A Puzzling Paucity of Double Peaked X-ray Pulsars
Twin Peaks
a r X i v :h e p -p h /0008122v 2 23 O c t 2000Twin Peaks aMischa Sall´e ,Jan Smit and Jeroen C.VinkInstitute for Theoretical Physics,University of Amsterdam,Valckenierstraat 65,1018XE Amsterdam,the NetherlandsThe on-shell imaginary part of the retarded selfenergy of massive ϕ4theory in 1+1dimensions is logarithmically infrared divergent.This leads to a zero in the spectral function,separating its usual bump into two.The twin peaks interfere in time-dependent correlation functions,which causes oscillating modulations on top of exponential-like decay,while the usual formulas for the decay rate fail.We see similar modulations in our numerical results for a mean field correlator,using a Hartree ensemble approximation.In our numerical simulations of 1+1dimensional ϕ4theory using the Hartree ensemble approximation 1we found funny modulations in a time-dependent correlation function.Fig.1shows such modulations on top of a roughly ex-ponential decay.The correlation function is the time average of the zero mo-mentum mode of the mean field,F mf (t )=ϕ(t )X (t )= t 2t 1dt ′X (t +t ′)/(t 2−t 1),taken afterwaiting a long time t 1for the system to be in approximate equilibrium.This equilibrium is approximately thermal and F mf (t )is analogous to the sym-metric correlation function of the quantum field theory at finite temperature,F (t )= 12πe −ipt12ρ(p 0),(1)and the latter in turn in terms of the retarded selfenergy Σ(p 0),ρ(p 0)=−2Im Σ(p 0)a Presentedby J.Smit.1mass in the propagators of the diagrams in Fig.2,after adding a counterterm that sets the real part of Σto zero at p 0=m .The one loop diagram is-14-12-10-8-6-4-2100200300400500600l o g (a b s [〈φt ’ φt ’+t 〉−〈φt ’〉〈φt ’+t 〉])tmt’m=31•103...61•103N=64, Lm=14.8-2.63-tm/233N=128, Lm=29.1-4.05-tm/105Figure1:Numerically computed correlation ln |F mf (t )|versus time t in units of the inverse temperature dependent mass m .The coupling is weak,λ/m 2=0.11and the tempera-ture T/m ≈1.4for the smaller volume (with significant deviations from the Bose-Einstein distribution)and ≈1.6for the larger volume (reasonable BE).++. . .123Figure 2:Diagrams leading to thermal damping.present only in the ‘broken phase’(for which ˆϕ =0;there is really only a symmetric phase in 1+1dimensions,but this is due to symmetry restoration by nonperturbative effects which will not obliterate the one-loop damping.)The corresponding selfenergy has been calculated in 2,for example.It only leads todamping for frequencies p 20>4m 2,which are irrelevant for the quasiparticledamping at p 20=m 2.So from now on we concentrate on the two-loop diagram.2After analytic continuation to real time onefinds that it is given by the sum of two terms,Σ1+Σ2(see e.g.3).Thefirst has an imaginary part corresponding to1↔3processes requiring p20>9m2,so it does not contribute to plasmon damping.The second is given byΣ2=−9λ2E1E2E3(1+n1)n2n3−n1(1+n2)(1+n3)m2+(p2+p3)2,E i=m =9λ2e m/T−1 2 ln mindeed an oscillating modulation on top of the roughly exponential decay.The decay corresponding to exp(−γt),withγgiven by(6),is also indicated in the plot:it does not do a good job in describing the average decay beyond thefirst interference minimum.The‘Twin Peaks’phenomenon implies that the usual definition of damping rate(5)is unreliable in1+1dimensions.Acknowledgements.We thank Gert Aarts for useful conversations.This work is supported by FOM/NWO.1.J.C.Vink,these proceedings.2.H.A.Weldon,Phys.Rev.D28,2007(1983).3.E.Wang and U.Heinz,Phys.Rev.D53,899(1996).1512.5107.552.5Figure3:The spectral functionρ(p0)near p0=m=1corresponding to the selfenergy shown in Figs.4,5(T=m,λ=0.4m2).-2-4-6-8-10-12050100150200Figure4:Plot of ln|F(t)|versus mt for T=m,λ=0.4m2.The straight line represents exp(−γt).4。
摘录不饱和聚酯文献中的经典句子
1.To access the description of a composite material, it will be necessary to specify the nature of components and their properties, the geometry of the reinforcement, its distribution, and the nature of the reinforcement–matrix interface.2. However, most of them are not chemically compatible with polymers3. That’s why for many years, studies have been conducted on particles functionalization to modulate the physical and/or chemical properties and to improve the compatibility between the filler and the matrix [7].4. Silica is used in a wide range of products including tires, scratch-resistant coatings, toothpaste,medicine, microelectronics components or in the building5. Fracture surface of test specimens were observed by scanning electron microscopy6.Test specimens were prepared by the following method from a mixture composed with 40 wt% UPE, 60 wt% silica Millisil C6 and components of ‘‘Giral.’7.Grafted or adsorbed component amounts on modified silica samples were assessed by thermogravimetric analysis (TGA) using a TGA METTLER-TOLEDO 851e thermal system. For the analysis, about 10–20 mg of samples were taken and heated at a constant rate of 10 C/min under air (purge rate 50 mL/min) from 30 to 1,100 C.8.Nanocomposites with different concentrations of nanofibers wereproduced and tested, and their properties were compared with those of the neat resin.9.Basically, six different percentages were chosen, namely 0.1, 0.3, 0.5, 1, 2, 3 wt %.10.TEM images of cured blends were obtained with a Philips CM120 microscope applying an acceleration voltage of 80 kV.Percolation threshold of carbon nanotubes filled unsaturated polyesters 11.For further verification, the same experiment was carried out for the unmodified UP resin, and the results showed that there were no endothermic peaks12.The MUP resin was checked with d.s.c, scanning runs at a heating rate of 10°C min 1. Figure 4a shows that an endothermic peak appeared from 88 to 133°C, which indicates bond breaking in that temperature range.13.On the basis of these results, it is concluded that a thermally breakable bond has been introduced into the MUP resin and that the decomposition temperature is around I lO°C.14.The structures of the UP before and after modification were also checked with FTi.r. Figure 5 shows a comparison of the i.r. spectra of the unmodified and modified UP resins.15This is probably a result of the covalent bonding ofthe urethane linkage being stronger than the ionic bondingof MgO.16.These examples show that different viscosity profiles can be designed with different combinations of the resins and thickeners according to the needs of the applications.17. A small secondary reaction peak occurred at higher temperatures, probably owing to thermally induced polymerization. 18.Fiber-reinforced composite materials consist of fibers of high strength and modulus embedded in or bonded to a matrix with a distinct interfaces between them.19.In this form, both fibers and ma-trix retain their physical and chemical identities,yet they provide a combination of properties that cannot be achieved with either of the constituents acting alone.20.In general, fibers are the principal load-bearing materials, while the surrounding matrix keep them in the desired location, and orientation acts as a load transfer medium between them and protects them from environmental damage.21.Moreover, both the properties, that is,strength and stiffness can be altered according to our requirement by altering the composition of a single fiber–resin combination.22.Again, fiber-filled composites find uses in innumerable applied ar- eas by judicious selection of both fiber and resin.23.In recent years, greater emphasis has been rendered in the development of fiber-filled composites based on natural fibers with a view to replace glass fibers either solely or in part for various applications. 24.The main reasons of the failure are poor wettability and adhesion characteristics of the jute fiber towards many commercial synthetic resins, resulting in poor strength and stiffness of the composite as well as poor environmental resistance.25.Therefore, an attempt has been made to overcome the limitations of the jute fiber through its chemical modification.26.Dynamic mechanical tests, in general, give more information about a composite material than other tests. Dynamic tests, over a wide range of temperature and frequency, are especially sensitive to all kinds of transitions and relaxation process of matrix resin and also to the morphology of the composites.27.Dynamic mechanical analysis (DMA) is a sensitive and versatile thermal analysis technique, which measures the modulus (stiffness) and damping properties (energy dissipation) of materials as the materials are deformed under periodic stress.28.he object of the present article is to study the effect of chemical modification (cyanoethylation)of the jute fiber for improving its suitability as a reinforcing material in the unsaturated polyesterres in based composite by using a dynamic mechanical thermal analyzer.30.General purpose unsaturated polyester resin(USP) was obtained from M/S Ruia Chemicals Pvt. Ltd., which was based on orthophthalic anhydride, maleic anhydride, 1,2-propylene glycol,and styrene.The styrene content was about 35%.Laboratory reagentgrade acrylonitrile of S.D.Fine Chemicals was used in this study without further purification. 31.Tensile and flexural strength of the fibers an d the cured resin were measured by Instron Universal Testing Machine (Model No. 4303).32.Test samples (60 3 11 3 3.2 mm) were cut from jute–polyester laminated sheets and were postcured at 110°C for 1 h and conditionedat 65% relative humidity (RH) at 25°C for 15 days.33.In DMA, the test specimen was clamped between the ends of two parallel arms, which are mounted on low-force flexure pivots allowing motion only in the horizontal plane. The samples in a nitrogen atmosphere were measured in the fixed frequency mode, at an operating frequency 1.0 HZ (oscillation amplitude of 0.2 mm) and a heating rate of 4°C per min. The samples were evaluated in the temperature range from 40 to 200°C.34.In the creep mode of DMA, the samples were stressed for 30 min at an initial temperature of 40°C and allowed to relax for 30 min. The tem- perature was then increased in the increments of 40°C, followed by an equilibrium period of 10min before the initiation of the next stress relax cycle. This program was continued until it reached the temperature of160°C. All the creep experiments were performed at stress level of20 KPa (approximate).35.The tensile fracture surfaces of the composite samples were studied with a scanning electron microscope (Hitachi Scanning electron Microscope, Model S-415 A) operated at 25 keV.36.The much im proved moduli of the five chemically modified jute–polyester composites might be due to the greater interfacial bond strength between the ma trix resin and the fiber.37.The hydrophilic nature of jute induces poor wettability and adhesion characteristics with USP resin, and the presence of moisture at the jute–resin interface promotes the formation of voids at the interface. 38.On the other hand, owing to cyanoethylation, the moisture regain capacity of the jute fiber is much reduced; also, the compatibility with unsaturated polyester resin has been improved and produces a strong interfacial bond with matrix resin and produces a much stiffer composite.39.Graphite nanosheets(GN), nanoscale conductive filler has attracted significant attention, due to its abundance in resource and advantage in forming conducting network in polymer matrix40.The percolation threshold is greatly affected by the properties of the fillers and the polymer matrices,processing met hods, temperature, and other related factors41.Preweighted unsaturated polyester resin and GN were mixed togetherand sonicated for 20 min to randomly disperse the inclusions.42.Their processing involves a radical polymerisation between a prepolymer that contains unsaturated groups and styrene that acts both asa diluent for the prepolymer and as a cross-linking agent.43.They are used, alone or in fibre-reinforced composites, in naval constructions, offshore applications,water pipes, chemical containers, buildings construction, automotive, etc.44.Owing to the high aspect ratio of the fillers, the mechanical, thermal, flame retardant and barrier properties of polymers may be enhanced without a significant loss of clarity, toughness or impact strength.45.The peak at 1724 cm-1was used as an internal reference, while the degree of conversion for C=C double bonds in the UP chain was determined from the peak at 1642 cm-1and the degree of conversion for styrene was calculated through the variation of the 992 cm-1peak46. Paramount to this scientific analysis is an understanding of the chemorheology of thermosets.47．Although UPR are used as organic coatings, they suffer from rigidity, low acid and alkali resistances and low adhesion with steel when cured with c onventional ‘‘small molecule’’ reagents.48．Improvements of resin flexibility can be obtained by incorporating long chain aliphatic com-pounds into the chemical structure of UPR. 47．In this study, both UPR and hardeners were based on aliphatic andcycloaliphatic systems to produce cured UPR, which have good durability with excellent mechan-ical properties.50．UPR is one of the widely used thermoset polymers in polymeric composites, due to their good mechanical properties and relatively inexpensive prices.51．[文档可能无法思考全面，请浏览后下载，另外祝您生活愉快，工作顺利，万事如意!]。
Effect of Stress Concentration on Magnetic Flux Leakage Signals from Blind-Hole Defects in Stressed
Res Nondestr Eval(1996)8:83–100©1996Springer-Verlag New York Inc.Effect of Stress Concentration on Magnetic Flux Leakage Signals from Blind-Hole Defects in Stressed Pipeline Steel T.W.Krause,R.W.Little,R.Barnes,R.M.Donaldson,B.Ma,and D.L.Atherton Department of Physics,Queen’s University,Kingston,Ontario,K7L3N6,CanadaAbstract.Stress-dependent magneticflux leakage(MFL)signals of the normal surface compo-nent(radial)MFL signal from blind-hole defects in pipeline steel were investigated.Three different stress rigs with uniaxial stress andfield configurations were used.A double-peak feature in the MFL signal was defined quantitatively by a saddle amplitude,which was taken as the difference between the average of the double peaks and the corresponding saddle point.Results indicated that the saddle amplitude increased linearly with increasing tensile surface stress and decreased, or did not exist,for increasing compressive surface stress.The stress-dependent saddle amplitude was shown to increase with increasing defect depth.Finite-element calculations indicated that stress concentration also increased with increasing defect depth.The measurements and analy-sis demonstrate that the stress-dependent saddle amplitude behavior in the radial MFL signal is associated with surface-stress concentrations near the blind-hole defects.IntroductionMagneticflux leakage(MFL)techniques are commonly used for the in-line inspection of pipelines for metal loss defects such as corrosion pits[1].The in-service operating pressures of gas pipelines generate large circumferential stresses that may reach70%of the yield strength of the pipe.These in-service stresses affect theflux leakage patterns and have been studied previously[2]–[7].In the presence of stress,defects act as“stress raisers”[8].Dependent upon the defect depth[9],the defects may generate stress con-centrations that exceed the yield strength in their vicinity.Stress raising around defects also may lead to enhanced stress corrosion cracking[10].There are two effects that may contribute to the generation of the stress-dependent MFL signal:1)the bulk effect of stress on the magnetic properties[11]–[16]and2)the effect of the defect as a stress raiser that is also dependent on the depth of the defect [9].Metal loss resulting from increasing defect depth increases the level of magnetic saturation in the vicinity of the defect and,therefore,increases the MFL signal.Similarly, by affecting the stress-dependent magnetic properties of the steel in the vicinity of the defect,the application of a bulk stress also affects the peak-to-peak MFL(MFL pp) signal.Stress concentrations in the vicinity of the defect have a similar effect.From a previous consideration[17],under a bending stress the two-dimensional solution for a100%through-wall defect or hole generates a peak stress level at the edge of the84Krause et al. hole that is2.4times that of the nominal background stress[8,17].Finite-element calculations and stress measurements[17]indicate that,for the same bending stress,the stress concentration for a round-bottomed pit that is50%of the through-wall thickness is1.2times the nominal stress.For a plate under uniform tensile stress,the maximum stress at the edge of a full cylindrical through-hole is three times that of the nominal stress [8,18].Stress concentrations occur at the two edges of the defect that are tangential to the applied stress direction.An increase in the pipe wallflux density typically results in an increase in the MFL signal due to increased saturation of the steel in the defect region.The effect of stress on the MFL pp signal has been shown to increase for increasingflux densities in the range of 0.65to1.24T[9,13]–[16].It is expected,therefore,that stress concentration combined with increasingflux density may similarly affect the MFL signal.Observations of a double-peak feature that increases in amplitude with increasing applied tensile stress have been made for normal-surface component(radial)MFL signals for various uniaxial orientations of stress andfield applied to pipeline steel[5,11].In particular,the amplitude of the double-peak feature(hereafter referred to as the saddle amplitude)has been observed to increase linearly with increasing levels of applied stress and has been associated with stress patterns around the defect itself[12,14].In this paper we provide evidence that strongly supports this claim.Further,it is demonstrated that the double-peak feature in the MFL signal may be associated primarily with stress concentrations that appear in the vicinity of the defect near the surface of the steel pipeline sample,and also that the stress concentration and resultant saddle amplitude in the MFL signal increase with increasing defect depth.Experimental ApparatusThe experimental apparatus is described in detail elsewhere[11,12].The apparatus used to measure the radial component of theflux leakagefield from a defect on the same side of the sample as the measuring apparatus(near side)consisted of a Hall probe,an amplifier to amplify the Hall signal,and a computer for data acquisition.The radialflux leakage signal was measured at scanned positions set at1-mm intervals(0.5mm for the semicircular pipe section)across the area of the defect.The radialflux leakage signal was taken as the average of100measurements taken at each position.Pipeline Sample and Stressing ApparatusSamples of pipeline steel used in this study were cut from a610-mm(24-in.)diameter X70steel pipe of9-mm wall thickness.Thefirst sample used was a102-mm(4-in.)wide semicircular section cut in the pipe hoop direction.Other samples used were4.27-m long axial strips that were also102mm(4in.)wide.The pipeline steel composition is given elsewhere[17].There were three separate experimental test rigs.Thefirst apparatus is the semi-circular hoop bending rig shown in Fig.1.The second and third apparatus use the single-strip beam-bending arrangement and the composite beam-bending arrangement,Magnetic Flux Leakage Signals from Blind-Hole Defects85Fig.1.The semicircular pipe section and bending stress rig for the production of surface stress in semicircular sections of pipe steel.both described elsewhere[11,12].Surface stresses up to±300MPa were applied using the three stress rigs.This is below the yield stress of the pipe steel,which is at500MPa. All three sets of apparatus have a13-mm diameter ball-milled external pit machined to50%of the steel wall thickness.The composite beam apparatus also has two more 13-mm diameter ball-milled external pits machined to depths of25and75%.An area of about40mm by40mm around the defect was stripped of its epoxy coating to expose the pipe steel.The defect area was magnetized to a maximum axialflux density of1.6T using ferrite magnets.For the semicircular pipe section,steel hingedfingers were used to couple theflux from the magnets into the steel pipe,while for the two beams,steel brushes shaped to the curvature of the beams coupledflux into the steel samples. Semicircular Pipe Section Stress RigIn thefirst stress rig,shown in Fig.1,a semicircular pipe section is held stationary by a fixed clamp,while the other is connected to a movable clamp.The movable clamp is free to travel along a horizontal threaded rod as the rod is rotated with the handle,the result being the application of a hoop-bending stress.When the clamp is moved inward,tension is created on the outside and compression on the inside pipe surface,with the opposite being true if the clamp were to be moved outward.A“clamp position versus stress”calibration was obtained theoretically[17]and verified using strain gauges(placed well away from the defect region).86Krause et al. Single BeamThe single-strip beam is a102-mm wide strip of steel cut in the axial direction from the 610-mm diameter pipe with a thickness of9mm and a length of4.27m.The low rigidity of the single beam allows bending by simply hanging masses of about5kg from one end of the beam or supporting it at a raised height while the middle length of the beam is supported and the opposite end of the beam isfixed in position.Composite BeamThe third apparatus utilizes a composite beam and an arrangement to bend the beam [11,12].The composite beam is made from two axial strips of pipeline steel that are separated at afixed distance of29mm by an alternatingfiberglass–wood composite. The composite materials are bonded together with high-strength epoxy resin.Under a bending stress the neutral axis of the beam is outside the pipeline steel regions,so that nearly uniform stress is generated through the thickness of the steel walls.Because the composite beam is much more rigid,the beam is stressed by placing it parallel to a comparably rigid pipe section of equal length separated by a wood saddle in the middle. At one end the beam and pipe are held together by a clamp or chain,and at the other end the beam and pipe are pulled together by another clamp with a scissor jack.For tests using tensile stress the steel strip with the defect in it is on the side facing away from the rigid pipe,with the composite beam above the pipe.For compressive stress the steel strip is on the side facing toward the pipe and with the beam underneath the pipe,so that the detector can be placed on top of the beam.Stress CyclesThree different procedures of applyingfield and stress are used to perform the mea-surements:1)the“normal cycle,”which involves magnetizing the beam with no applied stress and maintaining the appliedfield during the stressing of the beam;2)the“opposite cycle,”which is similar to the“normal cycle”except that the magnetization is generated with thefield in the opposite polarity;and3)the“after-cycle,”which involves removing the magnet before each stressing increment and then replacing it so that the beam is remagnetized after each change of stress.In all three methods,the defects are scanned at fixed levels of stress.Of the three cycles,the after-cycle is the most similar to an actual pipeline pigging measurement.Measurements of the peak-to-peak magneticflux leakage(MFL pp)signal in the normal-cycle mode across a50%penetration round-bottomed blind-hole–simulated de-fect for various levels of applied tensile and compressive stress in the semicircular pipe section were performed using the hoop-bending stress rig shown in Fig.1.Starting from0MPa,tensile stress up to250MPa was applied followed by changes in stress to 250MPa compressive stress and,finally,back to a0-MPa stress level.The MFL signal was recorded at various levels of applied stress.The stress in the pipe section was ad-justed by varying the distance between the ends of the semicircular pipe section in the stress rig to various strain gauge calibrated settings.Magnetic Flux Leakage Signals from Blind-Hole Defects87 For the composite beam tensile stress scans were performed,first for all three defects and stress cycles,and then followed by compressive stress scans,since a reorientation of the beam was required.No compressive stress scans were performed for the single beam.Variation of Pipeline Steel Flux DensityThe totalflux density within the semicircular pipe section was measured by removing the magnetizing system,noting theflux change,reversing the polarity of the magnetizer, applying it again,and noting theflux change again.The average of the twoflux readings was taken and theflux density within the pipe and was found to be1.54T.The totalflux density within the single-beam stress rig was determined in the same manner and was found to be1.6T.Two techniques were used to vary theflux density within the composite beam pipe wall and are described in detail elsewhere[9,13].Thefirst technique consisted of changing the size of the magnets used,and the second involved the application of partial shorting bars.The steel bars diverted some of theflux from the magnets and therefore reduced theflux density in the pipe wall.An integrating voltagefluxmeter,connected to a13-turn coil wound around one section of steel beam and through a hole in the center of the composite beam assembly,was used to determine theflux density within the pipe wall. The four pipe wallflux densities generated within the composite beam pipe wall using these two techniques were0.65T,0.84T,1.03T,and1.24T.AnalysisThe peak-to-peak radial component of the magneticflux leakage(MFL pp)signal is ob-tained by taking the difference between the maximum(positive)and minimum(negative) components of the MFL signal.Positive saddle amplitude values are obtained from the MFL signal by evaluating the difference between the average of the two positive peaks and the positive saddle point.Negative saddle amplitude values are obtained in the same manner,except that the negative double MFL peaks and the negative saddle point are used for the evaluation.Both the variation of the MFL pp signal and the saddle amplitude as functions of stress were investigated.Finite-Element CalculationsA three-dimensionalfinite-element method was used to model the stress pattern surround-ing the defect.Finite-element modeling was performed using the ANSYS Revision4.4 by Swanson Analysis Systems.A ten-node tetrahedral element with three directional degrees of freedom at each node was used to mesh the solid model.The volumes were defined using a solid modeling approach,where the geometry of the object was described by specifying key points,lines,areas,and volumes.ANSYS thenfilled in the solid model with nodes and elements based on the user-defined element shape and size.88Krause et al.Fig.2.(a)Surface and contour plots of the radial magneticflux leakage from the near side of a13-mm-diameter ball-milled50%defect in the semicircular pipe section under a tensile stress of250MPa during a normal cycle.Thefinite-element calculations modeled aflat plate with a ball-milled defect.The plate dimensions were taken as50mm×50mm with a thickness of9mm,which was the same as that of the pipeline steel samples.The radius of curvature of the ball-mill that generated the defect was taken as6.35mm.The full defect radius was,therefore,only attained at71%defect depth.This may have affected the calculations since the defect radius was changing continuously with respect to the mesh distribution up to71%of the wall thickness.Young’s modulus was taken as210GPa and Poisson’s ratio as0.28. Calculations were performed for a nominal stress of190MPa.ResultsSemicircular Pipe Section:MFL pp MeasurementsFigures2a and2b show surface and contour plots of the radial magneticflux density leakagefield over the defect for tensile and compressive stresses of250MPa,respectively. Both scans are from the normal-cycle procedure using constant magnetization.The amplitude of a signal is obtained by taking the difference between the maximum andMagnetic Flux Leakage Signals from Blind-Hole Defects89Fig.2.(b)Surface and contour plots of the radial magneticflux leakage from the near side of a13-mm-diameter ball-milled pit in the semicircular pipe section under compressive stress at250MPa during a normal cycle.minimum values offlux density over the area of the scan(MFL pp).The profile of the contours is typical for all scans,with slight variations with changing paring the two scans,a more pronounced double-peak feature is observed for the tensile surface stress case than for the compressive surface stress case.The MFL pp signal as a function of stress for the semicircular pipe section under bending-hoop stress is shown in Fig.3.Starting at0MPa,the variation of the MFL pp signal with surface stress demonstrates an initial increase with the application of tensile stress followed by a decrease and a large hysteresis loop as the stress is cycled from 250MPa to−250MPa.Under a compressive stress the variation of the MFL pp signal is smaller,as is the hysteresis.Thefinal zero-stress MFL pp signal is greater than the initial starting point.Arrows indicate the order in which the data were taken.Variation of Saddle Amplitude with StressResults obtained from an analysis of the positive and negative saddle amplitudes as a function of surface stress in the normal cycle are shown for the semicircular pipe section in Fig.4.Positive and negative saddle amplitudes are present for the zero-stress case.90Krause et al.Fig.3.Peak-to-peak MFL signal from the near side as a function of surface stress in the normal cycle for a13-mm-diameter ball-milled50%defect on the semicircular pipe section under hoop-bending stress with an applied pipe wallflux density of1.54Tesla at0MPa.Since hysteresis is present,arrows indicate the direction in which the data were taken.The positive saddle amplitude increases linearly from a minimum at250MPa compressive stress to a maximum at200MPa tensile stress.Some hystersis is evident.In comparison, the negative saddle amplitude is smaller in magnitude,more hysteretic,and slightly less linear.For the single-beam stress rig,observations of a saddle amplitude that depended linearly on stress were made for there tensile surface stress measurements equal to and greater than200MPa measured in the normal cycle.In this rig a saddle was not observed for zero or applied compressive stresses.As in the semicircular pipe section,the magnitude of the positive saddle amplitudes was greater than the corresponding negative saddle amplitudes.The variations of the positive and negative saddle amplitudes with stress for the composite beam for the three defect depths in the normal cycle at1.24T are shown in Fig.5for tensile stress values.For the composite beam no saddle was observed for any zero or compressive stress values,which is in contrast to the semicircular pipe section where a saddle amplitude that was a decreasing function of increasing compressive stress was observed.This result is considered further in the discussion.The results for the composite beam indicate an increasing variation of saddle amplitude with stress forMagnetic Flux Leakage Signals from Blind-Hole Defects91Fig.4.Positive(•)and negative( )saddle amplitudes as functions of surface stress using the semi-circular pipeline apparatus with afield of1.54T during the normal cycle are plotted for the13-mm ball-milled50%defect.increasing defect depth.For the25and50%depth defects the positive saddle amplitudes are greater in magnitude than the negative saddle amplitude values for equivalent levels of stress,while at75%this difference is not as great.The dependence of the positive and negative saddle amplitudes upon stress in the composite beam for the three different defect depths for measurements performed in the after-cycle at1.24T are shown in Fig.6.In contrast to the normal-cycle measurements for the25and50%defects,the magnitude of the negative saddle amplitudes is greater than that of the positive saddle amplitudes,while there is no observed difference between the magnitudes for the75%defect.The rate of change of the saddle amplitude with stress is greatest for the75%defect and least for the25%defect.Stress-Dependent Saddle Amplitude SlopesLinear bestfits were applied to the saddle amplitude data as a function of stress for the three different stress rigs.The slopes of saddle amplitude variation with stress for the normal cycle in the three different stress rigs are shown in Table1.Several observations can be made for the normal-cycle stress applied in the three different stress rigs.These92Krause et al.Fig.5.Saddle amplitudes as a function of stress in the composite beam apparatus from13-mm ball-milled defects in afield of1.24T in the normal cycle are plotted for the25%defect for the positive( ) and negative( ),for the50%defect for the positive( )and negative( ),and for the75%defect for the positive( )and negative(•)saddle amplitudes.Table1.Bestfit slopes for normal-cycle MFL pp and saddle amplitude with different defect depths in the composite beam and50%defect in the semicircular pipe section and single beam.%MFL pp vs.Stress-dependent Stress-dependent+Sad.amp.−Sad.amp. Defect stress slope saddle amplitude saddle amplitude MFL pp slope MFL pp slope depth(10−12T/Pa)pos.(10−13T/Pa)neg.(10−13T/Pa)(=col.3/col.2)(=col.4/col.2) Composite Beam(B=1.24T)25% 1.6210.130.0650% 5.1760.140.1275%11.019.119.50.1740.177 Semicircular Pipe Section(B=1.54T)50%—118——Single Beam(B=1.6T)50% 2.3 1.68±39±30.350.43Fig.6.Saddle amplitudes as a function of stress in the composite beam apparatus from13-mm ball-milled defects in afield of1.24T in the after-cycle are plotted for the25%defect for the positive( ) and negative( ),for the50%defect for the positive( )and negative( ),and for the75%defect for the positive( )and negative(•)saddle amplitudes.are:1)the slope directions of the positive and negative saddles as a function of stress are all positive;2)the rate of change of saddle amplitude as a function of stress for all three stress rigs is of the same order of magnitude,in contrast to the MFL pp signal variations with stress,which demonstrate little correlation between the three different stress rigs: 3)the magnitude of the saddle amplitudes obtained from the positive saddle curves is greater than the corresponding negative saddle curves in the normal cycle;4)no change in the saddle amplitudes was observed under compressive stress for bending stress applied in the axial direction in both the single and composite beams;5)the magnitudes of the saddle amplitudes for the semicircular pipe section are approximately four times greater than those observed for the single and composite beams,and do not go to zero even with the largest application of compressive stress;and6)there is a general increase in the positive and negative saddle amplitude slopes with increasing defect depth.The slopes obtained from the after-cycle and opposite-cycle also demonstrate an increasing saddle amplitude slope with increasing defect depth,although increased in-tercepts for the25and50%defects for the negative saddle amplitude variation are observed.This increase can be seen for the after-cycle in a comparison of Figs.5and6. The sum of the positive and negative saddle amplitude slopes(the total saddle amplitudeFig.7.The sum of positive and negative saddle amplitude stress slopes plotted as a function of% defect depth for the normal cycle( ),after-cycle,( )and opposite cycle( )in the composite beam (B=1.24T).The solid and dashed curves are lines to guide the eye.slope)obtained from the three stress cycle results are plotted as a function of percent defect depth in Fig.7.The total saddle amplitude slope is plotted as a function offlux density for the after-cycle in Fig.8.For all three cycles the results indicated an increasing total saddle am-plitude with increasingflux density.The stress concentration factor is a constant for constant defect depth and,therefore, may be related to the slope of the saddle amplitude variation with stress.However,for the zero-stress case,the radialflux leakage signal demonstrates a considerable increase with increasing defect depth[19,20].Therefore,to perform a comparison of the variation of the saddle amplitude with stress for different defect depths with calculated values of the stress concentration,it is necessary to normalize the stress-dependent saddle amplitude slopes by their respective zero-stress MFL pp signals.A comparison of the normalized saddle amplitude slopes with the maximum and surface maximum stress concentrations obtained fromfinite-element calculations is shown in Fig.9.The stress-dependent saddle amplitude slopes have been averaged over the three cycles,normalized by their respective zero stress MFL pp signals,and scaled to the calculated maximum surface stress at75% defect depth.The normalized and scaled saddle amplitude slopes have beenfitted in Fig.9with anFig.8.Sum of positive and negative saddle amplitude stress slopes plotted as a function of pipe wall flux density for the after-cycle( )in the composite beam(B=1.24T).The solid curve is simply a line to guide the eye.empirical formulation given byA=a sinh(bD),(1)where A is the sum of the positive and negative saddle amplitude slopes,D is the percent defect depth,and a and b arefitting parameters given by(a,b)=(0.71,0.018). Equation(1)holds in the limit of a0%defect since the total saddle amplitude A goes to zero as the MFL pp signal goes to zero.Thefinite-element calculations indicate that both the maximum and surface maximum stress concentration are increasing functions of percent defect depth.Starting at0%defect depth,the maximum stress concentration increases more rapidly than both the surface maximum and the normalized and scaled saddle amplitude slope values.Slower increases in thefinite-element calculations are observed in the vicinity of70%,which corresponds with the defect depth in thefinite-element model where the radius of the defect reaches its maximum of6.35mm.After90%the surface maximum concentration becomes the maximum stress concentration.The hyperbolic sine function,Eq.(1),coincides with the finite-element calculations above75%defect depth and with the theoretical fractional change in stress concentration at100%defect depth.Fig.9.Normalized change in maximum stress( )and maximum surface stress(⊕)as a function of%defect depth as obtained fromfinite-element calculations.The total saddle amplitude stress slopes ( )for the composite beam normalized by their respective zero-stress MFL pp signals and averaged over the three different stress cycles have been scaled to the maximum surface stress(SurfaceσMAX)finite-element calculations at75%defect depth.The dashed lines are spline curves through the pointsobtained from thefinite-element calculations and the solid line is a bestfit of the empirical relation,Eq.(1).DiscussionSemicircular Pipe Section:MFL pp MeasurementsThe application of a bending stress in the semicircular pipe section complicates the prediction of the magneticflux leakage stress behavior of the pipe since,if the upper surface of the pipe with the near-side defect is under tensile stress,then the inner surface will be under compressive stress.A further complication in this system is the direction of the magnetic easy axis with respect to the direction of the applied stress.The magnetic easy axis is at90◦to the direction of the applied stress,and,therefore,the magnetic properties of the pipeline steel are different[21]from those where the stress and easy axis are aligned in the same direction[22].Geometric properties of the semicircular pipe stress rig also may play a role in affecting the stress-dependent variation of the MFL pp signal,since the radius of curvature and therefore the length of theflux path in the semicircular pipe section changes as a function of stress with respect to thefixed length of the magnetizer.Furthermore,different levels of pipe wallflux density at equivalent stress levels for increasing and decreasing applied stresses may arise because of hystereticflux coupling in the hingedfinger–semicircular stress system.This may explain the severe hysteresis observed in the radial MFL pp signal for the semicircular pipe section under tensile stress shown in Fig.3.The application of a hoop-bending stress that is either tensile or compressive results in an overall decrease of the MFL pp signal for either surface tensile or surface compressive applied stress.However,there is an initial increase of the MFL pp signal under a surface tensile stress of50MPa.This may be attributed to the presence of a residual compres-sive surface stress present within the pipe.This suggestion is supported by spring-back measurements observed when the pipe section was cut in half[22].Stress-Dependent Saddle Amplitude:Stress Concentration FactorsThe variation of the MFL pp signal with stress appears to be associated primarily with the bulk effects of stress[9],[11]–[13]and pipe wallflux density[9,13]on the magnetic properties of steel in the general vicinity of the defect.However,we propose that the double-peak feature in the MFL pp signal and the variation of the saddle amplitude with stress is associated with the near-surface variation of stress in the immediate vicinity of the defect,which acts as a local stress raiser[17].Measurements of the MFL pp signal with almost uniform bulk stress in the composite beam stress rig indicate an increase of the MFL pp signal with increasing uniaxial tensile stress[9,13].Similarly,the variation of the saddle amplitude as a function of stress at the near-side surface of the defect demonstrated the same positive dependence.The rate of change of the saddle amplitude as a function of stress was also of the same order of magnitude in all three apparatus.Since it is the surface stress in all three apparatus that is monitored,we associate the saddle amplitude behavior as a function of stress with the corresponding variation of surface stress in the pipeline steel in the vicinity of the defect.Normalization of the stress-dependent saddle amplitude variation by the stress-de-pendent MFL pp slope for the case of the composite beam is shown in Table1.The results indicate that the saddle amplitude increases with defect depth faster than the stress-dependent MFL pp signal.Also shown in Table1are the positive and negative saddle amplitude slopes for the single beam normalized by the stress-dependent MFL pp slope for the50%defect.The values for the normalized saddle amplitude slopes obtained in this manner are more than twice those obtained for the50%defect in the composite beam. Normalization of the semicircular pipe section stress-dependent saddle amplitude by the corresponding MFL pp stress-dependent signal generates a nonlinear stress variation since the MFL pp signal varies nonlinearly over the applied tension–compression stress cycle.As was shown elsewhere[9,13],the single and composite beams demonstrate a compressive stress dependence,while no saddle amplitude is observed in this applied stress region.These results demonstrate that the variation of the MFL pp signal as a function of the bulk stress effect cannot explain the observed stress-dependent variation of the saddle amplitude.Furthermore,the slope of the saddle amplitude as a function of measured surface stress for the50%defect in the three different stress rigs,two of which are under a bending surface stress,are all of the same order.These points indicate。
用初中英语简要介绍双缝实验
用初中英语简要介绍双缝实验The Double-Slit ExperimentThe double-slit experiment is a fundamental experiment in quantum mechanics that demonstrates the wave-particle duality of light and other quantum particles. It was first performed by the English physicist Thomas Young in 1801, and it has since become one of the most famous experiments in the history of science.The basic setup of the double-slit experiment is as follows. A source of light, such as a laser or a monochromatic light source, is directed towards a barrier that has two narrow slits cut in it. The light passing through the slits is then projected onto a screen or a detector. When the light passes through the two slits, it creates an interference pattern on the screen, with alternating bright and dark regions.This interference pattern is a clear demonstration of the wave-like nature of light. If light were simply a stream of particles, one would expect to see two separate bright spots on the screen, corresponding to the two slits. However, the interference pattern shows that the light is behaving like a wave, with the waves from the two slits interfering with each other.The double-slit experiment can also be performed with other quantum particles, such as electrons or atoms. When these particles are directed towards the double slit, they also exhibit an interference pattern, indicating that they too have a wave-like nature.The wave-particle duality of quantum particles is a fundamental concept in quantum mechanics. It means that particles can exhibit both wave-like and particle-like properties, depending on the experiment being performed. This is a departure from the classical view of the world, where objects were either waves or particles, but not both.The double-slit experiment has been used to demonstrate the wave-particle duality of various quantum particles, including electrons, neutrons, atoms, and even large molecules. In each case, the interference pattern observed on the screen is a clear indication of the wave-like nature of the particles.One of the most interesting aspects of the double-slit experiment is the role of the observer. When the experiment is set up to detect which slit the particle goes through, the interference pattern disappears, and the particles behave like classical particles. This suggests that the act of measurement or observation can affect the behavior of quantum particles.This is a concept known as the "observer effect" in quantum mechanics, and it has profound implications for our understanding of the nature of reality. It suggests that the very act of observing or measuring a quantum system can alter its behavior, and that the observer is not a passive participant in the experiment.The double-slit experiment has also been used to explore the concept of quantum entanglement, which is another fundamental concept in quantum mechanics. Quantum entanglement occurs when two or more quantum particles become "entangled" with each other, such that the state of one particle is dependent on the state of the other.In the double-slit experiment, the interference pattern can be used to demonstrate the phenomenon of quantum entanglement. For example, if two particles are entangled and then directed towards the double slit, the interference pattern observed on the screen will depend on the state of the entangled particles.Overall, the double-slit experiment is a powerful and versatile tool for exploring the fundamental nature of reality at the quantum level. It has been used to demonstrate the wave-particle duality of light and other quantum particles, the observer effect, and the phenomenon of quantum entanglement. As such, it remains one ofthe most important and influential experiments in the history of science.。
市售干海参中非法添加的蔗糖和无机成分的X射线衍射质量控制
市售干海参中非法添加的蔗糖和无机成分的X射线衍射质量控制路大勇1,2，项太平1（1.吉林化工学院材料科学与工程学院，吉林吉林 132022）（2.吉林省高校特种功能材料重点实验室，吉林吉林 132022）摘要：粉末X射线衍射（PXRD）是一种简单快捷的无损检测技术，该技术罕有海参及其非法添加剂的检测应用。
本研究建立一种干海参中非法添加糖分的PXRD鉴定方法。
对随机采购的8种市售干海参刺参（呈甄干海参、棒棰岛干海参、辽刺参、精品海参、俄罗斯海参、野生海参、财神岛干海参、长生岛干海参），获得PXRD谱及特征标记峰。
运用有机分子晶体的PXRD谱模拟方法，鉴定糖分来源及其含量。
结果表明：海参体壁没有任何种类的有机分子晶体，海参沙嘴主要成分为具有菱方结构的碳酸镁钙（Mg0.1Ca0.9CO3），人为掺入的蔗糖能够在干海参中结晶，形成能被PXRD技术探测的系列衍射峰。
辽刺参中掺有糖分，被鉴定为蔗糖，其含量达4.45 g/100 g；呈甄干海参、棒棰岛干海参、辽刺参、精品海参、俄罗斯海参、野生海参、财神岛干海参、长生岛干海参中盐分含量分别为：3.62 g/100 g、4.40 g/100 g、3.55 g/100 g、2.87 g/100 g、1.60 g/100 g、15.56 g/100 g、2.35 g/100 g、3.90 g/100 g；呈甄干海参、棒棰岛干海参、精品海参、俄罗斯海参、野生海参、财神岛干海参、长生岛干海参中含沙量分别为：2.12 g/100 g、0.62 g/100 g、0.14 g/100 g、0.22 g/100 g、0.38 g/100 g、0.85 g/100 g、0.90 g/100 g。
因此，PXRD技术适合于市售干海参糖分和盐分的质量控制。
关键词：干海参；食品安全；粉末X射线衍射；盐分；蔗糖；碳酸镁钙文章篇号：1673-9078(2021)05-262-270 DOI: 10.13982/j.mfst.1673-9078.2021.5.0906 X-ray Diffraction Quality Control of the Illegally Added Sucrose and Inorganic Components in Commercial Dried Sea CucumberLU Da-yong1,2, XIANG Tai-ping1(1.College of Materials Science and Engineering, Jilin Institute of Chemical Technology, Jilin 132022, China)(2.Key Laboratory for Special Functional Materials in Jilin Provincial Universities, Jilin 132022, China)Abstract: Powder X-ray diffraction (PXRD) is a simple and rapid non-destructive test technique, which has rarely been applied to the detection of sea cucumber and its illegal additives. In this work, a PXRD identification method was set up for detecting illegally-added sugar in dried sea cucumber. Eight kinds of commercial dried sea cucumbers (Cheng Zhen dried Sea cucumber, Bangchui Island dried sea cucumber, Liao sea cucumber, high-quality sea cucumber, Russian sea cucumber, wild sea cucumber, Caishen Island dried sea cucumber and Changsheng Island dried sea cucumber) were purchased randomly, and their PXRD patterns and characteristic mark peaks were obtained. The PXRD spectrum simulation of organic molecular crystals was applied to identify the origin and content of the sugar in the sea cucumbers. The results indicated that there were no organic molecular crystals existed in the body walls of sea cucumber, and the main component of sea cucumber sand mouth was magnesium calcium carbonate (Mg0.1Ca0.9CO3) with a rhombohedral structure. The artificially incorporated sucrose could crystallize 引文格式：路大勇,项太平.市售干海参中非法添加的蔗糖和无机成分的X射线衍射质量控制[J].现代食品科技,2021,37(5):262-270,337LU Da-yong, XIANG Tai-ping. X-ray diffraction quality control of the illegally added sucrose and inorganic components in commercial dried sea cucumber [J]. Modern Food Science and Technology, 2021, 37(5): 262-270,337收稿日期：2020-09-28基金项目：长白山学者特聘教授支持计划（2015047）；吉林省中医药科技委托重点项目（2020037）作者简介：路大勇（1967-），男，博士，教授，研究方向：高介电陶瓷材料、变温测试技术、晶体药物及中药质量控制、无机-有机复合材料、胆结石精准鉴定与医疗262in dried sea cucumber, thereby forming a series of diffraction peaks that were detected by PXRD technique. Sucrose was illegally added to Liao sea cucumber at a content of 4.45 g/100 g. The salt contents of Cheng Zhen dried Sea cucumber, Bangchui Island dried sea cucumber, Liao sea cucumber, high-quality sea cucumber, Russian sea cucumber, wild sea cucumber, Caishen Island dried sea cucumber and Changsheng Island dried sea cucumber were 3.62 g/100 g, 4.40 g/100 g, 3.55 g/100 g, 2.87 g/100 g, 1.60 g/100 g, 15.56 g/100 g, 2.35 g/100 g and 3.90 g/100 g, respectively. The sand contents of Cheng Zhen dried sea cucumber, Bangchui Island dried sea cucumber, high-quality sea cucumber, Russian sea cucumber, wild sea cucumber, Caishen Island dried sea cucumber and Changsheng Island dried sea cucumber were 2.12 g/100 g, 0.62 g/100 g, 0.14 g/100 g, 0.22 g/100 g, 0.38 g/100 g, 0.85 g/100 g and 0.90 g/100 g, respectively. Thus, the PXRD technique is suitable for quality control of sugars and salt in commercial dried sea cucumber.Key words: dried sea cucumber; food safety; powder X-ray diffraction; salt; sucrose; magnesium calcium carbonate海参隶属于棘皮动物门（Echinodermata）海参纲（Holothrioider），是一种传统的名贵海产品，被誉为“八珍之首”。
Strong-Coupling Theory of High Temperature Superconductivity
INTRODUCTION
The seminal work by Bardeen, Cooper and Schrieffer (BCS)[1] extended further by Eliashberg [2] to the intermediate coupling regime solved one of the major scientific problems of Condensed Matter Physics in the last century. While the BCS theory provides a qualitatively correct description of some novel superconductors like magnesium diboride and doped fullerenes, if the phonon dressing of carriers (i.e. polaron formation) is properly taken into account, high-temperature superconductivity (HTS) of cuprates represents a challenge to the conventional theory. Here I discuss a multi-polaron approach to the problem based on our extension of the BCS theory to the strong-coupling regime [3]. Attractive electron correlations, prerequisite to any HTS, are caused by an almost unretarded electron-phonon (e-ph) interaction sufficient to overcome the direct Coulomb repulsion in this regime. Low energy physics is that of small polarons and bipolarons (real-space electron (hole) pairs dressed by phonons). They are itinerant quasiparticles existing in the Bloch states at temperatures below the characteristic phonon frequency. Since there is almost no retardation (i.e. no Tolmachev-Morel-Anderson logarithm) reducing the Coulomb repulsion, e-ph interactions should be relatively strong to overcome the direct Coulomb repulsion, so carriers must be polaronic to form pairs in novel superconductors. I identify the Fr¨ ohlich electron-phonon interaction as the most essential for pairing in superconducting cuprates. Many experimental observations have been satisfactorily understood in the framework of the bipolaron theory [3] providing evidence for a novel state of electronic matter in layered cuprates, which is a charged Bose-liquid of small mobile bipolarons. Here the band structure and essential interactions in oxide superconductors are discussed
混凝土裂缝扩展的断裂过程准则与解析_徐世烺
第25卷增刊II V ol.25 Sup.II 工 程 力 学 2008年 12 月 Dec. 2008ENGINEERING MECHANICS20———————————————收稿日期：2008-06-16基金项目：国家杰出青年科学基金项目(59625814)作者简介：*徐世烺(1953―)，男，湖北咸宁人，教授，博士，主要从事混凝土断裂力学理论与应用及新型材料与结构的研究工作(E-mail: slxu@)；赵艳华(1974―)，女，山西人，副教授，博士，主要从事混凝土断裂性能的研究工作(E-mail: zyhua74@).文章编号：1000-4750(2008)Sup.II-0020-14混凝土裂缝扩展的断裂过程准则与解析*徐世烺，赵艳华(大连理工大学土木水利学院，辽宁，大连116024)摘 要：该研究工作对混凝土这一多相的复合材料，通过实验和理论相结合的科学手段，建立了一套完整的描述混凝土裂缝发展的断裂理论以及分析方法。
根据实验观测结果提出了双K 断裂参数，可以反映混凝土裂缝发展特性。
在线形渐进叠加假定基础上，给出了双K 断裂参数的解析表达式。
根据分布于断裂过程区上粘聚力对裂缝扩展阻力的增强作用，得到了双K 断裂参数适用的解析解，并通过实验分析了各种可能因素对双K 断裂参数的影响。
在考虑粘聚力影响条件下，提出了裂缝扩展阻力的新K R 曲线，并将双K 断裂参数与之对应起来。
研究工作又通过能量的观点提出了与双K 断裂参数相对应的以能量释放率为参数的双G 断裂参数。
通过数值计算和实验分析证实了能量法和应力场法在描述混凝土断裂性能方面的等效性。
关键词：混凝土；断裂力学；断裂韧度；裂缝扩展；双K 断裂参数；新K R 阻力曲线；双G 断裂参数；裂缝粘聚力 中图分类号：TU528; O346.1 文献标识码：AANALYSIS AND CRITERION OF FRACTURE PROCESS FOR CRACKPROPAGATION IN CONCRETE*XU Shi-lang , ZHAO Yan-hua(School of Civil and Hydraulic Engineering, Dalian University of Technology, Dalian, Liaoning 116024, China)Abstract: For concrete-like multi-phase materials, systematic theories and analysis methods of crack propagation were established by combing fracture theories and testing techniques. Double-K fracture parameters were therein introduced based on experimental observations, which could be used to characterize crack propagation. Based on the hypothesis of linear asymptotic superposition, an analytical expression for double-K fracture parameters was given, and a practical estimation of their values was also provided according to the reinforcement to the crack extension resistance by cohesive force acting along the fracture process zone. And experiments were conducted to examine some possible influence factors on double-K fracture parameters. A novel K R curve was presented to depict crack propagation resistance. Parallel to double-K fracture parameters, double-G fracture parameters in the form of energy release rate were put forward. Numerical calculation and experimental analysis verified that the two methods, stress intensity factor and energy release rate, are equivalent in describing fracture features of concrete.Key words: concrete; fracture mechanics; fracture toughness; crack propagation; double-K fracture parameters;new K R resistance curve; double-G fracture parameters; cohesive force断裂力学是研究结构裂缝发展规律的有效工具，其中适用于玻璃等脆性材料的线弹性断裂力学(LEFM)已发展的较为成熟和完善，针对金属的弹塑性断裂力学(EPFM)也有了长足的发展。
Nuclear physics aspects of double beta decay
Petr Vogel
Kellogg Radiation Laboratory 106-38 California Institute of Technology Pasadena, CA 91125, USA Lecture notes for course CLXX “MEASUREMENTS OF NEUTRINO MASS” Int. School of Physics “Enrico Fermi”, Varenna, June 2008
arXiv:0807.2457v1 [hep-ph] 15 Jul 2008
Summary. — Comprehensive description of the phenomenology of the ββ decay is given, with emphasis on the nuclear physics aspects. After a brief review of the neutrino oscillation results and of motivation to test the lepton number conservation, the mechanism of the 0νββ is discussed. Its relation to the lepton flavor violation involving charged leptons and its use as a diagnostic tool of the 0νββ mechanism is described. Next the basic nuclear physics of both ββ -decay modes is presented, and the decay rate formulae derived. The nuclear physics methods used, the nuclear shell model and the quasiparticle random phase approximation, are described next, and the choice of input parameters is discussed in the following section. Finally, the numerical values of the nuclear matrix elements, and their uncertainty, are presented. In the appendix the relation of the search for the neutrino magnetic moment to the Dirac versus Majorana nature of neutrinos is described. PACS 21.60.-n – . PACS 23.40.Bw – . PACS 23.40.Hc – .
Sliding microindentation fracture of brittle materials Role of elastic stress fields
Sliding microindentation fracture of brittle materials:Role of elastic stress ®eldsY.Ahn a ,T.N.Farrisb,*,S.ChandrasekarbaDepartment of Mechanical Engineering,Hanyang University,Seoul,South KoreabSchools of Engineering,Purdue University,1282Grissom Hall,West Lafayette,IN 47907-1282,USAReceived 5April 1997;revised version received 15August 1997AbstractAn analytical model of the stress ®eld caused by sliding microindentation of brittle materials is developed.The com-plete stress ®eld is treated as the superposition of applied normal and tangential forces with a sliding blister approxi-mation of the localized inelastic deformation occurring just underneath the indenter.It is shown that lateral cracking is produced by the sliding blister stress ®eld and that median cracking is caused by the applied contact forces.The model is combined with measurements of the material displacement around an indentation to show that the relative magnitude of tensile stresses governing lateral crack and median crack growth varies with the magnitude of the applied load.The model also predicts a range of loads at which the lateral crack will grow only after the indenter is removed from the surface.These predictions are consistent with observations of the di erent regimes of cracking observed under a sliding pyramidal indenter in soda±lime glass and other brittle solids.Ó1998Elsevier Science Ltd.All rights reserved.1.IntroductionMicroscopic observations of machined ceramic surfaces show that brittle fracture contributes sub-stantially to material removal in abrasive machin-ing processes.A careful examination of the fractures in machined ceramics reveals striking similarities with fractures about quasi-static and sliding indentations produced by sharp indenters in brittle solids.It was,therefore,decided to devel-op a model for characterizing the stress ®elds pro-duced by sliding,sharp indenters in brittle solids (Ahn et al.,1993).This model is an extension of that proposed by Yo e (1982)to describe the stress ®elds and fractures generated under a qua-si-static indentation by a pointed indenter in brittlematerials.The paper begins with a review of the deformation produced under a pointed indenter which leads to a discussion of the Yo e model fol-lowed by a summary of the sliding microindenta-tion model.When a sharp indenter is quasi-statically ap-plied onto the surface of a brittle solid,the classi-cal theory relating the hardness to the yield stress of metals (Tabor,1951)no longer applies since yielding no longer occurs at a constant maximum shear stress or at a constant volume (Bridgman and Simon,1953).A large body of experimental observations has shown that in brittle materials,the volume of material displaced by the penetra-tion of the indenter is accommodated by compac-tion or shear deformation,or both,and this may occur either uniformly or irregularly.In silicate glasses,which have a relatively open structure,the displaced material is most readilyaccommodatedMechanics of Materials 29(1998)143±152*Corresponding author.E-mail:farrist@.0167-6636/98/$±see front matter Ó1998Elsevier Science Ltd.All rights reserved.PII:S 0167-6636(98)00012-Xby compaction within a zone underneath the ind-enter.However,in soda±lime glasses and in most ceramics shear deformation dominates with some compaction also taking place underneath the ind-enter.The experimental model used by Yo e to describe the deformation underneath a sharp con-ical indenter in soda±lime glass is based on the work of Peter (1970),amongst others,who showed that the mean contact pressure under a sharp ind-enter remains constant and relatively independent of the indenter geometry.This model assumes that as a conical indenter is applied to the solid surface,yielding initially occurs in a hemi-spherical bowl under the indenter and continues until the yielded zone attains its stable preferred state for that pres-sure.As the indenter is loaded further,no addi-tional ¯ow occurs within this bowl,but fresh yielding takes place in an adjoining thin hemi-spherical shell.This process continues and ``it is as if a set of nested hemi-spherical bowls separated by plastic ®ller were forced down in turn,one with-in the other,and become locked in the positions shown in Fig.1(a)(Yo e,1982)''.The yielding process occurs through a combination of shear de-formation and compaction within the yielded zone.Part of the material displaced by the indenter is accommodated by compaction within the yield-ed zone while the remaining material is pushed into the surroundings.At the end of the indenta-tion process,the elastic half-space is left with an over-large hemi-spheroid ®xed in a hemi-spherical cavity on its surface.This mis®t leads to a residual stress in the region outside of the cavity.Conse-quently,as the material reacts to this residual stress,cracking may occur within the solid.The ``blister''®eld proposed by Yo e (1982)was for describing the development of cracksbelow a conical indenter acting on a brittle solid.Yo e assumed that the inelastic zone underneath the indenter is hemi-spherical in shape with a radi-us equal to the contact radius (Fig.1(a)).The stress distribution in the surrounding elastic zone was obtained as the superposition of two stress ®elds ±the Boussinesq ®eld for the point force which idealized the indentation pressure distribu-tion and a doublet force system which idealized the localized inelastic deformation.The doublet force system for the blister ®eld consisted of super-position of a point center of expansion in an in®-nite elastic solid with an additional doublet to satisfy the free surface normal stress boundary condition.Such a doublet force system leads to a volume increase of the inelastic deformation zone that must be taken up by compaction or elastic de-formation of the remainder of the solid.The vol-ume increase is a measure of the ``strength''of the blister ®eld.The strength of the blister ®eld varies with the applied force;this variation is char-acterized by a material property which has thus far de®ed a precise estimation.Qualitatively,Yo e's model has predicted the origin and growth of radi-al,median,and lateral crack systems quite well.In particular it is consistent with the observation that for a certain range of loads,the lateral crack forms and grows during unloading.Its only disad-vantage is from a quantitative point of view as a procedure for determining the strength of the blis-ter ®eld for various indenter geometries is not yet available.Models to describe the sliding indentation frac-ture process in ceramics have not yet evolved to a stage where the inelasticity under the indenter is accounted for completely (Swain,1979;Misra and Finnie,1979;Chen et al.,1991).This is in large part due to the di culty introduced by a lack of information concerning the constitutive behav-ior of ceramics in large hydrostatic compressive stress ®elds such as that existing underneath a mic-roindentation.It seems that a reasonable ®rst step for modeling the sliding indentation stress ®elds would be to extend Yo e's work on static indenta-tion to the sliding situation.This extension should include the load-history e ects of inelastic defor-mation left behind by the sliding indenter and the elastic e ects due to the frictionalforce.Fig.1.(a)Indentation by yielding of successive bowls and (b)force doublet used for blister ®eld.144Y.Ahn et al./Mechanics of Materials 29(1998)143±152In this paper,an extension of Yo e's blister ®eld is proposed to model sliding microindentation stress®elds.This extension,called the sliding blis-ter®eld,is discussed in Section2.In Section3,the predictions of this theory are compared to the ex-perimental observations of Ahn(1992)of fractures around sliding indentations made through exami-nation of the fractured specimens after testing. There is also brief discussion of recent in-situ,ex-perimental observations of cracking(Bulsara, 1997)that are explained qualitatively by the sliding blister®eld model.2.Sliding blister stress®eldsA schematic illustration of the sliding microin-dentation geometry and the location of the inelas-tic deformation zone is shown in Fig.2.The pointed indenter is loaded normal to the surface by the load P acting in the z-direction and tangen-tially by the force Q acting in the x-direction.As we are interested in details of the stress®eld out-side the inelastic zone,for simplicity we use the Boussinesq and Cerruti solutions for concentrated point forces rather than the actual contact pressure distribution acting between the indenter and spec-imen surface.It is assumed that the inelastic defor-mation occurs in a region whose boundary in front of the sliding indentation takes the shape of one-fourth of a sphere with radius a equal to the half-width of the groove.Note that this is analo-gous to one-half of Yo e's nested bowls but that the load history behind the indenter is somewhat di erent from the quasi-static case.During steady sliding,the inelastic zone behind the indenter takes the shape of a half cylinder of radius a and length equal to the total sliding distance.In the following, the well known solutions for the concentrated nor-mal and tangential loading of a half-space is given followed by the sliding blister®eld solution. Recalling the coordinate system of Fig.2,the Boussinesq®eld for the concentrated normal force P acting normal to the surface of a semi-in®nite half-space at the origin is(Johnson,1985)r n x2p1À2mr1Àzqx2Ày2rzy2q&'À3zx2q!Y1 r n y2p1À2mr1Àzqy2Àx2rzx2q&'À3zy2q!Y2 s n xy2p1À2mr21Àzqxyr2Àxyzq3&'À3xyzq5!Y3 r n z À32pz3qY s n yz À32pyz2qY s n zx À32pxz2qY4 where r2 x2 y2and q2 x2 y2 z2de®ne the distance from the load to the®eld point in the xy plane and the total distance,respectively,and m is Poisson's ratio.The corresponding stress compo-nents due to the concentrated tangential force Q acting at the origin in the positive x-direction are given by(Johnson,1985)r t x À2p3x3q5À 1À2mxq3À3xq q z 2@4x3q3 q z 22x3q2 q z 3A5Y 5 r t y À2p3xy2qÀ 1À2mxqÀxq q z 2@4xy2q3 q z 22xy2q2 q z 3A5Y 6 s t xy À2p3xy2q1À2myq q z 2@4Àx2yq3 q z 2À2x2yq2 q z 3A5Y 7Fig.2.Schematic side view of sliding microindentation andmoving coordinate system.Y.Ahn et al./Mechanics of Materials29(1998)143±152145r t z À2p3xz2q5Y s t yz À2p3xyzq5Ys t zx À2p3x2zqX 8The superscripts n and t denote normal and tan-gential loading,respectively.The loads applied to the indenter are supported by these elastic stresses which decay as1a q2as q3I.These stresses are also singular at the point of load application,how-ever we do not investigate crack formation and growth there as it is part of the inelastic zone in which these equations do not apply.In addition to the stresses due to the loading of the indenter,there are stresses induced in the elas-tic zone due to the mis®t of the deformation occur-ring in the inelastic zone.For normal quasi-static indentation,Yo e(1982)calculates this stress using a single blister®eld.During sliding these mis®t strains accumulate behind the indenter.In the sequel,this e ect is approximated by accumu-lating blister®elds behind the sliding indenter. The calculation of the e ect of the accumulated blister®eld begins with the blister®eld derived by Yo e(1982)to describe quasi-static(normal)in-dentation residual stresses.Yo e's blister®eld is made up of the doublet force system shown in Fig.1(b)which consists of the superposition of two full-space elastic stress systems.These two sys-tems are a center of dilatation or three orthogonal doublets,and a doublet of twice this strength ap-plied in opposite sense perpendicular to the surface of the half-space.The resulting stress system,two outward double forces in the surface plane and an inward double force of equal magnitude perpendic-ular to it,satis®es the free surface condition along the surface of the half-space.The stress compo-nents of the resulting blister®eld are(Yo e,1982)r b x 2e1À2m x2 2y2r qÀ5 4m x2qÀ1À2m 2x2 3y2 z2r2q515x2z2q7Y 9r b y 2e1À2m 2x2 y2r qÀ5 4m y2qÀ1À2m 3x2 2y 2z2r2q515y2z2q7Y 10s b xy2eÀ1À2m xyr2q35À4m xyq5À1À2m xyz2r2q5À15xyz2q7!Y 11r b z2eÀ3z2q3À5z2q!Ys b yz2eÀ6yzqÀ15yz3q!Ys b zxÀ6xzÀ15xz3!Y 12where A is the strength of the blister®eld.It isclear from Eq.(12)that the blister®eld is associat-ed with zero surface traction.The accumulated blister®eld due to sliding istreated by taking the strength of the blister®eldper unit sliding length,B,as e f n d n.De®ninga function f such thatr b x ef r x Y y Y z Ythe residual stress due to the sliding blister®eld isr r xf n f r xÀn Y y Y z d n Xwhere the indenter slides from x to x .Theremaining components of the residual or slidingblister®eld stresses are calculated using the sameprocedure.The experimental con®guration of inte-rest corresponds to sliding the indenter over alength,large compared to the contact size,and ex-amination of the stresses near the indenter's presentlocation.This special case corresponds to f n f,a constant, ÀI Y 0,for which integrationleads to the following residual stress®eld:r r x2fÀ2m y2Àz2y2 z2 2xy2 z2 q5Â 2m x4y2À2x2y4 6m x2y4À2y6 4m y6À2m x4z2À4x2y2z2 2m x2y2z2À3y4z2 6m y4z2À2x2z4À4m x2z4 z6À2m z6 Y 13r r y2fÀ2y2 y2À3z2y2 z2 3xy2 z2 3q5Â 2x4y46x2y6À2m x2y6 4y8À2m y8À6x4y2z2À7x2y4z2À6m x2y4z2À2y6z2À8m y6z2À12x2y2z4À6m x2y2z4À15y4z4À12m y4z4x2z6À2m x2z6À8y2z6À8m y2z6 z8À2m z8 Y14146Y.Ahn et al./Mechanics of Materials29(1998)143±152r r z2f 2z 2 z 2À3y 2 y 2 z 2 3 xz 2 y 2 z 2 3q 5Â 6x 4y 215x 2y 4 9y 6À2x 4z 2 10x 2y 2z 2 12y 4z 2À5x 2z 4À3y 2z 4À6z 6 Y15s r xy2f Ày 2 1Àm x 2 2 1Àm y 2Àz 2À2m z 2q 5Y s r yz2f À4yz y 2Àx 2 y 2 z 23 xyz y 2 z 2 2q 5Â 4x 4y 210x 2y 4 6y 6À4x 4z 2 3y 4z 2À10x 2z 4À12y 2z 4À9z 6 Y 16 s r zx2f Àz 2x 2 2y 2Àz 2 q X 17 In the above expressions for the residual stress ®eld,the origin is located at the present indenter location (Fig.2).The complete stress ®eld is obtained by adding the elastic ®elds due to the normal and tangential loads to the residual stress ®eld as r r n r t r r Ys s n s t s r X3.Results and discussionWith the derivation of the sliding indentation stress ®eld in place,it is now possible to analyze observations of the microcracking about scratches in brittle solids made by Swain (1979),Misra and Finnie (1979),Ahn (1992),and Bulsara (1997).Fig.3shows a schematic view of the crack pat-terns which have emerged from the studies,most of which have been carried out at light loads in so-da±lime glass,silicon,polycrystalline alumina,and Ni±Zn ferrite.The typically observed crack pat-terns are median,lateral,and chevron (radial)cracks.The load regimes at which the various cracks occur in soda±lime glass are summarized in Table 1which is obtained based on observa-tions of the fractured specimen.In situ observations indicate that these cracks initiate at or close to the boundary between the in-elastic deformation zone and the surrounding elas-tic solid.The subsequent growth of these cracks occurs in the elastic region.Bulsara (1997)ob-serves that for most loads at which the median and lateral cracks occur,the cracks propagate such that the crack front moves with the load.However,near loads of about 1N applied with a Vickers indenter in soda±lime glass the lateral crack does not appear until the indenter is lifted from the sur-face.Once the load is removed,the lateral crack forms beneath the end of the scratch and propa-gates rapidly along the entire length of the scratch and until the beginning of the scratch track where it stops.The assumption that these cracks are initiated and propagated by tensile stresses which occur in the elastic material immediately adjoining the in-elastic zone allows for predictions of crack forma-tion and growth through a consideration of the stress ®elds.The stress ®elds are now examined in detail to determine whether the peak tensile stresses are consistent with the occurrence of ex-perimentally observed cracking.Under this as-sumption,the occurrence of the median crack is thus related to r y x Y 0Y ,the lateral crack toTable 1Classi®cation of fracture patterns in soda±lime glass under a sliding Vickers indenter (Ahn,1992)Normal load (N)Fracture pattern$0±0.05No crack$0.05±0.8Median crackingMedian and lateral cracking$0.8±3with lateral crack growth to the surface at higher loads$3±6Median cracking and crushed scratchtrackFig.3.Schematic view of cracking induced by sliding microin-dentation of brittle solids.Y.Ahn et al./Mechanics of Materials 29(1998)143±152147r z x Y 0Y ,and the radial crack to r x x Y Y 0 .There-fore,the magnitudes of these stresses are now com-pared to predict which crack patterns are most likely to occur at a given load.The calculations will refer to detailed experimental observations in soda±lime glass.Hence its Young's modulus,E 70GPa,and Poisson's ratio,m 0X 25,are used in Eqs.(1)±(17)for the ensuing calculations.3.1.Residual stressFig.4shows the residual normal stress distribu-tions as a function of x for locations at which me-dian,lateral and radial cracks occur.For comparison to subsequent plotting of the complete stress ®eld,the residual stresses are nondimension-alized using P /2a 2(the average contact pressure)and plotted for the case B /P 0.005.The stresses correspond to the indenter having moved from x ÀI to x 0,its present location.The residual stress ®eld equals the complete stress ®eld for large negative values of x /a .The residual stress r r z x Y 0Y is tensile below the scratch with its max-imum value just behind the indenter at x $À2a 3 .On the other hand,the normal stresses r r y x Y 0Yand r rx x Y Y 0 ,are compressive almost everywhere behind the indenter.The tensile nature of r r z x Y 0Y behind the indenter is a possible cause of lateral cracking in a plane perpendicular to the z -axis in the wake of the indenter.Such lateral cracking was commonly observed by Ahn (1992)at normal loads in the range of 0X 8$3Newtons.The residual stress ®eld is in plane strain in the y ±z plane once the indenter passes su ciently faraway from that point,i.e.for su ciently large neg-ative values of x /a .Fig.5shows the residual stress distribution in this plane strain ®eld.The normal stress r r z À2 Y y Y reaches its maximum tensile value at y 0which is consistent with lateral crack initiation behind the indenter.If the growth of this crack is determined by the maximum local tensile stress,then the direction of crack propagation may be also predicted using the residual shear stress in Fig.5.The sign of the shear stress for j y j ` is consistent with lateral crack growth that begins parallel to the x ±y plane subsequently turn-ing slightly out the plane and growing towards the surface as indicated schematically in Fig.2.The fact that r r y is tensile away from y 0is also con-sistent with lateral crack growth towards the sur-face.These conclusions are drawn from the assumption that the crack grows perpendicular to the maximum principal stress if it is tensile.However,the stress results alone do not explain well why the observed lateral crack is much longer than the width of the scratch.A more detailed fracture mechanics analysis that includes the e ect of the cracking on the stress ®eld is required to ful-ly explain the lateral crack growth plete stress ®eldThe complete stress ®eld requires the nor-mal (P )and tangential forces (Q )which are related by lYFig.4.Residual normal stress distribution at the edge of the in-elastic zone (B /P0.005).Fig.5.Plane strain residual normal and shear stress distribu-tions versus position perpendicular to the scribing direction (B /P 0.005).148Y.Ahn et al./Mechanics of Materials 29(1998)143±152where l is the coe cient of friction.When sliding a Vickers diamond indenter against soda±lime glass at extremely slow speeds (5mm/min)and at low loads (0.1$4N),Ahn (1992)measured l 0X 13Æ0X 033.Thus,to compare the stress ®eld with crack observations the following calculations use l 0X 13.Figs.6and 7illustrate the complete normal stress ®eld acting in the uncracked body at the locations where the median,lateral,and radial cracks are observed to occur.In particular,the stresses are given for two ratios of B /P .The nor-mal stress r y has its maximum at x %0so that me-dian cracking is expected just underneath the indenter.The normal stress r x has a maximum at x %À1X 3 .Thus radial cracks could be initiated at a distance behind the moving indenter.In the range of x T $À2 ,the normal stress r z main-tains its maximum value,so that any lateral crack-ing that does occur is expected to propagate the full length of the scratch driven by the residual stress ®eld.For f a `$0.005(see Fig.6),the maxima of the tensile stress r x and r z are smaller than that of r y .This is consistent with observa-tions of median cracking without lateral cracking for some load ranges.In summary,the tensile stresses which deter-mine the various types of cracking are r z À2a 3 Y 0Y for lateral cracking,r y 0Y 0Y for median cracking,and r x À1X 3 Y Y 0 for radial cracking.Furthermore,the formation of median cracking alone is generally expected only for small values of B /P i.e.when the strength of the residual stress ®eld,B ,is small or P is large.Also it can be said that lateral cracking is driven by residual stressrather than the applied loads.The residual stress that drives lateral cracking has a slight peak just behind the location of the indenter (Fig.4).4.Sliding blister ®eld strengthThe stress ®elds derived from the sliding inden-tation model depend on the factor B which may be termed,by analogy with Yo e's blister ®eld con-stant,A ,as the strength of the sliding indentation blister ®eld.At present there exists no well de®ned experiment which can be used to unambiguously obtain the values of A or B .Next B is estimated from certain experimental observations.Bridgman and Simon (1953)showed that most glasses undergo a certain amount of compaction under stress.For calculating B ,it will be assumed that any compaction of the glass which occurs un-der the sliding indenter is completely accommodat-ed within the inelastic zone.Furthermore,the remaining volume of material displaced by the ind-enter is assumed to be pushed out of the inelastic zone.For static indentation with a sharp indenter,the increase in volume of any hemi-sphere of radi-us q (q b Y inelastic zone radius)is indepen-dent of q and the volume change is given by D 2p e1À2m3qY 18where A is the strength of the doublet producing the static indentation blister ®eld and G is the shearmodulus.plete normal stress distributions at the edge of the inelastic zone (B /P0.0025).plete normal stress distributions at the edge of the inelastic zone (B /P 0.025).Y.Ahn et al./Mechanics of Materials 29(1998)143±152149Fig.8shows a schematic of a typical pro®le ta-ken across a scratch track in glass produced by a sliding Vickers indenter at light loads ($0X 05±0X 1N);see Ahn (1992)for actual scratch pro®les.Small humps appear on either side of the scratch track,which in the absence of any cracking around the indentation,is mostly due to upward ¯ow of the material.Such a pro®le suggests that some of the material displaced by the indenter is also ac-commodated by this upward ¯ow.The upward plastic ¯ow factor,F p ,is de®ned,using Fig.8,as p pw yeh À w efg w hipw yfiY 19where w yeh is the area of the triangle having ver-tices O ,A ,and D .While estimating B ,it is neces-sary to also account for this upward ¯ow of the material.By analogy with the static indentation blister ®eld,we can estimate the increase in volume around an in®nitely long scratch due to the sliding indentation blister ®eld asliml 3I lÀlf D x Àn Y y Y z d n liml 3I 2 2l tan h 2 33tan hÀp 2l8p 33 d c !p p Y 20 where d c a is the compaction ratio for glass andp p is the upward plastic ¯ow factor.The terms in the ®rst parenthesis of the right-hand side of Eq.(20)represent the impression volume of the sliding indentation and the terms in the second pa-renthesis represent the original volume of plastic deformation zone.The parameters a and h are de-®ned in Fig.8.Combining Eqs.(18)and (20)givesf3q 22p 1À2m1tan h Àp 2d cp p 21and B can now be estimated if the compaction ra-tio (d c a )and F p are known.The value of compaction ratio for soda±lime glass can be estimated using a curve ®t of the data of Cheng et al.(1990)for the compaction of soda±lime glass under hydrostatic pressure.Their equa-tion isd c % 0X 951À0X 729p 1X 934p 2 0X 260p 31 p2Y 22where p is the applied hydrostatic pressure in GPa.In order to estimate the values of a ,h ,and F p ,ex-perimental measurements of the width (2a )and depth a tan h of a scratch track in soda±lime glass were carried out for various applied loads (0.05±0.8N).From the experimental data the half-width of the track,a l m ,can be expressed as a function of P (N)as 9X 48 0X 57X23The average value of h was obtained from Talysurf pro®les of a number of scratch tracks as 83.6° ing the pro®lometric measurements,the average value of F p was estimated as 0.055.Combining the above leads to an estimation of the blister ®eld strength,B ,as a function of normal load,P .This is shown in Fig.9.The value of B in-creases monotonically with applied load P .Due to the nature of the increase in B with P showninFig.8.Sketch of surface pro®le across a scratch track made by a sliding Vickers indenter in soda±lime glass (load $0.05±1N).The ratio of vertical to horizontal magni®cation is5:1.Fig.9.Strength of residual stress ®eld as a function of applied load.150Y.Ahn et al./Mechanics of Materials 29(1998)143±152。
A New Equation of State for Carbon Dioxide Covering the Fluid Region
1514
1514 1516 1516 1516 1516 1517 1517 1518 1518
3.3 3.4 3.5 3.6 3.7 3.8 4.
Melting Pressure. . . . . . . . . . . . . . . . . . . . . . .. Sublimation Pressure. . . . . . . . . . . . . . . . . . . .. Vapor Pressure ....................... " Saturated Liquid Density. . . . . . . . . . . . . . . .. Saturated Vapor Density. . . . . . . . . . . . . . . . .. Caloric Data on the Liquid-Vapor Phase Boundary. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Experimental Basis of the New Equation of State. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 4.1 Thermal Properties .................... " 4.2 Specific Isobaric Heat Capacity. . . . . . . . . . .. 4.2.1 Experimental Results for the Specific Isobaric Heat Capacity. . . . . . . . . . . . .. 4.2.2 Results for the Specific Isobaric Heat
Colloids and Surfaces B Biointerfaces
operational stability. Another problem associated with enzyme electrodes is their rather slow heterogeneous electron transfer rates. The following three facts and/or the combination of them can be the major causes of the low electron transfer rate: (1) the electroactive prosthetic groups are often deeply buried within the complex structure of enzymes; (2) the enzymes adsorbed on the electrodes might have been denatured; and (3) the orientations of the enzymes on the electrodes might be unfavorable to the electron transfer [5,6]. Enzyme immobilization has become a vital step in overcoming these problems [7–11].
BEC-BCS crossover, phase transitions and phase separation in polarized resonantly-paired su
arXiv:cond-mat/0607803v2 [cond-mat.supr-con] 23 Jan 2007
Background and Motivation
One of the most in the study of degenerate atomic gases has been the observation1–9 of singlet paired superfluidity of fermionic atoms interacting via an s-wave Feshbach resonance10–18 . A crucial and novel feature of such experiments is the tunability of the position (detuning, δ ) of the Feshbach resonance, set by the energy of the diatomic molecular (“closed-channel”) bound state relative to the open-channel atomic continuum, which allows a degree of control over the fermion interactions that is unprecedented in other (e.g., solid-state) contexts. As a function of the magnetic-field controlled detuning, δ , fermionic pairing is observed to undergo the Bose-Einstein condensate to Bardeen-Cooper-Schrieffer (BEC-BCS) crossover19–29 between the Fermi-surface momentum-pairing BCS regime of strongly overlapping Cooper pairs (for large positive detuning) to the coordinate-space pairing BEC regime of dilute Bosecondensed diatomic molecules (for negative detuning). Except for recent experiments30–35 that followed our original work36 , and a wave of recent theoretical37–83 activity, most work has focused on the case of an equal mixture of two hyperfine states (forming a pseudo-spin 1/2 system), observed to exhibit pseudo-spin singlet superfluidity near an s-wave Feshbach resonance. Here we present an extensive study of such systems for an unequal number of atoms in the two pairing hyperfine states, considerably extending results and calculational details beyond those reported in our recent Letter36 . Associating the two pairing hyperfine states with up (↑) and down (↓) projections of the pseudo-spin 1/2, the density difference δn = n↑ − n↓ between the two states is isomorphic to an imposed “magnetization” m ≡ δn (an easily controllable experimental “knob”), with the chemical potential dif-
负折射率隐身衣英文版
Ran Duan,1 Elena Semouchkina,2,* and Ravi Pandey1
1Leabharlann Abstract: The geometric optics principles are used to develop a unidirectional transmission cloak for hiding objects with dimensions substantially exceeding the incident radiation wavelengths. Invisibility of both the object and the cloak is achieved without metamaterials, so that significant widths of the cloaking bands are provided. For the preservation of wave phases, the λ-multiple delays of waves passing through the cloak are realized. Suppression of reflection losses is achieved by using half-λ multiple thicknesses of optical elements. Due to periodicity of phase delay and reflection suppression conditions, the cloak demonstrates efficient multiband performance confirmed by full-wave simulations.
Particle-Imaging Techniques For Experimental Fluid Mechanics
I
Speckle Patterns
Particulate Markers
(N.»l)
I I
LSV
Particle Images
I
I I
I
I II
I
Fluorescent
Molecular Markers
Photochromic
I
I
I
I
(N.«l)
Particle-Image Velocimetry
A technique that uses particles and their images falls into the category commonly known as particle-image ve/ocimetry, or PI V, which is the principal subject of this article. Before comparing the characteristics of PIV with the other methods displayed in Figure I, it is helpful to examine
PIV
I
NI» l
High Image Density PIV
Low Image Density PlY PlY
NI«l
Figure 1
Particle-image velocimetry and other forms of pulsed-light velocimetry.
PARTICLE-IMAGING TECHNIQUES
where ilx is the displacement of a marker, located at x at time t, over a short time interval Llt separating observations of the marker images. The particles are usually solids in gases or liquids but can also be gaseous bubbles in liquids or liquid droplets in gases or immiscible liquids. Other types of markers include (a) patches of molecules that are activated by laser beams, causing them either to fluoresce (Gharib et al 1985), or to change their optical density by photochromic chemical reactions (Popovich & Hummel 1967, Ricka 1987), and (b) speckle patterns caused by illumi nating groups of particles with coherent light. Regardless of the marker type, locations at various instants are recorded optically by pulses of light that freeze the marker images on an optical recording medium such as a photographic film, a video array detector, or a holographic film. Since these methods share many similarities, it is useful to group them under the single topic of pulsed-light velocimetry, or PLV. The various P LV techniques are organized in Figure I.
量子纠缠 双缝干涉 英语 范例
量子纠缠双缝干涉英语范例Engaging with the perplexing world of quantum entanglement and the double-slit interference phenomenon in the realm of English provides a fascinating journey into the depths of physics and language. Let's embark on this exploration, delving into these intricate concepts without the crutchesof conventional transition words.Quantum entanglement, a phenomenon Albert Einstein famously referred to as "spooky action at a distance," challengesour conventional understanding of reality. At its core, it entails the entwining of particles in such a way that the state of one particle instantaneously influences the stateof another, regardless of the distance separating them.This peculiar connection, seemingly defying the constraints of space and time, forms the bedrock of quantum mechanics.Moving onto the enigmatic realm of double-slit interference, we encounter another perplexing aspect of quantum physics. Imagine a scenario where particles, such as photons or electrons, are fired one by one towards a barrier with twonarrow slits. Classical intuition would suggest that each particle would pass through one of the slits and create a pattern on the screen behind the barrier corresponding tothe two slits. However, the reality is far more bewildering.When observed, particles behave as discrete entities, creating a pattern on the screen that aligns with the positions of the slits. However, when left unobserved, they exhibit wave-like behavior, producing an interferencepattern consistent with waves passing through both slits simultaneously. This duality of particle and wave behavior perplexed physicists for decades and remains a cornerstoneof quantum mechanics.Now, let's intertwine these concepts with the intricate fabric of the English language. Just as particles become entangled in the quantum realm, words and phrases entwineto convey meaning and evoke understanding. The delicate dance of syntax and semantics mirrors the interconnectedness observed in quantum systems.Consider the act of communication itself. When wearticulate thoughts and ideas, we send linguistic particles into the ether, where they interact with the minds of others, shaping perceptions and influencing understanding. In this linguistic entanglement, the state of one mind can indeed influence the state of another, echoing the eerie connectivity of entangled particles.Furthermore, language, like quantum particles, exhibits a duality of behavior. It can serve as a discrete tool for conveying specific information, much like particles behaving as individual entities when observed. Yet, it also possesses a wave-like quality, capable of conveying nuanced emotions, cultural nuances, and abstract concepts that transcend mere words on a page.Consider the phrase "I love you." In its discrete form, it conveys a specific sentiment, a declaration of affection towards another individual. However, its wave-like nature allows it to resonate with profound emotional depth, evoking a myriad of feelings and memories unique to each recipient.In a similar vein, the act of reading mirrors the double-slit experiment in its ability to collapse linguistic wave functions into discrete meanings. When we read a text, we observe its words and phrases, collapsing the wave of potential interpretations into a singular understanding based on our individual perceptions and experiences.Yet, just as the act of observation alters the behavior of quantum particles, our interpretation of language is inherently subjective, influenced by our cultural background, personal biases, and cognitive predispositions. Thus, the same text can elicit vastly different interpretations from different readers, much like the varied outcomes observed in the double-slit experiment.In conclusion, the parallels between quantum entanglement, double-slit interference, and the intricacies of the English language highlight the profound interconnectedness of the physical and linguistic worlds. Just as physicists grapple with the mysteries of the quantum realm, linguists navigate the complexities of communication, both realmsoffering endless opportunities for exploration and discovery.。
双键含量的英语
双键含量的英语In the realm of chemistry, the concept of double bonds is pivotal. These are strong covalent links between atoms, characterized by the sharing of two pairs of electrons.The presence of double bonds significantly influences a molecule's reactivity and stability. For instance, they can alter the way substances interact with other chemicals, affecting everything from solubility to chemical reactions.Understanding double bonds is not just important for theoretical knowledge; it's also crucial for practical applications. In fields like pharmaceuticals and materials science, manipulating double bonds can lead to the creation of new compounds with desired properties.Moreover, the study of double bonds extends beyond the lab. It's a fundamental aspect of organic chemistry that students must grasp, often starting in high school and continuing through university-level courses.The versatility of double bonds is evident in the variety of molecules they can form. From simple hydrocarbons to complex proteins, these bonds are the backbone of many organic structures.In conclusion, the study of double bonds is an essential part of understanding the molecular world. Their role inshaping the properties and behaviors of substances is a testament to the intricate and fascinating nature of chemistry.。
割嘴的英文翻译1
Plasma Chem Plasma Process(2010)30:121–140DOI10.1007/s11090-009-9204-0O R I G I N A L P A P E RComputational Analysis of a Double Nozzle Structure Plasma Cutting TorchShaofeng Guo•Qianhong Zhou•Wenkang Guo•Ping XuReceived:9April2009/Accepted:9November2009/Published online:20November2009ÓSpringer Science+Business Media,LLC2009Abstract Double arcing phenomenon is a limit to increasing the capacity of the plasma cutting torch.In an attempt to enhance the ability of being invulnerable to the double arcing,a double nozzle structure is introduced in this paper.The reason why the double nozzle structure is less vulnerable to the double arcing phenomenon than single nozzle structure is explored.Double nozzle structure allows the longer nozzle which may cause stronger shock wave.In order to evaluate the influence of shock wave on the cutting ability,the influence of nozzle length on the double nozzle structure plasma arc is investigated.The modeling results show that the longer nozzle produces the stronger shock wave outside the nozzle outlet,but the energyflux and momentumflux become concen-trated after the shock wave and increases with the increasing of nozzle length.So the double nozzle structure improves the cutting ability of the plasma torch and meanwhile be less vulnerable to the double arcing phenomenon.Keywords Double nozzle structureÁDouble arcingÁCutting abilityIntroductionOriginally developed in1960s,plasma arc cutting(PAC)has been widely used in the modern industry of metal cutting.In the1990s dual gas torches and their processes were improved to produce precision plasma cutting systems capable of competing with lasers in some applications[1,2].The precision plasma cutting is also calledfine or high definition (HD)or high tolerance plasma arc cutting(HTPAC)[2–4].With the increasing importance of PAC in the industry and the development of computer science,many scientific papers S.Guo(&)ÁW.GuoÁP.XuPlasma Laboratory,Institute of Modern Physics,Fudan University,Shanghai200433,People’s Republic of Chinae-mail:shaofengFD@Q.ZhouInstitute of Applied Physics and Computational Mathematics,Beijing100094,People’s Republic of Chinahave been published on the physical characteristics of plasma cutting arc experimentally [5–10]and computationally[11–15]in recent years.The numerical simulation of plasma torches for metal cutting can give a deep insight in the physics of arc discharge and be a useful tool for torch design[16].One of the phenomena that puts a limit to increasing capabilities of the PAC process is double arcing[1].Nemchinsky[12]proposed the mechanism of the double arcing phe-nomenon which is that it appears when the voltage drop across the cold gas envelope wrapping the hot plasma channel reaches the electrical breakdown voltage of the envelope. Figure1,cited from[12],shows the double arcing phenomenon.In the normal mode of operation,the nozzle is electrically neutral:it is not electrically connected to any part of the circuit.During a double arcing event,the arc,which normally connects cathode and work, is split into two:one connecting the cathode and the nozzle,the other connecting the nozzle and work[1].So the double arcing phenomenon requires at least two points inside the nozzle channel where the electrical breakdown happens.This event leads to catastrophic damage of the nozzle and electrode[1].The challenge of today’s research in HTPAC is to increase the energy density generated by the systems.An increased energy density allows the HTPAC system to achieve higher cutting thickness without losing the overall quality of the cut[2].Increasing the current is one of the effective approaches to achieve the high energy density[16,17],but the high current can lead to double arcing phenomenon which can result in the catastrophic damage to the nozzle[1]. An efficient method to avoid the double arcing is to separate the nozzle into two insulated partitions[17].The resulting structure is called a‘‘double nozzle structure’’in the present paper which is different from the dual gas structure in the papers[1,2,10,16,18].The dual gas structure is composed of a nozzle and a shield cap.For the dual gas structure,the diameter of the shield cap is larger than that of the nozzle,for example the diameters of nozzle and shield cap of the HT2000in papers[10,18]are2and4mm,respectively,and the channel length of the nozzle is larger than that of the shield cap.For the double nozzle structure in the present paper,the diameter and the channel length of the one nozzle is equal to the other nozzle.There is a common function for two structures which is constricting the plasma arc to increase the energy density of the plasma jet.There are also different functions for two structures.The shield gas in the dual gas structure can protect the nozzle from the moltenmaterials ejected from the work-piece in the cutting process.The vast majority of the shield gas is not discharged but is to impinge on the plasma gas.The double nozzle structure can effectively prevent the nozzle from the double arcing phenomenon and the secondary gas takes part in the process of discharge as well as impinging on the plasma arc.Figure2shows the schemes of single nozzle structure cited from paper[11],dual gas structure cited from paper[10]and double nozzle structure introduced in the present paper,respectively.The dual gas torch,taking into account a shield cap with secondary gas impinging on the primary plasma column,can protect the nozzle from the damage of the fused metal droplets from the kerf region.Here we don’t take into account a shield cap because our focus is on the function of limiting the double arcing,and still,the double nozzle structure with a shield cap will add the third gas or shield gas which will absolutely increase the complexity of the simulation.The influence of shield gas on the plasmafield is another problem.The research of the double nozzle structure added with a shield cap is our future work.Our previous works[17,19]showed that RNG k–e model taking into account the low Reynolds number is preferable for the thermal plasma modeling and that the nozzle length has essential effects on the characteristics of the plasma arc for the single nozzle structure torch.In this paper emphasis is placed on the computational simulation of the plasma arc characteristics for the double nozzle structure based on the RNG k–e model taking into account the low Reynolds number.In the following section,the assumptions,governing equations,boundary conditions and the details of turbulence models are presented.The reason why the double nozzle structure is less susceptible to the double arcing phenomenon than single nozzle structure is presented in section‘‘Results and Discussion’’,and in order to investigate the influence of longer nozzle on the cutting ability of the plasma torch,four vital parameters,r E,g E,r p and g P,are defined and the results are discussed there,then conclusion is summarized in the next section.Mathematical and ModelAssumptionsIn this paper,the following assumptions are employed:(a)The plasmaflow is two-dimensional axisymmetric and steady state.The lateralattachment of the arc on the work-piece cannot be described.Instead,the metal plateis assumed with a hole containing a porous anode.(b)In a real plasma cutting operation,there are several 20°inclined pipes set in a ring to obtain vortex injection in the plane perpendicular to the torch axis [10].In two-dimension,the several inclined pipes are assumed to be a ring inlet with the same mass flow rate.The ratio of the azimuthal and axial velocity at inlet is tan 20°,the ratio of the radial and axial velocity at inlet is also tan 20°.(c)The continuum assumption is valid.The plasma is considered as a Newtonian fluidfollowing Navier–Stokes equations.(d)The plasma gas is air and assumed to be in local thermodynamic equilibrium state,whose thermodynamic and transport coefficients are calculated by Murphy [20,21].(e)The arc radiation is taken into account by net emission coefficient.(f)Hall currents and gravitational effects are considered negligible.These assumptions are generally accepted by published papers [7,8,11–13,15–19],and they all derived results which are in a good agreement with the experiment.For the non-transferred arc plasma,taking into account the Steenbeck law,arc root position makes 3D necessary.The nozzle plasma torch,taking into account the lateral arc attachment,necessitates the 3D.The present study had the aim of reducing double arcing by using a double nozzle,and this configuration has been investigated by the authors.The symmetric boundary conditions and porous anode hypothesis is enough for the motivations.So we think 3D in the present paper might make no erning EquationsConsidering the above assumptions,the fluid equations governing a thermal plasma are the same as for a compressible fluid with the addition of several source terms,and are given by the equations of conservation of mass,momentum,and energy.The electromagnetic equations are given by Maxwell’s equations which can be expressed in a reduced form in terms of the electric potential and magnetic vector potential as the current conservation equation and a form of the magnetic induction equation.The set of equations can be written in the general convecto-diffusion form:r Áðq v */Þ¼r ÁC /r /ÀÁþS /ð1Þwhere q is mass density and v *is velocity having axial,radial and azimuthal components,m z ,m r ,and m h .For each equation,the conserved quantity /,the diffusion coefficient C /and the source term S /are given explicitly in Table 1.In Table 1,h ,p and V are enthalpy,static pressure and electric potential,j r ¼Àr o V =o r and j z ¼Àr o V =o z are the radial and axial components of current density,A r and A z are the radial and axial components of magnetic vector potential.Knowing the magnetic potential,the calculation of the magnetic field for an axisymmetric coordinate system is:B h ¼o A r o z Ào A z o r c p and r are specific heat and electric conductivity,respectively.The effective viscosity isl e ¼l þl tand effective thermal conductivityk e ¼k þk twhere l and k are the plasma viscosity and thermal conductivity.l t and k t are the tur-bulence viscosity and turbulence thermal conductivity.The thermodynamic and transport property tables of air plasma provided by Murphy [20,21]with the temperature range of 300–30,000K (with 100K temperature intervals)and for nine different pressure values (0.1,0.2,0.5,0.8,1.0,2.0,5.0,8.0and 10atm)are used in our model.The source term S /in the energy equation accounts for the Joule effect,the electronic enthalpic flux and the radiation losses 4pe N where e N is the net emission coefficient (NEC)taken,in our case,for a 0.1mm radius.The NEC of air is obtained from Ref.[22]for one atmosphere,which has been multiplied by factor p /p atm for other pressure [15].Computational Domain and Boundary ConditionsThe double nozzle structure in the present paper is that the nozzle is composed of two co-axial parts made of copper with the same diameter and channel length.There is a ring made of insulated material between the two parts of the nozzle.Pores are distributed uniformly over the circle of the ring whose function is to be the secondary gas inlet.In the real plasma cutting operation,the distance between the nozzle exit and the metal piece is around 3–6mm [7,10].In the present paper the distance between the nozzle exit and the metal plate is 5mm.The metal plate is modeled with a hole containing a porous anode.The modeled domain for the computational simulation is presented in Fig.3.OABCD is the cathode part.The dimensions are that OA,OD and CD are 5,13and 3mm,respec-tively.AP is the primary gas inlet (inlet 1)which is 3.5mm.PNML and KJI are the first nozzle and second nozzle respectively.The length of ML equals to that of KJ.The distance from the cathode tip to the nozzle bore inlet is 5.2mm.LK is the secondary gas inlet (inlet2)which is 2mm.HG locates at the radius of 10mm.GF is the metal plate and FE is the porous anode which is 2mm.OE is the symmetry axis of the plasma torch.For the simulation,the length of the nozzle varies from 6to 12mm with 2mm interval according to need.Considering that the nozzle length in the present paper (6–12mm)is much longer than normal (for example 5mm in paper [7])and that there are papers [11,13]whoseTable 1Terms of governing equationsEquation/C /S /Mass continuity100Axial momentumm z l e Ào p o z þ1r o o r r l e o v r o z þo o z l e o v z o z À23l e o o z r Áv ~ðÞþj r B h Radial momentumm r l e Ào p o r þ1r o o r r l e o v r o r ÀÁþo o z l e o v z o r À2l e v r r 2þq v 20r À23l e o o r r Áv * Àj z B h Azimuthal momentumm h l e Àq v r v h r Àl e v h r 2Àv h r o l e o r Enthalpy h k e c p v *Ár p þ2l e o v r o r ÀÁ2þv 2r ÀÁ2þo v z o z 2 !þl e o v r o z þov z o r 2þl e o v h o r Àvh r ÀÁ2þl e o v h o r ÀÁ2À23l e 1r o o r rv r ðÞþo v z o z h i 2þj 2r þj 2z À4pe N þ5k j z p o h þj r p o h Electron potentialV r 0Axial potential vectorA z1l 0j zRadial potential vector A r 1l 0j r ÀAr 2configurations are nozzle diameter 1.7mm for 20–200A current,we choose that the nozzle radius and work current are 0.85mm and 100A,respectively.The flow rate of primary gas inlet has two values,which are 2and 4m 3h -1,respectively.The flow rate of secondary gas inlet has two values,which are 0and 2m 3h -1respectively.Maintaining the total quantity of working gas constant,there are two combination modes of the gas flow rate of primary gas inlet and secondary gas inlet.One mode is ‘‘4_0’’which means that the flow rate of the primary gas inlet is 4m 3h -1and the flow rate of the secondary gas inlet is 0.The other mode is ‘‘2_2’’which means that the flow rate of the primary gas inlet and secondary gas inlet are both 2m 3h -1.For mode ‘‘4_0’’,the secondary gas inlet is treated as wall in the computation.That means the mode ‘‘4_0’’is equivalent to the single nozzle structure and the mode ‘‘2_2’’to the double nozzle structure.The details of the boundary conditions are presented in Table 2,where the ratio of the azimuthal and axial velocity at inlets AP and KL is tan 20°,and the ratio of radial and axial velocity at inlet KL is tan 20°.We give the standard volumetric gas flow rate as inlet boundary condition in Table 2.In Fluent the inlet boundary condition is given mass flow rate by multiplying standard vol-umetric flow rate by standard mass density of air.The mass flow rate is one of the boundary conditions that can be accepted in Fluent Software.The velocity at inlets is obtained by Fluent according to various thermal dynamic parameters there.The boundary conditions imposed on the components of the magnetic vector potential are standard [7,8,23–25]and,although not mathematically rigorous,do not violate Ampere’s law.The Fig.3Computational domainTable 2Boundary conditionsPm T V A AP–4,2m 3h -1300K o V o n ¼0o A o n ¼0ABC–0500K o V o n ¼0o A o n ¼0CD–03,500K r o V o n ¼j c o A o n ¼0DE –o v o r ¼0;v r ¼v h ¼0o T o r ¼0o V o r ¼0o A o r ¼0EF –o v o n ¼0o T o n ¼00o A o n ¼0FG–01,000K 0o A o n ¼0GHI1atm –300K 00IJK–0500K o V o n ¼0o A o n ¼0KL–2,0m 3h -1300K o V o n¼0o A o n¼0LMNP –0500K o V o n ¼0o A o n¼0exponential,parabolic and constant current density distributions are adopted for a pre-liminary study on the influence of the current density distribution on plasma characteristics.It is found that there is no significant difference except in the vicinity of the cathode tip[24].In this study,the current density j c is chosen as the parabolic form:j c Àj max 1Àbr 2ÀÁð2Þwhere j max is the j c at r =0.Turbulence ModelIn our previous study [17],it is obtained that the ReNormalization Group (RNG)k –e model taking into account the low Reynolds number effect is preferable for modeling PAC.The (RNG)k –e model [26]is derived from the instantaneous Navier–Stokes equations,using a mathematical technique called ‘renormalization group’methods.The analytical derivation results in a model with constants different from those in the standard k –e model and additional terms in e equation that improves the accuracy for rapidly strained flows.The effect of swirl on turbulence is included in the RNG model.The transport equations for the RNG k –e model are as follows:o o x i q ku i ðÞ¼o o x j a k l e o k o x jþG k Àqe ÀY M ð3Þo o x i qe u i ðÞ¼o o x j a e l e o e o x j þC 1e G k e k ÀC 2e q e 2kÀR e ð4ÞThe value of C l derived using RNG theory is 0.0845.The inverse effective Prandtl numbers,a k and a e ,are set equal to 1.393,C 1e and C 2e are set equal to 1.42and 1.68,respectively.The term R e is given byR e ¼C l qg 31Àg =g 0ðÞe 21þbg e 2kwhere g ¼Sk =e ;g 0¼4:38;b ¼0:012:For most of the region,the plasma flow is not fully developed turbulent flows.In order to obtain an accurate description of how the effective transport varies with the effective Reynolds number,the differential equation is derived in RNG theory d q 2ffiffiffiffiffiel p ¼1:72^v ffiffiffiffiffi^v3p À1þC v d ^v ð5Þwhere ^v¼l e =l and C v %100.Equation 5is integrated to obtain the accurate description,allowing the model to better handle low-Reynolds-number flows.Results and DiscussionThe system of partial differential equations which constitutes the model is discretized and solved iteratively by the CFD commercial code FLUENT 6.3,enhanced with dedicated UDF to handle the source terms and the extra scalar equations needed for the electro-magnetic variables.Considering the compressibility of plasma flow,the coupled algorithm[27]which solves the momentum and pressure-based continuity equations together,isemployed.The reason that the double nozzle structure can prevent the double arcing phenomenon is presented.The influences of the double nozzle structure on the charac-teristics of the plasma arc column are presented.Physical Reason for the Double Nozzle StructureBased on the mechanism of double arcing phenomenon,it can be prevented by decreasing the electricfield across the cold gas envelope or by increasing the thickness of the cold gas envelope.The double nozzle structure introduced in this paper can fully realize a reduction of the electricfield across the cold gas envelope and partially realize an increase in the thickness of the cold gas envelope.The effects are produced because the double structure separates a single nozzle into two insulated partitions so as to decrease the voltage drop across the cold gas envelope,and the secondary gas enhances the cooling effective so as to increase the thickness of the cold gas envelope.Figure4shows the temperature contour for the single nozzle structure and double nozzle structure.The single nozzle structure is mode‘‘4_0’’and the double nozzle structure is mode‘‘2_2’’.For the single nozzle structure,the nozzle length is6mm.For the double nozzle structure,ML,LK,and KJ in Fig.3are all2mm.It indicates that the high temperature region increases gradually for the single nozzle structure,but shrinks in the vicinity of the secondary gas inlet for the double nozzle structure.According to Refs. [20,21],the air is insulated for temperature below about7,000K due to its small electrical conductivity.So it is reasonable to consider the region lower than7,000K as cold gas envelope or insulating region,and the region higher than7,000K as high temperature region or conductive region.Figure5shows contour of7,000K between the nozzle inlet and outlet for the single nozzle structure and double nozzle structure.The origin is the center point of the nozzle inlet.It indicates that the conductive region increases gradually along the axis for the single nozzle structure,but that for the double nozzle structure increases before the secondary inlet and then begins to shrink from the beginning of thesecondary gas inlet and then gradually increases after the secondary gas inlet.Between the nozzle inlet and the secondary gas inlet,the cold gas envelope is thinner for the double nozzle structure than that for the single nozzle structure.From the secondary gas inlet to the nozzle outlet,the cold gas envelope is thicker for the double nozzle structure than that for the single nozzle structure.However the difference of the thickness of the cold gas envelope for two structures is trivial at less than 60l m.Figure 6shows the axial distribution of electrical potential between the nozzle inlet and the metal plate for the single nozzle structure and double nozzle structure.The straight lines m and j are the positions of the nozzle inlet and nozzle outlet for both the single anddouble nozzle structure respectively.The straight lines l and k are the positions of the head and end of the secondary gas inlet.The point M and K are the cross points of real line and lines m and k respectively.The point S is the cross point of dashed line and line m.The bold line SN is the electrical potential of the nozzle for single nozzle structure.The bold lines DN1and DN2are the electrical potential of thefirst and second nozzle for the double nozzle structure respectively.The electrical potential of the nozzle is close to the electrical potential of the axial position of the head of the nozzle[1,12].It means that the electrical potential of the nozzle for the single nozzle structure is approximately equal to the value of point S in Fig.6,and the electrical potential of thefirst nozzle and second nozzle for the double nozzle structure are approximately equal to the values of point M and K respec-tively.So the electricalfield across the cold gas envelope can be estimated by formulaE¼VðxÞÀVðnozzleÞdwhere d is the thickness of the cold gas envelope which can be calculated from Fig.5, V(nozzle)is the electrical potential of the points M,K,and S respectively,V(x)is the axial electrical potential.Figure7shows the electricalfield across the cold gas envelope along the axis for the single nozzle structure and double nozzle structure.The origin is the center of the nozzle inlet.Ahead of the secondary gas inlet,the electricalfield for the double nozzle structure is slightly lower than that for the single nozzle structure.Behind the secondary gas inlet,the electricalfield for the double nozzle structure is much lower than that for the single nozzle structure.It can be drawn from Figs.5and7that before the secondary gas inlet,the cold gas envelope for the double nozzle structure is slightly thinner than that for single nozzle structure but the electricalfield across the cold gas envelope for the double nozzle structure is a little lower than that for the single nozzle structure. Moreover,it can be drawn from Figs.5and7that after the secondary gas inlet,the cold gas envelope for double nozzle structure is thicker than that for the single nozzle structure, and electricalfield across the cold gas envelope for double nozzle structure is much lowerthat r E tends toward the same near the plate for different current while g E increases markedly for the high current.Discussions above indicate that the change of nozzle radius or work current cause the quantitatively changes of the characteristics of plasma flow,for example shock wave effect,r E and g E etc.,but wouldn’t cause qualitatively change of the function of the double nozzle structure plasma torch.ConclusionIn this paper,a double nozzle structure plasma arc is investigated.The physics model for the numerical simulation adopted in the present paper was validated by our previous works 123[17,19].The purposes of the paper are to illuminate the physical reason of the double nozzle structure capable of avoiding the double arcing phenomenon,and to investigate the effects of nozzle length on the cutting ability of the plasma torch.Compared with single nozzle structure,between the nozzle inlet and secondary gas inlet of double nozzle structure,the effect of slightly thinning the cold gas envelope cancels out the effect of a little decreasing the electricalfield across the cold gas envelope.However, between the secondary gas inlet and nozzle outlet,a double nozzle structure not only makes the cold gas envelope a little thicker but more importantly makes the electricalfield across the cold gas envelope there much lower than that of the single nozzle structure.So the double nozzle structure can effectively avoid the appearing of the double arcing phenomenon according to the mechanism proposed by Nemchinsky[1,12].Although the longer nozzle produces stronger shock wave,the radius of the circle section s1through which half of the full energyflux transport,r E,begin to focus after the shock wave then tend towards the same near the plate,and the radius of the circle section s2,through which half of the full momentumflux transport,r p,can hardly vary with different nozzle lengths,and g E which means the energyflux through s1,and g P which means the momentumflux through s2,increase with increasing of the nozzle length,so the longer nozzle can likely be able to lead to a better quality of cut kerf.The influence of smaller nozzle radius and higher work current is similar to that of longer nozzle.But the nozzle length can not be extended at will since the energy loss due to the radiation is proportional to the nozzle length[12,17]and the longer nozzle length makes the pressure of gas inlet too high to work normally.Acknowledgments The authors would like to thank Prof.A.B.Murphy from CSIRO Materials Science and Engineering,Australia for his helpful advice and thermodynamic and transport property data for air plasma.References1.Nemchinsky VA,Severance WS(2006)What we know and what we do not know about plasma arccutting.J Phys D Appl Phys39:R4232.Bini R,Colosimo BM,Kutlu AE,Monno M(2008)Experimental study of the features of the kerfgenerated by a200A high tolerance plasma arc cutting system.J Mater Process Technol196:345 3.Hoult AP,Pashby IR,Chan K(1995)Fine plasma cutting of advanced aerospace materials.J MaterProcess Technol48:8254.Kirkpatrick Ian(1998)High definition plasma—an alternative to laser technology.Aircr Eng AerospTechnol70:2155.Ramakrishnan S,Rogozinski MW(1997)Properties of electric arc for metal cutting.J Phys D ApplPhys30:6366.Pardo C,Gonzalez-Aguilar J,Rodriguez-Yunta A,Calderon MAG(1999)Spectroscopic analysis of anair plasma cutting torch.J Phys D Appl Phys32:21817.Freton P,Gonzalez JJ,Gleizes A,Peyret FC,Caillibotte G,Delzenne M(2002)Numerical andexperimental study of a plasma cutting torch.J Phys D Appl Phys35:1158.Freton P,Gonzalez JJ,Peyret FC,Glezes A(2003)Complementary experimental and theoreticalapproaches to the determination of the plasma characteristics in a cutting plasma torch.J Phys D Appl Phys36:12699.Girard L,Teulet Ph,Razafinimanana M,Gleizes A,Camy-Peyret F,Ballot E,Richard F(2006)Experimental study of an oxygen plasma cutting torch:I.Spectroscopic analysis of the plasma jet.J Phys D Appl Phys39:154310.Peters J,Heberlein J,Lindsay J(2007)Spectroscopic diagnostics in a highly constricted oxygen arc.JPhys D Appl Phys40:396011.Ramakrishnan S,Gershenzon M,Polivka F,Kearny TN,Rogozinsky MW(1997)Plasma generation forthe plasma cutting process.IEEE Trans Plasma Sci25:937123。
- 1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
- 2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
- 3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。
a r X i v :a s t r o -p h /0211425v 1 19 N o v 2002Astronomy &Astrophysics manuscript no.paper February 2,2008(DOI:will be inserted by hand later)A Puzzling Paucity of Double Peaked X-ray PulsarsT.Bulik 1,D.Gondek-Rosi´n ska 2,1,A.Santangelo 3,T.Mihara 4,M.Finger,5,M.Cemeljic 61Nicolaus Copernicus Astronomical Center,Bartycka 18,00716Warsaw,Poland2LUTH,Observatoire de Paris,Place Jules Janssen,F-92195Meudon Cedex,France 3IFCAI-CNR,Via Ugo La Malfa 153,90146Palermo,Italy 4RIKEN,2-1Hirosawa,Wako,Saitama 351-0198,Japan 5NASA MSFC,Hunstville,AL USA 6AIP,An der Sternwarte 16,D-14482Potsdam,Germany Received /AcceptedAbstract.Accretion powered pulsars exhibit a variety of lightcurves.In this paper we propose to classify the observed lightcurves as single or double pulsed.We analyze the lightcurves of 86accretion powered pulsars and assign them to these classes.We present three datasets:first in which the classification can be easily done,second for which the classification is more difficult and not certain,and third for which we were unable to classify the pulsar because of lack of published data.We analyze a simple model in which the angles between the magnetic and rotation axis β,and between the rotation axis and the line of sight θare random,and show that it is inconsistent with the data.We also present a model in which the angle between the magnetic axis and rotation axis is restricted and compare it with the data.This leads to an upper limit on the angle β<40◦.We conclude that there must be a mechanism that leads to alignment of the magnetic and spin axis in X-ray pulsars.Key words.neutron stars –X-rays1.The lightcurves of accretion powered X-ray pulsarsAccreting neutron stars were discovered nearly more than 30years ago (Shklovsky 1967),with Cen X-3the first one discovered which showed pulsations (Giacconi et al.1971).Currently we know nearly one hundred accreting neutron stars,and in more than eighty of them pulsations were identified (Liu et al.2000,2001a).Accreting neutron stars in binaries exhibit a wide range of X-ray light curves.They vary as a function of the photon energy,and moreover in the transient sources the pulse shapes change with the variation of the luminosity.The pulse period in accreting sources is identified with the rotation of a magnetized star.As the matter from the companion star falls onto the neutron star it is channeled onto the magnetic poles by the strong magnetic field of the neutron star.Thus the polar caps are the places where most of the emission takes place.Several theoretical mod-els of radiation of magnetized accretion powered neutron stars have been proposed.The magnetized radiative transfer is solved using a dif-ference scheme (Meszaros &Nagel 1985;Bulik et al.1992),or using Monte Carlo scheme (Lamb et al.1990;Isenberg et al.1998),for a review see Meszaros (1992).The ra-diation from each polar cap produces one pulse in thelight curve.Depending on the emission cap physics and the strength of the magnetic field each pulse may have some additional structure.When during the rotation of an accreting pulsar we see two polar caps the lightcurve should exhibit two distinct pulses (peaks),and if only one cap is seen then the lightcurve is single peaked.Each pul-sar can be classified as single or double peaked depending on the location of the observer and the inclination be-tween the rotation and the magnetic axes.In this paper we classify the observed pulsars into two classes:first the single pulsed light curves as these for which the geometry is such that only one cap is seen,and the double pulsed light curves as those for which two caps are seen.At low X-ray energies this distinction may not be clear,however in the high energy band we clearly distinguish single or double pulses,and there are no triple (or multiple)pulsed lightcurves,see e.g.Nagase (1989);Bildsten et al.(1997).By high energy band we mean at least above 10keV,or in the pulsars where cyclotron lines were found,above the cyclotron lines.The paper is organized as follows:in section 2we sum-marize the observations,in section 3we analyze the ex-pected shapes and expected fraction of single and double peaked lightcurves,in section 4we discuss the results.We summarize the conclusions in section 5.2T.Bulik et al.:A Puzzling Paucity...2.Pulsar observationsIn this section we review the existing observations of X-ray pulsars and attempt to classify their lightcurves ac-cording to the number of pulses in their lightcurves.Wesummarize our classification in Tables1,2,and3.Foreach pulsar we have searched the literature for X-ray ob-servations,and verified if the pulsar was observed in theband above10keV.The pulsars with such observationsare listed in Table1.There are47entries in the Table outof which21have been classified as double and26as sin-gle.Additionally we have listed25pulsars in Table3forwhich no lightcurve above10keV was available.There are3pulsars with likely double light curves and22with singlein Table3.We see that in each table there are more singlepulsed than double pulsed objects.For completion we alsolist14pulsars in Table4for which no information on thetype of the lightcurve was available.We define three setsof data corresponding to the three Tables:dataset S1withthe data of Table1,dataset S2with the combined data ofTables1and3,and dataset S3with all the data,and theentries of Table4are assumed to be double peaked.3.The expected pulsars light curvesLet us assume that an accreting neutron star has a purecentered dipolefield.In such case the geometry of accre-tion powered pulsars is characterized by two angles:θ-the angle between the rotation axis and direction to theobserver,andβthe angle between the magnetic and rota-tion axes.The parameter space when only one cap is seenis determined by the condition:θ<90−β−∆g,(1)where∆g is the gravitational light deflection of a rayemitted parallel to the surface of the neutron star.Herewe assume that the magnetic beaming is not very strongand that there are X-ray photons emitted parallel to thesurface of the neutron star.Ignoring the gravitationallight bending effects,i.e.in the classical Newtonian case,∆g=0◦,the parameter space for seeing just one cap isshown as the region below the solid line in Figure1.Thus,if the anglesβandθare chosen randomly the fraction ofsingle pulsed objects should be1−π/4≈0.214.The re-gion for the single peaked light curves would be smallerif the radiation were strongly beamed.However,in thiscase the double peaked light curves would exhibit narrowpulses,contrary to what is observed-see e.g.Figure7inBildsten et al.(1997).For a set of data,like pulsars,with a well defined prop-erty,i.e.either single or double pulsed,and a given proba-bility p that each pulsar will belong to one or another classthe probability of observing n single peaked lightcurvesand m double peaked in an observation of randomly cho-sen n+m objects is given by the binomial distribution:P n,m=(n+m)!T.Bulik et al.:A Puzzling Paucity (3)Table1.X-ray pulsars in group one,i.e.these that are easily classifiable as single an double pulsed.Part1System P spin Type Comments References4T.Bulik et al.:A Puzzling Paucity...Table2.X-ray pulsars in group one,i.e.these that are easily classifiable as single an double pulsed.Part2 System P spin Type Comments ReferencesT.Bulik et al.:A Puzzling Paucity (5)Table3.X-ray pulsars in group two,i.e.with no pulse shape above10keV or were difficult to classify.System P spin Type Comments References6T.Bulik et al.:A Puzzling Paucity...Table4.X-ray pulsar in group three,for which no reliable pulse shapes were found. System P spin Type Comments ReferencesT.Bulik et al.:A Puzzling Paucity...7Fig.3.The probability of observing the data in models parameterized by the the maximum angle between the magnetic and rotation axis βmax .The solid line corre-sponds to the data set S 1,and the short-dashed line cor-responds to the data set S 2.The long-dashed line corre-sponds to the data set S 3.polar emission and against significant emission from the accretion column.We have obtained a a limit on the possible inclination angles of the magnetic axis with respect to the rotation axis βmax <50◦.A hint of such distribution was already shown by Leahy (1991).He analyzed the lightcurves of 20pulsars using a simple model with the beam dependence on the emission angle as cos 2φand cos 4φwhere φis the direction to the normal of the surface.For each pulsar he found the angles θand βhowever he fits were degenerate in these angles,so that it was not clear a priori which an-gle is which.The resulting distribution was inconsistent with the assumption that both angles are random,and Leahy (1991)concluded that the mean angle between the magnetic and rotation axis is as small 15◦.Bulik et al.(1995)modeled lightcurves of 4U 1538-52and Vela X-1observed by Ginga,and obtained the inclination angles below 50◦for their fits with best significance.Kraus et al.(1996)analyzed the pulse profiles of Cen X-3and recon-structed the geometry and beam pattern for this object.They found that the most likely inclination angles of the magnetic axis to the rotation axis are ∼20◦.Cemeljic &Bulik (1998)have noticed that the light curves of some accretion powered pulsars exhibit sud-den dips.Such dips can be interpreted as accretion flow eclipses,i.e.be caused by the absorption of the X-ray flux when the accretion column passes the line of sight.Such phenomena have been noted for at least three objects:A0535-262(Cemeljic &Bulik 1998),GX1+4(Giles et al.2000),and LS992(Reig &Roche 1999b).Fig.5.The value of the gravitational light bending as a function of the emission angle,measured from the ra-dial direction for photons emitted at different initial radii.The maximum gravitational light deflection is the value of deflection for the initial angle of 90◦,i.e.parallel to the surface.11.522.5M [M sol ]1.52.53.54.5R /r gSS1SS2BPAL12BBB1BBB2SDBFig.6.The ratio of the stellar radius to the gravitational radius as a function of mass for several neutron star equa-tions of state.The labels are BPAL12-Prakash et al.(1997),SBD -Sahu et al.(1993),BB1and BB2-Baldo et al.(1997),while SS1and SS2correspond to the MIT Bag model of strange quark matter (Witten 1984)with two different densities at zero pressure.If such eclipses happen when the accretion column passes through the line of sight then they should take place when |θ−β|<γ,where γis the angular width of the ac-cretion column.The region corresponding to γ=10◦is shaded in Figure 1.We see that such eclipses should fre-8T.Bulik et al.:A Puzzling Paucity...quently take place in double pulsed light curves,if the magnetic axis is randomly oriented with respect to the ro-tation axis.Moreover within the single pulsed light curves a significant fraction,-approximately20-30%should ex-hibit such dips,and this fraction increases as the amount of gravitational light bending increases.Yet the only three cases when such dips have been found are in single pulsed light curves.The lightcurve of A0535-262seems to be double peaked,however Cemeljic &Bulik(1998)pointed out that it can be interpreted as a single pulse divided by the accretionflow eclipse.This lack of double peaked pulsars with accretionflow eclipses (dips)may mean that the region of parameter space for double peaked light curves with dips is either empty or scarcely populated!Again we are drawn to the conclusion that the magnetic axis needs to be aligned with the rota-tion axis.If the magnetic axis inclination is restricted to the regionβmax<50◦,than one expects that the accre-tionflow eclipses to be observed only in the one pulsed lightcurves,as is the case.While this by itself is not a sig-nificant result,the identification of accretionflow eclipses is consistent with the conclusion that the range of allowed values ofβis limited.One should mention here that there may possibly be a selection bias against seeing double pulsed objects.In the case of nearly perpendicular rotators the two pulses will be similar.It is therefore possible that the lack of double pulsed objects is due to misidentification of the pulse period which should be two times longer as reported. The fraction of such misidentified objects depends on the exact shape of the beam.For wide uncollimated beams the two pulses look similar for a range of anglesβas large as the width of the beams.However,our limit isβmax<50◦, so the beams would have to be very wide.Additionally,the beam shape would have to be veryfine tuned in order to compensate the viewing geometry effects over such large range of angles.The sample of accreting pulsars presented here is dom-inated by transient Be/X-ray sytems.One should note that for the disk fed persistent sources(SMC X-1,SMC X-2,Cen X-3,LMC X-4,RX J0648.1-4419)there are two double peaked objects out offive sources,still below the expected≈79%,but this is not a significant discrep-ancy.In the case of wind fed persistent sources(Vela X-1,1E1145.1-6141,4U1907+09,4U1583-53,GX301-2,2S 0114+650)there are four double peaked out of six objects. However,because of the small number of these sources it is impossible to obtain any significant conclusion just from statistical analysis.However,as already mentioned above detailed modeling of two wind fed pulsars(4U1538-52 and Vela X-1)and one disk fed(Cen X-3)resulted in low values ofβ.5.ConclusionsWe analyzed the shapes of accretion powered pulsar light curves,looking for the expected fraction of single and dou-ble peaked light curves,as well as these exhibiting accre-tionflow eclipses.Wefind that the expected number of sin-gle peaked lightcurves is small;certainly less than about one infive lightcurves should be single peaked.On the other hand the observations show that quite a large frac-tion of accreting pulsars have single peaked lightcurves in hard X-rays.In order to explain that we are drawn to conclude that the magnetic axes in accretion pow-ered pulsars tend to be aligned with the rotation axis. Such alignment decreases the expected number of double peaked lightcurves,as seen in Figure1.We have compared the models parametrized by the maximal inclination of the magnetic to the rotation axisβmax and the value of the maximum gravitational light deflection∆g with the data.We obtain upper limits at the99%confidence level βmax<50◦and∆g<33◦.Our results are based on the classification of the neu-tron star lightcurves as single or double pulsed.In order to avoid possible misclassification we have attempted to use the data above10keV,or above the cyclotron line wherever possible.Moreover,we have attempted to clas-sify as many pulsars as double when we were in doubt. In order to rid of the possible systematic effects we have repeated the analysis for the three datasets,and in the third dataset we included all the unclassifiable pulsars as the double peaked objects to be conservative.The deficit of double pulsed objects is significant for every dataset that we analyzed.Moreover we note that the paucity of the double peaked pulsars is so strong that our results still hold even if there are still a few misidentifications in our analysis.We have also shown that if the pulsar beam is strongly collimated the deficit of double peaked objects becomes more significant.Acknowledgements.This research has been supported by the KBN grants2P03D02117and PBZ-KBN-054/P03/2001,and the EU Programme”Improving the Human Research Potential and the Socio-Economic Knowledge Base”(Research Training Network Contract HPRN-CT-2000-00137).TB is grateful for the hospitality of the Observatoire de Paris in Meudon and for the support of the CNRS/PAN Jumelage programme. ReferencesAngelini,L.,Church,M.J.,Parmar,A.N.,Balucinska-Church,M.,&Mineo,T.1998,A&A,339,L41 Aoki,T.,Dotani,T.,Ebisawa,K.,et al.1992,PASJ,44, 641Baldo,M.,Bombaci,I.,&Burgio,G.F.1997,A&A,328, 274Bildsten,L.,Chakrabarty,D.,Chiu,J.,et al.1997,ApJS, 113,367Bulik,T.,Kluzniak,W.,&Zhang,W.2000,A&A,361, 153Bulik,T.,Meszaros,P.,Woo,J.W.,Hagase, F.,& Makishima,K.1992,ApJ,395,564Bulik,T.,Riffert,H.,Meszaros,P.,et al.1995,ApJ,444, 405Burderi,L.,Di Salvo,T.,Robba,N.R.,La Barbera,A., &Guainazzi,M.2000,ApJ,530,429T.Bulik et al.:A Puzzling Paucity (9)Caraveo,P.A.,Bignami,G.F.,&Goldwurm,A.1989, ApJ,338,338Cemeljic,M.&Bulik,T.1998,Acta Astronomica,48,65 Chakrabarty,D.,Bildsten,L.,Grunsfeld,J.M.,et al. 1997,ApJ,474,414Chakrabarty,D.,Koh,T.,Bildsten,L.,et al.1995,ApJ, 446,826Coe,M.J.,Roche,P.,Everall,C.,et al.1994,A&A,289, 784Corbet,R.,Marshall,F.E.,Lochner,J.C.,Ozaki,M.,& Ueda,Y.1998,IAU Circ.,6803,1Corbet,R.H.D.,Finley,J.P.,&Peele,A.G.1999a,ApJ, 511,876Corbet,R.H.D.,Marshall,F.E.,Coe,M.J.,Laycock, S.,&Handler,G.2001,ApJ,548,L41Corbet,R.H. D.,Marshall, F. E.,Peele, A.G.,& Takeshima,T.1999b,ApJ,517,956Corbet,R.H.D.&Peele,A.G.1997,ApJ,489,L83 Cusumano,G.,Israel,G.L.,Mannucci,F.,et al.1998, A&A,337,772Cusumano,G.,Maccarone,M.C.,Nicastro,L.,Sacco,B., &Kaaret,P.2000,ApJ,528,L25Dennerl,K.,Haberl,F.,&Pietsch,W.1995,IAU Circ., 6184,2Finger,M.H.,Koh,D.T.,Nelson,R.W.,et al.1996, Nature,381,291Finger,M.H.,Macomb,D.J.,Lamb,R.C.,et al.2001, ApJ,560,378Giacconi,R.,Gursky,H.,Kellogg,E.,Schreier,E.,& Tananbaum,H.1971,ApJ,167,L67Giacconi,R.,Murray,S.,Gursky,H.,et al.1972,ApJ, 178,281Giles,A.B.,Galloway,D.K.,Greenhill,J.G.,Storey, M.C.,&Wilson,C.A.2000,ApJ,529,447 Grevenev,S.A.,Pavlinsk,M.N.,&Syunyaev,R.A.1992, Soviet Astronomy Letters,18,228Haberl,F.,Dennerl,K.,Pietsch,W.,&Reinsch,K.1997, A&A,318,490Haberl,F.,Pietsch,W.,Motch,C.,&Buckley,D.A.H. 1996,IAU Circ.,6445,2Hall,T.A.,Finley,J.P.,Corbet,R.H.D.,&Thomas, R.C.2000,ApJ,536,450Huckle,H.E.,Mason,K.O.,White,N.E.,et al.1977, MNRAS,180,21PHughes,J.P.1994,ApJ,427,L25Hulleman,F.,in’t Zand,J.J.M.,&Heise,J.1998,A&A, 337,L25Imanishi,K.,Yokogawa,J.,Tsujimoto,M.,&Koyama,K. 1999,PASJ,51,L15in’t Zand,J.J.M.,Baykal,A.,&Strohmayer,T.E.1998, ApJ,496,386Isenberg,M.,Lamb,D.Q.,&Wang,J.C.L.1998,ApJ, 505,688Israel,G.L.,Angelini,L.,Campana,S.,et al.1998, MNRAS,298,502Israel,G.L.,Campana,S.,Covino,S.,et al.2000,ApJ, 531,L131Israel,G.L.,Mereghetti,S.,&Stella,L.1994,ApJ,433,L25Israel,G.L.,Stella,L.,Angelini,L.,White,N.E.,& Giommi,P.1995,IAU Circ.,6277,1Israel,G.L.,Stella,L.,Angelini,L.,et al.1997,ApJ,474, L53Iwasawa,K.,Koyama,K.,&Halpern,J.P.1992,PASJ, 44,9Kelley,R.L.,Rappaport,S.,&Ayasli,S.1983,ApJ,274, 765Kinugasa,K.,Torii,K.,Hashimoto,Y.,et al.1998,ApJ, 495,435Koh,D.T.,Bildsten,L.,Chakrabarty,D.,et al.1997, ApJ,479,933Koyama,K.,Kawada,M.,Kunieda,H.,Tawara,Y.,& Takeuchi,Y.1990a,Nature,343,148Koyama,K.,Kawada,M.,Takeuchi,Y.,et al.1990b,ApJ, 356,L47Koyama,K.,Kawada,M.,Tawara,Y.,et al.1991a,ApJ, 366,L19Koyama,K.,Kunieda,H.,Takeuchi,Y.,&Tawara,Y. 1990c,PASJ,42,L59—.1991b,ApJ,370,L77Kraus,U.,Blum,S.,Schulte,J.,Ruder,H.,&Meszaros, P.1996,ApJ,467,794Lamb,D.Q.,Wang,J.C.L.,&Wasserman,I.M.1990, ApJ,363,670Leahy,D.A.1991,MNRAS,251,203Levine,A.,Rappaport,S.,Deeter,J.E.,Boynton,P.E., &Nagase,F.1993,ApJ,410,328Liu,Q.Z.,van Paradijs,J.,&van den Heuvel,E.P.J. 2000,A&AS,147,25—.2001a,A&A,368,1021—.2001b,A&A,368,1021Lochner,J.C.,Marshall,F.E.,Whitlock,L.A.,&Brandt, N.1998,IAU Circ.,6814,1Macomb,D.J.,Finger,M.H.,Harmon,B.A.,Lamb, R.C.,&Prince,T.A.1999,ApJ,518,L99 Makishima,K.,Ohashi,T.,Kawai,N.,et al.1990,PASJ, 42,295Marsden,D.,Gruber,D.E.,Heindl,W.A.,Pelling,M.R., &Rothschild,R.E.1998,ApJ,502,L129 McClintock,J.E.,Nugent,J.J.,Li,F.K.,&Rappaport, S.A.1977,ApJ,216,L15Mereghetti,S.,Tiengo,A.,Israel,G.L.,&Stella,L.2000, A&A,354,567Meszaros,P.1992,”High-energy radiation from magne-tized neutron stars Meszaros.”(Chicago:University of Chicago Press,c1992.),47...+Meszaros,P.&Nagel,W.1985,ApJ,298,147 Nagase,F.1989,PASJ,41,1Oosterbroek,T.,Orlandini,M.,Parmar,A.N.,et al.1999, A&A,351,L33Pakull,M.,van Amerongen,S.,Bakker,R.,&van Paradijs,J.1983,A&A,122,79Paul,B.,Agrawal,P.C.,Mukerjee,K.,et al.2001,A&A, 370,529Polidan,R.S.,Pollard,G.S.G.,Sanford,P.W.,&Locke, M.C.1978,Nature,275,29610T.Bulik et al.:A Puzzling Paucity...Prakash,M.,Bombaci,I.,Prakash,M.,et al.1997,Phys. Rep.,280,1Reig,P.&Coe,M.J.1999,MNRAS,302,700Reig,P.&Roche,P.1999a,MNRAS,306,100—.1999b,MNRAS,306,95Remillard,R.,Levine,A.,Takeshima,T.,et al.1998, IAU Circ.,6826,2Reynolds,A.P.,Bell,S.A.,&Hilditch,R.W.1992, MNRAS,256,631Robba,N.R.,Burderi,L.,Wynn,G.A.,Warwick,R.S., &Murakami,T.1996,ApJ,472,341Robba,N.R.&Warwick,R.S.1989,ApJ,346,469 Sahu,P.K.,Basu,R.,&Datta,B.1993,ApJ,416,267+ Santangelo,A.,Cusumano,G.,dal Fiume,D.,et al.1998, A&A,338,L59Saraswat,P.&Apparao,K.M.V.1992,ApJ,401,678 Saraswat,P.,Mihara,T.,Corbet,R.,&Ebisawa,K.1997, in All-Sky X-Ray Observations in the Next Decade, 109–+Schmidtke,P.C.,Cowley,A.P.,McGrath,T.K.,& Anderson,A.L.1995,PASP,107,450 Schwentker,O.1994,A&A,286,L47Scott,D.M.,Finger,M.H.,Wilson,R.B.,et al.1997, ApJ,488,831Seward,F.D.,Charles,P.A.,&Smale,A.P.1986,ApJ, 305,814Shklovsky,I.S.1967,ApJ,148,L1Stollberg,M.T.,Finger,M.H.,Wilson,R.B.,et al.1999, ApJ,512,313Sugizaki,M.,Nagase,F.,Torii,K.,et al.1997,PASJ,49, L25Tamura,K.,Tsunemi,H.,Kitamoto,S.,Hayashida,K.,& Nagase,F.1992,ApJ,389,676Tananbaum,H.,Gursky,H.,Kellogg,E.M.,et al.1972, ApJ,174,L143Tawara,Y.,Yamauchi,S.,Awaki,H.,et al.1989,PASJ, 41,473Thorsett,S.E.&Chakrabarty,D.1999,ApJ,512,288 Torii,K.,Kinugasa,K.,Katayama,K.,et al.1998a,ApJ, 508,854Torii,K.,Kinugasa,K.,Katayama,K.,Tsunemi,H.,& Yamauchi,S.1998b,ApJ,503,843Torii,K.,Sugizaki,M.,Kohmura,T.,Endo,T.,&Nagase, F.1999,ApJ,523,L65Tsujimoto,M.,Imanishi,K.,Yokogawa,J.,&Koyama,K. 1999,PASJ,51,L21Ueno,M.,Yokogawa,J.,Imanishi,K.,&Koyama,K.2000, PASJ,52,L63Wijnands,R.&van der Klis,M.1998,Nature,394,344 Wilson,C.A.&Finger,M.H.1998,IAU Circ.,7048,2 Wilson,C.A.,Finger,M.H.,Harmon,B.A.,et al.1997, ApJ,479,388Witten,E.1984,Phys.Rev.,30,272Woo,J.W.,Clark,G.W.,Levine,A.M.,Corbet,R.H.D., &Nagase,F.1996,ApJ,467,811Yokogawa,J.,Imanishi,K.,Tsujimoto,M.,Kohno,M.,& Koyama,K.1999,PASJ,51,547Yokogawa,J.,Imanishi,K.,Ueno,M.,&Koyama,K.2000, PASJ,52,L73Yokogawa,J.&Koyama,K.1998,IAU Circ.,7028,1。