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磁共振(磁谐振耦合)无线充电技术鼻祖级文章-英文原文

Wireless Power Transfer via Strongly Coupled Magnetic ResonancesAndré Kurs,1* Aristeidis Karalis,2 Robert Moffatt,1 J. D. Joannopoulos,1 Peter Fisher,3Marin Soljačić11Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA. 2Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA 02139, USA. 3Department of Physics and Laboratory for Nuclear Science, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.*To whom correspondence should be addressed. E-mail: akurs@Using self-resonant coils in a strongly coupled regime, we experimentally demonstrate efficient non-radiative power transfer over distances of up to eight times the radius of the coils. We demonstrate the ability to transfer 60W with approximately 40% efficiency over distances in excess of two meters. We present a quantitative model describing the power transfer which matches the experimental results to within 5%. We discuss practical applicability and suggest directions for further studies. At first glance, such power transfer is reminiscent of the usual magnetic induction (10); however, note that the usual non- resonant induction is very inefficient for mid-range applications.Overview of the formalism. Efficient mid-range power transfer occurs in particular regions of the parameter space describing resonant objects strongly coupled to one another. Using coupled-mode theory to describe this physical system (11), we obtain the following set of linear equationsIn the early 20th century, before the electrical-wire grid, Nikola Tesla (1) devoted much effort towards schemes to a&m(t)=(iωm-Γm)a m(t)+∑iκmn a n(t)+F m(t)n≠m(1)transport power wirelessly. However, typical embodiments (e.g. Tesla coils) involved undesirably large electric fields. During the past decade, society has witnessed a dramatic surge of use of autonomous electronic devices (laptops, cell- phones, robots, PDAs, etc.) As a consequence, interest in wireless power has re-emerged (2–4). Radiative transfer (5), while perfectly suitable for transferring information, poses a number of difficulties for power transfer applications: the efficiency of power transfer is very low if the radiation is omnidirectional, and requires an uninterrupted line of sight and sophisticated tracking mechanisms if radiation is unidirectional. A recent theoretical paper (6) presented a detailed analysis of the feasibility of using resonant objects coupled through the tails of their non-radiative fields for mid- range energy transfer (7). Intuitively, two resonant objects of the same resonant frequency tend to exchange energy efficiently, while interacting weakly with extraneous off- resonant objects. In systems of coupled resonances (e.g. acoustic, electro-magnetic, magnetic, nuclear, etc.), there is often a general “strongly coupled” regime of operation (8). If one can operate in that regime in a given system, the energy transfer is expected to be very efficient. Mid-range power transfer implemented this way can be nearly omnidirectional and efficient, irrespective of the geometry of the surrounding space, and with low interference and losses into environmental objects (6).Considerations above apply irrespective of the physical nature of the resonances. In the current work, we focus on one particular physical embodiment: magnetic resonances (9). Magnetic resonances are particularly suitable for everyday applications because most of the common materials do not interact with magnetic fields, so interactions with environmental objects are suppressed even further. We were able to identify the strongly coupled regime in the system of two coupled magnetic resonances, by exploring non-radiative (near-field) magnetic resonant induction at MHzfrequencies. where the indices denote the different resonant objects. The variables a m(t) are defined so that the energy contained in object m is |a m(t)|2, ωm is the resonant frequency of thatisolated object, and Γm is its intrinsic decay rate (e.g. due to absorption and radiated losses), so that in this framework anuncoupled and undriven oscillator with parameters ω0 and Γ0 would evolve in time as exp(iω0t –Γ0t). The κmn= κnm are coupling coefficients between the resonant objects indicated by the subscripts, and F m(t) are driving terms.We limit the treatment to the case of two objects, denoted by source and device, such that the source (identified by the subscript S) is driven externally at a constant frequency, and the two objects have a coupling coefficient κ. Work is extracted from the device (subscript D) by means of a load (subscript W) which acts as a circuit resistance connected to the device, and has the effect of contributing an additional term ΓW to the unloaded device object's decay rate ΓD. The overall decay rate at the device is therefore Γ'D= ΓD+ ΓW. The work extracted is determined by the power dissipated in the load, i.e. 2ΓW|a D(t)|2. Maximizing the efficiency η of the transfer with respect to the loading ΓW, given Eq. 1, is equivalent to solving an impedance matching problem. One finds that the scheme works best when the source and the device are resonant, in which case the efficiency isThe efficiency is maximized when ΓW/ΓD= (1 + κ2/ΓSΓD)1/2. It is easy to show that the key to efficient energy transfer is to have κ2/ΓSΓD> 1. This is commonly referred to as the strongcoupling regime. Resonance plays an essential role in thisDS S D'' power transfer mechanism, as the efficiency is improved by approximately ω2/ΓD 2 (~106 for typical parameters) compared to the case of inductively coupled non-resonant objects. Theoretical model for self-resonant coils. Ourexperimental realization of the scheme consists of two self- resonant coils, one of which (the source coil) is coupled inductively to an oscillating circuit, while the other (the device coil) is coupled inductively to a resistive load (12) (Fig. 1). Self-resonant coils rely on the interplay between distributed inductance and distributed capacitance to achieve resonance. The coils are made of an electrically conducting wire of total length l and cross-sectional radius a wound into Given this relation and the equation of continuity, one finds that the resonant frequency is f 0 = 1/2π[(LC )1/2]. We can now treat this coil as a standard oscillator in coupled-mode theory by defining a (t ) = [(L /2)1/2]I 0(t ).We can estimate the power dissipated by noting that the sinusoidal profile of the current distribution implies that the spatial average of the peak current-squared is |I 0|2/2. For a coil with n turns and made of a material with conductivity σ, we modify the standard formulas for ohmic (R o ) and radiation (R r ) µ0ω l a helix of n turns, radius r , and height h . To the best of our knowledge, there is no exact solution for a finite helix in the literature, and even in the case of infinitely long coils, the solutions rely on assumptions that are inadequate for our R o = 2σ 4πa µ πωr 42 ωh 2 (6)system (13). We have found, however, that the simple quasi- R =0 n 2 + (7)static model described below is in good agreementr ε 12 c3π3 c(approximately 5%) with experiment.We start by observing that the current has to be zero at the ends of the coil, and make the educated guess that the resonant modes of the coil are well approximated bysinusoidal current profiles along the length of the conducting wire. We are interested in the lowest mode, so if we denote by s the parameterization coordinate along the length of the conductor, such that it runs from -l /2 to +l /2, then the time- dependent current profile has the form I 0 cos(πs /l ) exp(i ωt ). It follows from the continuity equation for charge that the linear charge density profile is of the form λ0 sin(πs /l ) exp(i ωt ), so the two halves of the coil (when sliced perpendicularly to its axis) contain charges equal in magnitude q 0 = λ0l /π but opposite in sign.As the coil is resonant, the current and charge density profiles are π/2 out of phase from each other, meaning that the real part of one is maximum when the real part of the other is zero. Equivalently, the energy contained in the coil is 0The first term in Eq. 7 is a magnetic dipole radiation term(assuming r << 2πc /ω); the second term is due to the electric dipole of the coil, and is smaller than the first term for our experimental parameters. The coupled-mode theory decay constant for the coil is therefore Γ = (R o + R r )/2L , and its quality factor is Q = ω/2Γ.We find the coupling coefficient κDS by looking at the power transferred from the source to the device coil,assuming a steady-state solution in which currents and charge densities vary in time as exp(i ωt ).P =⎰d rE (r )⋅J (r ) =-⎰d r (A&S (r )+∇φS (r ))⋅J D (r ) at certain points in time completely due to the current, and at other points, completely due to the charge. Usingelectromagnetic theory, we can define an effective inductance L and an effective capacitance C for each coil as follows:=-1⎰⎰d r d r ' µJ &S(r ')+ρS(r ') 4π |r -r |ε0≡-i ωMI S I Dr '-r|r '-r |3⋅J D (r )(8)L =µ04π |I 0 |⎰⎰d r d r 'J (r )⋅J (r ')|r -r '|where the subscript S indicates that the electric field is due to the source. We then conclude from standard coupled-mode theory arguments that κDS = κSD = κ = ωM /2[(L S L D )1/2]. When 1 1 ρ(r )ρ(r ') the distance D between the centers of the coils is much larger= C 4πε 0 |q 0 | ⎰⎰d r d r ' |r -r '|(4)than their characteristic size, κ scales with the D -3dependence characteristic of dipole-dipole coupling. Both κ and Γ are functions of the frequency, and κ/Γ and the where the spatial current J (r ) and charge density ρ(r ) are obtained respectively from the current and charge densities along the isolated coil, in conjunction with the geometry of the object. As defined, L and C have the property that the efficiency are maximized for a particular value of f , which is in the range 1-50MHz for typical parameters of interest. Thus, picking an appropriate frequency for a given coil size, as we do in this experimental demonstration, plays a major role in optimizing the power transfer.1 2Comparison with experimentallydeterminedU =2 L |I 0 |parameters. The parameters for the two identical helical coils built for the experimental validation of the power 1 2 transfer scheme are h = 20cm, a = 3mm, r = 30 cm, and n = =2C|q 0 | (5)5.25. Both coils are made of copper. The spacing between loops of the helix is not uniform, and we encapsulate theuncertainty about their uniformity by attributing a 10% (2cm) uncertainty to h . The expected resonant frequency given these22dimensions is f0 = 10.56 ± 0.3MHz, which is about 5% off from the measured resonance at 9.90MHz.The theoretical Q for the loops is estimated to be approximately 2500 (assuming σ = 5.9 × 107 m/Ω) but the measured value is Q = 950±50. We believe the discrepancy is mostly due to the effect of the layer of poorly conductingcopper oxide on the surface of the copper wire, to which the current is confined by the short skin depth (~20μm) at this frequency. We therefore use the experimentally observed Q and ΓS= ΓD= Γ = ω/2Q derived from it in all subsequent computations.We find the coupling coefficient κ experimentally by placing the two self-resonant coils (fine-tuned, by slightly adjusting h, to the same resonant frequency when isolated) a distance D apart and measuring the splitting in the frequencies of the two resonant modes. According to coupled-mode theory, this splitting should be ∆ω = 2[(κ2-Γ2)1/2]. In the present work, we focus on the case where the two coils are aligned coaxially (Fig. 2), although similar results are obtained for other orientations (figs. S1 and S2).Measurement of the efficiency. The maximum theoretical efficiency depends only on the parameter κ/[(L S L D)1/2] = κ/Γ, which is greater than 1 even for D = 2.4m (eight times the radius of the coils) (Fig. 3), thus we operate in the strongly- coupled regime throughout the entire range of distances probed.As our driving circuit, we use a standard Colpitts oscillator whose inductive element consists of a single loop of copper wire 25cm in radius(Fig. 1); this loop of wire couples inductively to the source coil and drives the entire wireless power transfer apparatus. The load consists of a calibrated light-bulb (14), and is attached to its own loop of insulated wire, which is placed in proximity of the device coil and inductively coupled to it. By varying the distance between the light-bulb and the device coil, we are able to adjust the parameter ΓW/Γ so that it matches its optimal value, given theoretically by (1 + κ2/Γ2)1/2. (The loop connected to the light-bulb adds a small reactive component to ΓW which is compensated for by slightly retuning the coil.) We measure the work extracted by adjusting the power going into the Colpitts oscillator until the light-bulb at the load glows at its full nominal brightness.We determine the efficiency of the transfer taking place between the source coil and the load by measuring the current at the mid-point of each of the self-resonant coils with a current-probe (which does not lower the Q of the coils noticeably.) This gives a measurement of the current parameters I S and I D used in our theoretical model. We then compute the power dissipated in each coil from P S,D=ΓL|I S,D|2, and obtain the efficiency from η = P W/(P S+ P D+P W). To ensure that the experimental setup is well described by a two-object coupled-mode theory model, we position the device coil such that its direct coupling to the copper loop attached to the Colpitts oscillator is zero. The experimental results are shown in Fig. 4, along with the theoretical prediction for maximum efficiency, given by Eq. 2. We are able to transfer significant amounts of power using this setup, fully lighting up a 60W light-bulb from distances more than 2m away (figs. S3 and S4).As a cross-check, we also measure the total power going from the wall power outlet into the driving circuit. The efficiency of the wireless transfer itself is hard to estimate in this way, however, as the efficiency of the Colpitts oscillator itself is not precisely known, although it is expected to be far from 100% (15). Still, the ratio of power extracted to power entering the driving circuit gives a lower bound on the efficiency. When transferring 60W to the load over a distance of 2m, for example, the power flowing into the driving circuit is 400W. This yields an overall wall-to-load efficiency of 15%, which is reasonable given the expected efficiency of roughly 40% for the wireless power transfer at that distance and the low efficiency of the Colpitts oscillator.Concluding remarks. It is essential that the coils be on resonance for the power transfer to be practical (6). We find experimentally that the power transmitted to the load drops sharply as either one of the coils is detuned from resonance. For a fractional detuning ∆f/f0 of a few times the inverse loaded Q, the induced current in the device coil is indistinguishable from noise.A detailed and quantitative analysis of the effect of external objects on our scheme is beyond the scope of the current work, but we would like to note here that the power transfer is not visibly affected as humans and various everyday objects, such as metals, wood, and electronic devices large and small, are placed between the two coils, even in cases where they completely obstruct the line of sight between source and device (figs. S3 to S5). External objects have a noticeable effect only when they are within a few centimeters from either one of the coils. While some materials (such as aluminum foil, styrofoam and humans) mostly just shift the resonant frequency, which can in principle be easily corrected with a feedback circuit, others (cardboard, wood, and PVC) lower Q when placed closer than a few centimeters from the coil, thereby lowering the efficiency of the transfer.When transferring 60W across 2m, we calculate that at the point halfway between the coils the RMS magnitude of the electric field is E rms= 210V/m, that of the magnetic field isH rms= 1A/m, and that of the Poynting vector is S rms=3.2mW/cm2 (16). These values increase closer to the coils, where the fields at source and device are comparable. For example, at distances 20cm away from the surface of the device coil, we calculate the maximum values for the fields to be E rms= 1.4kV/m, H rms= 8A/m, and S rms= 0.2W/cm2. The power radiated for these parameters is approximately 5W, which is roughly an order of magnitude higher than cell phones. In the particular geometry studied in this article, the overwhelming contribution (by one to two orders of magnitude) to the electric near-field, and hence to the near- field Poynting vector, comes from the electric dipole moment of the coils. If instead one uses capacitively-loaded single- turn loop design (6) - which has the advantage of confining nearly all of the electric field inside the capacitor - and tailors the system to operate at lower frequencies, our calculations show (17) that it should be possible to reduce the values cited above for the electric field, the Poynting vector, and the power radiated to below general safety regulations (e.g. the IEEE safety standards for general public exposure(18).) Although the two coils are currently of identical dimensions, it is possible to make the device coil small enough to fit into portable devices without decreasing the efficiency. One could, for instance, maintain the product of the characteristic sizes of the source and device coils constant, as argued in (6).We believe that the efficiency of the scheme and the power transfer distances could be appreciably improved by silver-plating the coils, which should increase their Q, or by working with more elaborate geometries for the resonant objects (19). Nevertheless, the performance characteristics of the system presented here are already at levels where they could be useful in practical applications.References and Notes1. N. Tesla, U.S. patent 1,119,732 (1914).2.J. M. Fernandez, J. A. Borras, U.S. patent 6,184,651(2001).3.A. Esser, H.-C. Skudelny, IEEE Trans. Indust. Appl. 27,872(1991).4.J. Hirai, T.-W. Kim, A. Kawamura, IEEE Trans. PowerElectron. 15, 21(2000).5.T. A. Vanderelli, J. G. Shearer, J. R. Shearer, U.S. patent7,027,311(2006).6.A. Karalis, J. D. Joannopoul os, M. Soljačić, Ann. Phys.,10.1016/j.aop.2007.04.017(2007).7.Here, by mid-range, we mean that the sizes of the deviceswhich participate in the power transfer are at least a few times smaller than the distance between the devices. For example, if the device being powered is a laptop (size ~ 50cm), while the power source (size ~ 50cm) is in thesame room as the laptop, the distance of power transfer could be within a room or a factory pavilion (size of the order of a fewmeters).8. T. Aoki, et al., Nature 443, 671 (2006).9.K. O’Brien, G. Scheible, H. Gueldner, 29th AnnualConference of the IEEE 1, 367(2003).10.L. Ka-Lai, J. W. Hay, P. G. W., U.S. patent7,042,196(2006).11.H. Haus, Waves and Fields in Optoelectronics(Prentice- Supporting Online Material/cgi/content/full/1143254/DC1SOM TextFigs. S1 to S530 March 2007; accepted 21 May 2007Published online 7 June 2007; 10.1126/science.1143254 Include this information when citing this paper.Fig. 1. Schematic of the experimental setup. A is a single copper loop of radius 25cm that is part of the driving circuit, which outputs a sine wave with frequency 9.9MHz. S and D are respectively the source and device coils referred to in the text. B is a loop of wire attached to the load (“light-bulb”). The various κ’s represent direct couplings between the objects indicated by the arrows. The angle between coil D and the loop A is adjusted to ensure that their direct coupling is zero, while coils S and D are aligned coaxially. The direct couplings between B and A and between B and S are negligible.Fig. 2. Comparison of experimental and theoretical values for κ as a function of the separation between coaxially aligned source and device coils (the wireless power transfer distance.) Fig. 3. Comparison of experimental and theoretical values for the parameter κ/Γ as a function of the wireless power transfer distance. The theory values are obtained by using the theoretical κ and the experimentally measured Γ. The shaded area represents the spread in the theoretical κ/Γ due to the 5% uncertainty in Q.Fig. 4. Comparison of experimental and theoretical efficiencies as functions of the wireless power transfer distance. The shaded area represents the theoretical prediction for maximum efficiency, and is obtained by inserting theHall, Englewood Cliffs, NJ, 1984).12.The couplings to the driving circuit and the load donot theoretical values from Fig. 3 into Eq. 2 [with Γκ2/Γ2 1/2 W /ΓD= (1 +have to be inductive. They may also be connected by awire, for example. We have chosen inductive coupling in the present work because of its easier implementation. 13.S. Sensiper, thesis, Massachusetts Institute of Technology(1951).14.We experimented with various power ratings from 5W to75W.15.W. A. Edson, Vacuum-Tube Oscillators (Wiley, NewYork,1953).16.Note that E ≠cμ0H, and that the fields are out of phaseand not necessarily perpendicular because we are not in a radiativeregime.17.See supporting material on Science Online.18.IEEE Std C95.1—2005 IEEE Standard for Safety Levelswith Respect to Human Exposure to Radio FrequencyElectromagnetic Fields, 3 kHz to 300 GHz (IEEE,Piscataway, NJ,2006).19. J. B. Pendry, Science 306, 1353 (2004).20. The authors would like to thank John Pendry forsuggesting the use of magnetic resonances, and Michael Grossman and Ivan Čelanović for technical assistance.This work was supported in part by the Materials Research Science and Engineering Center program of the National Science Foundation under Grant No. DMR 02-13282, by the U.S. Department of Energy under Grant No. DE-FG02-99ER45778, and by the Army Research Officethrough the Institute for Soldier Nanotechnologies under Contract No. DAAD-19-02-D0002.) ]. The black dots are the maximum efficiency obtained from Eq. 2 and the experimental values of κ/Γ from Fig. 3. The red dots present the directly measured efficiency,as described in thetext.。

2001年考研英语真题及解析（黄皮书）2

2001年考研英语真题及解析（黄皮书）2第一部分英语知识应运试题解析一、文章总体分析本文是一篇报道性的文章，介绍了自露丝玛莉·韦斯特案件发生后，政府、法院、媒体各方面对于付款给证人的反应。

文章第一段介绍了政府的反应：要禁止报界买断证人新闻的举动。

第二至六段介绍了以大法官埃尔温勋爵为代表的法院在这个问题上的态度。

最后一段介绍了露丝玛莉·韦斯特案件的始末。

在该案件中由于很多证人通过讲述他们的经历而从媒体获得报酬，结果导致被告数罪并罚，被判十项无期徒刑。

结论为付款给证人的做法成为一个颇有争议的问题。

二、试题具体解析1. [A] as to关于，至于[B] for instance举例[C] in particular特别地[D] such as例如[答案] D[解析]本题考核的知识点是：逻辑关系。

解答该题时，考生需要判断空格前后部分prominent cases和The trial of Rosemary West 之间的关系，前者泛指“一些著名的案件”，后者是一个具体的案件，即“对露丝玛莉·韦斯特案件的审判”，可见两者是例证关系。

因此，所填入的选项应是一个表示“例如”或“像……一样”的连接词。

首先排除as to和in particular。

for instance（或for example）可表示“举例”，但放在句中多为插入语，且后面不可直接加宾语。

如：Here in Chicago, for instance, the movement was growing by leaps and bounds.（比如在芝加哥，运动正在迅猛发展）。

选项中只有介词短语such as可以接名词做宾语，表达“例如…，象这种的”的含义。

首段第一句话的结构比较复杂，中心句为The government is to ban payments to witnesses by newspapers（政府要禁止报界付钱给证人），现在分词结构seeking to buy up... Rosemary West 做后置定语，用来修饰newspapers，意为“试图收买涉及一些要案证人的报纸”。

Singularity of the density of states in the two-dimensional Hubbard model from finite size

a r X i v :c o n d -m a t /9503139v 1 27 M a r 1995Singularity of the density of states in the two-dimensional Hubbard model from ﬁnitesize scaling of Yang-Lee zerosE.Abraham 1,I.M.Barbour 2,P.H.Cullen 1,E.G.Klepﬁsh 3,E.R.Pike 3and Sarben Sarkar 31Department of Physics,Heriot-Watt University,Edinburgh EH144AS,UK 2Department of Physics,University of Glasgow,Glasgow G128QQ,UK 3Department of Physics,King’s College London,London WC2R 2LS,UK(February 6,2008)A ﬁnite size scaling is applied to the Yang-Lee zeros of the grand canonical partition function for the 2-D Hubbard model in the complex chemical potential plane.The logarithmic scaling of the imaginary part of the zeros with the system size indicates a singular dependence of the carrier density on the chemical potential.Our analysis points to a second-order phase transition with critical exponent 12±1transition controlled by the chemical potential.As in order-disorder transitions,one would expect a symmetry breaking signalled by an order parameter.In this model,the particle-hole symmetry is broken by introducing an “external ﬁeld”which causes the particle density to be-come non-zero.Furthermore,the possibility of the free energy having a singularity at some ﬁnite value of the chemical potential is not excluded:in fact it can be a transition indicated by a divergence of the correlation length.A singularity of the free energy at ﬁnite “exter-nal ﬁeld”was found in ﬁnite-temperature lattice QCD by using theYang-Leeanalysisforthechiral phase tran-sition [14].A possible scenario for such a transition at ﬁnite chemical potential,is one in which the particle den-sity consists of two components derived from the regular and singular parts of the free energy.Since we are dealing with a grand canonical ensemble,the particle number can be calculated for a given chem-ical potential as opposed to constraining the chemical potential by a ﬁxed particle number.Hence the chem-ical potential can be thought of as an external ﬁeld for exploring the behaviour of the free energy.From the mi-croscopic point of view,the critical values of the chemical potential are associated with singularities of the density of states.Transitions related to the singularity of the density of states are known as Lifshitz transitions [15].In metals these transitions only take place at zero tem-perature,while at ﬁnite temperatures the singularities are rounded.However,for a small ratio of temperature to the deviation from the critical values of the chemical potential,the singularity can be traced even at ﬁnite tem-perature.Lifshitz transitions may result from topological changes of the Fermi surface,and may occur inside the Brillouin zone as well as on its boundaries [16].In the case of strongly correlated electron systems the shape of the Fermi surface is indeed aﬀected,which in turn may lead to an extension of the Lifshitz-type singularities into the ﬁnite-temperature regime.In relating the macroscopic quantity of the carrier den-sity to the density of quasiparticle states,we assumed the validity of a single particle excitation picture.Whether strong correlations completely distort this description is beyond the scope of the current study.However,the iden-tiﬁcation of the criticality using the Yang-Lee analysis,remains valid even if collective excitations prevail.The paper is organised as follows.In Section 2we out-line the essentials of the computational technique used to simulate the grand canonical partition function and present its expansion as a polynomial in the fugacity vari-able.In Section 3we present the Yang-Lee zeros of the partition function calculated on 62–102lattices and high-light their qualitative diﬀerences from the 42lattice.In Section 4we analyse the ﬁnite size scaling of the Yang-Lee zeros and compare it to the real-space renormaliza-tion group prediction for a second-order phase transition.Finally,in Section 5we present a summary of our resultsand an outlook for future work.II.SIMULATION ALGORITHM AND FUGACITY EXPANSION OF THE GRAND CANONICALPARTITION FUNCTIONThe model we are studying in this work is a two-dimensional single-band Hubbard HamiltonianˆH=−t <i,j>,σc †i,σc j,σ+U i n i +−12 −µi(n i ++n i −)(1)where the i,j denote the nearest neighbour spatial lat-tice sites,σis the spin degree of freedom and n iσis theelectron number operator c †iσc iσ.The constants t and U correspond to the hopping parameter and the on-site Coulomb repulsion respectively.The chemical potential µis introduced such that µ=0corresponds to half-ﬁlling,i.e.the actual chemical potential is shifted from µto µ−U412.(5)This transformation enables one to integrate out the fermionic degrees of freedom and the resulting partition function is written as an ensemble average of a product of two determinantsZ ={s i,l =±1}˜z = {s i,l =±1}det(M +)det(M −)(6)such thatM ±=I +P ± =I +n τ l =1B ±l(7)where the matrices B ±l are deﬁned asB ±l =e −(±dtV )e −dtK e dtµ(8)with V ij =δij s i,l and K ij =1if i,j are nearestneigh-boursand Kij=0otherwise.The matrices in (7)and (8)are of size (n x n y )×(n x n y ),corresponding to the spatial size of the lattice.The expectation value of a physical observable at chemical potential µ,<O >µ,is given by<O >µ=O ˜z (µ){s i,l =±1}˜z (µ,{s i,l })(9)where the sum over the conﬁgurations of Ising ﬁelds isdenoted by an integral.Since ˜z (µ)is not positive deﬁnite for Re(µ)=0we weight the ensemble of conﬁgurations by the absolute value of ˜z (µ)at some µ=µ0.Thus<O >µ= O ˜z (µ)˜z (µ)|˜z (µ0)|µ0|˜z (µ0)|µ0(10)The partition function Z (µ)is given byZ (µ)∝˜z (µ)N c˜z (µ0)|˜z (µ0)|×e µβ+e −µβ−e µ0β−e −µ0βn (16)When the average sign is near unity,it is safe to as-sume that the lattice conﬁgurations reﬂect accurately thequantum degrees of freedom.Following Blankenbecler et al.[1]the diagonal matrix elements of the equal-time Green’s operator G ±=(I +P ±)−1accurately describe the fermion density on a given conﬁguration.In this regime the adiabatic approximation,which is the basis of the ﬁnite-temperature algorithm,is valid.The situa-tion diﬀers strongly when the average sign becomes small.We are in this case sampling positive and negative ˜z (µ0)conﬁgurations with almost equal probability since the ac-ceptance criterion depends only on the absolute value of ˜z (µ0).In the simulations of the HSﬁelds the situation is dif-ferent from the case of fermions interacting with dynam-ical bosonﬁelds presented in Ref.[1].The auxilary HS ﬁelds do not have a kinetic energy term in the bosonic action which would suppress their rapidﬂuctuations and hence recover the adiabaticity.From the previous sim-ulations on a42lattice[3]we know that avoiding the sign problem,by updating at half-ﬁlling,results in high uncontrolledﬂuctuations of the expansion coeﬃcients for the statistical weight,thus severely limiting the range of validity of the expansion.It is therefore important to obtain the partition function for the widest range ofµ0 and observe the persistence of the hierarchy of the ex-pansion coeﬃcients of Z.An error analysis is required to establish the Gaussian distribution of the simulated observables.We present in the following section results of the bootstrap analysis[17]performed on our data for several values ofµ0.III.TEMPERATURE AND LATTICE-SIZEDEPENDENCE OF THE YANG-LEE ZEROS The simulations were performed in the intermediate on-site repulsion regime U=4t forβ=5,6,7.5on lat-tices42,62,82and forβ=5,6on a102lattice.The ex-pansion coeﬃcients given by eqn.(14)are obtained with relatively small errors and exhibit clear Gaussian distri-bution over the ensemble.This behaviour was recorded for a wide range ofµ0which makes our simulations reli-able in spite of the sign problem.In Fig.1(a-c)we present typical distributions of theﬁrst coeﬃcients correspond-ing to n=1−7in eqn.(14)(normalized with respect to the zeroth power coeﬃcient)forβ=5−7.5for diﬀer-entµ0.The coeﬃcients are obtained using the bootstrap method on over10000conﬁgurations forβ=5increasing to over30000forβ=7.5.In spite of diﬀerent values of the average sign in these simulations,the coeﬃcients of the expansion(16)indicate good correspondence between coeﬃcients obtained with diﬀerent values of the update chemical potentialµ0:the normalized coeﬃcients taken from diﬀerentµ0values and equal power of the expansion variable correspond within the statistical error estimated using the bootstrap analysis.(To compare these coeﬃ-cients we had to shift the expansion by2coshµ0β.)We also performed a bootstrap analysis of the zeros in theµplane which shows clear Gaussian distribution of their real and imaginary parts(see Fig.2).In addition, we observe overlapping results(i.e.same zeros)obtained with diﬀerent values ofµ0.The distribution of Yang-Lee zeros in the complexµ-plane is presented in Fig.3(a-c)for the zeros nearest to the real axis.We observe a gradual decrease of the imaginary part as the lattice size increases.The quantitative analysis of this behaviour is discussed in the next section.The critical domain can be identiﬁed by the behaviour of the density of Yang-Lee zeros’in the positive half-plane of the fugacity.We expect toﬁnd that this density is tem-perature and volume dependent as the system approaches the phase transition.If the temperature is much higher than the critical temperature,the zeros stay far from the positive real axis as it happens in the high-temperature limit of the one-dimensional Ising model(T c=0)in which,forβ=0,the points of singularity of the free energy lie at fugacity value−1.As the temperature de-creases we expect the zeros to migrate to the positive half-plane with their density,in this region,increasing with the system’s volume.Figures4(a-c)show the number N(θ)of zeros in the sector(0,θ)as a function of the angleθ.The zeros shown in theseﬁgures are those presented in Fig.3(a-c)in the chemical potential plane with other zeros lying further from the positive real half-axis added in.We included only the zeros having absolute value less than one which we are able to do because if y i is a zero in the fugacity plane,so is1/y i.The errors are shown where they were estimated using the bootstrap analysis(see Fig.2).Forβ=5,even for the largest simulated lattice102, all the zeros are in the negative half-plane.We notice a gradual movement of the pattern of the zeros towards the smallerθvalues with an increasing density of the zeros nearθ=πIV.FINITE SIZE SCALING AND THESINGULARITY OF THE DENSITY OF STATESAs a starting point for theﬁnite size analysis of theYang-Lee singularities we recall the scaling hypothesis forthe partition function singularities in the critical domain[11].Following this hypothesis,for a change of scale ofthe linear dimension LLL→−1),˜µ=(1−µT cδ(23)Following the real-space renormalization group treatmentof Ref.[11]and assuming that the change of scaleλisa continuous parameter,the exponentαθis related tothe critical exponentνof the correlation length asαθ=1ξ(θλ)=ξ(θ)αθwe obtain ξ∼|θ|−1|θ|ναµ)(26)where θλhas been scaled to ±1and ˜µλexpressed in terms of ˜µand θ.Diﬀerentiating this equation with respect to ˜µyields:<n >sing =(−θ)ν(d −αµ)∂F sing (X,Y )ν(d −αµ)singinto the ar-gument Y =˜µαµ(28)which deﬁnes the critical exponent 1αµin terms of the scaling exponent αµof the Yang-Lee zeros.Fig.5presents the scaling of the imaginary part of the µzeros for diﬀerent values of the temperature.The linear regression slope of the logarithm of the imaginary part of the zeros plotted against the logarithm of the inverse lin-ear dimension of the simulation volume,increases when the temperature decreases from β=5to β=6.The re-sults of β=7.5correspond to αµ=1.3within the errors of the zeros as the simulation volume increases from 62to 82.As it is seen from Fig.3,we can trace zeros with similar real part (Re (µ1)≈0.7which is also consistentwith the critical value of the chemical potential given in Ref.[22])as the lattice size increases,which allows us to examine only the scaling of the imaginary part.Table 1presents the values of αµand 1αµδ0.5±0.0560.5±0.21.3±0.3∂µ,as a function ofthe chemical potential on an 82lattice.The location of the peaks of the susceptibility,rounded by the ﬁnite size eﬀects,is in good agreement with the distribution of the real part of the Yang-Lee zeros in the complex µ-plane (see Fig.3)which is particularly evident in the β=7.5simulations (Fig.4(c)).The contribution of each zero to the susceptibility can be singled out by expressing the free energy as:F =2n x n yi =1(y −y i )(29)where y is the fugacity variable and y i is the correspond-ing zero of the partition function.The dotted lines on these plots correspond to the contribution of the nearby zeros while the full polynomial contribution is given by the solid lines.We see that the developing singularities are indeed governed by the zeros closest to the real axis.The sharpening of the singularity as the temperature de-creases is also in accordance with the dependence of the distribution of the zeros on the temperature.The singularities of the free energy and its derivative with respect to the chemical potential,can be related to the quasiparticle density of states.To do this we assume that single particle excitations accurately represent the spectrum of the system.The relationship between the average particle density and the density of states ρ(ω)is given by<n >=∞dω1dµ=ρsing (µ)∝1δ−1(32)and hence the rate of divergence of the density of states.As in the case of Lifshitz transitions the singularity of the particle number is rounded at ﬁnite temperature.However,for suﬃciently low temperatures,the singular-ity of the density of states remains manifest in the free energy,the average particle density,and particle suscep-tibility [15].The regular part of the density of states does not contribute to the criticality,so we can concentrate on the singular part only.Consider a behaviour of the typedensity of states diverging as the−1ρsing(ω)∝(ω−µc)1δ.(33)with the valueδfor the particle number governed by thedivergence of the density of states(at low temperatures)in spite of theﬁnite-temperature rounding of the singu-larity itself.This rounding of the singularity is indeedreﬂected in the diﬀerence between the values ofαµatβ=5andβ=6.V.DISCUSSION AND OUTLOOKWe note that in ourﬁnite size scaling analysis we donot include logarithmic corrections.In particular,thesecorrections may prove signiﬁcant when taking into ac-count the fact that we are dealing with a two-dimensionalsystem in which the pattern of the phase transition islikely to be of Kosterlitz-Thouless type[23].The loga-rithmic corrections to the scaling laws have been provenessential in a recent work of Kenna and Irving[24].In-clusion of these corrections would allow us to obtain thecritical exponents with higher accuracy.However,suchanalysis would require simulations on even larger lattices.The linearﬁts for the logarithmic scaling and the criti-cal exponents obtained,are to be viewed as approximatevalues reﬂecting the general behaviour of the Yang-Leezeros as the temperature and lattice size are varied.Al-though the bootstrap analysis provided us with accurateestimates of the statistical error on the values of the ex-pansion coeﬃcients and the Yang-Lee zeros,the smallnumber of zeros obtained with suﬃcient accuracy doesnot allow us to claim higher precision for the critical ex-ponents on the basis of more elaborateﬁttings of the scal-ing behaviour.Theﬁnite-size eﬀects may still be signiﬁ-cant,especially as the simulation temperature decreases,thus aﬀecting the scaling of the Yang-Lee zeros with thesystem rger lattice simulations will therefore berequired for an accurate evaluation of the critical expo-nent for the particle density and the density of states.Nevertheless,the onset of a singularity atﬁnite temper-ature,and its persistence as the lattice size increases,areevident.The estimate of the critical exponent for the diver-gence rate of the density of states of the quasiparticleexcitation spectrum is particularly relevant to the highT c superconductivity scenario based on the van Hove sin-gularities[25],[26],[27].It is emphasized in Ref.[25]thatthe logarithmic singularity of a two-dimensional electrongas can,due to electronic correlations,turn into a power-law divergence resulting in an extended saddle point atthe lattice momenta(π,0)and(0,π).In the case of the14.I.M.Barbour,A.J.Bell and E.G.Klepﬁsh,Nucl.Phys.B389,285(1993).15.I.M.Lifshitz,JETP38,1569(1960).16.A.A.Abrikosov,Fundamentals of the Theory ofMetals North-Holland(1988).17.P.Hall,The Bootstrap and Edgeworth expansion,Springer(1992).18.S.R.White et al.,Phys.Rev.B40,506(1989).19.J.E.Hirsch,Phys.Rev.B28,4059(1983).20.M.Suzuki,Prog.Theor.Phys.56,1454(1976).21.A.Moreo, D.Scalapino and E.Dagotto,Phys.Rev.B43,11442(1991).22.N.Furukawa and M.Imada,J.Phys.Soc.Japan61,3331(1992).23.J.Kosterlitz and D.Thouless,J.Phys.C6,1181(1973);J.Kosterlitz,J.Phys.C7,1046(1974).24.R.Kenna and A.C.Irving,unpublished.25.K.Gofron et al.,Phys.Rev.Lett.73,3302(1994).26.D.M.Newns,P.C.Pattnaik and C.C.Tsuei,Phys.Rev.B43,3075(1991);D.M.Newns et al.,Phys.Rev.Lett.24,1264(1992);D.M.Newns et al.,Phys.Rev.Lett.73,1264(1994).27.E.Dagotto,A.Nazarenko and A.Moreo,Phys.Rev.Lett.74,310(1995).28.A.A.Abrikosov,J.C.Campuzano and K.Gofron,Physica(Amsterdam)214C,73(1993).29.D.S.Dessau et al.,Phys.Rev.Lett.71,2781(1993);D.M.King et al.,Phys.Rev.Lett.73,3298(1994);P.Aebi et al.,Phys.Rev.Lett.72,2757(1994).30.E.Dagotto, A.Nazarenko and M.Boninsegni,Phys.Rev.Lett.73,728(1994).31.N.Bulut,D.J.Scalapino and S.R.White,Phys.Rev.Lett.73,748(1994).32.S.R.White,Phys.Rev.B44,4670(1991);M.Veki´c and S.R.White,Phys.Rev.B47,1160 (1993).33.C.E.Creﬃeld,E.G.Klepﬁsh,E.R.Pike and SarbenSarkar,unpublished.Figure CaptionsFigure1Bootstrap distribution of normalized coeﬃcients for ex-pansion(14)at diﬀerent update chemical potentialµ0for an82lattice.The corresponding power of expansion is indicated in the topﬁgure.(a)β=5,(b)β=6,(c)β=7.5.Figure2Bootstrap distributions for the Yang-Lee zeros in the complexµplane closest to the real axis.(a)102lat-tice atβ=5,(b)102lattice atβ=6,(c)82lattice at β=7.5.Figure3Yang-Lee zeros in the complexµplane closest to the real axis.(a)β=5,(b)β=6,(c)β=7.5.The correspond-ing lattice size is shown in the top right-hand corner. Figure4Angular distribution of the Yang-Lee zeros in the com-plex fugacity plane Error bars are drawn where esti-mated.(a)β=5,(b)β=6,(c)β=7.5.Figure5Scaling of the imaginary part ofµ1(Re(µ1)≈=0.7)as a function of lattice size.αm u indicates the theﬁt of the logarithmic scaling.Figure6Electronic susceptibility as a function of chemical poten-tial for an82lattice.The solid line represents the con-tribution of all the2n x n y zeros and the dotted line the contribution of the six zeros nearest to the real-µaxis.(a)β=5,(b)β=6,(c)β=7.5.。

article

Journal of the Korean Physical Society,Vol.35,No.1,July1999,pp.16∼20CsI(Tl)Scintillator Telescope Measurement of Charged Particles Extracted from the KCCH MC-50CyclotronS.H.Park∗,C.Lee,H.Park,J.H.Kim,J.H.Ha,E.Seo,J.S.Kim,H.Bhang and J.C.KimDepartment of Physics,Seoul National University,Seoul151-742Y.D.KimDepartment of Physics,SeJong University,Seoul143-747J.H.Lee,Y.K.Kwon and C.S.LeeDepartment of Physics,Chung-Ang University,Seoul156-756J.H.ChangKorea Atomic Energy Research Institute,Taejon305-600H.Y.Lee and S.A.ShinDepartment of Physics,Ewha Womans University,Seoul120-750J.S.Chai and Y.S.KimCyclotron Application Laboratory,Korea Cancer Center Hospital,Korea Atomic Energy Research Institute,Seoul139-240K.H.YooDaebul University,Young-Am,JeonNam526-890(Received7September1998)A telescope was made with a150-µm-thick silicon surface barrier detector(∆E)and a cylindricalCsI(Tl)scintillator(E).A50-MeV proton beam from the MC-50cyclotron was incident on a nat Agfoil,and outgoing particles were measured with the telescope.Particle identiﬁcation was performedwith the telescope,and particles were identiﬁed to be protons,deuterons,and tritons with the helpof the range-energy relation.The diﬀerential cross sections for the nat Ag(p,p)reaction leading to theground state of nat Ag were measured and compared with the result of an optical model calculation.This result showed some possibility for charged particle experiments using the cyclotron at theKorea Cancer Center Hospital.I.INTRODUCTIONMany eﬀorts have been attempted to do nuclear exper-iments using the azimuthally varyingﬁeld-type(AVF) MC-50cyclotron at the KCCH(Korea Cancer Center Hospital),including measurements of the characteristics of the beam[1],in-beamγ-ray spectroscopy[2],the de-tection of neutrons[3].Charged-particle experiments us-ing this facility,however,have been limited because of ∗E-mail:psh@phya.snu.ac.kr,Telefax:02-871-1085the sensitivity of the energy measurement to the beam-energy resolution.Since the cyclotron was designed for medical treatment instead of science experiment,the beam optics and the emittance are not high enough to carry out physics experiment.This results in certain limits on the experimental energy and the position reso-lution.Detecting charged particles in air leads to addi-tional uncertainties generated by the energy losses and the stragglings.Given the limited conditions,systematic studies of the optical parameters[4]and studies of the spectra of sec-ondary particles[5]can be carried out at the the MC-50 -16-CsI(Tl)Scintillator Telescope Measurement of ···–S.H.PARK et al.-17-Fig.1.Sytematic diagram of the detector setup.cyclotron in KCCH.We attempted to measure the an-gular distributions of the scatterings of the beam oﬀa heavy target for the ﬁrst time in Korea by using the KCCH MC-50cyclotron,so as to enhance the feasibility of the facility for nuclear physics experiments.In charged-particle spectroscopy,the telescope method has usually been applied to identify the detected par-ticle.The energy loss per unit distance traveled by a non-relativistic particle of charge z and mass m can be expressed by the Bethe formula [6]asdE =C 1mz 2ln C 2Ewhere C 1and C 2are constants,and E is the particle energy.From the relation of the signals from the ∆E and the E detectors,it is possible to determine the mass and the charge of the scattered particle.A thin silicon detector can be used as a possible ∆E detector because of its small stopping power and because of its resolution high enough to resolve the dE diﬀerence for the given particle energy.An inorganic scintillator be used as a possible E de-tector.NaI(Tl)coupled to a photomultiplier tube has wide application among inorganic scintillators in nuclear physics,especially in γ-ray detection.NaI(Tl),though,has some drawbacks as a particle detector.It usually tends to be bulky and is sensitive to a magneticﬁeld.Fig.2.Drawing of the MC-50cyclotron facility at the Ko-rea Cancer Center Hospital.The experiment was performed on the zero-degreeline.Fig.3.Block diagram of the electronics used in this exper-iment.(TFA:Timing Fast Ampliﬁer,CFD:Constant Fraction Discriminator,GDG:Gate Delay Generator,ADC:Analog-to-Digital Converter,DAQ Pro:Data Acquisition Program)Moreover,the crystal is hygroscopic and should be en-capsulated.This lead to a loss of energy resolution and to a higher energy threshold.CsI(Tl)has some superior properties compared to NaI(Tl).The crystal has good mechanical and thermal stability so that it is easy to fab-ricate the crystal into various shapes.The crystal is less hygroscopic so that sealing it like NaI(Tl)is not necces-sary.The scintillator can be used without high-quality polishing.Moreover,the longer wavelength of the scin-tillation emission (570nm)is outside the peak response of most photomultipliers,and that can be overcome by using a photodiode readout.A photodiode is verycom-Fig.4.Two-dimensional plot of ∆E versus E of scattered particles.-18-Journal of the Korean Physical Society,Vol.35,No.1,July1999Fig. 5.Gaussianﬁttings for the energy spectrum of the protons.pact and is insensitive to a magneticﬁeld without using a higher voltage.The energy resolution of a CsI(Tl)scin-tillator with a PIN diode readout has been reported to be1%for50-MeV protons[7].In this work,the diﬀerential cross-sections of the pro-tons scattering oﬀa natural silver target(nat Ag(p,p)) were measured using a telescope made of a silicon sur-face barrier(SSB)detector and a CsI(Tl)scintillator. The results were compared with optical-model calcula-tions.The performance of the CsI(Tl)scintillator was investigated experimentally.Also,the extended usage of the KCCH MC-50cyclotron was carefully examined in the current study.II.EXPERIMENTWe fabricated a CsI(Tl)scintillator with a diameter of25mm,and a length of30mm,which was compa-rable to the range of about100-MeV protons.The pin silicon photodiode,Hamamatsu S2744,was coupled to the rearﬂat surface of the scintillator because the spec-tral response of the photodiode was better suited to the use of a CsI(Tl)scintillator.The sensitive area of the PIN diode had a rectangular shape of20.0mm by10.0Fig. 6.Deuteron energy spectra at diﬀerent angles:(a) 30◦,(b)40◦,(c)50◦,(d)60◦,(e)70◦,and(f)80◦.mm.The PIN diode was directly coupled to the scintil-lator.All surfaces of the scintillator were sanded,andboth the front and the rear surfaces of the scintillatorwere polished.The front was wrapped with1-µm-thickaluminized mylar,and the side of the scintillator wascovered with teﬂon tape.The scintillator and the PINdiode were coupled in the back and wrapped by usingblack tape for light tightness.In order to check the re-sponse of the detector toγ-rays,the energy spectra of 60Co and132Csγ-sources were taken and compared with the NaI(Tl)scintillator spectra.The FWHM at the1.33-MeV peak from60Co was85keV using NaI(Tl)scintil-lator,and it was93keV with the CsI(Tl)scintillator.A particle detector telescope was made by using a thinsilicon surface barrier detector(∆E)and a CsI(Tl)scin-tillator(E).The∆E detector used was an ORTEC TB-015-050-150SSB detector with full depletion length of150µm.High voltages of+30V and+150V were ap-plied to the PIN diode and the∆E detector,respectively.The silicon detector and the CsI(Tl)scintillator were in-serted into a cylindrically shaped aluminum mount.Acopper collimator with a diameter of5mm was put inthe front of the silicon detector.A systematic diagramof the telescope is shown in Fig.1.Table.1.The optical potential parameters used for the optical-model-calculation.V r o a4W D r o a V s r s a s (MeV)(fm)(fm)(MeV)(fm)(fm)(MeV)(fm)(fm) Previous[10]54.3 1.210.6837.2 1.240.71 6.0 1.250.68CsI(Tl)Scintillator Telescope Measurement of···–S.H.PARK et al.-19-Fig.7.Angular distribution of nat Ag(p,p)leading to the ground state of nat Ag.The curve is the result of an optical-model calculation.The experiment was carried out using the AVF MC-50 cyclotron,and its schematic beam transport features are shown in Fig.2.The target chamber was placed at the zero-degree beam line in the gantry room.The cham-ber was made of stainless steel.It had a window made of0.0762-mm-thick mylar on the left side of the cham-ber.The particles penetrated the mylar foil and were detected outside the chamber.A0.013-mm-thick natu-ral Ag target was placed in the center of the chamber. The electronics diagram for∆E−E coincidence is displayed in Fig.3.The pre-ampliﬁer,which was con-nected to the pin diode of the CsI(Tl)scintillator,had been specially designed for this purpose.The main gate for the ADC was made by the coincidence of the timing signals of the PIN diode for the CsI(Tl)scintillator and the pre-ampliﬁer for the∆E detector.The signals from the CsI(Tl)scintillator induced byγ-rays were rejected by the coincidence.The data from the analog-to-digital converter(ADC)were processed through the computer automated measurement and control(CAMAC)system, and the data acquisition was done using the KODAQ data sorting code[8].The count rate in our data acquisition was maintained at a rate of500counts per second to avoid energy spread-out in the CsI(Tl)scintillator caused by the highγ-ray background activity.Data were taken at angles from35◦to80◦in increments of5◦.A plastic scintillator was set at45◦with respect to the beam direction to monitor the condition of the incident beam at each detection angle. The anode signal from the plastic scintillator was atten-uated to one tenth and changed to a logic signal through the octal discriminator.The discrimination levels were set to be200mV and transferred to the TTL signal by passing through the gate delay generator(GDL),and the number of signal counts was measured by the counter.III.EXPERIMENTAL RESULTS ANDOPTICAL MODEL CALCULATIONProton,deuteron,and triton events were well resolved in a2-dimensional plot of∆E and E,as shown in Fig.4.The proton and the deuteron gates are drawn in this ﬁgure.The nat Ag foil was reported to consist of51.8%107Ag, and48.2%109Ag[9].The ground states and low-lying excited states(0.311MeV and0.415MeV states in109Ag [10];0.423MeV,and0.324MeV states in107Ag[11]) appeared to be too close to be resolved with the CsI(Tl) scintillator and photodiode,for which the FWHM of the detected signal for35-MeV proton was assumed to be 350keV[7].Hence,an additional Gaussian relating the mentioned excited states and to the main ground-state structure was used inﬁtting the ground-state peak of the current data for each angle,and the elastic-scattering cross section of the protons oﬀthe natural Ag target was extracted based on theﬁt.Theﬁts are shown in Fig.5. The FWHM from the elastic peak of the nat Ag(p,p) reaction was observed to be620keV.Considering the beam energy resolution,which was estimated to be500 keV for the35-MeV proton beam[3],we think that the detector resolution itself(Γ=370keV)appears to be acceptable for charged-particle experiments.Anderson et al.[12]investigated the level structure of 106Ag through the107Ag(p,d)reaction.They suggested low-lying excited106Ag states were populated so closely that they could hardly be resolved in the deuteron en-ergy spectrum in the current work,as is shown in Fig.6. We also found that the ratio of continuum events to the elastic scatterings increased as the detection angle was moved backward.Theoretical calculations were done for the diﬀerential cross-section for the elastic scatterings.Optical-model calculations were carried out using the DWUCK4code [13].The optical-model potential used in the calculations wasU(r)=−Ve+1+4iW Dddx1e+1+ ¯h mπc2V s1rddr1e s+1(L·σ)+V c,where x x=r−r xa x,and V c is the Coulomb potential due to a uniformly charged sphere of radius1.25A13fm.The optical model parameters extracted by Ford et al.[10,11] were used as references.Allowing the parameters V and W D to vary in order to search for the appropriate param-eters giving the bestﬁt,we could use an optical-model calculation to regenerate angular distribution matching-20-Journal of the Korean Physical Society,Vol.35,No.1,July1999in optimized way to the experimental results.The elastic scattering oﬀthe107Ag and the109Ag nuclei were calcu-lated independently.The sum of the elastic cross sections oﬀthe Ag isotopes for each angle was then extracted by weighting with their respective natural abundunce frac-tion.The optical potential parameters extracted from the current work are listed in Table1.We normalized the measured diﬀerential cross-section by using the one calculated with the optical model.Fig.7displays the agreement of the experimental angular distribution with the theoretical calculation in elastic scattering.IV.SUMMARYWe studied the performance of a∆E−E Si-CsI(Tl) telescope for charged-particle detection by using the nat Ag(p,p)reaction.A CsI(Tl)scintillator with a PINdiode connection was used for the E detector.The CsI(Tl)scintillator was easily machined,and it was less hygroscopic.Since the ranges of charged particles through CsI(Tl)crystal are shorter than with other scin-tillators,it was possible to make a compact telescope. Protons,deuterons,and tritons were clearly identiﬁed by using this telescope.The detected energy resolution of CsI(Tl)was revealed to be good enough to be used for charged particle experiments.The angular distribution of the proton elastic-scattering by the nat Ag(p,p)reaction was measured by using this telescope,and optical-model calculations suc-cessfully regenerated the distribution with optical pa-rameters which had been newly searched for in the cur-rent experiment.The results also provide encouragement to keep on performing extensive physics reaction research using the KCCH AVF MC-50accelerator facility.ACKNOWLEDGMENTSThis work was supported by the Basic Science Re-search Institute Program,Ministry of Education,Korea 1997(Project No.BSRI-97-2417),and by the Nuclear R &D Program,Ministry of Science and Technology.REFERENCES[1]C.S.Lee,Y.S.Kim,J.H.Lee,J.C.Kim,J.Ha,J.H.Park,I.C.Kim,S.H.Park,Z.Jang,Y.B.Lee,Y.K.Kim,J.S.Chai and Y.S.Kim,J.Korean Phys.Soc.32, 20(1998).[2]J.H.Ha,Ph.D.Dissertation,Seoul National University,1998,unpublished.[3]J.H.Kim,H.Bhang,J.H.Ha,J.C.Kim,M.J.Kim,Y.D.Kim,H.Park,J.S.Chai,Y.S.Kim,H.Y.Lee,S.A.Shin,J.Y.Huh,C.S.Lee and J.H.Lee,J.KoreanPhys.Soc.32,462(1998).[4]E.Fabrici,S.Micheletti,M.Pignanelli and F.G.Resmini,Phys.Rev.C21,844(1980).[5]F.E.Bertrand and R.W.Peelle,Phys.Rev.C8,1045(1973).[6]Glenn F.Knoll,Radiation Detection and Measurement(Wiley,New York,1989),Chap.11.[7]W.G.Gong,Y. D.Kim,G.Poggi,Z.Chen, C.K.Gelbke,W.G.Lynch,M.R.Maier,T.Murakami,M.B.Tsang and H.M.Xu,Nucl.Inst.Meth.A268,190(1988).[8]Y.D.Kim,H.Bhang,O.Hashimoto,K.Maeda,K.Omata,H.Outa,H.Park and M.Youn,Nucl.Inst.Meth.A372,431(1996),and references therein.[9]K.S.Krane,Introductory Nuclear Physics(Wiley,NewYork,1988).[10]J.L.C.Ford,Jr.,Cheuk-Yin Wong,Taro Tamura,R.L.Robinson and P.H.Stelson,Phys.Rev.158,1194 (1967).[11]J.L.C.Ford,Jr.,R.L.Robinson,P.H.Stelson,TaroTamura and Cheuk-Yin Wong,Nucl.Phys.A142,525 (1970).[12]R.E.Anderson,R.L.Bunting,J.D.Burch,S.R.Chinn,J.J.Kraushaar,R.J.Peterson,D.E.Prull,B.W.Ridley and R.A.Ristinen,Nucl.Phys.A242,93(1975). [13]P.D.Kunz and E.Rost,unpublished.。

简谐振动运动方程的推导

v2+
1 2
kx2 =
E( v
表示物体的振
动速度, x 表示物体离开平衡位置的位移) 变形
图
( 2) 式两边平方有: 2kEx2= Cos2U, ,( 3) ( 2) 式微分 dx= 2kESinUdU,,( 4) ( 3) ( 4) 两式代入( 1) 式后化简:
X 收稿日期: 2000- 11- 05 作者简介: 蔡群( 1963- ) , 女, 浙江温州人, 副教授, 主要从事物理教学及研究
k m
,
可得二阶常系数线性齐次微分方程
dd2tx2 + X2x= 0 , ,( 1)
方程( 1) 的特征方程为: r2 + X2 = 0 它有两
个复根 r= ? iX
方程( 1) 式的两个特解为
x1= e+ iXt , x2= = e- iXt
其通解为: x = C1e+ iXt + C2e- iXt , ,( 2)
第 3卷
=
A21+ A22(
A1 A 21+
A22 CosXt
+ A2 SinXt) , ,( 3) A21+ A22
( A1= C1+ C2, A2= C1- C2 为常数)
令 A=
A 21+ A22 CosU0=
A1 A21+ A22
SinU0
=
A2 A21+ A22
代入( 3) 式得
x= A( CosU0CosXt+ SinU0SinXt ) 根据三角函数和角公式, 同样得到弹簧振
( C1, C2 为常数)
根据欧拉公式
e(A? iB) x= ( CosBx ? iSinBx) eAx

英语申请信函写作

考研英语申请信写作介绍及经典范文当一个人想得到某种机会或某些东西，如申请得到奖学金、求学、申请出国签证等，往往通过申请信来请求。

申请信如何分段，没有严格的规定，其内容一般应包括以下三个部分：申请的具体内容和缘由；自己的情况和条件；提出要求，如回信、面试等等。

对于不同的申请内容，在介绍自己情况的时候也要有不同的侧重。

例如在求学信中，应比较侧重介绍自己已有的学位及专业情况；在申请留学经济资助的信中，应着重介绍自己的学业及学术水平，因为国外很多学校颁发奖学金是以此为标准的。

写申请信应注意：第一，语气要诚挚友好千万不要表现出强求的意思；第二，对于申请的内容和原因一定要写得非常清楚；第三，尽管不能表现出强求的意思，但是期望得到的心情一定要表达出来。

以下是两封申请信，第一封是求学信，另一封是申请留学资助的，第一封信用的是齐头式，第二封信用的是缩进式，信头和信内地址都已省略。

［Directions］: You are a student of Huabei University,. Write an application to get a scholarship for your graduate study in another university in America. You should write about 100 words. Do not sign your own name at the end of your letter,using “Li Ming” instead. You do not need to write the address.［参考范文之一］Dear Sir or Madam:I am writing to apply for admission to your university to pursue my M.S. degree. I have read the annual prospectus issued by your university and found that it has the best graduate program of chemistry. I am greatly interested in the program.I graduated in 2004 from Huabei University, majoring in Chemistry and holding a B. S. degree. At university, I took many fundamental courses in Chemistry and my English is excellent as I had served as the head of English Association for two years. Since then I have been teaching Chemistry in Beijing Normal University. Through my teaching experience, I have not only deepened my understanding in this field, but mastered many complicated research skills as well.Two of my former professors and the present dean of our department have kindly written letters of recommendation for me, as enclosed with this letter.Thank you very much. I look forward to hearing from you soon. Sincerely yours,Li Ming［参考范文之二］Dear Sir or Madam:I wish to apply for admission to your department as a graduate student.I am writing to ask whether it will be possible for you to grant me a fullscholarship, considering my academic record and the fact that I have no relatives or friends in America who can act as my sponsor.I completed a four-year course in chemistry at Beijing University last June. During my four years in the university, I have passed all the required courses of study with satisfactory marks. With Chemistry as my major, I minored in Physics and Mathematics. Enclosed herewith is my transcript from the department concerned.My English is very good. I have been learning English since early childhood with the help of my father who is a professor of English in Fudan University, Shanghai. I therefore believe that I will not have language difficulties while studying in the United States.I should be most grateful if you would give my request favorable consideration. Thank you very much and look forward to your reply.Li LI英语留学申请信五例【例一】Post Office Box 2418Branch 28-5Post Code 100081Beijing, P.R.C.November 12, 1997The Registrar of AdmissionThe Graduate School ofthe Pennsylvania State UniversityU.S.A. 16802Dear Sir:I am deeply interested in your graduate school in the Department of MechanicalEngineering, and plan to apply for admission for the fall of 1998. My GPA in the university was 3.5, and I plan to take TOEFL and GRE in October and December, 1997, respectively.Please send catalog and application forms to me. I shall be greatly appreciated.Very truly yours,Wang Yang【例二】Department of Applied PhysicsTsinghua University, 100084Beijing, ChinaSept. 11th, 1999RE: Applying for AdmittanceOffice of Graduate AdmissionsBoston UniversityMassachusetts, U.S.A.Dear Sir,I am writing in the hope that I may obtain an opportunity to further my study in Applied Physics toward Master degree in your university.My name is Li Jin, an undergraduate student of the Department of Applied Physics, Tsinghua University(China). Next year in the summer, I will graduate and get my BS degree. I plan to continue my study and researchin this field under the instructions of first class professors and ina dynamic academic atmosphere. I chose Boston University because there are a congenial team of researchers, an array of databases and research projects in your school of Physics. I believe my interests are extremely congruent with the strengths of the school. And my solid academic background will meet your general entrance requirements for graduate study.I will appreciate it very much if you could send me the Graduate Application Forms, the Application Form for Scholarships/Assistantships, a detailed introduction to the School of Physics, and other relevant information. My mailing address is shown on the top of this letter.I am looking forward to hearing from you soon.Sincerely yours,Li Jin【例三】English CollegeBeijing Foreign Language UniversityBeijing 100083P.R. ChinaJune 16, 1999Office of AdmissionHuntington UniversityDear Sir,Thank you for your letter and the application forms. Enclosed you will find the completed forms and three checks (80 dollars) for the applicationfee and the first month s rent for dormitory. The additional 5 dollarswill be deposited at your college. I shall appreciate any favorable action you might take in admitting me to your college for the spring semester of 1998. I am most anxious to hear from you soon.Sincerely yours，Zhao Pengfei【例四】Department of Finance and EconmicsShanghai Jiaotong UniversityShanghai 200043May 1, 1999Graduate SchoolOxford UniversityLondonDear Sir:Thank you for your email and kind offer! Definitely, I would like to try to apply for a visa for the winter quarter. I understand that both you and Professor Black have tried very hard to help me with my situation and I appreciate your efforts.As it is true that nobody really knows why the visa officers refuse certain applicants and allow others, I have been told by several successful visareapplicants that reapplying with a new I 20 with a slightly differentoffer from the US schools would help. For example, a slight increase in financial aid and so on. I don't know whether this is something possible for you to consider for my situation. But I would really appreciate if you could consider some possibilities. I know that I have given you enough trouble and please ignore my request if it is too difficult for you to do. I will simply try my best to get my visa and come to your school. 英文留学申请信四例【例一】Communication DepartmentFudan UniversityShanghai 200056P.R.ChinaMarch 23, 2001Graduate SchoolUniversity of TorontoToronto, OntarioDear Sir,I have just received from your office an application form and information for international students. However, I have completed and submitted the same form and paid the admission/evaluation fee before.Would you please tell me if my application and fee have reached you or if the recent materials were sent to me by mistake?Thanks for your assistance.Yours sincerely,Luan Jinfu【例二】Department of ComputerBeijing UniversityBeijing 100087P.R. China1st May, 2000Office of AdmissionUniversity of AucklandPrivate Bag AucklandNew ZealandDear Sir,I am going to graduate from Department of Computer in Beijing University in June next year. I am very eager to enter the Graduate School of your university next fall to study applied computer for Ph.D. degree.I would appreciate it very much if you would send me a graduate catalog of your university and any other necessary information, and also a set of application forms for admission. Thank you for your kind assistance. Sincerely yours，Wang Feng【例三】Department of Applied MathematicsWuhan UniversityWuhan 430000P.R. ChinaMarch 16, 1999Office of Foreign AdmissionUniversity of WaterlooWaterloo, OntarioCanadaDear Admission Officer:I am ×××, the Chinese applicant who desires to pursue my Ph.D. study in your honored program.I am very sorry to inform you that I presently cannot afford the application fee you demand because of the following reasons:1 The high foreign currency exchange rate, US = 8.9 RMB;2.My relative low monthly income, about 200 RMB (equal to only );3.The extremely strict limitation in China to obtain foreign currency, esp. U.S. Dollar in near future. According to current foreign currency regulation, only citizens who get visa can have at most ,000 exchanged.I got excellent scores on TOEFL (63/62/67, total: 640, May, 1998) and GRE (V: 700, Q: 800, A: 800, total: 2,300, Nov. 5th, 1998). My graduate GPA is 3.7. I sincerely hope you can consider my situation and review my application first.Thanks a lot. Your kindness is greatly appreciated.Yours truly，Fang Lin【例四】Department of Chemical EngineeringTsinghua UniversityBeijing 100084ChinaJan. 6, 1994Office of Foreign AdmissionUniversity of BirminghamP.O. Box 363Birmingham B152TTU.K.Dear Sir:I wish to pursue a doctoral degree in Chemical Engineering at your institution. My desired date of entrance is fall, 1994. Please send me necessary application forms at your early convenience.If possible, I also wish to obtain a graduate assistantship so that I may support myself and obtain more practical experience while pursuing graduate study.I obtained my B. E. (Chemical Engineering) in 1989 and M. S. (Chemical Engineering) in 1992 from Tsinghua University. At present, I work as a teacher at the same university.考研英语作文留学和奖学金申请信范文留学申请信和奖学金申请信中须写明下列几点：（1）写明申请学校和所学专业。

植物中活性氧的产生及清除机制

17卷2期2001年3月生　物　工　程　学　报Chinese Journal of Biotechnology Vol.17No.2March 2001收稿日期:2000207226,修回日期:2000212218。

基金项目:国家海洋863资助项目(819208203)。

3联系作者。

济南军区总医院检验科(250031),Tel :86253122187681转66314。

33北京协和医科大学基础医学研究院博士生。

植物中活性氧的产生及清除机制杜秀敏3　殷文璇33　赵彦修　张　慧(山东师范大学逆境植物实验室,济南250014)摘　要　环境胁迫使植物细胞中积累大量的活性氧,从而导致蛋白质、膜脂、DNA 及其它细胞组分的严重损伤。

植物体内有效清除活性氧的保护机制分为酶促和非酶促两类。

酶促脱毒系统包括超氧化物歧化酶(SOD )、抗坏血酸过氧化物酶(APX )、过氧化氢酶(CA T )和谷胱甘肽过氧化物酶(GPX )等。

非酶类抗氧化剂包括抗坏血酸、谷胱甘肽、甘露醇和类黄酮。

利用基因工程策略增加这些物质在植物体内的含量,从而获得耐逆转基因植物已取得一定的进展。

关键词　活性氧,氧化损伤,酶促脱毒系统中图分类号　Q943 文献标识码　C 文章编号100023061(2001)022******* 全球由于环境胁迫给作物造成的品质下降,产量降低的损失是惊人的。

当作物生长的外在条件如温度、湿度、土壤中的水分、盐浓度等发生急剧变化或当大气污染(如SO 2、臭氧)、紫外线辐射、某些农药如Paraquat (一种光动除草剂)及病原体等作用于植物时,都会使植物体内产生大量的活性氧(Reactive Oxygen Species ,ROS ),形成氧化损伤。

这些比氧活泼的含氧化合物包括:超氧根阴离子(O 2・-)、氢氧根离(OH -)、羟自由基(・OH )、过氧化氢(H 2O 2)等。

产生的活性氧可导致蛋白质、膜脂和其它细胞组分的损伤[2]。

sample letters

Sample letters:Invitation Letter for the Conference on MathematicsSchool of Mathematics andSystem ScienceShandong University27 Shanda NanluJinan, Shandong 250100P. R. ChinaMarch 20, 2007Professor George SmithSchool of Mathematical SciencesThe University of NottinghamUniversity ParkNottinghamNG7 2RD UKDear Professor George Smith,I am pleased to invite you to attend the Ninth International Conference on Finite or Infinite Dimensional Complex Analysis to be held from July 24 to 28, 2007 in Jinan and Tai’an city, China. The conference is jointly organized by Shandong University and Shandong University of Science and Technology.The conference will first be opened in Jinan, and then move to Tai’an. And you are cordially invited to attend the Jinan part of the conference, July 24-26, 2007, at the Academic Exchange Center of Shandong University. You will be provided with local expenses, including hotel accommodation and meals for the duration of the conference.If you have any enquires, please contact our Conference Convener Ms Song Mei at (86)531 8836 **** or visit .I look forward to seeing you in Jinan.Yours sincerely,(Signature)Liu DonglinOrganizing CommitteeLetter of AcceptanceJuly 15, 2005Dear Dr. Pan Feng,I have received your letter dated June 22, inviting me to speak at the Opening Ceremony of the Fifth National Council Meeting of Translators Association of China to be held on November 4-6, 2005, in Beijing. I will speak on “Globalization and Diversity: What Do They Mean for Translators?”Thank you for your kind invitation.I wish the meeting a very fruitful and successful one.I look forward to seeing you at the Opening Ceremony in Beijing.Yours sincerely,(signature)Betty CohenLetter of RefusalDear Mr. Snow,Thank you very much for your kind invitation to speak before the Western Cartographers Association (WCA) Next month.Unfortunately, prior commitments make it impossible for me to accept your flattering offer. My work takes me abroad quite frequently, and I will be in Upper Volta the week your association meets.Please accept my sincere apologies, and I hope you will think of me again if the WCA needs a guest speaker at some future date.Yours sincerely,(signature)Jack VanceApplication Letter for a Working Group(Your address)January 22, 2012Dr. Melba RipleyThe School of ArchitectureUniversity of Louisiana100 Webber HallBaton Rouge, LA 70814Dear Dr. Ripley,I am a researcher at school of Materials Engineering, Purdue University. I have devoted nearly five years to the study of how inexpensive housing can be made of native materials in Third World countries; I was intrigued by the recent accomplishments of you and your students in designing and providing “instant” housing to victims of the recent hurricane in Central America. Therefore, I wish to learn about construction techniques of developing new structures in your working group for six months, preferably during April through September.During the past three years, I have been an assistant to Dr. Graham Benson who has shared the rostrum with you at many academic and global conferences on housing. Together we, along with a group of students, have spent the past two summers showing people in South Central Africa how to mix a specially prepared binder developed by our research lab with local materials to make durable homes in a matter of days. I would truly like to have the opportunity to do research work in your group so as to learn state-of-the-art technology in housing-building materials.I would greatly appreciate it if you could send me more information about application at your earliest convenience.Sincerely yours,Thomas Lamb Application Letter for a Graduate ProgramDepartment of PhysicsNanjing University22 Hankou Roan, Nanjing 21009P. R. ChinaNovember 3, 2009Mrs. Elizabeth WilliamsGraduate Adamissions OfficeUniversity OfficesWellington SquareOxford, OX1 2JDUKDear Mrs. Elizabeth Williams,I am a student in the Department of Physics, expecting to graduate with a bachelor’s degree in July next year. I am very much interested in pursuing a master’s degree in Particle Physics Department of Oxford University. From my review of graduate programs and discussion with my professors, I find that Oxford University has the largest particle physics group in the UK, with a large academic and support staff. I intend to enter in the autumn of 2010.In my undergraduate years, I have worked hard. As you can see from my curriculum vitae, my GPA in major courses is 3.8/4.0 and I have remained top 5% of about 100 students. I have also worked with Dr. Liu Wei and Professor Luo Lei on research topics like the applied physics at the enterprise level. Because of my excellence in study and research, I have been awarded scholarships three times. In addition, I am well-prepared linguistically to further my studies in the UK. My TELTS is 7.5 and my GRE is 130.I would be grateful if you would send me the application forms for admission and financial support at your earliest convenience. Thank you for your consideration.I look forward to hearing from you soon.Sincerely yoursLin Pengpeng Application Letter for Attending a Conference(Your address)March 15, 2007Dear Dr. Nelson,I am a Ph. D. candidate in School of Environmental Science and Engineering of Shandong University, P. R. China. I have heard from Prof. Wang Dongliang that the International Conference on Cities and Conservation will be held in the University of California, September 1-5, 2007. I am writing to you about the possibility of attending the forthcoming conference.I am currently doing research in Prof. Wang’s working group on water pollution prevention technology and water reuse, the area that I have always been interested in. I believe that attending such a conference will provide me with a very good opportunity to exchange ideas and expertise with attendees from different parts of the world and, more importantly, to learn from them.I would be grateful if you could send me more information about application form and financial support.I look forward to your early reply.Sincerely yours,Wei LinExercise:1.Fill in the blanks with suitable words:You are cordially (1) to participate in the Second International Conference (2) the Telemedical Information Society (TIS) 2001 which has (3) with the Second International Conference on Information Technology Applications in Biomedicine (ITAB) 2001 (4) be held in Amsterdam, the Netherlands, from April 12th to 14th, 2001.TIS-ITAB 2001 is the first combined International conference. It (5) be an opportunity for the international community to (6) ideas and develop a common vision for the future of the world healthcare. Contributions (7) the progress of developing a global telemetrically information society will (8) scientific papers, demonstrations, forums and future vision papers. The (9) committee has been working hard to make TIS-ITAB 2001 a truly (10) experience for all participants.2.The following is the body of a Letter of Acceptance, please translate it into English.我已收到您2002年3月9日邀请我参加于2002年11月5-8日在中国地质大学(武汉)学术交流中心举行的地球科学与可持续发展策略会议的来信。

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7A.1 & 2 - Smith, D & Zettl, AREQ Giancoli, PHYSICS FOR SCIENTISTS & ENGINEERS, V. I, 3rd edition, 2000, Prentice HallREQ Fishbane, Gasiorowicz & Thornton, PHYSICS FOR SCIENTISTS AND ENGINEERS, PORTABLE TA PROBLEM SOLVING GUIDE, V.1, Prentice-Hall7A LAB MANUAL to be purchased at Copy CentralH7A - Kolomensky, YREQ Kleppner, INTRODUCTION TO MECHANICS, '73, McGraw HillREQ French, VIBRATIONS AND WAVES, NortonREC Kittel, MECHANICS- BERKELEY PHYSICS COURSE, V.1, McGraw HillREC Feynman, LECTURES ON PHYSICS, V. 1, Addison-WesleyREC Resnick, Halliday, Krane, PHYSICS, V.1, WileyREC French, NEWTONIAN MECHANICS, Norton7A LAB MANUAL to be purchased at Copy Central7B.1-3 - Packard, R & Tremsin, AREQ Giancoli, PHYSICS FOR SCIENTISTS & ENGINEERS, V. I & II, 2000, Prentice HallREQ Fishbane, Elby's PHYSICS FOR SCIENTISTS & ENGINEERS, PORTABLE TA PROBLEM SOLVING GUIDE, V. 2, Prentice Hall7B LAB MANUAL to be purchased at Copy CentralH7B - Boggs, SREQ Purcell, EM, BERKELEY PHYSICS COURSE: ELECTRICITY & MAGNETISM, V. 2, 2nd ed, 1985, McGraw 7B LAB MANUAL to be purchased at Copy Central7C.1 & 2 - Yu, P & Estilaei, RREQ Giancoli, PHYSICS FOR SCIENTISTS & ENGINEERS, V. II, 2000, Prentice Hall7C LAB MANUAL to be purchased at Copy CentralH7C - Lee, AREQ Serway, MODERN PHYSICS, 2nd edition, 1997, Harcourt BraceREC Fowles, INTRODUCTION TO MODERN OPTICS, 2nd edition, 1975, Dover7C LAB MANUAL to be purchased at Copy Central8A.1 & 2 - Golightly, WREQ Halliday, Resnick & Walker, FUNDAMENTALS OF PHYSICS, V.1, 6th edition, 2000, Wiley 8A LAB MANUAL to be purchased at Copy Central_______ 8B. 1 - McFadden, JREQ Halliday, Resnick & Walker, FUNDAMENTALS OF PHYSICS, V. 2, 6th edition, 2000, Wiley 8B LAB MANUAL to be purchased at Copy Central8B.2 - Dalven, RREQ Halliday, Resnick & Walker, FUNDAMENTALS OF PHYSICS, V. 2, 6TH edition, 2000, Wiley 8B LAB MANUAL to be purchased at Copy CentralREC Dalven, MATH FOR PHYSICS, McGraw-Hill Custom Publishing10 - Muller, R.No texts required24.1 - Jacobsen, RNo texts required24.3 -Boggs, SREQ Begelman & Rees, GRAVITY'S FATAL ATTRACTION: BLACK HOLES IN THE UNIVERSE, Scientific Amer.105.1 - Qiu, ZREQ Marion & Thornton, CLASSICAL DYNAMICS OF PARTICLES & SYSTEMS, 4th edition, 1995, Saunders 105.2 - Bardakci, KREQ Marion & Thornton, CLASSICAL DYNAMICS OF PARTICLES & SYSTEMS, 4th edition, 1995, SaundersREC Symon, MECHANICS, Addison-WesleyREC Barger & Olsson, CLASSICAL MECHANICS, McGraw Hill110A.1 & 2 - Strovink, M & Kerth, LREQ Griffiths, INTRODUCTION TO ELECTRODYNAMICS, 3rd edition, 1999, Prentice Hall110B - Zolotorev, MREQ Griffiths, INTRODUCTION TO ELECTRODYNAMICS, 3rd edition, 1999, Prentice HallREQ Pedrotti & Pedrotti, INTRODUCTION TO OPTICS, Prentice Hall111.1 - Holzapfel, WREQ Sedra & Smith, MICROELECTRONIC CIRCUITS, 3rd ed., OxfordREQ Hayes & Horowitz, STUDENT MANUAL FOR THE ART OF ELECTRONICS, CambridgeREQ Horowitz & Hill, THE ART OF ELECTRONICS, Cambridge111.2-3 - Falcone, R & Davis, SPREQ Lyons, L., A PRACTICAL GUIDE TO DATA ANALYSIS FOR PHYSICAL SCIENCE STUDENTS, Cambridge REQ Milissinos, EXPERIMENTS IN MODERN PHYSICS, Academic Press112.1 - Lindenberg, AREQ Kittel & Kroemer, THERMAL PHYSICS, 2nd edition, 1980, FreemanREC Reif, FUNDAMENTALS OF STATISTICAL & THERMAL PHYSICS, McGraw Hill112.2 - Clarke, JREQ Kittel & Kroemer, THERMAL PHYSICS, 2nd ed., 1980, FreemanREC Reif, FUNDAMENTALS OF STATISTICAL & THERMAL PHYSICS, McGraw Hill_____________________________________________________________________________________________ 129A - Shapiro, MREQ Perkins, INTRODUCTION TO HIGH ENERGY PHYSICS, 4TH edition, Cambridge137A.1-2 - Marrus, R & Shen, YRREQ Bransden, QUANTUM MECHANICS, 2nd edition, 2000, Pearson Education137B.1 - Wohl, CREC Griffiths, INTRODUCTION TO QUANTUM MECHANICS, Prentice Hall137B.2 - Steiner, HREQ Bransden, QUANTUM MECHANICS, 2nd edition, 2000, Pearson Education_____________________________________________________________________________________________ 141A - Orenstein, JREQ Kittel, INTRODUCTION TO SOLID STATE PHYSICS, 7th edition, 1996, WileyC160A- Filippenko, AREQ Phillips, PHYSICS OF STARS, Wiley______ 208A - Chiao, RREQ Yariv, QUANTUM ELECTRONICS, 3rd edition, 1989, Wiley209* - Sadoulet, BREQ Jackson, J D, CLASSICAL ELECTRODYNAMICS, 3rd edition, 1998, Wiley*PHYSICS 209 FORMERLY PHYSICS 210AB_____________________________________________________________________________________________ 212 - Lee, D-HNo texts required221A - Murayama, HREQ Sakurai, MODERN QUANTUM MECHANICS, 1994, Addison-Wesley222 - COURSE CANCELLEDWILL NOT BE OFFERED FALL 2001226 - Kim, Y-KREQ TBA_____________________________________________________________________________________________ 229A - Suzuki, MNo texts required_____________________________________________________________________________________________ 229C - Gaillard, M.REC Wess & Bagger, SUPERSYMMETRY AND SUPERGRAVITY, PrincetonREC Weinberg, QUANTUM THEORY OF FIELDS, V. III, CambridgeREC Bialin & Love, SUPERSYMMETRIC GAUGE FIELD THEORY AND STRING THEORY, Oxford_____________________________________________________________________________________________ 230B - Halpern, MNo texts required240A - Louie, SREC Anderson, CONCEPTS OF SOLIDS, World ScientificREC Ziman, PRINCIPLES OF THE THEORY OF SOLIDS, CambridgeREC Madelung, INTRODUCTION TO SOLID STATE THEORY, Springer-VerlagREC Yu & Cardona, FUNDAMENTALS OF SEMICONDUCTORS, Springer-VerlagREC Ashcroft & Mermin, SOLID STATE THEORY, Holt, Rinehart & WinstonREC Kittel, QUANTUM THEORY OF SOLIDS, Wiley242A - Wurtele, JREQ Nicholson, INTRODUCTION TO PLASMA THEORY, Wiley(by reader available at Copy Central on Brancroft Avenue)251 - SmootNone。