the same; the initial phase difference between the two member wa ves of ② remains constant within t.Conditional ② means that several usually independent light sources meet without interference, even if they emit light at the same frequency.Thereason is that usually the light emitted by the light source is a large number of waves distributed irregularly in the initial phase, and each wave lasts no more than 10 seconds, that is, every 10 seconds or so, the initial phase of the wave is a random change.Moreover, the initial phase of the wave column emitted by any two independent light sources is again statistically independent.You can imagine that when these independent light source wave meet, only in a very short time to produce a certain stripe pattern, and every 10 seconds or so, with another pattern, so far not any detection or recording device can keep up with such sharp changes, thus observed the average effect of the large number of patterns, namely uniform light intensity distribution rather than light and dark stripes.However, modern special lasers have produced tens of kilometers of waves, even lasting on the order of 10 seconds.Therefore, it can be said that if a detector with the time-resolution ability t is shorter than 10 seconds (which is possible), the interference of the light waves emitted by two independent lasers of the same frequency can also be observed.In addition, taking the two-wave interference as an example also requires that: the amplitude of the ③ two waves mustnot differ greatly; the polarization surface of the ④ two waves at the superposition point must be roughly consistent. When the condition ③ is not satisfied, although the interference stripes can still arise in principle, but the light and dark difference of the stripes is very little, and the interference phenomenon is not obvious.Conditiona l ④ is necessary because when the polarization surface of the two optical waves is perpendicular to each other, the light intensity of the synthetic field is the same value and does not show alternating light and shade (to observe the light alternation, you must use the polarization element). The above four points are commonly known as coherence conditions.Two or more light sources or light waves that satisfy these conditions are called coherent light sources or coherent light waves.若干个光波（成员波）相遇时产生的光强分布不等于由各个成员波单独造成的光强分布之和，而出现明暗相间的现象。

Chapter 5 Syntax 句法I. Multiple Choices:1.D. Immediate Constituent2. B. semantic3. A. concord4. A. the future is not expressed by morphological change5. D. substitutability6. C. co-occurrence7. B. Predicate 8.B. syntactic 9. C. self-control10. D. Government 11. D. coordinateII. Fill in the blanks with the most suitable words:1. Cohesion refers to ties and connections which exist within texts. They are also called formal links between sentences and between clauses.2. A sentence structure that is made up of layers of word groups is called a hierarchical structure.3. Sentences are traditionally assumed to be made up of words in _linear___ direction.4. Provide linguistic terms for the following descriptions.1) a type of relation holding with each other at aparticular place in a structure:2) an operation that moves a phrase category from its original position generated byPS rules to another within a structure: transformation3) the branch of linguistics which studies the rules governing the combination ofwords into sentences: syntaxIII. Decide whether the following statements are true or false. Write T for true and F for false in the bracket before each of them:T 1. It is characteristic of Halliday’s theory that more attention is paid to paradigmatic relations than to syntagmatic relations, which is the main concern of Chomsky.F2. Tense and aspect are two important categories of the verb, and they were separated in traditional grammar. (they were not separated in traditional grammar)F 3. Paradigmatic relation in syntax is alternatively called horizontal relation.(Paradigmatic relation is also called vertical relation; horizontal relation is a term for syntagmatic relation.)T 4. All human languages utilize a finite set of discrete units to form an infinite set of possible sentences.F 5. The English sentence "If only I could fly!" is in imperative mood. subjunctivemoodF 6. GOVERNMENT may be defined as the requirement that the form of two or morewords in a syntactic relationship should agree with each other. concordT 7. The SYNTAGMATIC RELATION is a relation between one item and others in a sequence, or between elements which are all present.T 8. The deep structure may be defined the abstract representation of the syntactic properties of a construction, i.e. the underlying level of structural relations between its different constituents, such as the relation between the underlying subject and its verbs, or a verb and its object.F 9. Categorization is the process of classifying our experiences into same categoriesbased on commonalities and differences. As a major ingredient in the creation of human knowledge, it allows us to relate present experiences to past ones.different categoriesF 10. The syntagmatic relation is also known as vertical relation. horizontal relationF 11. "Singing an English song" is an exocentric construction. endocentricconstructionT 12. Single words and clauses can both be constituents.IV. Define the following terms:1. IC analysisIC analysis. IC analysis (immediate constituent analysis) refers to the analysis of a sentence in terms of its immediate constituents ---- word groups ( or phrases), which are in turn analyzed into the immediate constituents of their own, and the process goes on until the ultimate constituents are reached. In practice, for the sake of convenience, we usually stop at the level of word.2. paradigmatic relationparadigmatic relation: Saussure originally called associative, is a relation holding between elements replaceable with each other at a particular place in a structure, or between one element present and the others absent.3. Lexical ambiguityLexical ambiguity: It refers to ambiguity explained by reference to lexical meanings. For example, “I went to the bank” is lexically ambiguous in the sense that “bank” in this sentence could refer to a business establishment or a slop of landing adjoining a river.4. Grammatical ambiguityGrammatical ambiguity: Grammatical ambiguity occurs when the grammatical structure of a sentence allows two different interpretations, each of which gives rise toa different meaning.5. Concord (or: Agreement)Concord (or: Agreement) could be defined as the requirement that the forms of two or more words in a syntactic relationship should agree with each other in terms of some categories. For example, in English the determiner and the noun it precedes should concord in number as in “this man”, “these men”; “book”, “same books”.6. endocentric constructionEndocentric construction is one kind of syntactic constructions whose distribution is functionally equivalent to that of one or more of its constituents, i.e., a word or a group of words, which serves as a definable centre or head. An endocentric construction is also known as a headed construction, for example, in the noun phrase “all these last few days”, days is the head. And this phrase is an endocentric construction.V. Questions:1. What is the aim of IC analysis? Make an IC analysis of the following sentence bymeans of either brackets or a tree diagram.北外2010My brother said Mary liked the handbag.The aim of IC analysis is to discover and demonstrate the interrelationships of the words in a linguistic structure—the sentence or the word-combination. The IC analysis views the sentence not just as a linear sequence of elements but as sequence made up of “layers”of immediate constituents, each lower-level constituent being part of a higher-level constituent.Though IC analysis, the internal structure of a sentence may be demonstrated clearly and ambiguities, if any, will be revealed.We can analyze the sentence like this:SNP VPVSˈNP VPN V NPDet N Det NMy mother said Mary liked the handbag. OrMy mother said Mary liked the handbag. 2. Why did Chomsky make the distinction between Deep and Surface structures?人大2006In generative grammar, deep structure is the abstract syntactic representation of a sentence, the underlying level of structural organization which specifies all the factors governing the way the sentence should be interpreted. On the other hand, surface structure is the final stage in the syntactic representation of a sentence, which provides the input to the phonological component of the grammar, and which thus most closely corresponds to the structure we articulate and hear.According to Chomsky, it is necessary to make the distinction, since it is helpful to differentiate and analyze syntactic structures such as "John is easy to please" and"John is eager to please", and also to disambiguate structures like "the shooting of the hunters". More importantly, it reflects two of the stages of how the language is processed through the generative grammar: the deep structure, which is an underlying structure, has to be transformed to the surface structure via a set of transformational rules.3.Try to identify the possible paradigmatic relation between any items in thefollowing poem by Lu Xun (i.e. tell if there is such a relation between which and which items).岂有豪情似旧时，花开花落两由之。

Faraday Discuss .,1997,108,469È471Concluding RemarksR.M.Hochstrasser a and J.P.Simons ba Department of Chemistry ,University of Pennsylvania ,Philadelphia ,PA 19104,USAb Physical and T heoretical Chemistry L aboratory ,University of Oxford ,Oxford ,UK OX13QZThere are several Golden Rules associated with the presentation of Concluding Remarks at Faraday Discussions.The Ðrst of these,“ask someone else to give themÏhas,sadly,been obeyed because of Prof.HochstrasserÏs enforced immobility,occasioned by a prol-apsed disc.We wish him a speedy recovery.The second Rule,“if you have nothing to say,say nothingÏhas been compensated,fortunately,by Prof.HochstrasserÏs provision of the outline notes of some of the remarks he would have made,had it been possible.They are presented below.The third Rule,“say some nice thingsÏis the easiest of all to obey since Prof.Whitehead has organised so imaginative and timely a Discussion,which has been introduced with all of Prof.JortnerÏs customary dynamism.It has addressed many issues.How do we monitor and interpret the dynamics of photon-induced processes in clusters and condensed media?What is the nature of the chromophore when it is no longer isolated in the gas phase?How does it “communicateÏwith its environment?How does the environment inÑuence electronic motions,e .g .in atomic or molecular Rydberg states;or nuclear motions,e .g .through caging or chap-eroning of atomic or molecular fragments;or their coupling,through non-adiabatic dynamics?How does photon absorption lead to nuclear motion in the neighbouring environment?How do the interactions of the chromophore with the environment depend upon the nature of the environment,and the way it is coupled to it,e .g .through space or through bonds?What are the characteristic timescales of the interactions;are they separable?Can we trace the pathway from the initial energy localisation,through its delocalisation to its eventual dissipation?What is the nature of the “molecular and intermolecular circuitryÏthat governs this evolution?Most pertinently,as Prof.Hochstrasser asks:How do the structural and dynamical results obtained from simple systems help us to understand the behaviour of more complex materials?What do clusters,for example,teach us about liquid structure?What do we learn about the dynamic behaviour in liquids and solids,from the study of Ðnite-sized assemblies?What conditions require statistical as opposed to discrete (level by level)models of dynamics?What is reasonable (or unreasonable)about seeking a microscopic quantum mechanical description of liquids?Investigations of small molecules teach us about chemical bonding and the charac-teristics of accurate potential energy surfaces.Weaker interactions are often evaluated from studies of van der Waals complexes and Ðnite clusters.The dynamics in such systems are determined by forces obtained from these potentials.While the properties of molecules in large clusters,liquids or extended aggregates might,in some cases,be framed in terms of isolated molecule potentials there will be cases where this is not possible.The most appropriate description of the dynamics of complex systems depends upon how the energy is partitioned.Typically,for a solution phase problem,the Hamiltonian involves the molecular part,and the solvent part which are separately solved either exactly or approx-H M H S ,imately,and a coupling part,that slightly mixes them.This partitioning yields a V MS ,useful representation when the molecular or solvent states are only slightly modiÐed by469470Concluding Remarkstheir interactions.The molecular potential is especially valuable in this case and may dominate the motion of the molecular nuclei even though the dynamics may be in a statistical limit.The intermolecular perturbations cause irreversible relaxation corre-sponding to transitions between the molecular states,accompanied by energy transfer to and from the solvent bath.In order that energy can be transferred to it,the solvent must have unoccupied states.Energy transfer to the molecule requires occupied states of the bath.A fully worked out example where this approach is nearly exact is the coupling of an atom or molecule to a very weak radiation Ðeld.Another example would be molecu-lar dynamics in very weakly interacting solvents.Quantum dynamics in this limit can be handled along the lines of RedÐeld theory,in which the reduced molecular density matrix is expanded to second order in This approach gives rise to spectral shifts V MS .and to coherence transfer along with relaxation of both the population and the phase of the molecular levels.The nuclear motions are largely governed by a slightly modiÐed version of the molecular potential.In stochastic dynamics,the solvent e†ect is estimated from correlation functions of where the Ñuctuations in the interaction potential V MS (t ),due to the motion of very large numbers of solvent nuclei and electrons are modelled by statistical forms or calculated from molecular dynamics simulations.There are situations where the molecular potential is so severely modiÐed by the solvent Èsolute interaction that an alternative representation is more realistic.In such cases it may be that the system of interest is a supermolecule or cluster,consisting of the solute and strongly interacting solvent molecules.The Hamiltonian could then be parti-tioned to yield a term for the energy states of the cluster,and the surrounding bath,comprising those solvent molecules that do not interact strongly with the solute.The dynamics can be determined from one of the perturbation approaches mentioned earlier.In examples of this type the relevant nuclear dynamics are controlled by the potential surface of the cluster but the irreversible relaxation is caused by the weak coupling between the supermolecule and the solvent.Measurements and calculations of potential energy surfaces of solute Èsolvent clusters are sorely needed for this approach.Such a picture assumes that the long-range forces are weak and that the interactions between the solvent molecules are not much inÑuenced by the presence of the solute.These assumptions would surely be inappropriate in accounting for the dynamics and struc-ture of polar molecules or ions in water,to give just one example.When Coulombic forces are important in determining structure,and their Ñuctuations determine the dynamics,we can imagine that long-range interactions will have to be included.As chemical reactions take place and charges redistribute,there may be large changes in the energy from interactions with moving solvent molecules.The solvent nuclear dynamics have been measured by time-resolved Kerr e†ects in transparent media,by dynamic Stokes shifts and by three pulse photon echoes in dye systems and in proteins (see the paper by Fleming and co-workers in this Discussion 1).In the cases that were examined theoretically,the major part of the solvent reorganisation energy around charges appears to originate from the Ðrst solvation shell.While the experiments charac-terise correlation functions of the solvent,they usually do not provide a microscopic picture of the motions that cause the energy changes other than to classify them broadly,as vibrational,librational or di†usive.On the other hand we would like to know when there are changes in the solute potential surfaces as a result of solvation and when solvation can inÑuence reactive motions.Equally important is the experimental charac-terisation of the solvent structures as the solvation dynamics evolve.Simulations are able to predict the answers to all these questions so some experimental results will allow the theory to be tested.In experiments on the photodissociation of changes HgBr 2,2in the potential energy function of the released HgBr occur on the timescale of the solvation.They can be followed through the changes in the vibrational frequency.The fast process involves the breaking up of the solvent structure associated with the tri-atomic molecule and a slower process involves the construction of the equilibriumR .M .Hochstrasser and J .P .Simons 471solvent structure around the HgBr fragment.Similar results for solvent structure changes were seen for ClO ~.3These structures should be accessible to spectroscopic experiments.As shown in the paper by Neumark and co-workers,4the cage reaction of I and I ~in a cluster of induces slow solvent evaporation and fast vibrational relax-CO 2ation.These experiments show details of the solvent involvement in the reactive motions that have proved difficult to obtain in solution phase experiments.Of course,it is known from experiment that the energy of a solution phase reaction is used to heat up the surrounding solvent molecules,and that the rate of reaction can be altered if the heat di†usion is very slow compared with the reaction rate.However,at conventional liquid densities (10M )the number of solvent molecules over which the released energy is dis-tributed grows to approximately 25in 10ps,by classical heat di†usion.The task of Ðnding a microscopic level description of solvent e†ects on relaxation and chemical processes is daunting.Nuclear motions can be extremely complex even for relatively small molecules in the absence of intermolecular interactions.When the solvent Èsolute interactions are strong the solvent forces can introduce additional anhar-monicity into the “soluteÏmotions thereby causing nuclear trajectories that are e†ec-tively absent in the isolated solvent molecule.For example,in the gas phase IR spectrum of the asymmetric stretch region shows no sign of any perturbations.In aqueous N 3~,solution,however,the mode relaxes in ca .1ps due to very strong coupling between solute modes;the motion is a combined solvent Èsolute displacement.5Such motions could be characterised through IR and Raman studies of clusters.There are many things (of course)that we have not heard about at this Discussion.One of the most important is single molecule spectroscopy,which can reveal the dis-tribution of molecular properties associated with Ñuctuations in their environment.When the observation time is shorter than the Ñuctuation timescale,the ensemble average is no longer equal to the time average.Not much has been heard about mol-ecules at interfaces,which is where much chemistry and biochemistry actually takes place.Not much has been heard about optical control of reaction rates in condensed phases;can we tune the solvent response to the lifetime of the transition state?We have not heard much about self-assembled supramolecular systems where the dynamics of photon-induced processes may be controlled by synthetic designÈmuch as it is in a photosynthetic centre.Perhaps these will feature in a future Faraday Discussion.References1Y.Nagasawa,J-Y.Yu,M.Cho and G.R.Fleming,Faraday Discuss .,1997,108,23.2M.Lim,M.Wo†ord,P.Hamm and R.M.Hochstrasser,Chem .Phys .L ett .,1998,in press.3M.Lim,S.Gnanakaran and R.M.Hochstrasser,J .Chem .Phys .,1997,106,3485.4B.J.Greenblatt,M.T.Zanni and M.Neumark,Faraday Discuss .,1997,108,101.5J.C.Owrutsky,D.Raftery and R.M.Hochstrasser,Ann .Rev .Phys .Chem .,1994,45,519.。

Phase Congruency Detects Corners and EdgesPeter KovesiSchool of Computer Science&Software EngineeringThe University of Western AustraliaCrawley,W.A.6009pk@.auAbstract.There are many applications such as stereo matching,mo-tion tracking and image registration that require so called‘corners’tobe detected across image sequences in a reliable manner.The Harris cor-ner detector is widely used for this purpose.However,the response fromthe Harris operator,and other corner operators,varies considerably withimage contrast.This makes the setting of thresholds that are appropri-ate for extended image sequences difficult,if not impossible.This paperdescribes a new corner and edge detector developed from the phase con-gruency model of feature detection.The new operator uses the principalmoments of the phase congruency information to determine corner andedge information.The resulting corner and edge operator is highly local-ized and has responses that are invariant to image contrast.This resultsin reliable feature detection under varying illumination conditions withfixed thresholds.An additional feature of the operator is that the cornermap is a strict subset of the edge map.This facilitates the cooperativeuse of corner and edge information.1IntroductionWith the impressive reconstruction results that have been achieved by those working in projective geometry(see for example Hartley and Zisserman[1])there has been a renewed interest in the detection of so called‘corners’,or‘interest points’.The success of these reconstructions depend very much on the reliable and accurate detection of these points across image sequences.The definition of a corner is typically taken to be a location in the image where the local autocorrelation function has a distinct peak.A variety of op-erators have been devised to detect corners.These include those developed by Moravec[2],Harris and Stephens[3],Beaudet[4],Kitchen and Rosenfeld[5], and Cooper et al.[6].Corner detectors based on the local energy model of fea-ture perception have been developed by Rosenthaler et al.[7],and Robbins and Owens[8].More recently the SUSAN operator has been proposed by Smith and Brady[9].Of these the Harris operator probably remains the most widely used.A common problem with all these operators,except the SUSAN operator, is that the corner response varies considerably with image contrast.This makes the setting of thresholds difficult.Typically we are interested in tracking fea-tures over increasingly extended image sequences.The longer the sequence the309greater the variations in illumination conditions one can expect,and the set-ting of appropriate thresholds becomes increasingly difficult,if not impossible. Inevitably thresholds have to be set at levels lower than ideal because detecting too many features is a lesser evil than detecting not enough.Stereo and motion reconstruction algorithms are then faced with the problem of dealing with very large clouds of noisy corner points,often greatly compromising their operation. Matching operations,which usually have rapidly increasing running time as a function of input size,suffer greatly in these conditions.Typically,considerable effort has to be devoted to the cleaning up of the output of the corner detector and to the elimination of outliers.The success of this cleaning up and outlier elimination process is usually crucial to the success of the reconstruction algo-rithm.Indeed,a very significant proportion of Hartley and Zisserman’s book[1] is devoted to robust estimation techniques.Another difficulty many of these operators have is that the Gaussian smooth-ing that is employed to reduce the influence of noise can corrupt the location of corners,sometimes considerably.The SUSAN operator deserves some special comment here because it does not suffer from these problems outlined above. It identifies features by determining what fraction of a circular mask has values the same,or similar,to the value at the centre point.Thresholds are therefore defined in terms of the size of the mask and no image smoothing is required. However,the SUSAN operator assumes that edges and corners are formed by the junctions of regions having constant,or near constant,intensity,and this limits the junction types that can be modeled.To address the many problems outlined above this paper describes a new corner and edge detector developed from the phase congruency model of feature detection.The new operator uses the principal moments of the phase congruency information to determine corner and edge information.Phase congruency is a dimensionless quantity and provides information that is invariant to image con-trast.This allows the magnitudes of the principal moments of phase congruency to be used directly to determine the edge and corner strength.The minimum and maximum moments provide feature information in their own right;one does not have to look at their ratios.If the maximum moment of phase congruency at a point is large then that point should be marked as an edge.If the mini-mum moment of phase congruency is also large then that point should also be marked as a‘corner’.The hypothesis being that a large minimum moment of phase congruency indicates there is significant phase congruency in more than one orientation,making it a corner.The resulting corner and edge operator is highly localized and the invariance of the response to image contrast results in reliable feature detection under varying illumination conditions withfixed thresholds.An additional feature of the operator is that the corner map is a strict subset of the edge map.This facilitates the cooperative use of corner and edge information.This paper is organized as follows:first the phase congruency model of feature perception is reviewed.We then examine how the phase congruency responses over several orientations can be analyzed in terms of moments to provide both310edge and corner information.Finally the performance is assessed relative to thecommonly used Harris operator.2The Phase Congruency Model of Feature DetectionRather than assume a gradient,the LocalEnergy Model in an image wherethe Fourier in Figure 1[10].NoticeFig.1.Fourier first four terms.how the Fourier the step in the squarewave.Congruency of perceived feature [11].The angle at which the congruency occurs dictates the feature type,for example,step or delta.The Local Energy Model model was developed by Morrone et al.[10]andMorrone and Owens [12].Other work on this model of feature perception can befound in Morrone and Burr [13],Owens et al.[14],Venkatesh and Owens [15],and Kovesi [16–20,11].The work of Morrone and Burr [13]has shown that thismodel successfully explains a number of psychophysical effects in human featureperception.The measurement of phase congruency at a point in a signal can be seengeometrically in Figure 2.The local,complex valued,Fourier components at alocation x in the signal will each have an amplitude A n (x )and a phase angleφn (x ).Figure 2plots these local Fourier components as complex vectors adding head to tail.The magnitude of the vector from the origin to the end point is theLocal Energy ,|E (x )|.The measure of phase congruency developed by Morrone et al.[10]isP C 1(x )=|E (x )|n A n (x ).(1)Under this definition phase congruency is the ratio of |E (x )|to the overall pathlength taken by the local Fourier components in reaching the end point.If allthe Fourier components are in phase all the complex vectors would be alignedand the ratio of |E (x )|/ n A n (x )would be 1.If there is no coherence of phase311RealaxisImaginaryaxisE(x)φφ(x)nA n (x)_noise circleFig.2.Polar diagram showing the Fourier components at a location in the signal plottedhead to tail.The weighted mean phase angle is given by (x ).The noise circle representsthe level of E (x )one can expect just from the noise in the signal.the ratio falls to a minimum of 0.Phase congruency provides a measure that isindependent of the overall magnitude of the signal making it invariant to vari-ations in image illumination and/or contrast.Fixed threshold values of featuresignificance can then be used over wide classes of images.It can be shown that this measure of phase congruency is a function of thecosine of the deviation of each phase component from the meanP C 1(x )= n A n (cos(φ(x )−φ(x )) nA n (x ).(2)This measure of phase congruency does not provide good localization and it isalso sensitive to noise.Kovesi [18,19]developed a modified measure consisting ofthe cosine minus the magnitude of the sine of the phase deviation;this produces amore localized response.This new measure also incorporates noise compensation:P C 2(x )=n W (x ) A n (x )(cos(φn (x )−φ(x ))−|sin (φn (x )−φ(x ))|)−T n A n (x )+ε.(3)The term W (x )is a factor that weights for frequency spread (congruency overmany frequencies is more significant than congruency over a few frequencies).Asmall constant,εis incorporated to avoid division by zero.Only energy valuesthat exceed T ,the estimated noise influence,are counted in the result.Thesymbols denote that the enclosed quantity is equal to itself when its value ispositive,and zero otherwise.In practice local frequency information is obtainedvia banks of Gabor wavelets tuned to different spatial frequencies,rather than viathe Fourier transform.The appropriate noise threshold,T is readily determinedfrom the statistics of the filter responses to the image.For details of this phasecongruency measure and its implementation see Kovesi [19–21].3123Combining Phase Congruency Information over many OrientationsA weakness of previous implementations of phase congruency has been the way in which information over many orientations is used and combined.The defini-tion of phase congruency outlined above only applies to1D signals.To obtain an overall measure of phase congruency in2D local energy isfirst calculated in several orientations,typically six,using data from oriented2D Gabor wavelets. Equation3is modified so that the numerator is the weighted and noise com-pensated local energy summed over all orientations,and the denominator is the total sum offilter response amplitudes over all orientations and scales.While this approach produces a phase congruency measure that results in a very good edge map it ignores information about the way phase congruency varies with orientation at each point in the image.To include information about the way phase congruency varies with orienta-tion we can proceed as follows:calculate phase congruency independently in each orientation using equation3,compute moments of phase congruency and look at the variation of the moments with orientation.The principal axis,corresponding to the axis about which the moment is minimized,provides an indication of the orientation of the feature.The magnitude of the maximum moment,correspond-ing to the moment about an axis perpendicular to the principal axis,gives an indication of the significance of the feature.If the minimum moment is also large we have an indication that the feature point has a strong2D component to it, and should therefore be additionally classified as a‘corner’.Following the classical moment analysis equations[22]we compute the fol-lowing at each point in the image:a=(P C(θ)cos(θ))2(4)b=2(P C(θ)cos(θ)).(P C(θ)sin(θ))(5)c=(P C(θ)sin(θ))2,(6)where P C(θ)refers to the phase congruency value determined at orientationθ, and the sum is performed over the discrete set of orientations used(typically six).The angle of the principal axisΦis given byΦ=12atan2bb22,a−cb22.(7)The maximum and minimum moments,M and m respectively,are given byM=12(c+a+b2+(a−c)2)(8)m=12(c+a−b2+(a−c)2).(9) 313This calculation of the maximum and minimum moments,along with the prin-cipal axis,corresponds to preforming a singular value decomposition on a phasecongruency covariance matrix.The moments correspond to the singular values.3.1Comparison with the Harris OperatorA comparison with the Harris operator is appropriate given its widespreaduse.The analysis described above is similar to that adopted by Harris andStephens [3].However they consider the minimum and maximum eigenvalues,αand β,of the image gradient covariance matrix in developing their corner detector.The gradient covariance matrix is given by G = I 2x I x I y I x I y I 2y(10)where I x and I y denote the image gradients in the x and y directions.A ‘corner’is said to occur when the two eigenvalues are large and similar in magnitude.Toavoid an explicit eigenvalue decomposition Harris and Stephens devise a measureusing the determinant and trace of the gradient covariance matrixR =det(G )−k (tr (G ))2,(11)where det(G )=αβand tr (G )=α+β,the parameter k is traditionally set to0.04.This produces a measure that is large when both αand βare large.Howeverwe have the problem of determining what is large.Noting that elements of theimage gradient covariance matrix have units of intensity gradient squared we cansee that the determinant,and hence the measure R will have units of intensitygradient to the fourth.This explains why the Harris operator is highly sensitiveto image contrast variations which,in turn,makes the setting of thresholdsexceedingly difficult.Some kind of sensitivity to image contrast is common to allcorner operators that are based on the local autocorrelation of image intensityvalues and/or image gradient values.Unlike image intensity gradient values phase congruency values are normal-ized quantities that have no units associated with them.If the moments arenormalized for the number of orientations considered we end up with phase con-gruency moment values that range between 0and 1.Being moments these valuescorrespond to phase congruency squared.Accordingly we can use the maximumand minimum phase congruency moments directly to establish whether we have asignificant edge and/or corner point.It should be emphasized that the minimumand maximum moments provide feature information in their own right;one doesnot have to look at their ratios.We can define a priori what a significant valueof phase congruency moment is,and this value is independent of image contrast.4ResultsThe performance of the phase congruency operator was compared to the Har-ris operator on a synthetic test image,and on a real scene containing strong314shadows.The results are shown infigures3and4.Raw Harris corner strength and raw phase congruency corner and edge strength images are displayed for comparison.It should be noted that the Harris corner strength values varied by many orders of magnitude across the image depending on contrast.To facilitate the display of the Harris corner strength image what is actually shown here is the fourth root of the image.Even after this transformation large variations are still evident.In contrast the phase congruency edge and corner strength images are minimally affected by image contrast and are readily thresholded(in this case with a value of0.4on both images)to produce a clear set of features.In applying the Harris operator to the synthetic image the standard deviation of the smoothing Gaussian was deliberately set to a large value of3pixels to illustrate the problem the operator has in localizing‘T’junctions.Notice how the detected Harris corners are displaced inwards on the left hand grey scale, note also the double response where the line intersects the circle.The phase congruency operator,on the other hand,locates‘T’junctions precisely.Changing the number offilter scales used to compute phase congruency does not affect the localization,it only affects the relative significance of features at different scales. For the real scene the standard deviation of the smoothing Gaussian for the Harris operator was1pixel.For both images phase congruency was computed using Gaborfilters over4scales(wavelengths of4,8,16and32pixels)and over 6orientations.Another important point to note is that the phase congruency edge map includes the corner map,this is unusual for an edge detector!The fact that the phase congruency corner map is a strict subset of the phase congruency edge map greatly simplifies the integration of data computed from edge and corner information.This facilitates the process of building a model of the scene from point and edge data matched over two or more views.In contrast,if the edge and corner information is computed via separate means,say the Canny and Harris operators respectively,the edge data is unlikely to include the corner data.The Gaussian smoothing that is applied to reduce the influence of noise results in the Canny edges being weakened in strength,and rounded at corner locations.MATLAB code is available for those wishing to replicate the results presented here[21].5ConclusionPhase congruency provides a contrast invariant way of identifying features within images.By combining phase congruency information over multiple orientations into a covariance matrix,and calculating the minimum and maximum moments we produce a highly localized operator that can be used to identify both edges and corners in a contrast invariant way.The contrast invariance facilitates the tracking of features over extended image sequences under varying lighting con-ditions.An additional advantage of the operator is that the phase congruency corner map is a strict subset of the phase congruency edge map.This simplifies the integration of data computed from edge and corner information.315Originalimage.Fourth root of Harris cornerstrength image(σ=3).Phase congruency edge strengthimage.Phase congruency corner strengthimage.Harris corners with threshold107(maximum corner strength was3.4x109).Phase congruency corners withthreshold0.4(maximum possiblephase congruency value is1).parison of the Harris and phase congruency operators on a test image.316Original image.Fourth root of Harris corner strength im-age (σ=1).Phase congruency edge strength image.Phase congruency corner strength image.Harris corners with threshold 108(maxi-mum corner strength was 1.25x 1010).Phase congruency corners with threshold 0.4(maximum possible phase congruencyvalue is 1).parison of the Harris and phase congruency operators on an image withstrong shadows.317References1.Hartley,R.,Zisserman,A.:Multiple View Geometry in Computer Vision.Cam-bridge University Press(2000)2.Moravec,H.P.:Robot rover visual navigation.UMI Research Press(1981)3.Harris,C.,Stephens,M.:A combined corner and edge detector.In:Proceedings,4th Alvey Vision Conference.(1988)147–151Manchester.4.Beaudet,P.R.:Rotationally invariant image operators.In:International JointConference on Artificial 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Letters6(1987)303–31313.Morrone,M.C.,Burr,D.C.:Feature detection in human vision:A phase-dependentenergy model.Proc.R.Soc.Lond.B235(1988)221–24514.Owens,R.A.,Venkatesh,S.,Ross,J.:Edge detection is a projection.PatternRecognition Letters9(1989)223–24415.Venkatesh,S.,Owens,R.:On the classification of image features.Pattern Recog-nition Letters11(1990)339–34916.Kovesi,P.D.:A dimensionless measure of edge significance.In:The AustralianPattern Recognition Society,Conference on Digital Image Computing:Techniques and Applications.(1991)281–288Melbourne.17.Kovesi,P.D.:A dimensionless measure of edge significance from phase congruencycalculated via wavelets.In:First New Zealand Conference on Image and Vision Computing.(1993)87–94Auckland.18.Kovesi,P.D.:Invariant Measures of Image Features From Phase Information.PhDthesis,The University of Western Australia(1996)19.Kovesi,P.D.:Image features from phase congruency.Videre:Journal of ComputerVision Research1(1999)1–26/e-journals/Videre/.20.Kovesi,P.D.:Phase congruency:A low-level image invariant.Psychological Re-search64(2000)136–14821.Kovesi,P.D.:MATLAB functions for computer vision and image analysis(1996-2003).au/∼pk/Research/MatlabFns/.22.Horn,B.K.P.:Robot Vision.McGraw-Hill(1986)New York.318。

2011年技术物理学院08级（激光方向）专业英语翻译重点！！！作者：邵晨宇Electromagnetic电磁的principle原则principal主要的macroscopic宏观的microscopic微观的differential微分vector矢量scalar标量permittivity介电常数photons光子oscillation振动density of states态密度dimensionality维数transverse wave横波dipole moment偶极矩diode 二极管mono-chromatic单色temporal时间的spatial空间的velocity速度wave packet波包be perpendicular to线垂直be nomal to线面垂直isotropic各向同性的anistropic各向异性的vacuum真空assumption假设semiconductor半导体nonmagnetic非磁性的considerable大量的ultraviolet紫外的diamagnetic抗磁的paramagnetic顺磁的antiparamagnetic反铁磁的ferro-magnetic铁磁的negligible可忽略的conductivity电导率intrinsic本征的inequality不等式infrared红外的weakly doped弱掺杂heavily doped重掺杂a second derivative in time对时间二阶导数vanish消失tensor张量refractive index折射率crucial主要的quantum mechanics 量子力学transition probability跃迁几率delve研究infinite无限的relevant相关的thermodynamic equilibrium热力学平衡（动态热平衡）fermions费米子bosons波色子potential barrier势垒standing wave驻波travelling wave行波degeneracy简并converge收敛diverge发散phonons声子singularity奇点（奇异值）vector potential向量式partical-wave dualism波粒二象性homogeneous均匀的elliptic椭圆的reasonable公平的合理的reflector反射器characteristic特性prerequisite必要条件quadratic二次的predominantly最重要的gaussian beams高斯光束azimuth方位角evolve推到spot size光斑尺寸radius of curvature曲率半径convention管理hyperbole双曲线hyperboloid双曲面radii半径asymptote渐近线apex顶点rigorous精确地manifestation体现表明wave diffraction波衍射aperture孔径complex beam radius复光束半径lenslike medium类透镜介质be adjacent to与之相邻confocal beam共焦光束a unity determinant单位行列式waveguide波导illustration说明induction归纳symmetric 对称的steady-state稳态be consistent with与之一致solid curves实线dashed curves虚线be identical to相同eigenvalue本征值noteworthy关注的counteract抵消reinforce加强the modal dispersion模式色散the group velocity dispersion群速度色散channel波段repetition rate重复率overlap重叠intuition直觉material dispersion材料色散information capacity信息量feed into 注入derive from由之产生semi-intuitive半直觉intermode mixing模式混合pulse duration脉宽mechanism原理dissipate损耗designate by命名为to a large extent在很大程度上etalon 标准具archetype圆形interferometer干涉计be attributed to归因于roundtrip一个往返infinite geometric progression无穷几何级数conservation of energy能量守恒free spectral range自由光谱区reflection coefficient（fraction of the intensity reflected）反射系数transmission coefficient（fraction of the intensity transmitted）透射系数optical resonator光学谐振腔unity 归一optical spectrum analyzer光谱分析grequency separations频率间隔scanning interferometer扫描干涉仪sweep移动replica复制品ambiguity不确定simultaneous同步的longitudinal laser mode纵模denominator分母finesse精细度the limiting resolution极限分辨率the width of a transmission bandpass透射带宽collimated beam线性光束noncollimated beam非线性光束transient condition瞬态情况spherical mirror 球面镜locus（loci）轨迹exponential factor指数因子radian弧度configuration不举intercept截断back and forth反复spatical mode空间模式algebra代数in practice在实际中symmetrical对称的a symmetrical conforal resonator对称共焦谐振腔criteria准则concentric同心的biperiodic lens sequence双周期透镜组序列stable solution稳态解equivalent lens等效透镜verge 边缘self-consistent自洽reference plane参考平面off-axis离轴shaded area阴影区clear area空白区perturbation扰动evolution渐变decay减弱unimodual matrix单位矩阵discrepancy相位差longitudinal mode index纵模指数resonance共振quantum electronics量子电子学phenomenon现象exploit利用spontaneous emission自发辐射initial初始的thermodynamic热力学inphase同相位的population inversion粒子数反转transparent透明的threshold阈值predominate over占主导地位的monochromaticity单色性spatical and temporal coherence时空相干性by virtue of利用directionality方向性superposition叠加pump rate泵浦速率shunt分流corona breakdown电晕击穿audacity畅通无阻versatile用途广泛的photoelectric effect光电效应quantum detector 量子探测器quantum efficiency量子效率vacuum photodiode真空光电二极管photoelectric work function光电功函数cathode阴极anode阳极formidable苛刻的恶光的irrespective无关的impinge撞击in turn依次capacitance电容photomultiplier光电信增管photoconductor光敏电阻junction photodiode结型光电二极管avalanche photodiode雪崩二极管shot noise 散粒噪声thermal noise热噪声1.In this chapter we consider Maxwell’s equations and what they reveal about the propagation of light in vacuum and in matter. We introduce the concept of photons and present their density of states.Since the density of states is a rather important property，not only for photons，we approach this quantity in a rather general way. We will use the density of states later also for other(quasi-) particles including systems of reduced dimensionality.In addition,we introduce the occupation probability of these states for various groups of particles.在本章中，我们讨论麦克斯韦方程和他们显示的有关光在真空中传播的问题。

Ornstein–Uhlenbeck process - Wikipedia,the f...Ornstein–Uhlenbeck process undefinedundefinedFrom Wikipedia, the free encyclopediaJump to: navigation, searchNot to be confused with Ornstein–Uhlenbeck operator.In mathematics, the Ornstein–Uhlenbeck process (named after LeonardOrnstein and George Eugene Uhlenbeck), is a stochastic process that, roughly speaking, describes the velocity of a massive Brownian particle under the influence of friction. The process is stationary, Gaussian, and Markov, and is the only nontrivial process that satisfies these three conditions, up to allowing linear transformations of the space and time variables.[1] Over time, the process tends to drift towards its long-term mean: such a process is called mean-reverting.The process x t satisfies the following stochastic differential equation:where θ> 0, μ and σ> 0 are parameters and W t denotes the Wiener process. Contents[hide]1 Application in physical sciences2 Application in financialmathematics3 Mathematical properties4 Solution5 Alternative representation6 Scaling limit interpretation7 Fokker–Planck equationrepresentation8 Generalizations9 See also10 References11 External links[edit] Application in physical sciencesThe Ornstein–Uhlenbeck process is a prototype of a noisy relaxation process. Consider for example a Hookean spring with spring constant k whose dynamics is highly overdamped with friction coefficient γ. In the presence of thermal fluctuations with temperature T, the length x(t) of the spring will fluctuate stochastically around the spring rest length x0; its stochastic dynamic is described by an Ornstein–Uhlenbeck process with:where σ is derived from the Stokes-Einstein equation D = σ2 / 2 = k B T / γ for theeffective diffusion constant.In physical sciences, the stochastic differential equation of an Ornstein–Uhlenbeck process is rewritten as a Langevin equationwhere ξ(t) is white Gaussian noise with .At equilibrium, the spring stores an averageenergy in accordance with the equipartition theorem.[edit] Application in financial mathematicsThe Ornstein–Uhlenbeck process is one of several approaches used to model (with modifications) interest rates, currency exchange rates, and commodity prices stochastically. The parameter μ represents the equilibrium or mean value supported by fundamentals; σ the degree of volatility around it caused by shocks, and θ the rate by which these shocks dissipate and the variable reverts towards the mean. One application of the process is a trading strategy pairs trade.[2][3][edit] Mathematical propertiesThe Ornstein–Uhlenbeck process is an example of a Gaussian process that has a bounded variance and admits a stationary probability distribution, in contrast tothe Wiener process; the difference between the two is in their "drift" term. For the Wiener process the drift term is constant, whereas for the Ornstein–Uhlenbeck process it is dependent on the current value of the process: if the current value of the process is less than the (long-term) mean, the drift will be positive; if the current valueof the process is greater than the (long-term) mean, the drift will be negative. In other words, the mean acts as an equilibrium level for the process. This gives the process its informative name, "mean-reverting." The stationary (long-term) variance is given byThe Ornstein–Uhlenbeck process is the continuous-time analogue ofthe discrete-time AR(1) process.three sample paths of different OU-processes with θ = 1, μ = 1.2, σ = 0.3:blue: initial value a = 0 (a.s.)green: initial value a = 2 (a.s.)red: initial value normally distributed so that the process has invariant measure [edit] SolutionThis equation is solved by variation of parameters. Apply Itō–Doeblin's formula to thefunctionto getIntegrating from 0 to t we getwhereupon we seeThus, the first moment is given by (assuming that x0 is a constant)We can use the Itōisometry to calculate the covariance function byThus if s < t (so that min(s, t) = s), then we have[edit] Alternative representationIt is also possible (and often convenient) to represent x t (unconditionally, i.e.as ) as a scaled time-transformed Wiener process:or conditionally (given x0) asThe time integral of this process can be used to generate noise with a 1/ƒpower spectrum.[edit] Scaling limit interpretationThe Ornstein–Uhlenbeck process can be interpreted as a scaling limit of a discrete process, in the same way that Brownian motion is a scaling limit of random walks. Consider an urn containing n blue and yellow balls. At each step a ball is chosen at random and replaced by a ball of the opposite colour. Let X n be the number of blueballs in the urn after n steps. Then converges to a Ornstein–Uhlenbeck process as n tends to infinity.[edit] Fokker–Planck equation representationThe probability density function ƒ(x, t) of the Ornstein–Uhlenbeck process satisfies the Fokker–Planck equationThe stationary solution of this equation is a Gaussian distribution with mean μ and variance σ2 / (2θ)[edit ] GeneralizationsIt is possible to extend the OU processes to processes where the background driving process is a L évy process . These processes are widely studied by OleBarndorff-Nielsen and Neil Shephard and others.In addition, processes are used in finance where the volatility increases for larger values of X . In particular, the CKLS (Chan-Karolyi-Longstaff-Sanders) process [4] with the volatility term replaced by can be solved in closed form for γ = 1 / 2 or 1, as well as for γ = 0, which corresponds to the conventional OU process.[edit ] See alsoThe Vasicek model of interest rates is an example of an Ornstein –Uhlenbeck process.Short rate model – contains more examples.This article includes a list of references , but its sources remain unclear because it has insufficient inline citations .Please help to improve this article by introducing more precise citations where appropriate . (January 2011)[edit ] References^ Doob 1942^ Advantages of Pair Trading: Market Neutrality^ An Ornstein-Uhlenbeck Framework for Pairs Trading ^ Chan et al. (1992)G.E.Uhlenbeck and L.S.Ornstein: "On the theory of Brownian Motion", Phys.Rev.36:823–41, 1930. doi:10.1103/PhysRev.36.823D.T.Gillespie: "Exact numerical simulation of the Ornstein–Uhlenbeck process and its integral", Phys.Rev.E 54:2084–91, 1996. PMID9965289doi:10.1103/PhysRevE.54.2084H. Risken: "The Fokker–Planck Equation: Method of Solution and Applications", Springer-Verlag, New York, 1989E. Bibbona, G. Panfilo and P. Tavella: "The Ornstein-Uhlenbeck process as a model of a low pass filtered white noise", Metrologia 45:S117-S126,2008 doi:10.1088/0026-1394/45/6/S17Chan. K. C., Karolyi, G. A., Longstaff, F. A. & Sanders, A. B.: "An empirical comparison of alternative models of the short-term interest rate", Journal of Finance 52:1209–27, 1992.Doob, J.L. (1942), "The Brownian movement and stochastic equations", Ann. of Math.43: 351–369.[edit] External linksA Stochastic Processes Toolkit for Risk Management, Damiano Brigo, Antonio Dalessandro, Matthias Neugebauer and Fares TrikiSimulating and Calibrating the Ornstein–Uhlenbeck process, M.A. van den Berg Calibrating the Ornstein-Uhlenbeck model, M.A. van den BergMaximum likelihood estimation of mean reverting processes, Jose Carlos Garcia FrancoRetrieved from ""。

Accuracy 准确度AGC: Automatic gain control. 自动增益控制。

Airy Hypothesis艾里假说alias:假频amplitude spectrum振幅谱antiroots反山根Bouguer anomaly布格异常Bouguer correction布格改正continuation延拓density密度density contrast密度差depth of compensation补偿深度dot chart布点量板double Bouguer correction双重布格改正downward continuation向下延拓elevation correction高程改正field continuation位场延拓figure of the earth大地水准面free-air anomaly自由空间异常free-air correction自由空间改正free oscillation of the earth:地球自由震荡gal伽geodesy:大地测量学geoid大地水准面gradiomanometer压差密度计：gradiometer梯度仪gravimeter重力仪gravitational constant万有引力常数gravity重力gravity anomaly:重力异常gravity meter比重计：gravity reduction:重力改正gravity survey重力调查gravity unit重力单位Gutenberg discontinuity:古登堡不连续面horizontal cylinder水平圆柱体isostasy:地壳均衡说：isostatic correction:均衡改正：latitude correction:纬度改正local gravity局部重力值normal gravity正常重力：Poisson's equation：泊松方程：Pratt hypothesis:普拉特假说second-derivative map:二次微商图：topographic correction地形改正torsion balance扭秤Worden:沃尔登重力仪aeromagnetic航空磁测Airborne magnetometer:航空磁力仪alternating-field demagnetization:交变场退磁：Curie point:居里点declination:磁偏角diurnal variation:日变ferrimagnetism:亚铁磁性：ferromagnetic:铁磁性的field intensity:场强fluxgate magnetometer:磁通门磁力仪gamma:伽马gauss:高斯：geomagnetic pole:地磁极geomagnetic reversal: 地磁极倒转：geomagnetic-variation method:地磁变化法：geometric sounding:电磁几何测深：inclination:倾角inductivity:感应率：local magnetic anomalies:局部磁异常magnetic basement:磁性基底：magnetic dip:磁倾角magnetic disturbance磁扰magnetic equator:地磁赤道magnetic field磁场magnetic flux:磁通量magnetic intensity:磁场强度：magnetic interpretation methods磁测资料解释法magnetic meridian:地磁子午线：magnetic moment:磁矩：magnetic permeability:磁导率：magnetic polarization:磁极化：Magnetic pole:磁极：magnetic storms:磁暴：magnetization:磁化强度magnetometer:磁力仪：nanotesla:纳特斯拉：normal magnetic field:正常磁场oersted:奥斯特paleomagnetism:古地磁学：paramagnetic: 顺磁性的：permeability:磁导率，渗透率：polarity:极性：polarization:极化度，极化，偏振：reduction to the pole化向地磁极归极法：secular variation:长期变化：tesla:特斯拉weber:韦伯apparent resistivity: 视电阻率：conductivity:电导率：current electrode:供电电极：dielectric constant:介电常数：dielectric polarization:电介质极化：dipole array:偶极排列dipole-dipole array:偶极-偶极排列：electrical profiling:电剖面法：electrical sounding电测深electrical survey电法勘探，电测井electric field:电场electric susceptibility:电极化率：electrochemical SP:电化学自然电位：electrode电极：electrode equilibrium potential:电极平衡电位：electrode polarization:电极极化：electrode potential:电极电位electrode resistance:电极电阻：electrolyte:电解质：electromagnetic method:电磁法：electromagnetic spectrum:电磁波谱：electronic电子的ELF:极低频：EM:电磁的：emu:电磁单位：equipotential-line method:等位线法equipotential surface:等位面：far-field:远场：fixed-source method:定源法：free-space field:自由空间场：galvanometer:电流计heat flow unit:热流单位HFU:热流单位：horizontal-dipole sounding水平偶极测深induced polarization:激发极化：infinite electrode:无穷远电极：NMR核磁共振permittivity:电容率：polarization ellipse:极化椭圆：pole-dipole array:单极-偶极排列：pole-pole array:单极-单极排列：Primary field: 一次场：secondary field:二次场：self-potential:自然电位self-potential method:自然电位法skin depth:趋肤深度skin effect:趋肤效应sky wave:天波：sky-wave interference:天波干扰：SP:自然电位：spontaneous potential:自然电位：transient electromagnetic method:瞬变电磁法：abnormal events:异常同相轴absorption:吸收作用：acoustic声学的，声的acoustic impedance:声阻抗，波阻抗：acoustic wave: 声波，地震波：air gun:空气枪：air wave:空气波：angle of incidence:入射角：apparent velocity:视速度：apparent wavelength:视波长：arrival:波至：arrival time波至时间：attenuation:衰减average velocity:平均速度azimuth:方位角binary gain:二进制增益blind zone: 盲区：body waves:体波：break:波跳：buried focus effect:地下焦点效应：cable:电缆：chirp:线性调频脉冲:coefficient of anisotropy:各向异性系数coherence:相干性coherent:相关的：common-depth-point:共深度点：common-depth-point stack:共深度点叠加：common-offset gather:共偏移距道集：common-offset stack:共炮检距叠加（同距叠加）：common-range gather:共炮检距道集（选排）：Common reflection point: 共反射点：compressional wave:压缩波：configuration:排列形式：converted wave:转换波critical angle:临界角critical reflection:临界反射：curved path:弯曲射线路径deconvolution:反褶积：deep seismic sounding: DSS.深地震测深：diffraction: 绕射：diffraction stack:绕射叠加：dilatational wave:膨胀波dispersion:扩散，频散display:显示：diving waves:弓形射线波：Dix formula:Dix公式DSS:深地震测深：dynamic corrections动校正：earthquake:天然地震：earthquake seismology: 天然地震测震学：elastic:弹性的：elastic constants:弹性常数：elastic impedance:弹性阻抗：elastic wave:弹性波：electrodynamic geophone:电动检波器：epicenter:震中：event:同相轴：expanding spread: 扩展排列：extended spread:纵排列fathometer:水深计：Fermat’s principle:费马原理：first arrival:初至：first break:初至波：floating datum: 浮动基准面flute槽focus:震源fold: 覆盖次数format:数据格式：Gardner method:加德纳法：gather:道集：geophone:地震检波器：geophone interval:检波距：ground roll:地滚波：group interval:组合间距：group velocity:群速度：guided wave:导波：hammer冲击锤：head wave:首波：：hodograph:矢端线：Hooke's law:虎克定律：horizontal stacking:水平叠加：Huygens principle:惠更斯原理：impedance:阻抗incident angle:入射角：interval velocity:层速度：Kirchoff diffraction equation:基尔霍夫绕射方程：law of reflection:反射定律：law of refraction:透射定律：least-time path:最短时程：Lg-wave: Lg-波：longitudinal wave:纵波：long-path multiple:全程多次反射波：long wave长波：love wave:勒夫波low-velocity layer:低速层：marker bed:标准层：migration: 偏移，运移：minimum-phase:最小相位：multiple:多次波：multiple coverage:多次覆盖：multiplex:多路传输，多倍仪multiplexed format:多路编排格式：mute:切除：NMO: Normal moveout.正常时差。