Surveying on two-zone height of sublevel strip mining

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PS-InSAR技术在北京通州区地面沉降监测中的应用

25Vo1.16 No.01 March, 2021/第16卷第1期 2021年3月PS-InSAR 技术在北京通州区地面沉降监测中的应用孔祥如，罗勇，刘贺，王新惠，赵龙，沙特（北京市水文地质工程地质大队（北京市地质环境监测总站），北京 100195）摘要：地面沉降是通州区重要地质灾害，由此引发的地裂缝次生灾害现象严重影响通州区的发展建设。

以TerraSAR-X 卫星影像为数据基础，采用永久散射体干涉测量（PS-InSAR）技术获取通州区地面沉降2015—2018年监测数据，分析了通州区地面沉降时空分布特征以及地裂缝次生灾害的垂向形变特征。

结果表明：（1）通州区地面沉降主要集中在西部和北部地区，形成了以通州城区—梨园—台湖为中心的西部沉降区和以永顺—宋庄为中心的北部沉降区，每个沉降区内又分布着多个小的沉降漏斗，在区域上具有不均匀沉降的特征；（2）宋庄地裂缝两盘各存在一个沉降漏斗中心，裂缝带沿线存在多个小沉降漏斗，由裂缝带向两侧沉降量逐渐增大，垂直裂缝带方向存在显著的沉降梯度变化，差异沉降特征明显，建议在宋庄地裂缝成因机理研究过程中考虑差异沉降对地裂缝形成的影响。

关键词：地面沉降；监测技术；永久散射体干涉测量；通州区；地裂缝Application of PS-InSAR technology in the land subsidence survey inTongzhou District, BeijingKONG Xiangru, LUO Y ong, LIU He, WANG Xinhui, ZHAO Long, SHA T e(Beijing Institute of Hydrogeology and Engineering Geology (Beijing Institute of Geo-Environment Monitoring), Beijing 100195)Abstract: Land subsidence is an important geological disaster in T ongzhou District. The resulting secondary disasters such as ground fissures seriously affect the development and construction of T ongzhou District. Based on T erraSAR-X satellite images, the monitoring data of land subsidence in T ongzhou District from 2015 to 2018 were obtained using PS InSAR technology. This paper analyzes the spatial and temporal distribution characteristics of land subsidence and vertical deformation characteristics of secondary disasters of ground fissures in T ongzhou District. Through this study, we obtain the temporal and spatial distribution characteristics of land subsidence in Tongzhou District, and reveal the characteristics of differential land subsidence of Songzhuang ground fissure. The results show: (1) The land subsidence in T ongzhou District is mainly concentrated in the west and north areas, forming the western subsidence area with T ongzhou-city-proper-Liyuan-Taihu as the center and the northern subsidence area with Y ongshun-Songzhuang as the center. There are many small subsidence funnels in each subsidence area with基金项目：地面沉降成灾机理与防控技术研究，北京市财政重点项目（PXM2019_158305_000012）第一作者简介：孔祥如（1989- ），男，硕士，工程师，主要从事地面沉降、地裂缝等地质灾害监测与研究工作。

Double Resonant Raman Scattering in Graphite

Double Resonant Raman Scattering in GraphiteC.Thomsen and S.ReichInstitut für Festkörperphysik,Technische Universität Berlin,Hardenbergstrasse36,10623Berlin,Germany(Received9August2000)Weﬁnd that the electronic dispersion in graphite gives rise to double resonant Raman scattering for excitation energies up to5eV.As we show,the curious excitation-energy dependence of the graphite D mode is due to this double resonant process resolving a long-standing problem in the literature and invalidating recent attempts to explain this phenomenon.Our calculation for the D-mode frequency shift (60cm21͞eV)agrees well with the experimental value.PACS numbers:78.30.–j,81.05.TpSingle incoming or outgoing resonances are widelyknown in Raman spectroscopy and frequently used tostudy the electronic and vibrational properties of crystalsor molecules.They occur if the energy of the incoming orthe scattered photon matches the transition energy of an al-lowed electronic transition leading to a large enhancementof the Raman cross section[1].Closely related is the ideaof double resonant Raman scattering,where,in addition tothe incoming or outgoing resonances,the elementary exci-tation makes a real transition.Double resonances are muchstronger than single resonances.They were,however,onlyobserved under very speciﬁc experimental conditions:The energetic difference between two electronic bandswas adjusted to the phonon energy by applying electricor magneticﬁelds,uniaxial stress,or by a proper choiceof the parameters of semiconductor quantum wells[2–5].Double resonant conditions were thereby realized fordistinct excitation energies.In this Letter we study the double resonant Raman pro-cess for linearly dispersive bands as in semimetals.Weshow that double resonances are responsible for the ob-servation of the defect induced D mode in graphite andits peculiar dependence on excitation energy.The doubleresonance considered has a much stronger enhancementthan simple incoming or outgoing resonances explainingwhy the defect mode(and its second order peak)is sostrong compared to the graphite G point vibration.Theﬁrst order Raman spectra of graphite show besidesthe G point modes an additional defect induced peak,theso-called D mode[6–9].The D mode is related to theﬁnite crystallite size and disappears for perfect crystals[6,10].Its frequency was found to shift with excitationenergy at a rate of4050cm21͞eV over a wide excita-tion energy range[7,11–13],a phenomenon which hasnot been understood for almost20years.Tan et al.foundthat there is a curious discrepancy between the Stokes andanti-Stokes frequencies of the D mode,which they wereunable to explain[14].Various groups have recently at-tempted to explain the unusual excitation-energy depen-dence which was found also for the second order spectra,where the mode shifts at approximately twice the rate andis not defect induced.Sood et al.proposed a disorder in-duced double resonance above a gap Dഠ1eV in the band structure leading to a dependence of the phonon wave vec-tor q and hence the phonon frequency on the energy of the incoming light E1as qϳ͑E12D͒1͞2[12].There is,however,no such gap in the electronic structure of graphite;it is a semimetal with valence and conduction band crossing the Fermi level at the K point of the Bril-louin zone.Pócsik et al.introduced a new Raman mecha-nism for which the wave vector of the electron which is excited by the incoming resonant photon supposedly de-ﬁnes the wave vector of the scattered phonon[13].This ad hoc k෇q quasiselection rule was applied to particu-lar branches of the phonon band structure by Matthews et al.and Ferrari and Robertson[15,16].However,these explanations required a mysterious coupling of the opti-cal branches to a transverse acoustic branch in the phonon band structure or did not yield the correct shift of the D mode.Single resonances have not been identiﬁed in the graphite Raman spectra because the linear dispersion of the electronic bands allows these resonances to occur at all energies E1and for the entire D band independently of q.There is no reason why the quasimomentum where the electronic transitions occur is transferred selectively to the phonon seen in the Raman spectra,and it is impossible to understand the difference between Stokes and anti-Stokes frequencies.In other words,the“quasiselection rule”in-voked by Refs.[13,15,16]has no physical basis and cannot explain the experimental observations.To study the resonant Raman effect in a semimetal like graphite weﬁrst consider a one-dimensional example as depicted in Fig.1,where we have shown two linear bands with different Fermi velocities which cross at the Fermi level.The peculiarity of this electronic dispersion is that, in addition to single resonances,a double resonant transi-tion is possible for a wide variety of excitation energies. Theﬁrst step of the double resonance for a particular inci-dent laser energy E1is to create an electron-hole pair at the k point matching the energy difference between the con-duction and the valence band(i!a).It is obvious that for a monotonically increasing phonon dispersion v ph͑q͒there exists a(v ph,q)combination which can scatter the electron to a state on the second band(a!b).This52140031-9007͞00͞85(24)͞5214(4)$15.00©2000The American Physical Societyis the phonon for which double resonance occurs.Then the electron is elastically scattered back by the lattice de-fects (b !c )and recombines conserving k in the process (c !i ).For a larger incoming photon energy a larger phonon quasimomentum is required for this transition and hence a different phonon energy,if the phonon band is dis-persive.The double resonance occurs also for two emitted phonons at twice the energy where quasimomentum is con-served by equal and opposite q of the two emitted phonons,i.e.,it is not defect induced.The anti-Stokes process for a particular incoming energy is seen to be doubly resonant at a larger phonon momentum (and hence energy)than the Stokes process.For the linear bands in Fig.1we can calculate the Ra-man matrix element K 2f ,10explicitly by evaluating the usual expression [1]:K 2f ,10෇M f M ba M cb M oa ,b ,c 1͑E 12E e ai2i ¯h g ͒͑E 12¯h v ph 2E e bi2i ¯h g ͒͑E 12¯h v ph 2E eci 2i ¯h g ͒.(1)Here M o ,f are the (constant)transition matrix elementsfor the incoming and outgoing photons,M ba ,M cb rep-resents the phonon or impurity which scatters the elec-tron from state a to b and from state b to c ,and g ,the broading parameter,has been taken to be the same for all transitions.For a semimetal the electronic en-ergies are E eai ෇j k j ͑y 22y 1͒and E e bi ෇7q y 1͞2,and E eci ෇j k j ͑y 22y 1͒with y 1,0and y 2.0being the Fermi velocities.In one dimension the sum may be con-verted to an integral over k :K 2f ,10෇M f M ba M cb M o ͑2k 22q ͒͑y 22y 1͒3͑k 22q y 2y 22y 1͒͑k 21q y 1y 22y 1͒3Z `0dk͑k 12k ͒͑k 22k ͒,(2)with k 1෇͑E 12i ¯h g ͒͑͞y 22y 1͒and k 2෇͑E 12¯h v ph 2i ¯h g ͒͑͞y 22y 1͒.This integral is straightfor-wardly evaluated toK 2f ,10෇aM f M ba M cb M o22q y 2y 22y 121q y 1y 22y 1,(3)FIG.1.Schematic Raman double resonance in one dimensionfor linearly dispersive bands with Fermi velocities y 1and y 2.For a given incident energy E 1and a monotonically increasing phonon dispersion relation ¯h v ph ͑q ͒there is at most one q and ¯h v ph leading to double resonance.In this example the electron is scattered back to band 1by an impurity.where a ෇ln ͑k 2͞k 1͒͑2k 22q ͓͒͑͞y 22y 1͒2¯h v ph ͔is aslowly varying function of q .Physically Eq.(3)says that there is double resonance when the phonon quasimomen-tum is equal toq ෇E 12¯h v ph y 2or E 12¯h v ph2y 1.(4)The double resonance is particularly strong since two termsin the denominator of Eq.(1)go to zero simultaneously,and much stronger than the incoming resonance consid-ered by Refs.[13,15,16],where only one term in the de-nominator of Eq.(1)vanishes.In Fig.2we plot j K 2f ,10j of Eq.(3)as a function of phonon quasimomentum for two incoming photon ener-gies.For each photon energy there are two maxima,their separation depending on the Fermi velocities [Eq.(4)].For different incoming E 1the resonances occur at different q again as given by Eq.(4);for E 1between 1and 4eV the center q varies between 0.13and 0.6Å21(we chose as Fermi velocities y 1෇27and y 2෇6eV Åadapted from graphite)as compared to ഠ0.003Å21for a nondefect in-duced process excited at 3eV .For a dispersive phonon,if it is single valued and increasing with q ,there are two0.00.20.40.60.8E 1= 3 eVE 1= 2 eV|K 2f ,10| (a r b . u n i t s )q ph (Å-1)FIG.2.The absolute magnitude of the Raman matrix element in Eq.(3)for two incident photon energies and a model dis-persion.See text for details.By far the strongest enhancement occurs for the double resonance as given by Eq.(4).5215pairs ͑q ,v ph ͒which ful ﬁll condition (4).To give a rough estimate for a hypothetical linear dispersion of an opti-cal phonon we adapted from the K and G point valuesof graphite ¯h v Kph ෇1270cm 21and ¯h v G ph ෇1580cm 21;the double resonance for an incoming photon energy at E 1෇3eV according to Eq.(4)occurs for the center q ෇0.44Å21,and hence ¯h v ph ෇1350cm 21is the phonon energy actually observed.For a different E 1the phonon energy shifts accordingly.Note the large phonon quasi-momentum which can normally be observed only with neutron scattering.A difference in Stokes and anti-Stokes frequencies follows naturally from Eq.(4)when replacing v ph by 2v ph .After illustrating the principle of a double resonance with linearly dispersive electronic bands near the Fermi surface we now turn to a two-dimensional realistic de-scription of the bands in graphite and demonstrate that our interpretation explains quantitatively the experimental de-pendence of the D mode in graphite on excitation energy.For the electronic bands it is suf ﬁcient to consider only the bonding and antibonding bands which,up to about 6eV ,are the only bands involved in real optical transitions.The asymmetries between bonding (lower sign)and antibond-ing (upper sign)states we took into account [17]according to E c ,y ෇6g 0w ͑k ͓͒͞17sw ͑k ͔͒,where w ͑k ͒is the tight binding band centered around the K point of the Brillouin zone of graphite [18]:w ͑k ͒෇͕32cos k ?R 12cos k ?R 22cos k ?͑R 12R 2͒1p 3sin k ?R 12p 3sin k ?R 22p3sin k ?͑R 12R 2͖͒1͞2,(5)where R 1,2are the unit vectors of the graphene cell,g 0෇3.03eV,and s ෇0.129for a close approximation to thegraphite band structure [17].In the isotropic limit (for small k and neglecting s )the incoming transition occurs at E eai ෇E c 2E y ෇p 3a 0g 0k .Note,though,that forphoton energies in the visible and higher the incomingresonance does not occur close to the K point,and theanisotropy of the band structure must be taken into account.For example,for k ෇0.23Å21in the KM direction E e ai ෇2.7eV,while in the K G direction E eai ෇3.2eV.To obtain a realistic as possible two-dimensional nu-merical evaluation of the sum in Eq.(1)we included forE e͑a ,b ,c ͒i the full electronic dispersion curves of Eq.(5)and integrated j K 2f ,10j 2over k space.The phonondispersion in the energy range (1270,1620cm 21)wemodeled by simple functions such that they representclosely the ones calculated from force constant [19]orab initio [20]calculations.In particular,we ﬁxed theG point frequency to 1580cm 21,the M and K point ones to 1480and 1270cm 21,respectively,and included the overbending to 1620cm 21typical for the vicinity ofthe G point in graphite [10].Our results are not depen-dent on the details of these curves.We then proceeded to evaluate Eq.(1)by searching the Brillouin zone forincoming resonances and,where we found them,by in-tegrating ͕j ͓E 1͑k o ͒2͓E c ͑k f ͒2E y ͑k o ͔͒2¯h v ph ͑k f2k o ͒2i ¯hg ͔͓¯h v ph ͑k f 2k o ͒2i ¯h g ͔j 2͖21over k f in the entire Brillouin zone.We plotted the Raman intensities j K 2f ,10j 2as a function of phonon frequency v ph for three different incident laser energies in Fig.3.The peak is seen to shift to higher en-ergies with increasing E 1.In Fig.4we show the maxima of the intensities as a function of incident energy together with the experimental results on the D -mode ’s excitation dependence of various groups.The agreement is found tobe excellent,in particular,in view of the fact that no un-known parameter was introduced in our derivation and noﬁtting was performed.The slope for the D -mode ’s exci-tation energy dependence calculated by our model if taken to be linear is 60cm 21͞eV,the experimental slopes being slightly lower,ranging from 46to 51cm 21͞eV [11,13,15].The absolute values of the D -mode frequencies agree alsoexcellently.The relative strength of single and double resonances may be determined by the relative area A of the two-phonon peaks of the G point mode and the D mode,which are both Raman allowed.Experimentally we ﬁnd A 2D ͞A 2G ഠ40which independently con ﬁrms our interpreta-tion of the shifting D mode as due to a double resonance.We obtained the difference in Stokes and anti-Stokes fre-quencies as ഠ15cm 21(for E 1෇2eV)slightly depend-ing on E 1compared to ഠ7cm 21as reported in Ref.[14].The remaining discrepancy suggests a somewhat too small slope of our model phonon dispersions or a slightly too large electron dispersion.In conclusion,we investigated Raman double reso-nances,a mechanism which leads to a strong Raman signal at variable q vectors well within the Brillouin zone of solids.Our interpretation resolves the long-time not 130014001500E 1 = 4 e V E 1 = 3 e V E 1 = 2 e V |K 2f ,10|2(a r b . u n i t s )Raman Shift (cm -1)FIG.3.Calculated Raman spectrum of the D mode in graphitefor different incoming photon energies E 1.5216130013501400R a m a n s h i f t D -m o d e (c m -1)Excitation energy (eV)FIG.4.Measured and calculated frequencies of the D band as a function of the excitation energy.The open symbols corre-spond to experimental data,and the closed squares to the calcu-lated phonon energies in double resonance.The line is a linear ﬁt to the theoretical values with a slope of 60cm 21͞eV,the numbers give the corresponding slopes for the data.understood excitation-energy dependence of the D mode in ing a realistic electron and phonon band structure we calculated the absolute value as well as the rate at which the D mode shifts without adjusting any parameter to 60cm 21͞eV compared to ഠ50cm 21͞eV as observed experimentally.The recently introduced quasi-selection rule “k ෇q ”for the explanation of this phe-nomenon may be dismissed.We thank M.Cardona for pointing out an error in the initial version of this manuscript.[1]R.M.Martin and L.M.Falicov,in Light Scattering inSolids I,edited by M.Cardona,Topics in Applied Physics V ol.8(Springer,Berlin,1983),p.79.[2]ler,D.A.Kleinmann,and A.C.Gossard,SolidState Commun.60,213(1986).[3]F.Cerdeira,E.Anastassakis,W.Kauschke,and M.Car-dona,Phys.Rev.Lett.57,3209(1986).[4]A.Alexandrou,M.Cardona,and K.Ploog,Phys.Rev.B38,R2196(1988).[5]S.I.Gubarev,T.Ruf,and M.Cardona,Phys.Rev.B 43,1551(1991).[6]F.Tuinstra and J.L.Koenig,J.Chem.Phys.53,1126(1970).[7]R.P.Vidano,D.B.Fischbach,L.J.Willis,and T.M.Loehr,Solid State Commun.39,341(1981).[8]Y .Kawashima and G.Katagiri,Phys.Rev.B 52,10053(1995).[9]W.Kauschke,A.K.Sood,M.Cardona,and K.Ploog,Phys.Rev.B 36,1612(1987).[10]R.J.Nemanich and S.A.Solin,Phys.Rev.B 20,392(1979).[11]Y .Wang,D.C.Aolsmeyer,and R.L.McCreery,Chem.Mater.2,557(1990).[12]A.K.Sood,R.Gupta,C.H.Munro,and S.A.Asher,inProceedings of the XVI International Conference on Ra-man Spectroscopy,edited by A.M.Heyns (Wiley-VCH,Berlin,1998),p.62.[13]I.P óscik,M.Hundhausen,M.Koos,O.Berkese,andL.Ley,in Proceedings of the XVI International Confer-ence on Raman Spectroscopy (Ref.[12]),p.64.[14]P.H.Tan,Y .M.Deng,and Q.Zhao,Phys.Rev.B 58,5435(1998).[15]M.J.Matthews,M.A.Pimenta,G.Dresselhaus,M.S.Dresselhaus,and M.Endo,Phys.Rev.B 59,6585(1999).[16]A.C.Ferrari and J.Robertson,Phys.Rev.B 61,14095(2000).[17]R.Saito,G.Dresselhaus,and M.S.Dresselhaus,Phys.Rev.B 61,2981(2000).[18]S.Reich and C.Thomsen,Phys.Rev.B 62,4273(2000).[19]R.A.Jishi and G.Dresselhaus,Phys.Rev.B 26,4514(1982).[20]G.Kresse,J.Furthm üller,and J.Hafner,Europhys.Lett.32,729(1995).5217。

The properties of extragalactic radio sources selected at 20 GHz

a r X i v :a s t r o -p h /0603437v 3 16 S e p 2006Mon.Not.R.Astron.Soc.000,1–??(2000)Printed 5February 2008(MN L A T E X style ﬁle v1.4)The properties of extragalactic radio sources selected at20GHzElaine M.Sadler 1,Roberto Ricci 2,Ronald D.Ekers 2,J.A.Ekers 2,Paul J.Hancock 1,Carole A.Jackson 2,Michael J.Kesteven 2,Tara Murphy 1,Chris Phillips 2Robert F.Reinfrank 3,Lister Staveley–Smith 2,Ravi Subrahmanyan 2,Mark A.Walker 1,2,4,Warwick E.Wilson 2,Gianfranco De Zotti 5,61Schoolof Physics,University of Sydney,NSW 2006,Australia2AustraliaTelescope National Facility,CSIRO,P.O.Box 76,Epping,NSW 1710,Australia3Department of Physics and Mathematical Physics,University of Adelaide,Adelaide,SA 5005,Australia 4MAW Technology Pty Led,3/22CliﬀSt.,Manly 2095,Australia 5SISSA/ISAS,Via Beirut 2–4,I-34014Trieste,Italy6INAF,Osservatorio Astronomico di Padova,Vicolo dell’Osservatorio 5,I-35122Padova,Italy5February 2008ABSTRACTWe present some ﬁrst results on the variability,polarization and general properties of radio sources selected at 20GHz,the highest frequency at which a sensitive radio survey has been carried out over a large area of sky.Sources with ﬂux densities above 100mJy in the ATCA 20GHz Pilot Survey at declination −60◦to −70◦were observed at up to three epochs during 2002–4,including near-simultaneous measurements at 5,8and 18GHz in 2003.Of the 173sources detected,65%are candidate QSOs or BL Lac objects,20%galaxies and 15%faint (b J >22mag)optical objects or blank ﬁelds.On a 1–2year timescale,the general level of variability at 20GHz appears to be low.For the 108sources with good–quality measurements in both 2003and 2004,the median variability index at 20GHz was 6.9%and only ﬁve sources varied by more than 30%in ﬂux density.Most sources in our sample show low levels of linear polarization (typically 1–5%),with a median fractional polarization of 2.3%at 20GHz.There is a trend for fainter 20GHz sources to have higher fractional polarization.At least 40%of sources selected at 20GHz have strong spectral curvature over the frequency range 1–20GHz.We use a radio ‘two–colour diagram’to characterize the radio spectra of our sample,and conﬁrm that the ﬂux densities of radio sources at 20GHz (which are also the foreground point-source population for CMB anisotropy experiments like WMAP and Planck)cannot be reliably predicted by extrapolating from surveys at lower frequencies.As a result,direct selection at 20GHz appears to be a more eﬃcient way of identifying 90GHz phase calibrators for ALMA than the currently–proposed technique of extrapolation from radio surveys at 1–5GHz.Key words:surveys —cosmic microwave background —galaxies:radio continuum —galaxies:active —radio continuum:general1INTRODUCTIONMost large–area radio imaging surveys have been carried out at frequencies of 1.4GHz or below,where the long–term variability of the radio–source population is generally low.The catalogued ﬂux densities measured by such surveys can therefore continue to be used with a high level of conﬁdence for many years after the survey was made.It is not clear to what extent this is true for radio sur-veys carried out at higher frequencies,where the source pop-ulation becomes increasingly dominated by compact,ﬂat–spectrum sources which may be variable on timescales of a few years.We are currently carrying out a sensitive radio survey of the entire southern sky at 20GHz,using a wide-band ana-c2000RAS2Sadler et al.logue correlator on the Australia Telescope Compact Array (ATCA;see Ricci et al.2004a for an outline of the pilot study for this survey).We have therefore begun an investi-gation of the long–term variability of radio sources selected at20GHz,which will also help us estimate the likely long–term stability of our source catalogue.There is little information to guide us in what to expect. Only a few studies of radio–source variability have been car-ried out at frequencies above5GHz and these have generally targeted sources which were either known to be variable at lower frequencies,or were selected to haveﬂat or rising radio spectra at frequencies below about5GHz.Such objects may not be typical of the20GHz source population as a whole.The full AT20GHz(AT20G)survey,using the whole 8GHz bandwidth of the analogue correlator and coherently combining all three interferometer baselines,began in late 2004and has a detection limit of40–50mJy at20GHz,i.e. about a factor of two fainter than the sources discussed here. It will eventually cover the entire southern sky from decli-nation0◦to−90◦.Our reasons for carrying out a Pilot Survey in advance of the full AT20G survey were to characterize the high–frequency radio–source population,and to optimize the ob-servational techniques used in the two–step survey process (i.e.fast scans of large areas of sky with a wide-band ana-logue correlator,followed by snapshot imaging of candi-date detections)to maximize the completeness,reliability and uniformity of theﬁnal AT20G catalogue.Because of the slightly diﬀerent observational techniques used in2002, 2003and2004,the Pilot Survey data are not as complete or uniform as the AT20G data are intended to be.The Pi-lot Survey nevertheless provides an importantﬁrst look at the faint radio–source population at20GHz.Since correc-tions for extragalactic foreground confusion will be critical for next–generation CMB surveys,a better knowledge of the properties of high–frequency radio sources(and especially their polarization and variability)is particularly desirable.This paper presents an analysis of the radio–source pop-ulation down to a limitingﬂux density of about100mJy at 20GHz,based on observations in the declination zone−60◦to−70◦scanned by the AT20GHz Pilot Survey in2002 and2003.Our aim is to provide someﬁrst answers to the following questions:•How does the radio–source population at20GHz re-late to the‘ﬂat–spectrum’and‘steep–spectrum’populations identiﬁed at lower frequencies?•What fraction of radio sources selected at20GHz are variable on timescales of a few years,and how stable in time is a20GHz source catalogue?•What are the polarization properties of radio contin-uum sources selected at20GHz?2OBSER V ATIONS2.1The ATCA wide–band correlatorAn analogue correlator with8GHz bandwidth(Roberts et al.2006),originally developed for the Taiwanese CMB in-strument AMiBA(Lo et al.2001)is currently being used at the Australia Telescope Compact Array(ATCA)to carry out a radio continuum survey of the entire southern sky at2002Sep13–17218 3.430 2003Oct9–16317.6,20.46–730,30,60 Date ATCA Obs.Freq.N antconﬁg.(GHz)Table2.Log of follow–up ATCA imaging observations of sources detected in the scanning survey at20GHz.N ant shows the num-ber of antennas equipped with12mm receivers for each observing session.The angular resolution of the follow–up images is typi-cally8arcsec at4.8GHz,4arcsec at8.6GHz and15arcsec at 20GHz.20GHz.The wide bandwidth of this correlator,combined with the fast scanning speed of the ATCA,makes it pos-sible to scan large areas of sky at high sensitivity despite the small(2.3arcmin)ﬁeld of view at20GHz.Since delay tracking cannot be performed with this wide-band analogue correlator,all scanning observations are carried out on the meridian(where the delay for an east–west interferometer is zero).The fast-scanning survey measures approximate posi-tions andﬂux densities for all candidate sources above the detection threshold of the survey.Follow-up20GHz imaging of these candidate detections is then carried out a few weeks later,using the ATCA in a hybrid conﬁguration with its standard(delay–tracking)digital correlator.These follow–up images allow us to conﬁrm detections,and to measure ac-curate positions andﬂux densities for the detected sources. Finally,the conﬁrmed sources are also imaged at5and 8GHz to measure their radio spectra,polarisation and an-gular size.2.2Observations in the−60◦to−70◦declinationzoneTables1and2summarize the telescope and correlator con-ﬁgurations used for the observations discussed in this paper. There are three main data sets:(i)The ATCA Pilot Survey observations made in2002 and published by Ricci et al.(2004a).These are brieﬂy de-scribed in§2.4below.(ii)Data from a resurvey of the same declination zone at 20GHz in2003,together with near–simultaneous observa-tions at4.8and8.6GHz of the conﬁrmed sources(see§2.5). (iii)20GHz images made in2004of sources detected at 18GHz in2002and/or2003,as part of a program to monitorc 2000RAS,MNRAS000,1–??Extragalactic radio sources at20GHz3the long–term variability of the sources detected in the pilot survey(§2.6).Although our ATCA20GHz pilot survey covered the whole sky between declinations−60◦to−70◦,only sources with Galactic latitude|b|>10◦are discussed in this paper. While the source population at2<|b|<10◦is also dom-inated by extragalactic objects,it is very diﬃcult to make optical identiﬁcations of radio sources close to the Galactic plane because of the high density of foreground stars.Since one aim of this study is to examine the optical properties of high–frequency radio sources,we therefore chose to exclude the small number of extragalactic sources which lay within ten degrees of the Galactic plane,or within5.5degrees of the centre of the Large Magellanic Cloud.2.3Theﬂux density scale of the ATCA at20GHz At centimetre wavelengths,the ATCA primaryﬂux cali-brator is the radio galaxy PKSB1934–638(Reynolds1994). Planets have traditionally been used to set theﬂux density scale in the12mm(18–25GHz)band,and the planets Mars and Jupiter were used as primaryﬂux calibrators during the ﬁrst two years of operation of the ATCA12mm receivers in 2002–3.However,the use of planets to set theﬂux density scale has some signiﬁcant disadvantages(Sault2003):•Their angular size(4–25arcsec for Mars and30–48arcsec for Jupiter)means that they can be resolved out at20GHz on baselines greater than a few hundred metres.•Their(northern)location on the ecliptic means that they are visible above the horizon for a much shorter time than a southern source like PKSB1934–38,and shadowing of northern sources can also be a problem in some compact ATCA conﬁgurations.PKSB1934–638was monitored regularly in the12mm band over a six–month period in2003,using Mars as primaryﬂux calibrator(Sault2003).These observations showed that theﬂux density of PKSB1934–638remained constant(varying by less than±1–2%at20GHz),making it suitable for use as aﬂux calibrator at these high frequen-cies.From2004,therefore,PKSB1934–638was used as the primaryﬂux ATCA calibrator at20GHz,whereas Mars was used in our2002and2003observations.2.42002observations2.4.1Scanning observationsTheﬁrst observations of the declination strip−60◦to−70◦were made by Ricci et al.(2004a).Using a single analogue correlator with3GHz bandwidth and two ATCA antennas on a single30m baseline,they detected123extragalactic (|b|>5◦)sources at18GHz above a limitingﬂux density of100mJy.The2002observations did not completely cover the whole−60◦to−70◦declination strip because of tech-nical problems which interrupted some of the fast scanning runs.Figure4of Ricci et al.(2004a)shows the2002sky coverage and the missing regions,which are mainly in the RA range5–8h.The declination−60◦to−70◦strip was therefore reobserved at22GHz in2003,and full coverage was then achieved.The region overlapped by the2002and 2003observations gives a useful test of the completeness of the scanning survey technique,as discussed in§4.2.4.2Follow–up imaging andﬂux–density errorsFollow-up synthesis imaging of the candidate sources de-tected in the2002scans was carried out at18GHz with the ATCA as described by Ricci et al.(2004a).It is important to note that,because the candidate source positions obtained from the wide-band scans in2002were typically accurate to ∼1arcmin,and the primary beam of the ATCA antennas at20GHz is only∼2.3arcmin,about30%of the sources detected in the follow–up images were oﬀset by80arcsec or more from the pointing centre,and so required large (more than a factor of two)corrections to their observed ﬂux densities to correct for the attenuation of the primary beam.These corrections were made by Ricci et al.(2004a), but were not explicitly discussed in their paper.It has sub-sequently become clear that uncertainties in the primary beam correction at very large oﬀsets from theﬁeld centre can sometimes introduce large systematic errors into the ob-servedﬂuxes.For this reason,we now regard the18GHzﬂux density measurements listed by Ricci et al.(2004a)as unre-liable for sources observed at more than80arcsec from the imagingﬁeld centre.For follow–up imaging in2003and sub-sequent years,sources more than80arcsec from the imaging ﬁeld centre were re-observed at the correct position when-ever possible.2.52003observations2.5.1Scanning observationsIn2003,we used three analogue correlators and three ATCA antennas,giving us three independent baselines(of30,30 and60m).The correlators also had a new design with the potential for8GHz operation(Roberts et al.2006).The 2003fast scans were carried out using three ATCA antennas separated by30m on an east–west baseline,and scanned in a trellis pattern at15deg min−1with11–degree scans from declination−59.5◦to−70.5◦,interleaved with2.3arcmin separation and sampled at54ms.The system temperature was continually monitored at 17.6and20.4GHz and periods with high sky noise(i.e.due to clouds or rain)wereﬂagged out and repeated later.Cal-ibration sources were observed approximately once per day by tracking them through transit(±5min).Due to an unforeseen problem matching the wide-band receiver output to theﬁbre modulator,there was a15db slope across the bandpass.When we transformed the16lag channels observed into8complex frequency channels,the resulting bandpass was uncalibratable and unphysical.This occurred because we had an analogue correlator and there is no exact Fourier Transform relation between delay and frequency(Harris&Zmuidzinas2001).The actual bandpass was measured by taking the Fourier Transform of the time sequence obtained while tracking a calibrator source through transit.In this case we have a physical delay which changes as the earth rotates and we can get a sensible bandpass.In the end only two channels were usable,giving a total band width of3GHz. It was also impractical to make a phase calibration of thec 2000RAS,MNRAS000,1–??4Sadler etal.Figure parison of the 18GHz ﬂux densities measured in 2002and 2003for sources detected independently in the scanning process.Sources which were detected in 2002but not recovered in 2003are shown as open triangles with a ﬂux density limit of 100mJy for 2003.As discussed in the text,the error bars on the 2002ﬂux density measurements are signiﬁcantly larger than for 2003.Open squares show sources with oﬀsets of more than 80arcsec from the imaging ﬁeld centre in the 2002data.three interferometers with this data.As a result the sensi-tivity in 2003was only marginally better than that in 2002,and overlapping scans could not be combined coherently.To extract a candidate source list from the 2003raster scans,the correlator delays were cross-matched with the template delay pattern of a strong calibrator.The correlator coeﬃcient for each time stamp along the scans was recorded,and values from overlapping scans were incoherently com-bined to form images in 12equal-area zenithal projection maps (each two hours wide in right ascension).The source ﬁnding algorithm imsad implemented in Miriad was used to extract candidate sources above a 5σthreshold.2.5.2Follow–up imagingA list of 1350candidate sources detected in the scanning survey was observed at 17,19,21and 23GHz as noted in Table 2.As in 2002,the planet Mars was used as the primary ﬂux calibrator.In the 2003follow–up imaging,the data were reduced as the observations progressed,and sources which were more than 80arcsec from the imaging centre were reob-served if possible.This signiﬁcantly improved the accuracy of the ﬂux density measurements for the 2003images com-pared to those made in 2002,as can be seen in Figure 1.Images of each follow–up ﬁeld were made at 18and 22GHz using the multi–frequency synthesis (MFS)tech-nique (Conway et al.1990;Sault &Wieringa 1994).Since the signal-to-noise ratio in the 18GHz band was signiﬁ-cantly higher than at 22GHz,we used only the 18GHz data in our subsequent analysis.The median rms noise in thefollow–up images was 1.5mJy/beam at 18GHz,and sources stronger than ﬁve times the rms noise level (estimated from the Stokes-V images)were considered to be genuine detec-tions.The 364sources with conﬁrmed detections at 18GHz (including some Galactic plane sources)were imaged at 5and 8.6GHz in November 2003.The total integration time for these follow–up images was 80s (2cuts)at 17–19and 21–23GHz,and 180s (6cuts)at 5and 8GHz.2.62004observationsA sample of 200sources detected at 18GHz in 2002and/or 2003was re-imaged on 22October 2004in a series of tar-geted observations at 19and 21GHz,using the ATCA hy-brid conﬁguration H214.All these imaging observations were centred at the source position measured in 2002/3,so that positional oﬀsets from the imaging ﬁeld centre were negligi-ble.The 19and 21GHz data were combined to produce a single 20GHz image of each target source.The total inte-gration time at 20GHz was 240s (2cuts),and the median rms noise in the ﬁnal images was 0.7mJy rms.3DATA REDUCTION AND SOURCE–FITTING3.1Reduction of the follow–up imagesFor the 2003data,deconvolved images of the conﬁrmed sources were made at 5,8and 18GHz and positions and peak ﬂux densities were measured using the Miriad task maxﬁt ,which is optimum for a point source.We also used the Miriad task imﬁt to measure the integrated ﬂux density and angular extent of extended sources.Where necessary,the ﬁt-ted ﬂux densities were then corrected for the primary beam attenuation at frequencies between 17and 23GHz based on a polynomial model of the Compact Array antenna pattern.Positional errors were estimated by quadratically adding a systematic term and a noise term:the systematic term was assessed by cross-matching the 18GHz source po-sitions with the Ma et al.(1998)International Coordinate Reference Frame (ICRF)source positions;the noise term is calculated from the synthesized beam size divided by the ﬂux S/N.The median position erors are 1.3arcsec in right ascension and 0.6arcsec in declination.To estimate the ﬂux density errors,we quadratically added the rms noise from V-Stokes images to a multiplica-tive gain error estimated from the scatter between snapshot observations of the strongest sources.The median percent-age gain errors were 2%at 5and 8GHz,and 5%at 18GHz.For the 2004data,the 19and 21GHz visibilities were amplitude and phase calibrated in Miriad.As noted in §2.3,PKSB 1934-638was used as the primary ﬂux calibrator.The calibrated visibilities were combined to form 20GHz images using the MFS technique and peak ﬂuxes were worked out using the Miriad task maxﬁt .Position and ﬂux errors were determined in the same way as for the 2003data.3.2Polarization measurementsAs all four Stokes parameters were available,linear polar-ization measurements were carried out on the 2003andc2000RAS,MNRAS 000,1–??Extragalactic radio sources at20GHz5parison of18GHzﬂux densities measured in2002and2003with20GHzﬂux densities measured in2004.The horizontal dotted line shows the sensitivity limit of the2002and2003surveys.2004data.Q-Stokes,U-Stokes,and polarisedﬂux P=6Sadler et al.The columns in Table3are as follows:(1)The AT source name,followed by#if the source is resolved or double at20GHz(see§3.4).(2)The radio position(J2000.0)measured from the20GHz images.For resolved doubles,the listed position is the radio centroid.(3)For sources where we were able to make an optical iden-tiﬁcation on the Digitized Sky Survey,this column lists theb J magnitude from the Supercosmos database.(4)The object type of the optical ID,as classiﬁed in Su-percosmos:T=1for a galaxy,T=2for a stellar object(QSO candidate).T=0indicates either a blankﬁeld at the source position or a faint(>22mag)object for which the Supercos-mos star/galaxy separation is unreliable.(5)The18GHzﬂux density measured in2002,followed by its error.For resolved doubles,we list the integratedﬂux density over the source.Flux densities in square brackets[ ]are measurements made at oﬀsets of more than80arcsec from the imagingﬁeld centre at18–20GHz,and should beregarded as unreliable because of the large primary–beam correction.Flux densities followed by a colon are measured at oﬀsets of60–80arcsec from theﬁeld centre,but should be reliable.(7)The18GHzﬂux density measured in2003,and its error.(9)The20GHzﬂux density measured in2004,and its error.(11)The8.6GHzﬂux density measured in2003,and its er-ror.(13)The4.8GHzﬂux density measured in2003,and its er-ror.(15)The integratedﬂux density at843MHz and its error, from the Sydney University Molonglo Sky Survey(SUMSS) catalogue(Mauch et al.2003).(17)The fractional linear polarization at20GHz measured in2004,and its error.(19)The debiased variability index at20GHz,calculated as described in§5.1.(20)Alternative source name,from the NASA Extragalactic Database.(21)Notes on individual sources,coded as follows:C=listed in the online ATCA calibrator catalogue,E=possible EGRET gamma–ray source(Tornikoski et al. 2002),I=listed as an IRAS galaxy in the online NASA Extra-galactic Database(NED),M=galaxy detected in the near-infrared Two-Micron All-Sky Survey(2MASS),P=in the Parkes quarter-Jy sample(Jackson et al.2002), Q=listed as a QSO in NED,V=VLBI observation with the VSOP satellite(Hirabayashi et al.2000)W=source detected in theﬁrst–year WMAP data(Bennett et al.2003),X=listed as an X-ray source in NED,=polarization observation by Ricci et al.(2004b).3.4Extended sources at20GHzThe great majority of the sources detected in the20GHz Pilot Survey are unresolved in our follow–up images at5, 8and20GHz.The source–detection algorithm used in the Pilot Survey was optimized for point sources,and therewillGalaxyCandidate QSOMag.limitFigure4.Optical identiﬁcations for the20GHz radio sources in Table3.Galaxies and stellar objects(QSO candidates)are shown separately.Only27sources(13%of the sample)are unidentiﬁed down to b J<22mag.be some bias against extended sources with angular sizes larger than about30arcsec.For sources larger than1arcmin in size,the totalﬂux densities listed in Table3may also be underestimated.Only eleven of the173sources in Table3were resolved in our(15arcsec resolution)20GHz images.The overall properties of extended sources in the current sample are as follows:•Three objects,J0103–6439,J2157–6941and J2358–6052/J2359–6057,are very extended double–lobed radio sources which are too large to be imaged with these ATCA snapshots.As a result,the totalﬂux densities listed in Table 3are lower limits to the correct value.•Another seven sources are resolved in our ATCA im-ages,but still lie within the2.2arcmin primary beam of the ATCA at20GHz.Details of these objects are given in Ap-pendix A.•Five of the extended sources(J0103–6439,J0121-6309,J0257-6112,J0743–6726and J2157–6941)have aﬂat–spectrum core which dominates theﬂux density at20GHz. Since the number of extended sources is small,and they ap-pear to be somewhat diverse in nature,we defer any detailed discussion of the extended radio–source population to a later paper.3.5Optical identiﬁcation of the20GHz sources We examined all the sources in Table3in the SuperCOS-MOS online catalogue and images(Hambly et al.2001).An optical object was accepted as the correct ID for a20GHz radio source if it was brighter than b J=22mag.and lay within2.5arcsec of the radio position.For one source in Ta-ble3(J0715–6829)the optical image was saturated by lightc 2000RAS,MNRAS000,1–??Extragalactic radio sources at20GHz7 Figure5.Relation between SuperCOSMOS b J magnitude andredshift for those objects in our sample which have a publishedredshift.Open circles show galaxies from the20GHz andﬁlledcircles QSOs.The small crosses show a representative subsampleof2dFGRS radio galaxies selected at1.4GHz(Sadler et al.2002).The highest redshift so far measured for an object in this sampleis for J1940–6907,a QSO at z=3.154.from a nearby11th magnitude star and so no identiﬁca-tion could be attempted.Of the remaining172sources,146(85%)had an optical ID which met the criteria listed above.Monte Carlo tests(based on matching the SuperCOSMOScatalogue with radio positions randomly oﬀset from thosein Table3)imply that at least97%of these IDs are likelyto be genuine associations,rather than a chance alignmentwith a foreground or background object.As can be seen from Figure4,the majority(65%)of ra-dio sources selected at20GHz have stellar IDs on the DSSB images,and are candidate QSOs or BL Lac objects.20%of the radio sample are identiﬁed with galaxies and15%are faint objects or blankﬁelds.The overall optical identi-ﬁcation rate of85%for radio sources selected at20GHz issigniﬁcantly higher than the identiﬁcation rate for brightradio sources selected at1.4GHz(typically∼30%aboveB∼22mag),but is closer to that found by Bolton et al.(2004)for aﬂux–limited sample of radio sources selectedat15GHz,as discussed in§8.1.1.Figure5shows the relation between b J magnitude andredshift for the22sources(13%of the objects in Figure4)which currently have a published redshift.A represen-tative sample of nearby radio galaxies(Sadler et al.2002)selected from the2dF Galaxy Redshift Survey(2dFGRS;Colless et al.2001)is shown for comparison.Galaxies de-tected in our20GHz survey appear to span a narrow rangein optical luminosity similar to that seen in nearby radiogalaxies selected at lower frequencies,though we cautionthat the sub-sample of sources with published redshifts isinhomogeneous in nature and may be biased in luminosity<100600%101–12513431%126–1508563%151–2001212100%>200504794%8Sadler etal.Figure6.Examples of radio spectra for each of the four spectral classes identiﬁed in the text(Upturn,Rising,Steep and Peak),together with a spectrum classiﬁed as Flat(|α|<0.1for both0.84–5GHz and8–20GHz).Where available,a408MHzﬂux density from the MRC (Large et al.1981)is plotted in addition to the data from Table3.5RADIO SPECTRA OF THE20GHZSOURCES5.1Representative radio spectra at0.8to20GHzFigure6shows some representative radio spectra for sourcesin our sample.It is clear we see a wide variety of spectralshapes,most of which cannot beﬁtted by a single power–law over the frequency range1–20GHz.We can distinguishfour main kinds of spectra:(a)Sources with steep(falling)spectra over the whole range843MHz to20GHz(e.g.J0408–6545in Fig.6).(b)Sources with peaked(GPS)spectra,in which theﬂuxdensity rises at low frequency and falls at high frequency(e.g.J0201–6638).(c)Sources with inverted(rising)radio spectra over thewhole frequency range(e.g.J0113–6753).(d)Sources with an upturn in their spectrum,where theﬂuxdensity is falling at lower frequencies,but then turns up andbegins to rise above5–8GHz(e.g.J2213–6330).In addition,a small number of sources haveﬂat radiospectra in which theﬂux density is essentially constant overthe entire frequency range observed(e.g.J0220–6330in Fig.6).The radio spectral indexα=(log S1−log S2)。

Experimental evidence of accelerated energy transfer in turbulence

a r X i v :p h y s i c s /0607244v 2 [p h y s i c s .f l u -d y n ] 29 M a y 2007Experimental evidence of accelerated energy transfer in turbulencebb´e ,1C.Baudet,2and G.Bustamante 11Laboratorio de Turbulencia,Departamento de F´ısica,Facultad de Ciencia,Universidad de Santiago de Chile.Casilla 307,Correo 2,Santiago,Chile2Laboratoire des Ecoulements geophysiques et Industriels,UMR 5519CNRS/UJF/INPG.1025,Rue de la Piscine,38041Grenoble,France (Dated:21June 2005;Revised 09June 2006)We investigate the vorticity dynamics in a turbulent vortex using scattering of acoustic waves.Two ultrasonic beams are adjusted to probe simultaneously two spatial scales in a given volume of the ﬂow,thus allowing a dual channel recording of the dynamics of coherent vorticity structures.Our results show that this allows to measure the average energy transfer time between diﬀerent spatial length scales,and that such transfer goes faster at smaller scales.PACS numbers: 43.58.+z 47.27.JvMuch of the investigation in turbulence has been de-voted to the understanding of the mechanisms underly-ing the energy transfer through the turbulent cascade,a concept introduced by Richardson in 1922[1].A good deal of theoretical and numerical work has been dedi-cated to study shell models,which include the essential features expected in a turbulent cascade,but without some of the complications inherent to the Navier-Stokes equations.Though these models retain some of the dy-namics of the motion equations,they handle the velocity ﬁeld as a scalar.Thus the price payed is a complete loss of ﬂow geometry [2].Another approach is the study of random multiplicative cascade models,which adequately mimic the statistics of the local energy dissipation rate ǫat diﬀerent ﬂow scales,and the intermittency of small scales observed in a large number of experimental results.Although much progress was done,many issues related to the statistics of energy transfer,energy dissipation and small scale intermittency in turbulent ﬂows still remain without satisfactory answers.In particular,the dynamics of the energy transfer through the turbulent cascade has been only recently addressed in some theoretical works [3,4],but this aspect of turbulent ﬂows is still lacking experimental studies speciﬁcally addressing it.In this note we report an experimental result,obtained for the case of a vortex embedded in a turbulent ﬂow pro-duced in air by two coaxial centrifugal fans,each facing the other and rotating at ﬁxed angular velocities.This so-called von K´a rm´a n ﬂow has been used in a number of experiments in turbulence [5].When the fans rotate in the same direction with identical speeds,a strong vortex is produced between them [6].The advantage of this con-ﬁguration is that in a small volume we obtain an intense and well-deﬁned coherent vorticity structure,surrounded by a fully turbulent background.Details of this setup are given in a previous work [7].The parameters used in this case are:diameter of fans:D =30cm,height of vanes:h =2.2cm,distance between disks:H =30cm,rota-tion speed:f =30Hz,and diameter of central holes:d =2.5cm.The fans were driven by two DC motors,powered by independent constant voltage sources allow-ing to keep the disk rotation within 1%of the desired speed.Local measurements of the airﬂow speed were performed with a Dantec Streamline 90N10frame hous-ing a Constant Temperature Anemometer which drives a 5µm diameter and 2mm length platinum wire probe.A Streamline 90H02Flow Unit was used to calibrate it.To produce and detect the sound waves,four circular Sell type electrostatic transducers [9]were used,each having an active surface diameter of 14cm.Two B&K model 2713power ampliﬁers drove the emitters.The receivers used custom made charge ampliﬁers,whose output were connected to two Stanford Research model SR830lock-in ampliﬁers (LIA)through 2nd order high-pass RC ﬁlters having cut-oﬀfrequencies of 7.5kHz.The sine-wave out-put of each LIA internal generator was used as signal source for the corresponding emitter.The LIA output signals,comprising in-phase and quadrature components,were low-pass ﬁltered by an IOTech Filter-4888th order elliptic ﬁlter bank,using a cutoﬀfrequency of 4kHz.The resulting signal was digitized at 12.5kS/s with a 16-bit resolution National Instruments AT-MIO-16X multifunc-tion board,installed into a personal computer.A total of 220points per signal channel was collected in each of 77data sets.Fig.1(top)shows the device that produced the ﬂow,along with the four circular ultrasonic transducers,and the hot-wire probe.The transducers were arranged to perform measurements using an interferometric con-ﬁguration,described in detail in a previous work [8].The scattering angles were θ1=40◦and θ2=60◦.The magnitude of the scattering wave-vectors,q scatti =4πν0,i sin(θscatti/2)/c =|k ′−k |,i =1,2,were adjusted independently for each channel through their correspond-ing frequencies ν0,i .We acquired three sets of data,set-ting ν0,1=20kHz,40kHz,and 60kHz;while ν0,2took some 25values in the interval [16,90]kHz in each case.Notice that each probed scattering wave-vector,related to the z -component of the vorticity distribution,can be set arbitrarily close (even identical)to the other.Fig.1(bottom)displays a schematic upper view of the lower disk,hot-wire probe and ultrasonic transducers,along with distances and angles.This arrangement is symmet-ric with respect to the vertical plane AA.Also displayedFIG.1:Top:Partial view of the experimental setup.Bottom: a schematic drawing of the experimental setup(see text).is a schematic diagram of the measuring chain.Fig.2 (top)is a sketch of the volume probed by the ultrasonic beams,showing the relationships between scattering vec-tors and wave-vectors in the case of exact inter-channel tuning(same scattering wave-vector).As mentioned in previous works[6,7],the vortex performs a slow pre-cession motion around the axis of rotation of the fans. Even so,it remains inside the measurement volume,as shown inﬁg.2.A horizontal cut of the measurement volume is displayed as a shaded rhombus,the heavier shaded circle indicating the position of the vortex core. Air speed measurements with the probe wire aligned ver-tically,and located at about2cm of the disks’s rotation axis and some10cm above the lower disk,give the sam-ple record displayed inﬁg.2(bottom).The nearly peri-odic precession of the vortex is visible as a pattern with sharp dips—sometimes enlarged or doubled byﬂuctu-ations due to the turbulent background,each time the center of the vortex is close or coincides with the hot wire location.These events are signaled by arrows in ﬁg.2,the time interval between single events being about 1s.Accordingly,the spectrum displayed inﬁg.3(top) has a rather wide peak located at f0≈1Hz.The Tay-lor hypothesis is not met by thisﬂow,but this spec-trum gives an idea of the energy contents at diﬀerent scales.At higher frequencies(smaller scales),it meets only approximately the k−5/3K41law(represented by the straight line)in the inertial range,due to the pres-ence of the vortex in the bulk of theﬂow.In fact,we observe three regions,A,B,and C,where the spectrum looks self-similar,but with diﬀerent slopes.As we will see later,this could be related to the inﬂuence of the ﬂow anisotropy on the dynamics of the energytransfer FIG.2:Top:Diagram showing the relationship between wave-vectors,the volume probed by the ultrasonic beams (shaded region)and the size of the disks.The dark circle represents a cut of the vortex core.Bottom:A sample of the anemometer signal.Arrows signal events of minimal air speed,the vortex core being close to the hot wire probe there. The inset displays the velocity proﬁle of a non turbulent vor-tex,which helps in recognizing the vortex core in the turbu-lent signal.through the turbulent cascade.The acoustic signals are delivered by the LIAs as low frequency complex voltages, which are images of the spatial Fourier modesΩz(q j,t) of theﬂow vorticity,probed at well-deﬁned wave vectors q j=4πν0,j sin(θj/2)/c,j=1,2.Typical spectra of these signals are displayed inﬁg.3(bottom).The wide central peak,due to the intense coherent vorticity of the vortex, lies between two side bands produced by the background ﬂow.There is a close correspondence between the low fre-quency region of the velocity spectrum(up to50Hz)and the central region of the vorticity spectrum.The same is true for the high frequency region(>200Hz)of the spectra,both exhibiting a slowly decaying roll-oﬀ,with a slope close to−5/3related to the background turbulence of theﬂow.Now we address the separation of the coherent structure and the background turbulentﬂow.Fol-lowing ref.[8],we compute the coherence between two spatial Fourier modes of the vorticity,Ωz(q1,t) andΩz(q2,t).The coherence function,C(q1,q2,ν)= Ωz(q1,ν)Ω∗z(q2,ν) /FIG.3:Top:Power spectral density of the signal displayed inﬁg. 2.Three almost linear regions are labeled A,B,and C(see text),with slopesαA,B,C.The straight line represents the Kolmogorov spectrum,with slopeαK=−1.66.Bottom: Individual spectra of the signals delivered by the lock-in am-pliﬁers.The spectrum corresponding to the scattering angle of60degrees decreases slightly faster with the frequency shift. Scattered waves having the same central frequency of the in-cident beam have no frequency shift.central peak with a high level of coherence(0.9,being1 the maximum expected value;the value of0.9should be ascribed to incoherent noise)reveals that both channels are detecting the same coherent structure.This was veriﬁed“turning oﬀ”the vortex by rotating the disks in opposite directions at the same angular speed.In this case only a turbulent shear layer remains,and the plot of the coherence function displays only the side bands.By stacking plots of coherence for a sequence of values of q1,it is possible to build surfaces of coherence relating events at diﬀerentﬂow scales,as functions of ∆q=q2−q1and the frequency shiftν,as shown inﬁg.4. We can interpret them in as eddies at given scales draw-ing its energy from decaying structures at larger scales, in the frame of the Richardson’s turbulent cascade.As these surfaces represent a time average of the whole story,we perform a time cross-correlation analysis to conﬁrm this interpretation.This is done by computing the cross-correlationχ(q1,∆q,∆t)= |Ωz(q1,t)||Ωz(q1+∆q,t+∆t)| /FIG.5:Time lags corresponding to the coherence sur-faces ofﬁg. 4.a),b),and c)correspond to q1= 3.79,7.58,and11.4cm−1,respectively.The straight lines are linearﬁts to the measured points,with correlation coef-ﬁcient R2=0.60(0.75,0.66).Note that the slopes decrease with increasing q1.ical work[3].A rather crude explanation of this result follows:if E(q)is the spectral density of energy per unit mass—averaged in time,and we think ofδq/δτas be-ing an ordinary derivative,then E(q)δq/δτis the average energyﬂux density in k-space.But this is the average dissipation rate per unit massǫ.Thus,E(q)δq/δτ=ǫ, andδτ/δq=E(q)/ǫ.As E(q)decreases with increasing q,so doesδτ/δq.Notice that in this picture,the energy attached to a given eddy is transported towards larger wave numbers merely by reduction of its spatial scale(in directions perpendicular to its vorticity)due to stretch-ing by the velocityﬁeld of larger eddies.We can illustrate our view in the frame of K41the-ory[1]:we have E(q)=C Kǫ2/3q−5/3,where C K is the Kolmogorov constant.Thus,for homogeneous and isotropic turbulence,δτ/δq=C Kǫ−1/3q−5/3,which is of course a decreasing quantity.By rearranging terms,we have q−5/3δq=(ǫ1/3/C K)δt,which by integration yieldsq(t)=(q−2/30−22C Kǫ−1/3q−2/3,corre-sponding to the average time taken by the energy at thescale l0to cascade down to l=0+(q→∞),in aﬂuidwith vanishing viscosity—in the frame of K41theory.Putting C K≈0.5,ǫ∼102W/kg,estimated from thepower injected to theﬂow(≈70W)and the volume ofmoving air(∼0.5m3)and,for instance,q0≈3×102m−1,corresponding to the largest scale measured withour acoustic method,we get t0K∼4ms.This is onthe order of characteristic times inﬁg.5,showing thattransfer times in homogeneous turbulence do not diﬀertoo much from those in ourﬂow.Thus,our reasoningshows that the trend observed inﬁg.5can be understoodin terms of“classical”homogeneous and isotropic tur-bulence.In non-homogenous,non-isotropic turbulence,as in the present experiment,the behavior ofδτ/δq canbe estimated from the experimental spectrum shown inﬁg.3,where the Kolmogorov spectrum is plotted as astraight line,for comparison.In the large scales region(A),δτ/δq decreases faster than in K41turbulence,thecascade acceleration being larger.In the small scales re-gion(C),δτ/δq tends to reach the Kolmogorov slope,but the acceleration is slightly smaller than in K41.Re-gion(B),in which the cascade acceleration reaches itsminimum,is a transition zone from a non-isotropicﬂowat large scales,where vorticity is mainly parallel to thez-axis,to a more isotropic small-scaleﬂow.In all threeregions the spectrum seems to be self-similar,with dif-ferent scaling exponents.Of course,being this one aﬁrst experimental result revealing the accelerated natureof energy transfer through the turbulent cascade,morework will be necessary to state our conclusions on moresolid ground.We recall that we are measuring only thez-component of the vorticity and the modulus of the ve-locity component normal to the z-axis.It should benecessary to simultaneously measure at least one morecomponent of the vorticity.Additionally,the conditionsof validity for the Taylor hypothesis are not meet in thesehot-wire measurements—aﬂying probe would be muchbetter to study thisﬂow.At any rate,in the large-scalerange the vorticity in ourﬂow is mainly parallel to the z-axis.Thus,eddies in the large scale region have mostlyparallel vorticities,and the vortex stretching is largelyinhibited there,slowing down the energy transfer.Atsmaller scales,where a more isotropicﬂow exists,vortexstretching is reestablished,giving faster energyﬂux rates.Thus,in-between the acceleration should be greater thanin the isotropic case.This could explain in part our re-sults.To conclude,we remark that our reasoning suggestthat cascade acceleration may be a necessary but not suf-ﬁcient condition for small scale intermittency.Financial support for this work was provided byFONDECYT,under projects#1990169,#7990057and#1040291.[1]U.Frisch,Turbulence:the Legacy of A.N.Kolmogorov,(Cambridge University Press,Cambridge,1995)[2]L.Biferale,Annu.Rev.Fluid Mech.35,441(2003)[3]E.L´e vˆe que and C.R.Koudella,Phys.Rev.Lett.86,4033(2001).[4]Roberto Benzi,Luca Biferale,and Mauro SbragagliaPhys.Rev.E71,065302(R)(2005).[5]For example,experimental results in conﬁned vonK´a rm´a nﬂows are given in J.-F.Pinton,P. C.W.Holdsworth,and bb´e,Phys.Rev.E60,R2452 (1999);P.Odier,J.-F.Pinton,and S.Fauve,Phys.Rev.E58,7397(1998);O.Cadot,Y.Couder,A.Daerr,S.Douady,and A.Tsinober Phys.Rev.E56,427(1997);O.Cadot,S.Douady,and Y.Couder,Phys.Fluids7,630 (1995);J.Maurer,P.Tabeling,and G Zocchi,Europhys.Lett.26,31(1994);S.Douady,Y.Couder,and M.E.Brachet,Phys.Rev.Lett.67,983(1991).[6]bb´e,J.-F.Pinton,and S.Fauve,Phys.Fluids8,914(1996).[7]bb´e and J.-F.Pinton,Phys.Rev.Lett.81,1413(1998).[8]C.Baudet,O.Michel,and W.J.Williams,Physica D128,1(1999).[9]D.Anke,Acustica30,30(1974).[10]We have not dropped2πfactors here in the magnitudeof scattering vectors,which explain the diﬀerence in∆q scales in the aforementionedﬁgures.[11]This is like measuring the advection of a magnitude inthe Fourier space.Of course,here the“advection”mech-anism lies in the dynamics of the turbulent velocityﬁeld in the direct space.The idea of measuring a wind in the Fourier space by looking simultaneouly at two diﬀerent scales was proposed by S.Fauve in1990.。

The Detection and Characterization of cm Radio Continuum Emission from the Low-mass Protost

a r X i v :0705.1747v 1 [a s t r o -p h ] 12 M a y 2007Draft version February 1,2008Preprint typeset using L A T E X style emulateapj v.03/07/07THE DETECTION AND CHARACTERIZATION OF CM RADIO CONTINUUM EMISSION FROM THELOW-MASS PROTOSTAR L1014-IRSYancy L.Shirley 1,Mark J.Claussen 2,Tyler M.Bourke 3,Chadwick H.Young 4,Geoffrey A.Blake 5Draft version February 1,2008ABSTRACTObservations by the Cores to Disk Legacy Team with the Spitzer Space Telescope have identiﬁed a low luminosity,mid-infrared source within the dense core,Lynds 1014,which was previously thought to harbor no internal source.Followup near-infrared and submillimeter interferometric observations have conﬁrmed the protostellar nature of this source by detecting scattered light from an outﬂow cavity and a weak molecular outﬂow.In this paper,we report the detection of cm continuum emission with the VLA.The emission is characterized by a quiescent,unresolved 90µJy 6cm source within 0.′′2of the Spitzer source.The spectral index of the quiescent component is α=0.37±0.34between 6cm and 3.6cm.A factor of two increase in 6cm emission was detected during one epoch and circular polarization was marginally detected at the 5σlevel with Stokes V/I =48±16%.We have searched for 22GHz H 2O maser emission toward L1014-IRS,but no masers were detected during 7epochs of observations between June 2004and December 2006.L1014-IRS appears to be a low-mass,accreting protostar which exhibits cm emission from a thermal jet or a wind,with a variable non-thermal emission component.The quiescent cm radio emission is noticeably above the correlation of 3.6cm and 6cm luminosity versus bolometric luminosity,indicating more radio emission than expected.In this paper,we characterize the cm continuum emission in terms of observations of other low-mass protostars,including updated correlations of centimeter continuum emission with bolometric luminosity and outﬂow force,and discuss the implications of recent larger distance estimates on the physical attributes of the protostar and dense molecular core.Subject headings:radiation mechanisms:thermal,non-thermal —radio continuum:stars —stars:for-mation1.INTRODUCTIONIt is extremely diﬃcult to identify the incipient stages of low-mass (≈1M sun )star formation be-cause dense molecular cloud cores obscure nascent pro-tostars.Submillimeter dust continuum surveys (e.g.,Ward-Thompson et al.1994,Shirley et al.2000,Visser et al.2002,Kirk et al.2005)have identiﬁed several dense cores with no apparent internal sources,based on the lack of an IRAS point source and the diﬀuse na-ture of submillimeter dust emission.Observations by the Cores to Disk Legacy Team (c2d)with the Spitzer Space Telescope have identiﬁed a few mid-infrared sources that are embedded near the submillimeter continuum peaks of previously classiﬁed starless cores (e.g.Young et al.2004,Bourke et al.2006).These new objects are of low-luminosity (L int ≤0.1L ⊙)and presumably low-mass since they were not previously detected by IRAS.Some of these objects may be in the earliest stages of accre-tion.These newly identiﬁed low-mass,low-luminosity protostars warrant detailed follow-up studies to deter-mine their evolutionary status.The ﬁrst newly identiﬁed object detected in the c2d survey,L1014-IRS (Young,et al.2004),was mod-eled as a very low-luminosity (L int <0.1L ⊙),low-mass1Bart J.Bok Fellow,Steward Observatory,University of Ari-zona,933Cherry Ave.,Tucson,AZ 857212NRAO,P.O.Box 0,1003Lopezville Road,Socorro,NM 878013Harvard-Smithsonian Center for Astrophysics,60Garden St.MS42,Cambridge,MA 021384Nicholls State University,Thibodaux,LA 703105Division of Geological and Planetary Sciences 150-21,Califor-nia Institute of Technology,Pasadena,CA 91125(M <0.1M ⊙)object embedded within the Lynds 1014dark cloud (Lynds 1962)at a distance of approximately 200pc.This object has been classiﬁed as a VeLLO (Very Low-Luminosity Object)by the c2d team:an object with an internal protostellar luminosity ≤0.1L ⊙that is di-rectly associated with a dense molecular core.The recent study of Morita et al.(2006)has suggested a revised dis-tance estimate of 400to 900pc based on the possible age ranges of nearby T-Tauri stars that are spatially within 2◦of the L1014dense core.However,it is not clear that these T-Tauri stars are directly associated with L1014.Determining the evolutionary state of L1014-IRS has been the subject of several follow-up studies.The large scale molecular distribution in the dense core was deter-mined by the single-dish mapping survey of Crapsi et al.(2005).No evidence for a large scale CO outﬂow was detected;however,a molecular outﬂow was detected on small scales with the SMA (Bourke et al.2005).Near-infrared observations detect scattered light,presumably from the outﬂow cone,at 1.6µm and 2.2µm (Huard et al.2006).The SMA-detected CO outﬂow is aligned with the direction of the near-infrared scattered light cavity.High resolution molecular observations with BIMA indi-cate that the protostar is not at the peak of the molec-ular and dust column density in the core,but oﬀset by about 8′′in the plane of the sky (Lai et al.,in prepa-ration).This oﬀset is also seen in (sub)millimeter con-tinuum maps (Young et al.2004)and the near-infrared extinction map (Huard et al.2006).Despite these signiﬁcant observational eﬀorts,a single,consistent picture of the evolutionary state of L1014-IRS has not emerged.In order to better characterize the2physical nature of L1014-IRS,we have conducted cen-timeter radio continuum observations using ﬁve array conﬁgurations of the Very Large Array 6(VLA).Cen-timeter radio continuum emission is well correlated with the luminosity of protostellar sources (Anglada 1995)and is thought to arise from shock ionization from protostel-lar winds (Ghavamian &Hartigan 1998),from interac-tion of the protostellar jets with dense gas in the interface of the outﬂow cavity (Curiel et al.1987,1989,Shang et al.2004),or from accretion shock-driven photoionization (Neufeld &Hollenbach 1996).In this paper we report the detection and characteriza-tion of the cm radio continuum emission toward L1014-IRS (§3.1).We compare the detected cm emission with observations of other low-mass protostars (§4.1).We dis-cuss the non-detections of 22GHz H 2O masers and com-pare our upper limits to the recent maser monitoring surveys of low-mass protostars (§4.2).We also compare the derived source properties from the diverse studies of the protostar and dense core in terms of the range of distance estimates to L1014(§4.3).2.VLA OBSERVATIONSL1014-IRS was observed during 10epochs in 5ar-ray conﬁgurations (D,A,BnA,B,and C)with the Very Large Array (Table 1).All observations were centered on the published Spitzer mid-infrared source (α=21h 24m 07s .51,δ=+49◦59′09.′′0,J2000.0).Con-tinuum observations were made at 3.6cm,and 6.0cm,with two polarization pairs at adjacent frequencies,pro-viding a total equivalent bandwidth of 172MHz.We also attempted to detect H 2O masers by observing the J K a K c =616→523transition at 22.23508GHz with,typically,24.4kHz spectral resolution (0.3km/s)span-ning ±20km/s velocity coverage.For the 3.6and 6.0cm data,the data were reduced independently using the standard routines in AIPS++and AIPS .Complex gain calibration was performed by switching to the nearby quasar 2137+510,2.4◦from L1014-IRS,on time-scales of 15to 30minutes (Hamaker,Bregman,&Sault 1996a,b).The absolute ﬂux density and bandpass calibration were determined from observa-tions of the quasars 3C48and 3C283.The Stokes I and V images were deconvolved using the Cotton-Schwab algorithm (e.g.,Schwab 1984)and Clark-H¨o gbom algorithm (H¨o gbom 1974,Clark 1980)with a few thousand iterations and interactive CLEAN regions.Imaging the L1014-IRS ﬁeld was diﬃcult due to the presence of several bright sources within the VLA pri-mary beam (Figure 1a).Special care had to be taken in the CLEANing process (e.g.,Cornwell,Braun,&Briggs 1999)and multiple reductions with variations in the CLEAN parameters were performed.We have checked the consistency of our images by also reducing the data with the standard AIPS routines,and the ﬂuxes agree within the statistical errorbars.Generally,the images are made with natural weighting of the visibilities (Briggs 1995);however,uniform weighting was used to obtain better angular resolution for the full track (9hour)ob-servations on the days of July 1,2004and August 21,6The VLA is operated by NRAO.The National Radio Astron-omy Observatory is a facility of the National Science Foundation operated under a cooperative agreement by Associated Universi-ties,Inc.2004.3.RESULTS3.1.Radio Continuum DetectionsWe detected cm radio continuum emission from a source within 0.′′2of the Spitzer mid-IR source using the VLA at 3.6cm and 6cm (Figure 1).The initial detec-tions were made during 9hour tracks at 3.6cm and 6cm with the VLA in the D conﬁguration.Subsequent observations detected the source at 6cm in the other three VLA conﬁgurations,and again at 3.6cm in D con-ﬁguration.All of the 6cm observations,except for the initial 6cm detection on August 21,2004,indicate a constant ﬂux density source with an average 6cm ﬂux of 88±11µJy (8σ).The source is unresolved in all array conﬁgurations.The two detections at 3.6cm are also in agreement with each other despite being separated by 17months.The average 3.6cm ﬂux is 111±8µJy (14σ).The spectral index between two wavelengths (λ2>λ1)is deﬁned asα=ln(S λ1/S λ2)3to detect that variation due to the higher noise level in progressively shorter time blocks.A Stokes V source (circularly polarized)was marginally detected at the 5σlevel at 6cm on August 21,2004with a ﬂux of 84±17µJy at the position of the 6cm Stokes I source (Figure 1d).The fraction of circular polarization,f c =Stokes V/I =48±16%,is quite high if the detection is signiﬁcant.Since the Stokes V result was obtained during a full single track of VLA observa-tions,it will be diﬃcult to conﬁrm until L1014-IRS is observed with wider bandwidth (e.g.,with the eVLA).If the circular polarization signal is real,then this observa-tion indicates that the radio emission observed on August 21,2004must originate from a non-thermal mechanism (§4.1.2).3.2.Water Maser SearchWe searched for H 2O masers during seven epochs span-ning 22months by observing the J K a K c =616→523transition at 22.23508GHz.No H 2O masers were de-tected at any epoch.The combined 1σrms of the non-detection is 3.1mJy/beam with a channel spacing of 24.4kHz and a total bandwidth of 3.125MHz (∼40km/s).The individual observations are summarized in Table 1.4.DISCUSSION4.1.Centimeter Radio Continuum Emission4.1.1.Steady ComponentCentimeter continuum emission has been detected to-ward many but not all high-mass and low-mass proto-stars.The emission is most commonly thought to origi-nate from bremsstrahlung (free-free)emission from ion-ized gas,although some protostellar objects also display non-thermal emission.For high-mass protostars,the ion-ization mechanism is photoionization usually in the form of an embedded HII region (Churchwell 1990).For pro-tostars that are later in spectral type than B,the ioniz-ing radiation from the star is not enough to signiﬁcantly photoionize the surrounding envelope and an alternative mechanism is needed to explain the observed emission (Rodr´ıguez et al.1989,Anglada 1995).Since nearly all low-mass,embedded protostars are known to have molecular outﬂows (e.g.Wu et al.2004),the ioniza-tion is postulated to arise from shocks generated from a jet (e.g.,Cohen,Bieging,&Schwartz 1982,Bieging &Cohen 1989,Curiel et al.1987,1989,Rodr´ıguez &Reipurth 1996,Shang et al.2004).Direct evidence for this hypothesis comes from observations using interfer-ometers at high angular resolution.Elongated centime-ter continuum emission regions are observed with the same orientation as the large-scale molecular outﬂow to-ward a few protostars (e.g.,Anglada 1995;Bontemps,Ward-Thompson,&Andr´e 1996).In addition,the ob-served outﬂow force (M ⊙km/s/yr)theoretically provides enough energy in the shock to explain the observed cen-timeter ﬂuxes toward most low-mass protostars (Cabrit &Bertout 1992,Skinner et al.1993,Anglada 1995).Finally,the radio spectral index of many protostellar sources is consistent with optically thin (α≈−0.1)to partially optically thick free-free emission between 3.6cm and 6.0cm (2.0>α>−0.1,e.g.,Anglada et al.1998,Beltr´a n et al.2001).The centimeter continuum luminosity (e.g.,L 3.6=S 3.6D 2mJy kpc 2)of low-mass and intermediate-mass protostellar sources was ﬁrst cataloged from the litera-ture in the review by Anglada (1995).Anglada plotted the 3.6cm luminosity against the bolometric luminosity of protostars with L bol <103L ⊙and found a well corre-lated relationship (r =0.79),L 3.6=10−2.1(L bol /1L ⊙)0.7mJy kpc 2.This relationship has formed the basis for predictions of the amount of centimeter emission that is expected in searches for new low-mass protostars (e.g.,Harvey et al.2002,Stamatellos et al.2007).The 3.6cm luminosity correlation is directly related to the well established correlation of outﬂow force vs.bolometric lu-minosity (Bontemps et al.1996,Wu et al.2004);higher luminosity sources drive more powerful outﬂows that re-sult in a larger degree of shock ionization and therefore a larger 3.6cm luminosity (Anglada 1995).Since 1995,many more centimeter observations have been made and the spectral coverage of the photometry of protostars has increased.We have used the detailed summary tables of Furuya et al.(2003;Table 4)and Anglada (1995)supplemented by the surveys of Eiroa et al.(2005)and Anglada et al.(1998)to catalog the 3.6cm,6.0cm,and bolometric luminosities of detected protostellar sources.We updated the bolometric lumi-nosity of sources observed in the submillimeter surveys of Shirley et al.(2000),Mueller et al.(2003),and Young et al (2003).The resulting sample of 58sources at 3.6cm and 40sources at 6.0cm are plotted in Figure 2.We ﬁnd updated correlations oflog(L 3.6/1mJy kpc 2)=−(2.24±0.03)+(0.71±0.01)log(L bol /1L ⊙)(2)log(L 6.0/1mJy kpc 2)=−(2.51±0.03)+(0.87±0.02)log(L bol /1L ⊙),(3)with correlation coeﬃcients of r =0.66and r =0.74respectively.This sample is not complete as there are many more protostellar centimeter detections for which no L bol has been published.Nevertheless,we have up-dated the correlation of Anglada (1995)with twice as many points at 3.6cm and plotted the correlation at 6.0cm for the ﬁrst time.For comparison,we have plotted the 3.6cm and 6.0cm luminosities of L1014-IRS in Figure 2at the distances of 200,400,and 900pc.L1014-IRS is above the correlation at all distances indicating that we have detected more centimeter continuum ﬂux than expected.The spectral index of sources between 3.6cm and 6.0cm is used to argue for the interpretation that the emission mechanism is consistent with partially optically thick free-free emission.Optically thin free-free emission is expected to have a spectral index α=−0.1at cen-timeter wavelengths.In the optically thick limit,αap-proaches 2.0with intermediate values indicative of par-tially optically thick plasmas.We have also plotted the spectral index of sources from the literature that have been detected at both wavelengths and have a published L bol determination in Figure 2.No correlation of αis observed with bolometric luminosity,probably indicat-ing that the optical depth associated with the jet’s shock ionization is not dependent on the total protostellar lu-minosity or the strength of the molecular outﬂow.The median spectral index is α=0.5,with most protostellar sources having ﬂat or positive spectral indices.This me-dian value is close to the result expected for an ionized wind or jet with a 1/r 2density gradient (e.g.,Panagia &Felli 1975,Wright &Barlow 1975,Reynolds 1986).Unfortunately,most of the sources in Figure 2were not4observed at both wavelengths on the same day and vari-ability may result in signiﬁcant scatter in the plot.The spectral index of the quiescent emission of L1014-IRS(0.37±0.34)is consistent with ionized free-free emis-sion with a density gradient.The spectral index agrees well with the median of the ensemble of protostellar sources measured.We have also updated the correlation between outﬂow force,F out(M⊙km/s/yr),and centrimetric luminosity of Anglada(1995)using the molecular outﬂow compilations of Bontempts et al.(1996),Furuya et al.(2003),and Wu et al.(2004).The updated correlation of44sources is weak(r=0.55),log(F out/1M⊙km/s/yr)=−(3.15±0.07)+(0.67±0.03)log(L3.6/1mJy kpc2).(4) This correlation is interpreted as evidence that jets from the molecular outﬂow provide enough shock ionization to account to the observed centimeter continuum emission (e.g.,Anglada1995).Assuming maximum ionization ef-ﬁciency,the minimum outﬂow force needed to create the observed level of3.6cmﬂux was estimated by Curiel et al.(1987,1989)to be F out=10−3.5(L3.6/1mJy kpc2). This level is shown as a dashed line in Figure2d.The observed outﬂow force toward L1014-IRS ranges from 0.04−2.9×10−6M⊙km/s/yr for distances of200to 900pc(see Bourke et al.2005).At a distance of200pc, the upper limit on the outﬂow force is a factor of2lower than the Curiel theoretical minimum outﬂow force.The upper limit in the observed outﬂow force includes esti-mates of the missingﬂux due to interferometric spatial ﬁltering as well as the average opacity corrections for low-mass protostellar outﬂows(see Bourke et al.2005). Given the range of uncertainty in these estimates,the observed outﬂow force is below,but not necessarily in-consistent with the theoretical minimum outﬂow force needed to produce the observed3.6cm luminosity.The disagreement between the observed outﬂow force is more pronounced at larger distances,increasing to an order of magnitude below the theoretical curve for a distance of 900pc.The small observed molecular outﬂow force and the large observed centimeter continuum luminosities may indicate that another ionization mechanism is operating in L1014-IRS.There are a few other possibilities that have been discussed in the literature.We shall analyze the viability of two popular possibilities.Radiative transfer modeling of emission at24and70µm indicate aﬂux excess from a disk around L1014-IRS (Young et al.2004).Neufeld&Hollenbach(1996)pos-tulated that the supersonic infall of material onto a pro-tostellar disk will create an accretion shock with enough ionization to generate∼1mJy of continuum emission at centimeter wavelengths at distances of≈200pc.How-ever,this mechanism does not appear to be able to pro-vide enough ionization to explain the emission observed toward L1014-IRS.In order to produce90µJy emission at6cm at a distance of200pc,the protostellar mass has to be>2M⊙and the accretion rate onto the disk must be>10−4M⊙/yr(see Figure2of Neufeld&Hollenbach 1996).Estimates of the protostellar mass are very un-certain and highly distance dependent,however,2M⊙is likely larger than the L1014-IRS protostar and disk mass, even for the far distance estimate of900pc(see Young et al.2004).Furthermore,this accretion rate is an order of magnitude larger than the range of inferred accretion rates from the observed outﬂow momentumﬂux and the modeled internal luminosity of the source(≤3×10−5 M⊙/yr;Bourke et al.2006,Young et al.2004).Ion-ization from an accretion shock does not appear to be a likely explanation.A more plausible possibility is that there is a spheri-cal wind component.The expected continuum emission from self-shocked spherical winds have been modeled by numerous authors(e.g.,Panagia&Felli1975,Wright& Barlow1975,Reynolds1986,Gonz´a lez&Cant´o2002). The recent study of Gonz´a lez&Cant´o model a time variable wind that generates internal shocks(Raga et al. 1990)which produce ionization and centimeter contin-uum emission(see Ghavamian&Hartigan1998).Their models produce centimeter continuum emission of sev-eral hundreds ofµ-Janskys and spectral indices that are positive for mass loss rates of10−6M⊙/yr at a distance of150pc.Accounting for the larger distance estimates of200to900pc and potentially lower mass loss rates for L1014-IRS,then this type of emission may still account for theﬂux observed at3.6cm and6cm(∼100µJy). However,the spherical wind models is usually applied to evolved protostellar sources that are Class II(classi-cal T-Tauri stars)or later(e.g.,Evans et al.1987).If L1014-IRS is an older,more evolved protostar,then this may not be a problem(§4.3).4.1.2.Variable ComponentWhile the quiescent component of L1014-IRS is constant over5epochs with a positive spectral in-dex,the emission properties of L1014-IRS were signif-icantly diﬀerent during the single epoch of August21, 2004.The6cmﬂux was larger by a factor of two, S6.0(21AUG2004)=173±16µJy.Unfortunately,the spectral index of elevated emission was not determined since L1014-IRS was observed at a single wavelength. Circular polarization was detected at the5σlevel indi-cating non-thermal emission.Thus,L1014-IRS has vari-able centimeter emission,although the timescale of the variability is not constrained since it was seen to vary during only a single epoch.In general variability of centimeter continuum sources has not been properly addressed since observations of sources are limited to a few epochs.There has not been a systematic,monthly monitoring campaign of deeply embedded sources to characterize their centimeter vari-ability;however,there is observational evidence for vari-ability among deeply embedded protostellar sources.For instance,the Class0source,B335,is known to vary be-tween an upper limit of<80µJy(1994December)and 390µJy(2001January)at3.6cm(Avila et al.2001, Reipurth et al.2002).Another example is the variability and purported evidence for jet precession of the centime-ter continuum sources toward IRAS16293(Chandler et al.2005).Variability contributes scatter(de-correlation) of the luminosity correlations shown in Figure2.In ad-ditional to the known variable thermal sources,several non-thermal protostellar sources are known to be highly variable(e.g.T Tauri stellarﬂares,see White1996); but,most of those objects are more evolved than deeply embedded protostars.The observed increase in emission on August21,2004 and5σStokes V detection is indicative of variable non-5thermal emission toward L1014-IRS.While there have been a few high-mass protostars with observed nega-tive spectral indices(e.g.,Reid et al.1995;Garay et al.1996),most embedded(≤Class I)low-mass proto-stars with cm radio emission have positive spectral in-dices(see Figure2).There are only a few embedded low-mass protostars toward which negative spectral in-dex,non-thermal emission is detected(e.g.,Shepherd &Kurtz1999,Girart et al.2002).One case,R CrA IRS5,was detected with signiﬁcant circular polarization (Feigelson et al.1998).The authors postulate that the emission is due to gyrosynchrotron emission and may originate from magnetic reconnection events associated withﬂares(Feigelson et al.1998).The physical mecha-nism for generating the radioﬂare is still not well under-stood(e.g.,Basri2004)and it is questionable whether it applies to the embedded phase of low-mass protostars (see below).A second case,IRAS19243+2350,is a steep spectrum non-thermal source(α=−0.82±0.04)that is elongated in the direction of its CO outﬂow(Girart et al.2002).Girart et al.postulate that the emission may originate from a bi-conical synchrotron source tracing the protostellar jet,similar to observations of the high-mass source W3(OH)(Reid et al.1995,Wilner,Reid,& Menten1999).Non-thermal emission may be present in low-mass protostellar jets,but the level of emission may be dominated by the thermal,shock-ionized component of the jet.In the case of L1014-IRS,this non-thermal jet component would have to be variable.We shall dis-cuss several possibilities for the origin of the observed non-thermal emission toward L1014-IRS.In order to better understand the non-thermal emis-sion mechanism,we estimate the brightness tempera-ture of the emission to be T b=Sνλ2d2/2kR2emit= 0.14−2.8×106K for distances of200to900pc and an emitting region that is R emit=1AU in size.The brightness temperature is very sensitive to the assumed size of the emitting region.A R emit of1AU is appro-priate for a smallﬂare;but,smaller when compared to the solar coronal emitting region which is typically less than≈5AU(e.g.Leto et al.2000).Since the emission observed toward L1014-IRS was unresolved,even in the A-array conﬁguration,then we can only limit the size of the emission region to<90(D/200pc)AU.For instance, if we assumed that the emitting region was45AU(half of our A-array resolution),then the brightness temper-ature drops to<100K.This is too low even for the steady,thermal free-free component(T∼104K),unless the emission was very optically thick.This cannot be the case sinceτ>>1would implyαapproaching2.0 which is not observed.While the size of the emitting re-gion is severely unconstrained,the detection of circular polarization indicates non-thermal emission probably on small(<few AU)size scales,most likely due to gyrosyn-chrotron emission(e.g.,Ramaty1969;Dulk&Marsh 1982).Radioﬂares are observed toward very low-mass ob-jects including brown dwarfs(Berger et al.2002,Os-ten et al.2006),late M dwarfs(Berger2006),and T-Tauri stars(Bieging&Cohen1989;White,Pallavicini, &Kundu1992).The typical level of quiescent emis-sion toward low-mass stars and brown dwarfs is100µJy and theﬂares are1mJy(for nearby distances of≈30pc)with signiﬁcant circular polarization(f c≈50%) detected during theﬂaring events.The spectral lumi-nosity at6cm of L1014-IRS during the event is Lν= 4πD2Sν=4.7×1015(D/200pc)2erg s−1Hz−1.This is about2400times larger than the most luminous ob-served solarﬂares(Bastian2004)and about200times larger than theﬂares observed by Berger(2006)toward late M dwarfs.If the radio emission is due to aﬂare,it must be a powerfulﬂare since L1014-IRS is at least20 times farther away than the average distance of sources detected by Berger( d =10.6±5.1pc).However,it is not larger than the typical non-thermalﬂaring emission observed toward young T Tauri stars of Lν=1015−1018 erg s−1Hz−1(G¨u del2002).The ratio of spectralﬂare luminosity to bolometric luminosity,Lν/L bol=4×10−18 Hz−1,is also similar to the ratio observed toward classi-cal T-Tauri stars(see G¨u del2002).The timescale over which radioﬂares toward low-mass stars are observed tends to occur over minutes to hours. For instance,the low-mass brown dwarf,LP944-2,dis-covered by the2001NRAO summer students(Berger et al.2002),displaysﬂaring activity with an average timescale of10to15minutes.This is very diﬀerent from the activity observed toward L1014-IRS on August21, 2004.We detected no evidence for short-term variabil-ity within our detected emission.The source appears to have a nearly constantﬂux that is twice as high as the steady component for at least an8hour period.This elevated emission then appears to be longer in duration than that observed duringﬂaring events toward low-mass (proto)stars(G¨u del2002).An alternative possibility is that the elevated emission is not due to aﬂare,but due to rotational modulation of a non-thermal component associated with the magnetic connection between disk and accretion onto the star(i.e., Bieging&Cohen1989).Such a mechanism has been postulated for the T-Tauri star,V410Tauri,with a rota-tional period of1.9days.The observed emission toward V410is1mJy with a negative spectral index.If the accretion spot is blocked from view for a fraction of the stellar rotation period,then it is possibly that we could have observed the source with the accretion spot is in view on August21,2004and with the accretion spot blocked from view during the other epochs.The rota-tional period of L1014-IRS must be longer than8hours since elevated emission was observed during the entire8 hour track.A negative spectral index was observed to-ward V410Tauri,while a negative spectral has not been observed toward L1014-IRS.This hypothesis is highly speculative and would require a regular monitoring cam-paign to test.Unfortunately,it is currently not possible to strongly constrain the origin of the non-thermal component to-ward L1014-IRS.The expanded bandwidth of the eVLA is needed to permit a systematic monitoring campaign with high enough signal-to-noise in only a few hour ob-servations to routinely check for a Stokes V detection and to determine an instantaneous spectral index.4.2.Water Maser Non-detectionsA compact,weak molecular outﬂow has been detected toward L1014-IRS(Bourke et al.2005);therefore it may be possible to detect water masers if the jet is impinging on dense knots of material near the protostar.Previous。

国土三调数据与地理国情数据融合可行性分析

第35卷第6期2020年12月遥感信息RemoteSensingInformationVol.35,No.6Dec，2020国土三调数据与地理国情数据融合可行性分析龚国辉12,董春12,亢晓琛2(1.辽宁工程技术大学，辽宁阜新123000；.中国测绘科学研究院，北京100036)摘要：我国将逐渐构建自然资源统一调查监测体系，以此辅助空间规划、用途管制等重要工作，这对全面、精细的土地覆被数据提出了迫切需求。

文章综合考虑了地理国情监测数据的自然属性和第三次全国国土调查数据的管理属性，以广西壮族自治区港北区为例，首先经语义分析明确2类数据指标的潜在匹配关系，再利用空间分析技术进行实验验证，将相匹配类型的国土三调数据的属性补充到地理国情监测数据的一级类房屋建筑(区)中，获得了兼具精准自然属性和丰富管理属性的融合数据源，初步证实了2类数据补充融合的可行性。

关键词：地理国情监测；第三次全国国土调查；对比分析；管理属性；属性补充doi：10.3969/j.issn.1000-3177.2020.06.011中图分类号:P205文献标志码:A文章编号：1000-3177(2020)06-0067-09Fusion Feasibility Analysis of Geographical National SituationData and Third National Land Survey DataGONG Guohui12,DONG Chun1，,KANG Xiaochen2(1.Liaoning Technical University,Fuxin,Liaoning123000,China；2.Chinese Academy of Surveying and Mapping^Beijing100036,China)Abstract：Theunifiednaturalresourcessurveyand monitoringsystem wi l begradua l yestablishedinChinatoassistin importantworksuchasspatialplanningandusagecontrol，whichhasputforwardanurgentneedforcomprehensiveand detailedlandcoverdata Inthispaper，thenaturala t ributesofgeographicalnationalsituationdataandthe management a t ributesofthethird nationallandsurvey data werecomprehensivelyconsidered Gangbeidistrictof GuangxiZhuang autonomousregion wastaken as an example，and the potential matching relationship between the two types of data indicatorswasclarifiedthroughsemanticanalysis Thenthea t ributesofthematchingtypeofthethirdnationallandsurvey datawereaddedtothehousing buildings(areas)ofthefirstclassland-usetypesofthegeographicalnationalsituation monitoringdatathrough spatialanalysistechnology Such fusion data source with precise naturala t ributes and rich managementa t ributeswasobtained，whichpreliminarilyprovedthefeasibilityofsupplementaryfusionofthetwotypesof dataKeywords：geographical nationalsituation monitoring；third nationalland survey；comparative analysis；management a t ribute；a t ributesupplement收稿日期20191218修订日期：2020-09-29基金项目：国家自然科学基金项目（71773117.41701461）；国家社会科学基金重大项目（18ZDA066）；自然资源时空大数据变化统计关键技术研究项目（AR1910）。

网格降水预报时间降尺度方法改进

刘凑华,林建,曹勇,等.2021.网格降水预报时间降尺度方法改进[J].暴雨灾害,40(6):617-625LIU Couhua,LIN Jian,Cao Yong,et al.2021.Improvement of time downscaling method of grid precipitation forecast [J].Torrential Rain and Disasters,40(6):617-625网格降水预报时间降尺度方法改进刘凑华，林建，曹勇，代刊，郭云谦，唐健(国家气象中心，北京100081)摘要：网格降水预报时间降尺度的目标是将业务上准确率较高的24h 精细化网格降水主客观订正预报结果降尺度到更细的时间分辨率上，以保证不同时间间隔精细化降水预报的准确率和总量的一致性。

针对目前业务中降尺度方法以数值模式预报的单点降水量时间序列为比重实现对逐个网格点的预报拆分，拆分后雨带范围偏大、强度偏小和移动不合理等问题，增加位置订正、动态重构和频率匹配等算法来改进时间降尺度的效果。

基于ECMWF 模式预报时空演变，以国家气象中心2020年7月18日20时24h 网格降水预报拆分成逐1h 预报为实例，阐述了不同算法步骤的作用，并选取2020年1月1日—12月31日逐日08时起报的逐24h 网格降水预报进行时间降尺度批量对比试验。

个例分析和批量试验结果表明，改进后的时间降尺度方法可提升逐小时网格降水预报的合理性和准确率。

位置订正算法用于订正数值模式预报同网格预报之间的位置偏差，动态重构算法用于减少拆分后雨带中心移速和强度的不合理波动，而频率匹配则用于订正拆分后雨带范围偏大和强度偏弱的问题。

改进后的逐小时降水预报各等级ETS 和BIAS 评分均有所改善，尤其是对20mm 以上的短时强降水改进效果显著。

关键词：网格降水预报；时间降尺度；位置订正；动态重构；频率匹配中图法分类号：P456文献标志码：ADOI ：10.3969/j.issn.1004-9045.2021.06.006收稿日期：2021-07-21；定稿日期：2021-09-21资助项目：国家重点研发计划(2018YFC1507205，2017YFC1502004，2018YFC1508102)；国家科技支撑计划(2015BAC03B01)第一作者：刘凑华，主要从事预报检验方法和精细化网格预报技术研究。

小波多尺度分析尼泊尔M_(W)7.8地震前卫星重力变化

能够用重力手段监测地震是由于在大地震孕育和发生过程中，震源区附近会产生物质迁移和质量再分布现象,重力场也随之变化叫2002年3 月发射成功的GRACE重力卫星,具有高精度、高时间空间分辨率，能够监测出重力变化，其时变重力场能够提高人类认识地球内部物质迁移。重力场的变化量揭示了地球系统内部的物质运动、分布及变化，它主要是由地球流体圈层的质量迁移引起的，也可能与冰川均衡调整和地震现象造成的质量运动有关。
3
GRACE重力场小波多
尺度分解及结果分析
GRACE卫、、
变化相对较大且变化较快。、
空间尺度上具有差异，由浅入深可能表现为不同。
一般情况下，小波分解最大尺度选取的越大, 那么被滤除的细节部分就越多，分离出的成分越
；
就越多，重构后的信号就会丢失很多有用信号, 。一
观测信号比有用信号的量级要大，这时候较小的分解阶数就能很好的解决问题，相反的情况就需要分解的阶数较高。对于重力数据理论模型，不同尺度分解出来的重力数据“对应不同深度、不同密度的不均匀分布
Changes before Nepal MW7.8 Earthquake[J]. South China journal of seismology , 2021 , 41(1) ：73-77]
小波多尺度分析尼泊尔M 7.8地震前卫星重力变化
刘潇
(中畴四勘察设计院集团有限公司，武汉430063)
摘要：利用GRACE重力卫星RL05月重力场数据,获取尼泊尔大地震前后震源区周缘2010—2015年每月重力变化，以及震中点位重力时间序列。基于小波多尺度分析方法对卫星重力场进行分解,获得重力场细节和近似
孙文科倒尝试将GRACE运用在日本大地震的研究中，取得了不错的结果；邹正波勺等研究 GRACE重力变化的计算和分析，对球谐系数选取以及高斯平滑半径进行了讨论；王武星旳等利用 GRACE研究了汶川地震发震前的重力异常；已有研究成果表面GRACE卫星观测到的重力变化包含了浅部到深部的各种质量改变成分，可以通过位场分离的方法去识别与提取。小波多尺度分析方法将重力异常分解到不同的尺度空间中，尺度大小决定了重力异常所反映的地质体埋深“。

Understanding the value of high resolution regional climate modeling

UNDERST ANDING THE VALUE OF HIGH RESOLUTION REGIONAL CLIMATE MODELING 5.1James M.Done L.Ruby Leung,Christopher A.Davis and Bill Kuo1.National Center for Atmospheric Research,Boulder,CO2.Paciﬁc Northwest National Laboratory,Richland,WA1INTRODUCTIONA regional climate model(RCM)provides high resolutionclimate scenarios important for impact assessment andresource management.High resolution allows for a moreprecise description of regional topographic forcings dueto orography,land-sea contrasts and vegetation charac-teristics.Consequently,processes strongly forced by to-pography,such as orographic precipitation and monsooncirculations,improve at increased resolution(Giorgi andMarinucci,1996).Since better resolved small-scale pro-cesses may have improved large-scale impacts,RCMscan be used to study the upscale impact of regional forc-ings(e.g.the orographic shadowing effect)on the large-scale climate,in addition to climate downscaling.Withincreasing computational power that enables global cli-mate models to be applied at higher spatial resolution,itis important to assess the value of higher resolution(1-10km grid-spacing)regional climate modeling.Higherresolution does not necessarily imply more accurate cli-mate simulation(e.g.Boyle(1993),Sperber et al.(1994)and Senior(1995)).The sensitivity of physics parameter-izations to model grid-spacing may overwhelm any ben-eﬁts of higher resolution simulation(Duffy et al.,2003).There are also fundamental differences in how the solu-tions of short-term forecast models and RCMs depend onresolution.The Weather Research and Forecasting(WRF)model(Michalakes et al.,2001)is designed speciﬁ-cally for high-resolution limited-area applications.Themodel uses high order numerical accuracy to solve thefully compressible non-hydrostatic equations,and there-fore provides a suitable tool to understand the value ofhigh resolution(1-10km grid-spacing)regional climatemodeling.This study builds on previous regional climateresearch using theﬁfth-generation Pennsylvania StateUniversity-NCAR mesoscale model(MM5)(Leung et al.,2003,Leung and Qian,2003),and represents theﬁrststep in assessing the value of high resolution(1-10kmgrid spacing)regional climate modeling using version2of the WRF model.Model evaluation concentrates on the region of thewestern United States where topographic forcings playan important role in deﬁning the regional climate,andwhere it is thought high resolution regional climate mod-through31st January1991.For the parent domain (WRF30),initial,lateral and lower boundary conditions are derived from the NCEP-NCAR reanalyses at2.5hor-izontal grid spacing interpolated onto the WRF model grid.Solutions on the parent domain provide lateral boundary conditions for the nested domain.Relaxation at all boundaries has a combined linear/exponential func-tional form over10grid points,and lateral boundary con-ditions are updated every6hours.To aid long-term in-tegrations the lower boundary conditions of sea surface temperature,vegetation fraction and albedo are updated every6hours.The same physics parameterizations are used for both domains:boundary and surface-layer processes are represented by the Monin-Obukhov(Janjic Eta)sur-face scheme,the Noah land surface model and the Mellor-Y amada-Janjic(Eta)TKE boundary layer scheme; convection is parameterized by the Eta Kain-Fritsch scheme;explicit precipitation processes are parameter-ized by the Ferrier scheme;radiation is represented by the rapid radiative transfer model and the Dudhia short-wave scheme.Two datasets are used to analyzse the regional cli-mate of the western United States.Theﬁrst consists of daily rainfall amount and daily maximum and mini-mum2m temperature gridded at1/24(approximately 4.4km),developed by C.Daly and W.Gibson of the Spatial Climate Analysis Service at Oregon State Uni-versity and G.Taylor of the Oregon Climate Service at Oregon State University.This dataset is available at.A statis-tical topographic-precipitation relationship developed by Daly et al.(1994)is used to spatially interpolate the sta-tion observations to capture the mesoscale details of pre-cipitation distribution in regions of complex terrain.The second dataset consists of daily snow wa-ter equivalent,2m temperature and rainfall totals at the snowpack telemetry(snotel)stations in the western United States.There are a total of about650snotel sta-tions typically located in remote mountain sites;with83 snotel stations located within the WRF6domain as shown in Fig.2.3RESULTSPrecipitationThe WRF30average daily precipitation amount agrees well with observations in terms of spatial distribution,as shown in Fig.3.In agreement with40km MM5simula-tions by Leung and Qian(2003),WRF30shows a lack of precipitation along the coastal hills,good simulation over the Cascade Range and a slight overprediction over the basins beyond.The WRF30barrier height for the coastal hills is about half that at1/24grid-spacing(not shown) resulting in reduced topographic forcing and precipitation amounts are underpredicted,whereas for the larger scale Cascade Range the barrier height is more accurate and precipitation amounts are well simulated.As expected the WRF6precipitationﬁeld,shown in Fig.3,showsﬁner-scale structure associated withﬁner-scale topographic forcing.The WRF6precipitation also shows increased range in magnitude east-west across terrain maxima.A comparison with the1/24observa-tions interpolated onto the WRF6grid indicates theﬁne-scale structure is realistic,but shows that WRF6overesti-mates precipitation over the western slopes of the Cas-cade Range,yet underestimates precipitation over the coastal hills and over the low-lying areas between the coastal hills and the Cascades.The rain shadow effect in the lee of the Cascade Range is weaker in WRF30than observed,but is much improved in WRF6. TemperatureThe WRF30cold-season average2m temperature com-pares well with observations in terms of spatial distribu-tion and magnitude,as shown in Fig. 4.The range in magnitude is slightly less for WRF30than observed.The WRF6cold-season average2m temperature,shown in Fig.4,showsﬁner-scale structure associated withﬁner-scale topography,and also shows increased range in magnitude.A comparison with the1/24observations interpolated onto the WRF6grid shows thisﬁne-scale structure to be realistic.In contrast to WRF30,the WRF6 2m temperature shows a warm bias of up to1.5C over the basins in the lee of the Cascade Range.Both WRF30 and WRF6show cool biases over the northern Cascades and warm biases over the southern Cascades;possibly related to snow cover(see next section).SnowpackDecreased grid-spacing has a dramatic impact on simu-lated snowpack(snow water equivalent).The maximum cold-season average snowpack in WRF30is0.19m com-pared to1.73m in WRF6.For both WRF30and WRF6, snowpack accumulates where2m temperatures are low and where precipitation is signiﬁcant(not shown).Fig. 5shows WRF30snowpack conﬁned to the northern half of the Cascade Range,whereas snowpack in WRF6ex-tends across parts of the southern Cascasde Range and eastern Oregon State.Snowpack in WRF6has much higher amplitude of variability associated with the more precise description of terrain andﬁner-scale details of temperature and precipitation.A comparison of WRF6,WRF30and observed snowpack at the locations of83snotel stations within the WRF6domain,shown in Fig.6,shows snowpack sim-ulation is very poor,and indicates that increased model resolution brings only a slight improvement.The snotel station average snowpack for WRF30,WRF6and obser-vations is11mm,15mm and141mm respectively.Despite the more accurate station elevations in WRF6(see Fig.6),the station average2m tempera-ture biases for WRF30and WRF6are similar at+1C and +0.8C respectively,and the correlations between obser-vations and model simulations are generally poor.The model also underpredicts precipitation amounts at theFigure2:Terrain height(m)for WRF6and WRF30for the region of the WRF6domain.Crosses mark the locations of83snotel stations.snotel sites.The station average daily mean precipitation totals for WRF30,WRF6and observations are4.7mm, 3.3mm and7.3mm respectively.Snotel stations are generally located below maxima in terrain features and close to the WRF6snow-line(see Fig.5).In addition,the majority of stations are located on the eastern slopes of terrain maxima(see Fig.2);the opposite side to WRF6precipitation maxima(see Fig.3). The positive temperature bias and negative precipitation bias will contribute to poor snowpack simulation;however, snowpack may be more sensitive to details of the Noah land surface model.4CONCLUSIONSA high resolution regional climate simulation showed re-alistic small-scale spatial variability of precipitation and 2m temperature.Substantial increases in cold-season average snowpack occurred locally on using smaller grid-spacing,yet biases in temperature and precipitation and the details of the land surface model may have resulted in the poor comparison with observations at selected ob-serving stations.Locally,the long-term simulation of precipitation and snowpack were highly sensitive to the regional climate model grid-spacing.Analysis is in progress to determine the sensitivity of precipitation and snowpack over larger areas to model grid-spacing which has implications for regional hydrological modeling.5FUTURE WORKA more detailed evaluation of cold-season simulations is needed to further understand the value of high resolution regional climate modeling.In particular,the topography-precipitation and temperature-precipitation-snowpack re-lationships will be examined in more detail.Averages of seasonal simulations over a few years will determine the robustness of the preliminary results.Attention will then focus on understanding the impact of high resolution regional climate modeling on the warm-season North American Monsoon climate.The mon-soon climate will be evaluated based on the observational dataset described in this study and North American Mon-soon Experiment(NAME)radar composites.Simulations at4km grid-spacing,without a parameterization of con-vection,will be compared to a simulations using30km grid-spacing.Finally,rather than using RCMs for downscaling cli-mate information,their real value may lies in the ability to study the interaction between regional topographic forc-ings and the large-scale climate signal.This study has indicated there may be improvements to the large-scale climate signal using high resolution RCMs,evidenced by the improved rain shadow effect in the lee of the Cascade Range.More work is needed to establish the validity of the WRF model for high resolution long-term simulation for both upscaling and downscaling research.ACKNOWLEDGEMENTS.We thank Wei Wang and Jimy Dudhia for assistance with the WRF model.This work is supported by the NCAR FY04opportunity fund. REFERENCESBoyle,J.(1993).Sensitivity of dynamical quantities to horizontal resolution for a climate simulation using the ECMWF(cycle33)model.J.Climate,6,796–815. Daly, C.,Neilson,R.,and Phillips, D.(1994).A statistical-topographic model for mapping climatolog-Figure3:Daily average precipitation amount(mm)for WRF6,WRF30and observations interpolated from the1/24grid onto the WRF6and WRF30grids.The crosses mark the locations of83snotel stations.Figure4:Cold-season average2m temperature(K)for WRF6,WRF30and observations interpolated from the1/24grid onto the WRF6and WRF30grids.Crosses mark the locations of83snotel stations.Figure5:Cold-season average snowpack(snow water equivalent)(mm)for WRF6and WRF30.Crosses mark the locations of83 snotel stations.ical precipitation over mountainous terrain.J.Appl. Meteor.,33,140–158.Duffy,P.,Govindasamy, B.,Iorio,J.,,Milovich,J., Sperber,K.,Taylor,K.,Wehner,M.,and Thompson,S. (2003).High resolution simulations of global climate. Part I:Present climate.Climate Dyn.,21,371–390. Giorgi,F.and Marinucci,M.(1996).An investigation of the sensitivity of simulated precipitation to model resolution and its implications for climate studies.Mon. Wea.Rev.,124,148–166.Leung,L.and Qian,Y.(2003).The sensitivity of precip-itation and snowpack simulations to model resolution via nesting in regions of complex terrain.J.Hydrome-teor,4,1025–1043.Leung,L.,Qian,Y.,and Bian,X.(2003).Hydroclimate of the western united states based on observations and regional climate simulation of1981-2000.Part I: Seasonal statistics.J.Climate,16,1892–1911. Michalakes,J.,Chen,S.,Dudhia,J.,Hart,L.,Klemp, J.,Middlecoff,J.,and Skamarock,W.(2001).De-velopment of a next generation regional weather research and forecast model.In Developments in Teracomputing:Proceedings of the Ninth ECMWF Workshop on the Use of High Preformance Computing in Meteorology,Zweiﬂhofer W,Krietz N(eds).World Scientiﬁc:Singapore.Senior,C.(1995).The dependence of climate sensitivityon the horizontal resolution of a GCM.J.Climate,8, 2860–2880.Sperber,K.,Hameed,S.,Potter,G.,and Boyle,J.(1994). Simulation of the northern summer monsoon in the ECMWF model:Sensitivity to horizontal resolution. Mon.Wea.Rev.,122,2461–2481.Figure6:Scatter plots of observed and simulated surface variables at the locations of83snotel stations within the WRF6domain for WRF6(blue)and WRF30(red).。

毕业设计论文塑料注射成型

Modeling of morphology evolution in the injection moldingprocess of thermoplastic polymersR.Pantani,I.Coccorullo,V.Speranza,G.Titomanlio* Department of Chemical and Food Engineering,University of Salerno,via Ponte don Melillo,I-84084Fisciano(Salerno),Italy Received13May2005;received in revised form30August2005;accepted12September2005AbstractA thorough analysis of the effect of operative conditions of injection molding process on the morphology distribution inside the obtained moldings is performed,with particular reference to semi-crystalline polymers.The paper is divided into two parts:in the ﬁrst part,the state of the art on the subject is outlined and discussed;in the second part,an example of the characterization required for a satisfactorily understanding and description of the phenomena is presented,starting from material characterization,passing through the monitoring of the process cycle and arriving to a deep analysis of morphology distribution inside the moldings.In particular,fully characterized injection molding tests are presented using an isotactic polypropylene,previously carefully characterized as far as most of properties of interest.The effects of both injectionﬂow rate and mold temperature are analyzed.The resulting moldings morphology(in terms of distribution of crystallinity degree,molecular orientation and crystals structure and dimensions)are analyzed by adopting different experimental techniques(optical,electronic and atomic force microscopy,IR and WAXS analysis).Final morphological characteristics of the samples are compared with the predictions of a simulation code developed at University of Salerno for the simulation of the injection molding process.q2005Elsevier Ltd.All rights reserved.Keywords:Injection molding;Crystallization kinetics;Morphology;Modeling;Isotactic polypropyleneContents1.Introduction (1186)1.1.Morphology distribution in injection molded iPP parts:state of the art (1189)1.1.1.Modeling of the injection molding process (1190)1.1.2.Modeling of the crystallization kinetics (1190)1.1.3.Modeling of the morphology evolution (1191)1.1.4.Modeling of the effect of crystallinity on rheology (1192)1.1.5.Modeling of the molecular orientation (1193)1.1.6.Modeling of theﬂow-induced crystallization (1195)ments on the state of the art (1197)2.Material and characterization (1198)2.1.PVT description (1198)*Corresponding author.Tel.:C39089964152;fax:C39089964057.E-mail address:gtitomanlio@unisa.it(G.Titomanlio).2.2.Quiescent crystallization kinetics (1198)2.3.Viscosity (1199)2.4.Viscoelastic behavior (1200)3.Injection molding tests and analysis of the moldings (1200)3.1.Injection molding tests and sample preparation (1200)3.2.Microscopy (1202)3.2.1.Optical microscopy (1202)3.2.2.SEM and AFM analysis (1202)3.3.Distribution of crystallinity (1202)3.3.1.IR analysis (1202)3.3.2.X-ray analysis (1203)3.4.Distribution of molecular orientation (1203)4.Analysis of experimental results (1203)4.1.Injection molding tests (1203)4.2.Morphology distribution along thickness direction (1204)4.2.1.Optical microscopy (1204)4.2.2.SEM and AFM analysis (1204)4.3.Morphology distribution alongﬂow direction (1208)4.4.Distribution of crystallinity (1210)4.4.1.Distribution of crystallinity along thickness direction (1210)4.4.2.Crystallinity distribution alongﬂow direction (1212)4.5.Distribution of molecular orientation (1212)4.5.1.Orientation along thickness direction (1212)4.5.2.Orientation alongﬂow direction (1213)4.5.3.Direction of orientation (1214)5.Simulation (1214)5.1.Pressure curves (1215)5.2.Morphology distribution (1215)5.3.Molecular orientation (1216)5.3.1.Molecular orientation distribution along thickness direction (1216)5.3.2.Molecular orientation distribution alongﬂow direction (1216)5.3.3.Direction of orientation (1217)5.4.Crystallinity distribution (1217)6.Conclusions (1217)References (1219)1.IntroductionInjection molding is one of the most widely employed methods for manufacturing polymeric products.Three main steps are recognized in the molding:ﬁlling,packing/holding and cooling.During theﬁlling stage,a hot polymer melt rapidlyﬁlls a cold mold reproducing a cavity of the desired product shape. During the packing/holding stage,the pressure is raised and extra material is forced into the mold to compensate for the effects that both temperature decrease and crystallinity development determine on density during solidiﬁcation.The cooling stage starts at the solidiﬁcation of a thin section at cavity entrance (gate),starting from that instant no more material can enter or exit from the mold impression and holding pressure can be released.When the solid layer on the mold surface reaches a thickness sufﬁcient to assure required rigidity,the product is ejected from the mold.Due to the thermomechanical history experienced by the polymer during processing,macromolecules in injection-molded objects present a local order.This order is referred to as‘morphology’which literally means‘the study of the form’where form stands for the shape and arrangement of parts of the object.When referred to polymers,the word morphology is adopted to indicate:–crystallinity,which is the relative volume occupied by each of the crystalline phases,including mesophases;–dimensions,shape,distribution and orientation of the crystallites;–orientation of amorphous phase.R.Pantani et al./Prog.Polym.Sci.30(2005)1185–1222 1186R.Pantani et al./Prog.Polym.Sci.30(2005)1185–12221187Apart from the scientiﬁc interest in understandingthe mechanisms leading to different order levels inside a polymer,the great technological importance of morphology relies on the fact that polymer character-istics (above all mechanical,but also optical,electrical,transport and chemical)are to a great extent affected by morphology.For instance,crystallinity has a pro-nounced effect on the mechanical properties of the bulk material since crystals are generally stiffer than amorphous material,and also orientation induces anisotropy and other changes in mechanical properties.In this work,a thorough analysis of the effect of injection molding operative conditions on morphology distribution in moldings with particular reference to crystalline materials is performed.The aim of the paper is twofold:ﬁrst,to outline the state of the art on the subject;second,to present an example of the characterization required for asatisfactorilyR.Pantani et al./Prog.Polym.Sci.30(2005)1185–12221188understanding and description of the phenomena, starting from material description,passing through the monitoring of the process cycle and arriving to a deep analysis of morphology distribution inside the mold-ings.To these purposes,fully characterized injection molding tests were performed using an isotactic polypropylene,previously carefully characterized as far as most of properties of interest,in particular quiescent nucleation density,spherulitic growth rate and rheological properties(viscosity and relaxation time)were determined.The resulting moldings mor-phology(in terms of distribution of crystallinity degree, molecular orientation and crystals structure and dimensions)was analyzed by adopting different experimental techniques(optical,electronic and atomic force microscopy,IR and WAXS analysis).Final morphological characteristics of the samples were compared with the predictions of a simulation code developed at University of Salerno for the simulation of the injection molding process.The effects of both injectionﬂow rate and mold temperature were analyzed.1.1.Morphology distribution in injection molded iPP parts:state of the artFrom many experimental observations,it is shown that a highly oriented lamellar crystallite microstructure, usually referred to as‘skin layer’forms close to the surface of injection molded articles of semi-crystalline polymers.Far from the wall,the melt is allowed to crystallize three dimensionally to form spherulitic structures.Relative dimensions and morphology of both skin and core layers are dependent on local thermo-mechanical history,which is characterized on the surface by high stress levels,decreasing to very small values toward the core region.As a result,the skin and the core reveal distinct characteristics across the thickness and also along theﬂow path[1].Structural and morphological characterization of the injection molded polypropylene has attracted the interest of researchers in the past three decades.In the early seventies,Kantz et al.[2]studied the morphology of injection molded iPP tensile bars by using optical microscopy and X-ray diffraction.The microscopic results revealed the presence of three distinct crystalline zones on the cross-section:a highly oriented non-spherulitic skin;a shear zone with molecular chains oriented essentially parallel to the injection direction;a spherulitic core with essentially no preferred orientation.The X-ray diffraction studies indicated that the skin layer contains biaxially oriented crystallites due to the biaxial extensionalﬂow at theﬂow front.A similar multilayered morphology was also reported by Menges et al.[3].Later on,Fujiyama et al.[4] investigated the skin–core morphology of injection molded iPP samples using X-ray Small and Wide Angle Scattering techniques,and suggested that the shear region contains shish–kebab structures.The same shish–kebab structure was observed by Wenig and Herzog in the shear region of their molded samples[5].A similar investigation was conducted by Titomanlio and co-workers[6],who analyzed the morphology distribution in injection moldings of iPP. They observed a skin–core morphology distribution with an isotropic spherulitic core,a skin layer characterized by aﬁne crystalline structure and an intermediate layer appearing as a dark band in crossed polarized light,this layer being characterized by high crystallinity.Kalay and Bevis[7]pointed out that,although iPP crystallizes essentially in the a-form,a small amount of b-form can be found in the skin layer and in the shear region.The amount of b-form was found to increase by effect of high shear rates[8].A wide analysis on the effect of processing conditions on the morphology of injection molded iPP was conducted by Viana et al.[9]and,more recently, by Mendoza et al.[10].In particular,Mendoza et al. report that the highest level of crystallinity orientation is found inside the shear zone and that a high level of orientation was also found in the skin layer,with an orientation angle tilted toward the core.It is rather difﬁcult to theoretically establish the relationship between the observed microstructure and processing conditions.Indeed,a model of the injection molding process able to predict morphology distribution in theﬁnal samples is not yet available,even if it would be of enormous strategic importance.This is mainly because a complete understanding of crystallization kinetics in processing conditions(high cooling rates and pressures,strong and complexﬂowﬁelds)has not yet been reached.In this section,the most relevant aspects for process modeling and morphology development are identiﬁed. In particular,a successful path leading to a reliable description of morphology evolution during polymer processing should necessarily pass through:–a good description of morphology evolution under quiescent conditions(accounting all competing crystallization processes),including the range of cooling rates characteristic of processing operations (from1to10008C/s);R.Pantani et al./Prog.Polym.Sci.30(2005)1185–12221189–a description capturing the main features of melt morphology(orientation and stretch)evolution under processing conditions;–a good coupling of the two(quiescent crystallization and orientation)in order to capture the effect of crystallinity on viscosity and the effect ofﬂow on crystallization kinetics.The points listed above outline the strategy to be followed in order to achieve the basic understanding for a satisfactory description of morphology evolution during all polymer processing operations.In the following,the state of art for each of those points will be analyzed in a dedicated section.1.1.1.Modeling of the injection molding processTheﬁrst step in the prediction of the morphology distribution within injection moldings is obviously the thermo-mechanical simulation of the process.Much of the efforts in the past were focused on the prediction of pressure and temperature evolution during the process and on the prediction of the melt front advancement [11–15].The simulation of injection molding involves the simultaneous solution of the mass,energy and momentum balance equations.Theﬂuid is non-New-tonian(and viscoelastic)with all parameters dependent upon temperature,pressure,crystallinity,which are all function of pressibility cannot be neglected as theﬂow during the packing/holding step is determined by density changes due to temperature, pressure and crystallinity evolution.Indeed,apart from some attempts to introduce a full 3D approach[16–19],the analysis is currently still often restricted to the Hele–Shaw(or thinﬁlm) approximation,which is warranted by the fact that most injection molded parts have the characteristic of being thin.Furthermore,it is recognized that the viscoelastic behavior of the polymer only marginally inﬂuences theﬂow kinematics[20–22]thus the melt is normally considered as a non-Newtonian viscousﬂuid for the description of pressure and velocity gradients evolution.Some examples of adopting a viscoelastic constitutive equation in the momentum balance equations are found in the literature[23],but the improvements in accuracy do not justify a considerable extension of computational effort.It has to be mentioned that the analysis of some features of kinematics and temperature gradients affecting the description of morphology need a more accurate description with respect to the analysis of pressure distributions.Some aspects of the process which were often neglected and may have a critical importance are the description of the heat transfer at polymer–mold interface[24–26]and of the effect of mold deformation[24,27,28].Another aspect of particular interest to the develop-ment of morphology is the fountainﬂow[29–32], which is often neglected being restricted to a rather small region at theﬂow front and close to the mold walls.1.1.2.Modeling of the crystallization kineticsIt is obvious that the description of crystallization kinetics is necessary if theﬁnal morphology of the molded object wants to be described.Also,the development of a crystalline degree during the process inﬂuences the evolution of all material properties like density and,above all,viscosity(see below).Further-more,crystallization kinetics enters explicitly in the generation term of the energy balance,through the latent heat of crystallization[26,33].It is therefore clear that the crystallinity degree is not only a result of simulation but also(and above all)a phenomenon to be kept into account in each step of process modeling.In spite of its dramatic inﬂuence on the process,the efforts to simulate the injection molding of semi-crystalline polymers are crude in most of the commercial software for processing simulation and rather scarce in the ﬂeur and Kamal[34],Papatanasiu[35], Titomanlio et al.[15],Han and Wang[36],Ito et al.[37],Manzione[38],Guo and Isayev[26],and Hieber [25]adopted the following equation(Kolmogoroff–Avrami–Evans,KAE)to predict the development of crystallinityd xd tZð1K xÞd d cd t(1)where x is the relative degree of crystallization;d c is the undisturbed volume fraction of the crystals(if no impingement would occur).A signiﬁcant improvement in the prediction of crystallinity development was introduced by Titoman-lio and co-workers[39]who kept into account the possibility of the formation of different crystalline phases.This was done by assuming a parallel of several non-interacting kinetic processes competing for the available amorphous volume.The evolution of each phase can thus be described byd x id tZð1K xÞd d c id t(2)where the subscript i stands for a particular phase,x i is the relative degree of crystallization,x ZPix i and d c iR.Pantani et al./Prog.Polym.Sci.30(2005)1185–1222 1190is the expectancy of volume fraction of each phase if no impingement would occur.Eq.(2)assumes that,for each phase,the probability of the fraction increase of a single crystalline phase is simply the product of the rate of growth of the corresponding undisturbed volume fraction and of the amount of available amorphous fraction.By summing up the phase evolution equations of all phases(Eq.(2))over the index i,and solving the resulting differential equation,one simply obtainsxðtÞZ1K exp½K d cðtÞ (3)where d c Z Pid c i and Eq.(1)is recovered.It was shown by Coccorullo et al.[40]with reference to an iPP,that the description of the kinetic competition between phases is crucial to a reliable prediction of solidiﬁed structures:indeed,it is not possible to describe iPP crystallization kinetics in the range of cooling rates of interest for processing(i.e.up to several hundreds of8C/s)if the mesomorphic phase is neglected:in the cooling rate range10–1008C/s, spherulite crystals in the a-phase are overcome by the formation of the mesophase.Furthermore,it has been found that in some conditions(mainly at pressures higher than100MPa,and low cooling rates),the g-phase can also form[41].In spite of this,the presence of different crystalline phases is usually neglected in the literature,essentially because the range of cooling rates investigated for characterization falls in the DSC range (well lower than typical cooling rates of interest for the process)and only one crystalline phase is formed for iPP at low cooling rates.It has to be noticed that for iPP,which presents a T g well lower than ambient temperature,high values of crystallinity degree are always found in solids which passed through ambient temperature,and the cooling rate can only determine which crystalline phase forms, roughly a-phase at low cooling rates(below about 508C/s)and mesomorphic phase at higher cooling rates.The most widespread approach to the description of kinetic constant is the isokinetic approach introduced by Nakamura et al.According to this model,d c in Eq.(1)is calculated asd cðtÞZ ln2ðt0KðTðsÞÞd s2 435n(4)where K is the kinetic constant and n is the so-called Avrami index.When introduced as in Eq.(4),the reciprocal of the kinetic constant is a characteristic time for crystallization,namely the crystallization half-time, t05.If a polymer is cooled through the crystallization temperature,crystallization takes place at the tempera-ture at which crystallization half-time is of the order of characteristic cooling time t q deﬁned ast q Z D T=q(5) where q is the cooling rate and D T is a temperature interval over which the crystallization kinetic constant changes of at least one order of magnitude.The temperature dependence of the kinetic constant is modeled using some analytical function which,in the simplest approach,is described by a Gaussian shaped curve:KðTÞZ K0exp K4ln2ðT K T maxÞ2D2(6)The following Hoffman–Lauritzen expression[42] is also commonly adopted:K½TðtÞ Z K0exp KUÃR$ðTðtÞK T NÞ!exp KKÃ$ðTðtÞC T mÞ2TðtÞ2$ðT m K TðtÞÞð7ÞBoth equations describe a bell shaped curve with a maximum which for Eq.(6)is located at T Z T max and for Eq.(7)lies at a temperature between T m(the melting temperature)and T N(which is classically assumed to be 308C below the glass transition temperature).Accord-ing to Eq.(7),the kinetic constant is exactly zero at T Z T m and at T Z T N,whereas Eq.(6)describes a reduction of several orders of magnitude when the temperature departs from T max of a value higher than2D.It is worth mentioning that only three parameters are needed for Eq.(6),whereas Eq.(7)needs the deﬁnition ofﬁve parameters.Some authors[43,44]couple the above equations with the so-called‘induction time’,which can be deﬁned as the time the crystallization process starts, when the temperature is below the equilibrium melting temperature.It is normally described as[45]Dt indDtZðT0m K TÞat m(8)where t m,T0m and a are material constants.It should be mentioned that it has been found[46,47]that there is no need to explicitly incorporate an induction time when the modeling is based upon the KAE equation(Eq.(1)).1.1.3.Modeling of the morphology evolutionDespite of the fact that the approaches based on Eq.(4)do represent a signiﬁcant step toward the descriptionR.Pantani et al./Prog.Polym.Sci.30(2005)1185–12221191of morphology,it has often been pointed out in the literature that the isokinetic approach on which Nakamura’s equation (Eq.(4))is based does not describe details of structure formation [48].For instance,the well-known experience that,with many polymers,the number of spherulites in the ﬁnal solid sample increases strongly with increasing cooling rate,is indeed not taken into account by this approach.Furthermore,Eq.(4)describes an increase of crystal-linity (at constant temperature)depending only on the current value of crystallinity degree itself,whereas it is expected that the crystallization rate should depend also on the number of crystalline entities present in the material.These limits are overcome by considering the crystallization phenomenon as the consequence of nucleation and growth.Kolmogoroff’s model [49],which describes crystallinity evolution accounting of the number of nuclei per unit volume and spherulitic growth rate can then be applied.In this case,d c in Eq.(1)is described asd ðt ÞZ C m ðt 0d N ðs Þd s$ðt sG ðu Þd u 2435nd s (9)where C m is a shape factor (C 3Z 4/3p ,for spherical growth),G (T (t ))is the linear growth rate,and N (T (t ))is the nucleation density.The following Hoffman–Lauritzen expression is normally adopted for the growth rateG ½T ðt Þ Z G 0exp KUR $ðT ðt ÞK T N Þ!exp K K g $ðT ðt ÞC T m Þ2T ðt Þ2$ðT m K T ðt ÞÞð10ÞEqs.(7)and (10)have the same form,however the values of the constants are different.The nucleation mechanism can be either homo-geneous or heterogeneous.In the case of heterogeneous nucleation,two equations are reported in the literature,both describing the nucleation density as a function of temperature [37,50]:N ðT ðt ÞÞZ N 0exp ½j $ðT m K T ðt ÞÞ (11)N ðT ðt ÞÞZ N 0exp K 3$T mT ðt ÞðT m K T ðt ÞÞ(12)In the case of homogeneous nucleation,the nucleation rate rather than the nucleation density is function of temperature,and a Hoffman–Lauritzen expression isadoptedd N ðT ðt ÞÞd t Z N 0exp K C 1ðT ðt ÞK T N Þ!exp KC 2$ðT ðt ÞC T m ÞT ðt Þ$ðT m K T ðt ÞÞð13ÞConcentration of nucleating particles is usually quite signiﬁcant in commercial polymers,and thus hetero-geneous nucleation becomes the dominant mechanism.When Kolmogoroff’s approach is followed,the number N a of active nuclei at the end of the crystal-lization process can be calculated as [48]N a ;final Zðt final 0d N ½T ðs Þd sð1K x ðs ÞÞd s (14)and the average dimension of crystalline structures can be attained by geometrical considerations.Pantani et al.[51]and Zuidema et al.[22]exploited this method to describe the distribution of crystallinity and the ﬁnal average radius of the spherulites in injection moldings of polypropylene;in particular,they adopted the following equationR Z ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ3x a ;final 4p N a ;final 3s (15)A different approach is also present in the literature,somehow halfway between Nakamura’s and Kolmo-goroff’s models:the growth rate (G )and the kinetic constant (K )are described independently,and the number of active nuclei (and consequently the average dimensions of crystalline entities)can be obtained by coupling Eqs.(4)and (9)asN a ðT ÞZ 3ln 24p K ðT ÞG ðT Þ 3(16)where heterogeneous nucleation and spherical growth is assumed (Avrami’s index Z 3).Guo et al.[43]adopted this approach to describe the dimensions of spherulites in injection moldings of polypropylene.1.1.4.Modeling of the effect of crystallinity on rheology As mentioned above,crystallization has a dramatic inﬂuence on material viscosity.This phenomenon must obviously be taken into account and,indeed,the solidiﬁcation of a semi-crystalline material is essen-tially caused by crystallization rather than by tempera-ture in normal processing conditions.Despite of the importance of the subject,the relevant literature on the effect of crystallinity on viscosity isR.Pantani et al./Prog.Polym.Sci.30(2005)1185–12221192rather scarce.This might be due to the difﬁculties in measuring simultaneously rheological properties and crystallinity evolution during the same tests.Apart from some attempts to obtain simultaneous measure-ments of crystallinity and viscosity by special setups [52,53],more often viscosity and crystallinity are measured during separate tests having the same thermal history,thus greatly simplifying the experimental approach.Nevertheless,very few works can be retrieved in the literature in which(shear or complex) viscosity can be somehow linked to a crystallinity development.This is the case of Winter and co-workers [54],Vleeshouwers and Meijer[55](crystallinity evolution can be drawn from Swartjes[56]),Boutahar et al.[57],Titomanlio et al.[15],Han and Wang[36], Floudas et al.[58],Wassner and Maier[59],Pantani et al.[60],Pogodina et al.[61],Acierno and Grizzuti[62].All the authors essentially agree that melt viscosity experiences an abrupt increase when crystallinity degree reaches a certain‘critical’value,x c[15]. However,little agreement is found in the literature on the value of this critical crystallinity degree:assuming that x c is reached when the viscosity increases of one order of magnitude with respect to the molten state,it is found in the literature that,for iPP,x c ranges from a value of a few percent[15,62,60,58]up to values of20–30%[58,61]or even higher than40%[59,54,57].Some studies are also reported on the secondary effects of relevant variables such as temperature or shear rate(or frequency)on the dependence of crystallinity on viscosity.As for the effect of temperature,Titomanlio[15]found for an iPP that the increase of viscosity for the same crystallinity degree was higher at lower temperatures,whereas Winter[63] reports the opposite trend for a thermoplastic elasto-meric polypropylene.As for the effect of shear rate,a general agreement is found in the literature that the increase of viscosity for the same crystallinity degree is lower at higher deformation rates[62,61,57].Essentially,the equations adopted to describe the effect of crystallinity on viscosity of polymers can be grouped into two main categories:–equations based on suspensions theories(for a review,see[64]or[65]);–empirical equations.Some of the equations adopted in the literature with regard to polymer processing are summarized in Table1.Apart from Eq.(17)adopted by Katayama and Yoon [66],all equations predict a sharp increase of viscosity on increasing crystallinity,sometimes reaching inﬁnite (Eqs.(18)and(21)).All authors consider that the relevant variable is the volume occupied by crystalline entities(i.e.x),even if the dimensions of the crystals should reasonably have an effect.1.1.5.Modeling of the molecular orientationOne of the most challenging problems to present day polymer science regards the reliable prediction of molecular orientation during transformation processes. Indeed,although pressure and velocity distribution during injection molding can be satisfactorily described by viscous models,details of the viscoelastic nature of the polymer need to be accounted for in the descriptionTable1List of the most used equations to describe the effect of crystallinity on viscosityEquation Author Derivation Parameters h=h0Z1C a0x(17)Katayama[66]Suspensions a Z99h=h0Z1=ðx K x cÞa0(18)Ziabicki[67]Empirical x c Z0.1h=h0Z1C a1expðK a2=x a3Þ(19)Titomanlio[15],also adopted byGuo[68]and Hieber[25]Empiricalh=h0Z expða1x a2Þ(20)Shimizu[69],also adopted byZuidema[22]and Hieber[25]Empiricalh=h0Z1Cðx=a1Þa2=ð1Kðx=a1Þa2Þ(21)Tanner[70]Empirical,basedon suspensionsa1Z0.44for compact crystallitesa1Z0.68for spherical crystallitesh=h0Z expða1x C a2x2Þ(22)Han[36]Empiricalh=h0Z1C a1x C a2x2(23)Tanner[71]Empirical a1Z0.54,a2Z4,x!0.4h=h0Zð1K x=a0ÞK2(24)Metzner[65],also adopted byTanner[70]Suspensions a Z0.68for smooth spheresR.Pantani et al./Prog.Polym.Sci.30(2005)1185–12221193。

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