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Deconfinement and color superconductivity in cold neutron stars

a r X i v :a s t r o -p h /0504564v 2 15 S e p 2005Deconﬁnement and color superconductivity in cold neutron starsG.Lugones ∗and I.Bombaci †Dipartimento di Fisica “Enrico Fermi”Universit`a di Pisa and INFN Sezione di Pisa,Largo Bruno Pontecorvo 3,56127Pisa,Italy We study the deconﬁnement transition of hadronic matter into quark matter in neutron star conditions in the light of color superconductivity.Deconﬁnement is considered to be a ﬁrst order phase transition that conserves color and ﬂavor.It gives a short-lived (τ∼τweak )transitory colorless-quark-phase that is not in β-equilibrium.We deduce the equations governing deconﬁnement when quark pairing is allowed and ﬁnd the regions of the parameter space (pairing gap ∆versus bag constant B )where deconﬁnement is possible inside cold neutron stars.We show that for a wide region of (B,∆)a pairing pattern is reachable within a strong interaction timescale,and the resulting “2SC-like”phase is preferred energetically to the unpaired phase.We also show that although β-stable hybrid star conﬁgurations are known to be possible for a wide region of the (B,∆)-space,many of these conﬁgurations could not form in practice because deconﬁnement is forbidden,i.e.the here studied non-β-stable intermediate state cannot be reached.I.INTRODUCTIONA general feature of degenerate Fermi systems is that they become unstable if there exist any attractive inter-action at the Fermi surface.As recognized by Bardeen,Cooper and Schrieﬀer (BCS)[1]this instability leads to the formation of a condensate of Cooper pairs and the appearance of superconductivity.In QCD any attractive quark-quark interaction will lead to pairing and color su-perconductivity,a subject already addressed in the late 1970s and early 1980s [2,3]which came back a few years ago since the realization that the typical superconducting gaps in quark matter may be larger than those predicted in these early works (∆as high as ∼100MeV)[4].The phase diagram of QCD has been analyzed in the light of color superconductivity and model calculations suggest that the phase structure is very rich at high densities.Depending on the number of ﬂavors,the quark masses,the interaction channels,and other variables many possi-ble β-stable color superconducting phases of quark mat-ter are possible [5,6,7,8,9].There is at present some indication that the quark gluon plasma might have been produced in laboratory [10].However,it is not yet established whether decon-ﬁnement happens in nature in the high density,low tem-perature regime that is relevant for neutron stars.Un-fortunately,ﬁrst principle calculations are not available in this region of the QCD phase diagram.In turn we shall base our analysis on phenomenological considera-tions which could delineate at least a broad brush pic-ture of the physics involved.Matter in compact stars should be electrically neutral and colorless in bulk.Also,any equilibrium conﬁguration of such matter should re-main in β-equilibrium.Satisfying these requirements im-pose nontrivial relations between the chemical potentials of diﬀerent quarks.Moreover,such relationssubstan-2analyzed.To the best of our knowledge,all previous works about color superconductivity in compact stars have dealt with matter in β-equilibrium.This is the situation expected to appear in strange stars or hybrid stars as soon as they set-tle in a stable conﬁguration.However,during the decon-ﬁnement transition in neutron stars,matter is transito-rily out of equilibrium with respect to weak interactions.In fact,the transition from β-stable hadron matter to quark matter in cold neutron stars should occur trough a quantum nucleation process [12,13,15,16,17,18].Quantum ﬂuctuations could form bothvirtual drops of unpaired quark matter (hereafter the Q ∗unp phase)or vir-tual drops of color-superconducting quark matter (Q ∗∆phase).In both cases,the ﬂavor content of the quark matter virtual drop must be equal to that of the conﬁned β-stable hadronic phase at the same pressure (the central pressure of the hadronic star).In fact,since quark decon-ﬁnement and quark-quark pairing are due to the stronginteraction,the oscillation time ν−10of a virtual quark droplet in the potential energy barrier separating the hadronic from the quark phase,is of the same order of the strong interaction characteristic time (τstrong ∼10−23s).The latter is many orders of magnitude smaller than the weak interaction characteristic time (τweak ∼10−8s).Thus,quark ﬂavor must be conserved forming a virtual drop of quark matter [17,18,19,20,21].Which one ofthe two kind of droplets (Q ∗unp or Q ∗∆)will nucleate de-pends on the value of the corresponding Gibbs free energy per baryon (g unp ,g ∆).In fact,the latter quantity enters in the expression of the volume term of the energy barrier separating the conﬁned and deconﬁned phases (see e.g.eq.(7)in [18],where the Gibbs free energy per baryon is denoted by µi ,i =Q ∗,H ).Clearly,when g ∆<g unp the nucleation of a Q ∗∆drop will be realized.The direct formation by quantum ﬂuctuations of a drop of β-stable quark matter (Q phase)is also possi-ble in principle.However,it is strongly suppressed with respect to the formation of the non β-stable drop by afactor ∼G 2N/3Fermi being N the number of particles in the critical size quark drop.This is so because the formation of a β-stable drop will imply the almost simultaneous conversion of ∼N/3up and down quarks into strange quarks.For a critical size β-stable nugget at the center of a neutron star it is found N ∼100−1000,and there-fore the factor is actually tiny.This is the same reason that impedes that an iron nucleus converts into a drop of strange quark matter,even in the case in which strange quark matter had a lower energy per baryon (Bodmer-Witten-Terazawa hypothesis).Because of this reason it is assumed that a direct transition to β-stable quark mat-ter is not possible [33].Therefore,the β-stable state Q could be reached only after the β-decay of the interme-diate state Q ∗.This is in agreement with many other previous works,see e.g.[17,18,19,20,21].In this context,one question addressed by the present work is whether the system settles in a paired or in an un-paired state just after the deconﬁnement.On the otherhand,notice that although the above mentioned non-β-stable quark phase is very short-lived,it constitutes an unavoidable intermediate state that must be reached be-fore arriving to the ﬁnal β-stable conﬁguration,e.g.CFL quark matter (c.f.[22,23]).The second question we shall address is whether this intermediate phase can eventually preclude the transition to the ﬁnal β-stable state in spite of the latter having a lower energy.This is because the Q -phase can be formed only after the nucleation of a real(i.e critical size)drop of Q ∗unp or Q ∗∆matter,and its sub-sequent “long term”(t ∼τweak ∼10−8s)weak decay process.II.DECONFINEMENT OF HADRONIC MATTER INTO COLOR SUPERCONDUCTINGQUARK MATTERGiven the uncertainties in the nature of matter at high densities,the analysis is based on the extrapolation to higher densities of an hadronic model valid around the nuclear saturation density ρ0,and the extrapolation to ρ0of a quark model that is expected to be valid only for ρ→∞.Within this kind of analysis the (in general)dif-ferent functional form of both EOSs,induces the phase transition to be ﬁrst order.Notice that from lattice QCD calculations there are indications that the transition is ac-tually ﬁrst order in the high-density and low-temperature regime,although this calculations involve temperatures that are still larger than those in neutron stars,and do not include the eﬀect of color superconductivity [26].Deconﬁnement is analyzed here as a ﬁrst order phase transition that conserves the ﬂavor abundances in both phases.Therefore,it gives a transitory colorless-quark-phase that is not in β-equilibrium.For describing the just deconﬁned quark phase we shall model it as a free Fermi mixture of quarks and leptons and we will subtract the pairing and the vacuum energy.The thermodynamic potential can be written asΩ=Ωfree Q +ΩgapQ +ΩL +B,(1)withΩfree Q=f,c1π2∆2¯µ2,(3)3PressureG i b b s e n e r g y p e r p a r t i c l e G / n BFIG.1:Schematic comparison of the free energy of hadronic matter (H ),non-β-stable ”just-deconﬁned”matter (Q ∗),and β-stable quark matter (Q )for diﬀerent cases.In the case of panel a)the transition can never occur inside neutron stars in spite of the ﬁnal state (Q)having a lower energy per baryon.As explained in the text,a direct transition to Q is strongly suppressed.Since Q ∗has a larger energy per baryon than H for all pressures below the central pressure of the maximummass hadronic star (P maxc ),deconﬁnement cannot occur even if the Q phase has a lower energy.In panels b)and c)the phase Q ∗has a lower energy per baryon than H for somepressures below (P maxc ).Therefore,deconﬁnement is possibleif pressures between P 0and P maxc are reached inside a given neutron star.The diﬀerence between panels b)and c)is the energy per particle at zero pressure (indicated with a dot for Q and with an asterisk for H ).In b)quark stars are the so called strange stars,because they can be made up of quark matter from the center up to the surface (P=0).In case c)they are hybrid stars,because at zero pressure H has a lower energy than Q .For a ﬁxed hadronic equation of state,these possibilities correspond to diﬀerent values of the parameters of the quark model (the vacuum energy density B and the superconducting gap ∆).which results from E cf =3π2+2A3π2(5)for quarks that do not pair.The number density of each ﬂavor in the quark phase is given byn f =cn fc ,(6)and the baryon number density n B byn B =13 cn c =14Y H f=Y Qff=u,d,s,L(8)being Y H f≡n H f/n H B and Y Q i≡n Qf /n Q B the abundancesof each particle in the hadron and quark phase respec-tively(we shall omit the super-indexes H and Q in the following).In other words,the just deconﬁned quark phase must have the same“ﬂavor”composition than the β-stable hadronic phase from which it originated. Additionally,the deconﬁned phase must be locally col-orless;therefore,it must be composed by an equal num-ber or red,green and blue quarks:n r=n g=n b(9) being n r,n g and n b the number densities of red,green and blue quarks respectively,given by:n c= f n fc.(10) Color neutrality can be automatically fulﬁlled by im-posing that eachﬂavor must be colorless separately,i.e. n ur=n ug=n ub,n dr=n dg=n db,and n sr=n sg=n sb. But in general this conﬁguration will not allow pairing with a signiﬁcant gap.As already stated,for quarks hav-ing diﬀerent color andﬂavor the pairing gap may be as large as100MeV,while for particles having the same ﬂavor the gap is found to be about two orders of magni-tude smaller(see[25]and references therein).Pairing is allowed even in the caseδµ>∆but the corresponding gaps are small[6,28].Therefore,in order to allow pair-ing between quarks with a non negligible gap,the Fermi momenta of at least u r and d g quarks must be equal(the choice of these two particular colors andﬂavors is just a convention).This implies the equality of the correspond-ing number densitiesn ur=n dg.(11) The above condition represents a state that fulﬁlls all the physical requirements of the deconﬁned phase(e.g.is color and electrically neutral),and should be the actual state(forτ≪τweak)if it has the lowest free energy per baryon.Energy must be paid in order to equal at least two Fermi seas,but in compensation the pairing energy is recovered.The gained energy depends on the value of the pairing gap∆and,at least for suﬃciently large∆, is expected to be larger than the energy invested to force a pairing pattern.Also,notice that color conversion of quarks allows the adjustment of the Fermi seas within a givenﬂavor in a very short timescale(∼τstrong),i.e. several orders of magnitude faster thanβ-equilibration (τstrong≪τweak).We emphasize that this phase is not inﬂavor equilib-rium.After a weak interaction timescale this transitorypaireddbdgdrubugurncfunpaireddrdbdgubugurncf010*******-40-2020406080B = 100 MeV fm-3∆ = 150∆ = 100∆ = 50∆ = 0g∆-gunp[MeV/particle]P [MeV fm-3]FIG.2:Deconﬁnement of pure neutron matter.Upper panel: Sketch of the lowest energy conﬁguration of the paired and un-paired phases just after the deconﬁnement.Lower panel:The diﬀerence in the Gibbs energy per particle between paired and unpaired quark matter.For positive values of g∆−g unp the preferred phase just after the deconﬁnement is the unpaired one while for negative values it is the paired one.pairing pattern will be abandoned by the system in favor of the lowest-energyβ-stable conﬁguration.Depending on the density,the lowest energy state may be LOFF, gapless2SC,gapless CFL,standard CFL,(to name just some possibilities)as extensively discussed in the litera-ture.III.APPLICATION TO SIMPLIFIEDEQUATIONS OF STATEA.Deconﬁnement of pure neutron matterA simple solution can be found in the case of the de-conﬁnement of pure neutron matter,since strange quarks and electrons are not present in the hadronic gas.First, we apply the colorless conditions andﬂavor conserva-tion introduced in the previous section,in order deter-mine the abundances of each quark species.In order to allow pairing of at least two diﬀerent quarks species in the just deconﬁned phase,we impose the condition of Eq.(11),i.e.n ur=n ing one of the color-5 less conditions(n r=n g)it is found that n dr=n ug,implying that these quarks can also pair with a sig-niﬁcant gap.From the remaining colorless condition(n r=n b)it is found n ur+n dr=n ub+n db.The con-dition ofﬂavor conservation states n d=2n u;therefore,n dr+n dg+n db=2(n ur+n ug+n ub).Introducing theratio x=n ug/n ur weﬁnd from the above equations:n ub=0(12)n db12π2(1+x2/3)∆2µ2ur+.(18)1+xMinimizing g∆=g∆(P∆,x)with respect to x it is foundthat the minimum correspond to x= 1.Therefore,quarks u r−d g and u g−d r pair in a“2SC-like”patternlike the one shown in Fig.2.In order to determine whether the system settles in apaired or in an unpaired conﬁguration we compare theGibbs free energy per baryon of the above conﬁgurationwith the Gibbs free energy per baryon of an unpairedquark gas(both evaluated at the same pressure,and withthe sameﬂavor composition).For unpaired quark mat-ter the ground state of the colorless mixture(compatiblewithﬂavor conservation)is shown in Fig.2,and is de-scribed by n dr=n dg=n db=2n ur=2n ug=2n ub=26 conservation in the following simple formn d=ξn u,(20)beingξ≡Y H d/Y H u(c.f Eq(8)).In the case of the n-p-e−gas,the parameterξcan be expressed in terms of the proton fraction Y p=n p/n B of nuclear matter as ξ=(2−Y p)/(1+Y p).It is easy to check thatξ=2 corresponds to the deconﬁnement of pure neutron mat-ter,ξ=1to symmetric nuclear matter andξ=0.5to the unrealistic case of pure proton matter.We emphasize that in the case ofβ-stable n-p-e−system,ξis a function of density(or pressure)that depends only on the state of the hadronic matter that deconﬁnes.Therefore,ﬂavor conservation states that n dr+n dg+ n db=ξ(n ur+n ug+n ub).In addition,the condition of Eq.(8)applied to electrons yields:3n e=2n u−n d,(21) which conﬁrms thatﬂavor conservation automatically guarantees electric charge conservation.Finally,we im-pose that1)n dr=n ug in order to allow for paring be-tween quarks d r with u g,and2)n ur=n dg in order to allow for paring between quarks u r with d g. Introducing the ratio x=n ug/n ur,and using Eqs.(20)and(21)weﬁnd the particle number densities of eachﬂavor and color in the paired phase as a function of one of the particle densities(e.g.n ur),the parameter ξthat depends only of the state of the hadronic phase, and the free parameter x:n ug=x n ur(22)n ub=(1+x)2−ξ1+ξn ur(26)Note that the free parameter x that can be elimi-nated by minimizing the Gibbs energy per baryon g∆= ( fc n fcµfc+µe n e)/n B with respect to x at constant pressure P∆.The minimization gives x=1,which means that the conﬁguration of the paired phase that is energet-ically preferred is the one having n dr=n ug=n ur=n dg, as sketched in the upper panel of Fig. 2.In Fig.3we compare the Gibbs energy per baryon of the“2SC-like”paired phase and unpaired matter for diﬀerent values of the bag constant B and the pairing gap∆.Compar-ing with the pure neutron matter case of Fig.2it can be noticed that an increase in the proton fraction of the hadronic phase favors the formation of a paired quark phase after deconﬁnement.ncfsbsgsrunpaireddrdbdgubugurncfsbsgsrpaireddbdgdrubugur010*******-20-10102030ξ = 1.6∆ = 50∆ = 100∆ = 0η = 0.3g∆-gunp[MeV/particle]P [MeV fm-3]FIG.4:Deconﬁnement ofβ-stable hadronic matter including strange hadrons.Upper panel:Sketch of the particle num-ber conﬁguration just after deconﬁnement.The most general paired conﬁguration compatible with the condition n ur=n dg, n ug=n dr,ﬂavor conservation,and charge neutrality is the one sketched here.Lower panel:The diﬀerence in the Gibbs energy per baryon between both phases.For positive values of g∆−g unp the preferred phase just after the deconﬁnement is the unpaired one while for negative values it is the paired one. The curves correspond to B=60MeV fm−3(dashed line), B=100MeV fm−3(solid line),and B=140MeV fm−3 (doted line).We employed m s=150MeV.IV.DECONFINEMENT OF COLD HADRONICMATTERIn the following we analyze the deconﬁnement of a gen-eral hadronic system including strange hadrons and then we apply the results to a realistic EOS in order to study deconﬁnement inside cold neutron stars.A.Deconﬁnement of a general hadronic equationof state•Flavor conservation:After deconﬁnement the parti-cle densities of quarks u,d and s are the same as in the hadronic phase and can be determined by Eqs.(8).An-other equivalent way of expressing theﬂavor conservation7condition is in terms of two parametersξandη:n d=ξn u.(27)n s=ηn u.(28) whereξ≡Y H d/Y H u andη≡Y H s/Y H u depend only on the composition of the hadronic phase.These expressions are valid for any hadronic EOS.For hadronic matter contain-ing n,p,Λ,Σ+,Σ0,Σ−,Ξ−,andΞ0,we haveξ=n p+2n n+nΛ+nΣ0+2nΣ−+nΞ−2n p+n n+nΛ+2nΣ++nΣ0+nΞ0.(30)As typical values,we notice thatη=0corresponds to zero strangeness,and that at the center of the maxi-mum mass star(calculated with the hadronic equation of state of Glendenning and Moszkowski GM1[31])we haveξ=1.15andη=0.85.Notice thatξandηdeter-mine univocally the number of electrons present in the system through electric charge neutrality of the decon-ﬁned phase:3n e=2n u−n d−n s.(31)•Pairing condition:As made in the previous section for the n-p-e−gas,we impose that1)n dr=n ug in order to allow for paring between quarks d r with u g,and2) n ur=n dg in order to allow for paring between quarks u r with d g.•Color neutrality:The condition n r=n g leads immediately to n sr=n sg.Also,n r=n b leads to 2n ur+n sr=n ub+n db+n sb.The above conditions lead to the pairing pattern schematically shown in the upper panel of Fig.4.Note that these conditions still leave a degree of freedom that can beﬁxed by introducing an additional parameter h relating the particle number densities of two arbitrary quark species.Therefore,it is possible to impose the equality of two arbitrary Fermi seas in order to allow pairing between them.We have analyzed the10possible combinations and veriﬁed that6of them lead to a nega-tive value of the particle number density of at least one quark species.The other4possibilities allow pairing of particles that don’t have diﬀerent color andﬂavor,allow-ing pairing with a negligible gap.For this reason,it is more convenient to introduce h≡n sb/n sr,and minimize the free energy with respect to h.Using the above Eqs.weﬁnd the following linear set of equations:2n ur+n sr=n ub+n db+n sb(32)2n ur+n db=ξ(2n ur+n ub)(33)2n sr+h n sr=η(2n ur+n ub),(34)from which we obtain the number densities of each quark species in the paired phase as functions of only four quan-tities:n ub=24+η+2h−ηh−2ξ−hξ2−η+h+ηh+2ξ+hξn ur(36) n sb=6ηh2−η+h+ηh+2ξ+hξn ur(38) n e=2(2+h)(2−η−ξ)12π2+µ4eπ2¯µ2∆2−B,(40) g∆= fc n fcµfc n B,(41)where k fc=(µ2fc−m2fc)1/2,¯µ=µur,the chemical po-tentialsµfc are obtained fromn fc=µ3fcπ2f c=u r,u g,d r,d g(42)µfc=(3π2n fc)1/3f c=u b,d b(43)µfc=[(3π2n fc)2/3+m2s]1/2f c=s r,s g,s b(44) The minimization of g∆with respect to h gives h= 1and therefore the number densities are given by the following equations:n ub=4−2ξ1+ξn ur(46)n sb=2η1+ξn ur.(48)with n ug=n dr=n dg=n ur and n sg=n sr=n sb. Equations(40)-(48)constitute the equations of state for just deconﬁned quark matter.In the lower panel of Fig. 4we show∆g for particular values of the parameters (ξ=1.6,η=0.3).8∆ [M e V f m -3]B [Mev fm -3]FIG.5:The cparameter space ∆vs.B indicating the re-gions for which deconﬁnement is possible inside the maximum mass neutron star with the GM1EOS [31](M max =1.8M ⊙).We also indicate whether the ﬁnal state reached after β-equilibration of the just-deconﬁned phase has energy per baryon less or greater than the neutron mass (i.e.leads to the formation of strange stars or hybrid stars respectively).We adopted m s =150MeV for the strange quark mass.If (B,∆)fall inside the dashed region,deconﬁnement is not pos-sible even at the center of the maximum-mass star with this EOS.For (B,∆)inside the grey region the just-deconﬁned unpaired phase has always less energy per baryon than the just-deconﬁned paired phase.For (B,∆)in the white region the just-deconﬁned phase is always paired quark matter.The regions met at a point of coordinates (B ∗,∆∗)indicated with an asterisk and shown in Table I for diﬀerent values of the strange quark mass m s .The maximum of the grey region is indicated with a dot,and the corresponding value ∆max is shown in Table I for diﬀerent m s .032334781003003780150275498520024168979the maximum of the grey region(which is the same in Figs.5and6)and give the corresponding value∆max in Table I.We have also included in the parameter space the curve separating the regions in whichβ-stable quark matter has an energy per baryon smaller than the neutron mass from the region in whichǫ/n B(P=0)>m n(for simplicity, pairedβ-stable quark matter is assumed in all cases to be CFL).To the left of this curve theﬁnal state after β-equilibration is absolutely stable quark matter leading to the formation of strange stars.To the right,β-stable quark matter is restricted to the core of neutron stars (hybrid stars).The position of this curve also depends on the value of m s.In Figs.5and6it is shown for m s=150MeV(for more details the reader is refereed to [29]).V.DISCUSSIONIn this paper we have analyzed the deconﬁnement tran-sition from hadronic matter to quark matter,and investi-gated the role of color superconductivity in this process. We have deduced the equations governing deconﬁnement when quark pairing is allowed and,employing a realis-tic equation of state for hadronic matter,we have found the regions of the parameter space B versus∆where the deconﬁnement transition is possible inside neutron stars. The main results are shown in Figs.5and6and were explained in the last section.In the following we discuss some implications for neutron star structure.Stars containing quark phases fall into two main classes:hybrid stars(where quark matter is restricted to the core)and strange stars(made up completely by quark matter).This structural characteristic depends on whether the energy per baryon ofβ-equilibrated quark matter at zero pressure and zero temperature is less than the neutron mass(the so called“absolute stability”con-dition).In the absence of pairing,quark matter inβ-equilibrium has an energy per baryon(at P=0)smaller than the neutron mass only if B is in the range57MeV fm−3<∼B<∼90MeV fm−3.Within this range of B, unpairedβ-stable quark matter is the so called strange quark matter,and it is possible the existence of stars made up entirely by the quark phase.For B>∼90MeV fm−3unpairedβ-stable quark matter at P=0and T=0 decays into hadrons,and therefore it can be present only in the core of neutron stars.The size of the core(if any) depends on the value of B:the larger the value of B, the smaller the size of the quark matter core(for a given neutron star mass).Pairing enlarges substantially the region of the param-eter space whereβ-stable quark matter has an energy per baryon smaller than the neutron mass[29,30].Al-though the gap eﬀect does not dominate the energetics, being of the order(∆/µ)2∼a few percent,the eﬀect is substantially large near the zero-pressure point(which determines the stability and also the properties of the outer layers and surface of the star).As a consequence,a “CFL strange matter”is allowed for the same parameters that would otherwise produce unbound strange matter without pairing[29].The line separating strange mat-ter from non-absolutely stable quark matter is shown in dotted line in Figs.5and6,according to[29]. Concerning just deconﬁned quark matter(i.e.not in β-equilibrium)it has been already shown that the transi-tion to unpaired quark matter is not possible in a1.6M⊙neutron star if the Bag constant is B>∼126MeV fm−3, because the transition pressure is never reached inside the star,even in the proto-neutron star phase[21].The results when pairing is allowed have been shown in the previous section,where we have shown the“deconﬁne-ment”parameter space for the maximum mass neutron star with the GM1EOS(1.8M⊙),and for a1.6M⊙neutron star.As it is evident from Figs.5and6,de-conﬁnement is facilitated for large∆(i.e.it is possible for a larger range of B).This result can be roughly un-derstood if we think paired matter as unpaired matter with an eﬀective bag constant depending on the chemi-cal potential(or on density):B eﬀ(∆,µ)=B−A10pairs(B,∆)fall comfortably inside the dashed region of Fig.6where deconﬁnement is not allowed.For the same value of B,heavier stars(∼1.8M⊙)could deconﬁne, since(B,∆)would be inside the grey region of Fig.5, but the resulting conﬁguration would be not structurally stable and would form a black hole(c.f.[32]).Although the EOSs are diﬀerent in[32]and in the present work, this should not aﬀect this generic trend.Notice that qualitatively similar results have been found in[18,21] for unpaired quark matter.A stated in the Introduction,the transition from nu-clear matter to quark matter proceeds by bubble nucle-ation.However,notice that for largeB the results with typical surface tensionσ=10−30MeVfm−2do not dif-fer much from the case in bulk[17,18].This means that we don’t expect that the dashed region of Figs.5and 6will change signiﬁcantly when including surface eﬀects.Anyway,even if the surface tension were very large,the here presented bulk case is still relevant because it gives a lower limit for the transition:i.e.,if deconﬁnement is not possible in bulk,it will be even more diﬃcult when including surface eﬀects.In other words,the dashed line of Figs.5and6could move to the left in a more re-ﬁned study,but not to the right.A complete study of the astrophysical implications is in progress and will be published elsewhere.VI.ACKNOWLEDGEMENTSG.L.wants to thank FAPESP for support during an early phase of this work.We thank Jorge Horvath and Ettore Vicari for stimulating discussions.[1]J.Bardeen,L.N.Cooper and J.R.Schrieﬀer,Phys.Rev.108,1175(1957).[2]B.Barrois,Nucl.Phys.B129,390(1977)[3]D.Bailin and A.Love,Phys.Rep.107,325(1984),andreferences therein.[4]M.G.Alford,K.Rajagopal and F.Wilczek,Phys.Lett.B422,247(1998);R.Rapp,T.Sch¨a fer,E.V.Shuryak and M.Velkovsky,Phys.Rev.Lett.81,53(1998);M.G.Alford,Ann.Rev.Nucl.Part.Sci.51,131(2001). [5]M.G.Alford,K.Rajagopal,S.Reddy and F.Wilczek,Phys.Rev.D64,074017(2001).[6]M.Huang and I.Shovkovy,hep-ph/0311155and refer-ences therein.[7]K.Rajagopal and F.Wilczek,hep-ph/0011333[8]S.B.Ruester,I.A.Shovkovy,D.H.Rischke,Nucl.Phys.A743(2004)127-146[9]G.Nardulli,Riv.Nuovo Cimento25,1(2002)[10]M.Gyulassy and L.McLerran,Nucl.Phys.A750,30-63(2005);E.Shuryak,J.Phys.G30,S1221(2004) [11]I. A.Shovkovy,S. B.R¨u ster and D.H.Rischke,arXiv:nucl-th/0411040(2004)[12]I.M.Lifshitz and Y.Kagan,Soviet Phys.JETP35,206(1972)[13]C.Alcock,E.Farhi,and A.Olinto,Astrophys.J.310,261(1986)[14]J.E.Horvath and H.Vucetich,Phys.Rev.D59,023003(1998)[15]J.E.Horvath,Phys.Rev.D49,5590(1994)[16]F.Grassi,Astrophys.J.492,263(1998)[17]K.Iida and K.Sato,Phys.Rev.D58,2538(1998)[18]I.Bombaci,I.Parenti,I.Vida˜n a,Astrophys.J.614,314(2004)[17,18,19,20,21][19]M.L.Olesen and J.Madsen,Phys.Rev.D49,2698(1994)[20]G.Lugones and O.G.Benvenuto,Phys.Rev.D58,083001(1998)[21]O.G.Benvenuto and G.Lugones,Mon.Not.R.A.S.304,L25(1999)[22]Z.Berezhiani,I.Bombaci,A.Drago,F.Frontera and A.Lavagno;Astrophys.J.586,1250(2003).[23]A.Drago,vagno and G.Pagliara;Phys.Rev.D69,057505(2004)[24]E.J.Ferrer,V.de la Incera and C.Manuel,e-PrintArchive:hep-ph/0503162[25]M.Alford and K.Rajagopal,JHEP06,031(2002)[26]F.Csikor,G.I.Egri,Z.Fodor,S.D.Katz,K.K.Szab´o,A.I.T´o th,JHEP0405,046(2004)and references therein.[27]see M.Buballa,hep-ph/0402234and references therein.[28]I.Shovkovy and M.Huang,Phys.Lett.B564,205(2003)[29]G.Lugones and J.E.Horvath,Phys.Rev.D66,074017(2002)[30]G.Lugones and J.E.Horvath,Astronomy and Astro-physics,403,173(2003)[31]N.K.Glendenning and S.A.Moszkowski,Phys.Rev.Lett.67,2414(1991).[32]M.Alford and S.Reddy,Phys.Rev.D67,074024(2003)[33]Notice that the nucleation of an initial quark dropletmight be induced in principle by external inﬂuences such as high energy cosmic rays or neutrinos[13].However,es-timates of the production rates of quark droplets by neu-trino sparking[14]show that this mechanism is not likely to drive a neutron to quark conversion for realistic values of the minimum center of mass energy necessary to pro-duce a quark-gluon plasma in heavy ion collisions.Ultra high energy neutrinos would be also harmless because the outer crust acts as a shield due to the huge cross section[14].In this paper we are assuming that the conversionmust proceed trough an intermediate“twoﬂavor”phase, but other possibilities cannot be deﬁnitely excluded.。

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wang_etal_07

Crustal structure beneath the eastern margin of the Tibetan Plateauand its tectonic implicationsChun-Yong Wang,1Wei-Bin Han,2Jian-Ping Wu,1Hai Lou,1and W.Winston Chan3Received7June2005;revised26February2007;accepted26March2007;published10July2007.[1]Two crustal cross sections through the eastern margin of the Tibetan Plateau arejointly determined from deep seismic sounding.The E–W trending line AA’passesthrough the western Sichuan plateau(including the Songpan-Garze terrane and theLongmenshan fault belt)and ends in the Sichuan basin(a part of the Yangtze craton).LineBB’has a trend of NNE and crosses the Songpan-Garze terrane.Two-dimensional crustalstructures along the profiles were jointly determined by the additional use of existingdeep seismic sounding data.Our seismic velocity models indicate that the western Sichuanplateau and the Sichuan basin have crustal thicknesses of62and43km,averagecrustal P wave velocities of6.27and6.45km/s and lower crustal(V p>6.5km/s)thicknesses of27and15km,respectively.Density models constructed from the seismicvelocity models are consistent with observed Bouguer gravity anomalies.We infer thatcollision between the Tibetan Plateau and the Yangtze craton has caused thickening of thelower crust and uplift of the western Sichuan plateau.We detect a low-velocity layer in theupper crust of the western Sichuan plateau but observe no equivalence in the Sichuanbasin;west dipping thrusts may detach into this low-velocity layer.The seismic phase P m Pin the western Sichuan plateau has low amplitude,suggesting high attenuation in the lowercrust(Q p of100–300).We suggest that the high attenuation is a consequence of lowercrustal flow caused by the large lower crustal thickness beneath the western Sichuanplateau.Citation:Wang,C.-Y.,W.-B.Han,J.-P.Wu,H.Lou,and W.W.Chan(2007),Crustal structure beneath the eastern margin of the Tibetan Plateau and its tectonic implications,J.Geophys.Res.,112,B07307,doi:10.1029/2005JB003873.1.Introduction[2]Continent-continent collision between the Indian and the Eurasian plates began at about45Ma,and has resulted in uplift of the Tibetan Plateau and major thickening of the underlying crust.Several models have been proposed to explain the mechanism of uplift and pattern of deformation for the Tibetan Plateau[e.g.,Molnar and Tapponnier,1975; Tapponnier et al.,1982;England and Houseman,1986]. Each of these models predicts different modes for the uplift and deformation of the Tibetan Plateau and in turn must explain the observed crustal and upper mantle structure [e.g.,Molnar and Chen,1978;Chen and Molnar,1981; Barazangi and Ni,1982;Hirn et al.,1984;Ni and Barazangi,1984;Zhao et al.,1993;Nelson et al.,1996; Owens and Zandt,1997].[3]Recent Global Positioning System(GPS)measure-ments of crustal motion in the central eastern Tibetan Plateau and its adjacent foreland indicate no significant shortening(<3mm/yr)within the Longmenshan region,although it rises over6km within less than100km horizontal distance.The presence of active rock uplift along this margin is remarkable,given the distinct lack of upper crustal shortening between the plateau and the Sichuan basin[Burchfiel et al.,1995;Chen et al.,2000;Zhang et al.,2004].Some authors[e.g.,Block and Royden,1990; Wernicke,1990;Bird,1991;Wdowinski and Axen,1992] proposed that in regions where the continental crust is hot, the middle or lower crust acts as a weak viscous layer capable of flow on geologic timescales.Thus lower crustal flow in the eastern margin of the Tibetan Plateau has been proposed as a mechanism by which the lateral pressure gradients within the crust are equilibrated,reducing varia-tions in topography and crustal thickness[Bird,1991; Royden et al.,1997].[4]Observations of crustal structure beneath the eastern margin of the Tibetan Plateau provide a test for tectonic models of the region and insight into the structure and kinematics of thickened continental crust.Several studies, including active source seismic refraction and wide-angle reflection experiments,referred to here as deep seismic sounding(DSS)experiments,have been carried out in the last25years[e.g.,Chen et al.,1986;Xiong et al.,1986;Cui et al.,1987,1996],but existing data are sparse and remain inconclusive.In this paper,we present the results of DSSJOURNAL OF GEOPHYSICAL RESEARCH,VOL.112,B07307,doi:10.1029/2005JB003873,2007 ClickHereforFullArticle1Institute of Geophysics,China Seismological Bureau,Beijing,China.2Sichuan Seismological Bureau,Chengdu,China.3Multimax Inc.,Herndon,Virginia,USA.western Sichuan plateau,which is the central eastern margin of the Tibetan Plateau,and the Sichuan basin.2.Regional Geologic Setting and Previous Geophysical Results2.1.Regional Geologic Setting[5]The study area includes the western Sichuan plateau and the Sichuan basin.The western Sichuan plateau con-tains the Songpan-Garze terrane and the Longmenshan fault belt.The Sichuan basin is situated in the western Yangtze craton.The Longmenshan and Jinpingshan mountains are the east boundary of the Tibetan Plateau,with the Songpan-Garze terrane to the west and the Yangtze craton to the east (Figures1and2a).The Yangtze craton has been in a stable sedimentary environment since late Paleozoic time,where thick sedimentary strata were deposited and have not been metamorphosed.During the Eocene and Oligocene,parts of the Yangtze craton have undergone folding[Ren et al., 1999].[6]Besides the Longmenshan fault belt,other fault zones in the study area include the Xianshuihe,Garze-Litang, Xiangcheng,Jinshajiang,and the Longriba faults in the western Sichuan plateau and Anninghe fault in the Yangtze craton(Figure2a).The Xianshuihe fault is a strike-slip fault dated from at least the Quaternary period,and it extends from the Garze region through Daofu,to Kangding,with a length of Bureau,1989;Allen et al.,1991].The strike-slip rate on theXianshuihe fault is12±4mm/yr[King et al.,1997;Larson etal.,1999].GPS measurements indicate that a crustal fragmentrotates clockwise around the Eastern Himalayan Syntaxis(EHS,Figure1),and that the block’s eastern boundary is asinistral fault system with a cumulative displacement rate of$10mm/yr relative to the South China Block[Chen et al., 2000;Zhang et al.,2004].The eastern boundary of this crustalfragment is along the Xianshuihe/Xiaojiang fault system.Focal mechanism solutions of earthquakes occurring on theXianshuihe fault indicate left-lateral strike-slip movementunder east–west trending principal compressional stress[Sichuan Seismological Bureau,1989].The Jinshajiang faultis the west boundary of the Songpan-Garze terrane,with theSanjiang tectonic zone farther to the west.The north–southtrending Anninghe fault is situated along the southwestmargin of the Yangtze craton.The Panxi tectonic zone(100km wide and300km long)is distributed along theAnninghe fault zone,with anomalous deep geophysicalstructures and rich mineral resources[Cui et al.,1987;Teng,1994].[7]The eastern margin of the Tibetan Plateau,i.e.,thetransitional zone between the Tibetan Plateau and Yangtzecraton has experienced strong crustal deformation andfaulting during both the Mesozoic and late Cenozoic epochs[Chen et al.,1994;Burchfiel et al.,1995;Kirby et al.,2002,2003].The first event produced the folding in the Songpan-Figure1.Topographic relief of the Tibetan Plateau and adjacent areas.Deep seismic sounding profiles are indicated by bold lines.The box indicates the study area depicted in Figure2.The eastern boundary of the Tibetan Plateau is defined by1,Longmenshan mountains;2,Jinpingshan mountains.Asterisk denotes the location of the Eastern Himalayan Syntaxis(EHS).appears much weaker than the first with only minor crustal shortening evidence but significant uplift of the plateau [Clark and Royden,2000].[8]Earthquakes regularly occur in the western Sichuan plateau(Figure2a).Significant historic events include those at Litang(M7.2)in1954,Kangding(M7.5)in1955, Zhuwei(M s6.8)in1967,Luhuo(M s7.9)in1973,Songpan (M s7.2)in1976,and Daofu(M s6.9)in1981[Gu,1983; Sichuan Seismological Bureau,1989;Jones et al.,1984; Allen et al.,1991;Papadimitriou et al.,2004].2.2.Previous Geophysical Studies[9]Crustal and upper mantle structures beneath the eastern margin of the Tibetan Plateau and its surrounding areas were previously outlined by several DSS profiles (Figure3).Near Longmenshan,the crustal thickness varies sharply from about40km in the Yangtze craton to53km in the Songpan-Garze terrane[Chen et al.,1986].The Huashixia-Shaoyang profile[Cui et al.1996]shows that the crustal structure to the north of the western Sichuan plateau,with a crustal thickness of about60km,is quite different from that presented by Chen et al.[1986].The Lijiang-Zhehai profile[Xiong et al.,1986]indicates that the crustal structure of the Panxi tectonic zone,situated to the southwest of the Sichuan basin,is characterized by a a low-velocity anomaly in the upper mantle(7.7to7.9km/ s).The Lijiang-Xinshizhen and the Lazha-Changheba pro-files provide supporting evidence for a low-velocity layer in the middle crust and a low-velocity anomaly in the upper-most mantle in the Panxi tectonic zone[Cui et al.,1987].In addition,the Simao-Zhongdian profile in western Yunnan shows that the crustal thickness in northwestern Yunnan, about70km south of the western Sichuan plateau,is58km [Lin et al.,1993].After collecting the arrival time data from a large industrial explosion(107kg TNT)and154local earthquakes,recorded at50seismic stations in the Sichuan and Yunnan regions,Zhao and Zhang[1987]presented one-dimensional(1-D)P wave velocity models of the western Sichuan plateau with a crustal thickness of61to64km and a P n velocity of7.80to7.84km/s,as well as models of the Sichuan basin that have a crustal thickness of40to41km and a P n velocity of8.15to8.20km/s.[10]The3-D velocity structure of the crust and upper mantle in southwestern China has been determined from traveltime data collected by regional seismic networks in the Sichuan and Yunnan regions[e.g.,Liu et al.,1989;Sun et al.,1991;Huang et al.,2002;Wang et al.,2003].Wang et al.[2003]demonstrate that a positive anomaly(2to4%) and a large-scale negative anomaly(3to5%)of P wave velocity exist in the upper crust of the Sichuan basin and theFigure2.(a)Geologic setting of the study area and locations of new seismic sounding profiles.Seismic stations are indicated by open triangles:AA’is the Zhubalong-Zizhong profile,and BB’is the Benzilan-Tangke profile.Stars denote position of shot points.Grey lines mark boundaries between tectonic units. Faults are indicated by bold lines with number:1,Longmenshan fault;2,Xianshuihe fault;3,Anninghe fault;4,Garze-Litang fault;5,Jinshajiang Fault;6,Xiangcheng fault;7,Longriba fault.Rivers are indicated by thin lines:a,Jingshajiang River;b,Yellow River.Circles denote earthquakes with M>5.0 since1960.(b)Layout of the observation(1)line AA’and(2)line BB’.Shot points are located according to their projection onto straight lines.Numbers beneath shot point indicate the distance from the shot point to the western end of line AA’,or the southern end of line BB’.Dashed lines denote records with no useful information.The ones denoted by‘‘S’’have the record sections presented in the auxiliary material.between these positive and negative anomalous areas coin-cides with the Longmenshan fault belt.Strike-slip faults, such as the Xianshuihe and Anninghe faults,are associated with local negative P wave velocity anomalies in the upper crust.Regionally,the crustal and the upper mantle structures in southwestern China are characterized by relatively low crustal P wave velocities,low P n velocities and large crustal thickness variations.[11]There is a350mGal difference of Bouguer gravity anomaly between the western Sichuan plateau and the Sichuan basin[Yuan,1996].A NNE trending zone of high gravity gradient,approximately150km wide and900km long,coincides with the Longmenshan fault belt[Li,1993]. The gravity field varies gradually between the Longmen-shan fault belt and the Jinshajiang fault belt(Figure3). [12]Heat flow values determined in the Songpan-Garze terrane range from36to87mW/m2,with an average value of62±16mW/m2,and values in the western Sichuan–central Yunnan area range from53to107mW/m2,with an average value of76±13mW/m2[Hu et al.,2000].Hot springs are distributed along the Xianshuihe,the Garze-Litang and the Anninghe faults.Most of the springs have temperatures above40°C,with several above80°C[Teng, 1994].3.Crustal Velocity Structures in the Study Area yout of the DSS Profiles[13]Our DSS project in the study area involves two intersecting profiles(line AA’and line BB’)with an over-lapping portion from Litang to Yajiang(Figure2a).Line AA’trends along latitude30°N.It begins at Zhubalong (ZBL)close to the Jinshajiang River,passes through Litang (LIT),Yajiang(YJ1),Kangding,Luding(LUD),Hongya (HYA),and ends at Zizhong(ZIZ),with a total length of 552.02km.Line AA’passes through the Songpan-Garze terrane,the Longmenshan fault belt,and the Yangtze craton, and joins the northern end of the Lazha-Changheba profile [Cui et al.,1987]at Kangding.Line BB’extends from Benzilan(BZL)close to the Jinshajiang River,through Xiangcheng,Litang,Yajiang(YJ2),Daofu(DFU), Ma’erkang(MEK),and to Tangke(TKE)by the Yellow River,with a NNE trend and a total length of649.07km. Line BB’passes through the Songpan-Garze terrane andFigure3.Bouguer gravity anomalies and the location of the DSS and deep seismic reflection profiles in the study area.Contour interval is25mGal.The Longmenshan fault belt is manifested as a large-scale gravity gradient belt trending NNE.Seismic profiles are indicated by straight lines and with numbers or letters:1,Huashixia-Shaoyang profile;2,Longmenshan triangle;3,Lijiang-Zhehai;4,Lijiang-Xinshizhen;5,Lazha-Changheba;6,Simao-Zhongdian;7,Hezuo-Tangke.AA’,Zhubalong-Zizhong; BB’,Benzilan-Tangke.[14]The DSS profiles utilize11explosions(Table1).All explosions were fired underwater at a local water depth of 8–15m,except shot LIT,which is a borehole explosion at a local depth of30m,and with charge distributed among 20holes.Shots ZBL and BZL are located at the western and southwestern boundaries of the Songpan-Garze terrane, respectively,whereas MEK and TKE lie in the northern Songpan-Garze terrane.LIT situates along the Garze-Litang fault belt.LUD and DFU are along the Xianshuihe fault belt.YJ1and YJ2are located between the Garze-Litang fault and the Xianshuihe fault.HYA lies in the west Sichuan basin,$60km east to the Longmenshan fault belt,and ZIZ lies in the central Sichuan basin(Figure2).[15]The seismic waves excited by all explosions were recorded by a total of about220three-component short-period digital seismographs(with maximum gain at1Hz), which were successively deployed along line AA’and line BB’,with recorder interval of2to4km.All recorders and shots were synchronized through GPS clocks.The sampling interval on records is10ms.Timing errors of recorders and explosions are less than0.01s.The profiles are crooked (Figure2a),but a2-D velocity structure along each profile was assumed.The observation system is online,reversed and overlapped(Figure2b).On the abscissas of distance, shot points ZBL,LIT,YJ1,LUD,HYA,and ZIZ on line AA’are located at0.00,121.38,193.71,306.16,394.71, and552.02km,respectively.Shot points BZL,YJ2,DFU, MEK,and TKE on line BB’are located at0.00,267.83, 334.54,505.68,and649.07km,respectively.The low-pass-filtered(8Hz)record sections along lines AA’and BB’were plotted with a reduced velocity of6.0km/s(Figures4–10and the auxiliary material)and were interpreted shot by shot.The2-D crustal velocity structures along lines AA’and BB’were jointly determined.13.2.General Analysis of Seismic Phases[16]Our seismic phase identification and analysis is based on the assumption that the crust is horizontally layered and that seismic velocity generally increases with depth[Meissner,1986].On the record sections,seismic phases P g and P m P can be directly identified.The first arrival phase P g is the head wave or diving wave propagat-ing within the crystalline basement,and P m P is the Moho reflection.The distance range for observing phase P g is from approximately20to100km.The critical distance of phase P m P varies from140to180km.The P n phase is refracted through the uppermost mantle and can be identi-fied as the first arrival beyond about200km.Besides phases P g,P m P and P n,there are3or4crustal reflection phases,which can be traced as secondary arrivals on the record sections.In the order of arrival times,these phases are labeled as P1,P2,P3,and P4in the western Sichuan plateau,and are labeled as P1,P3and P4in the Sichuan basin,which is also related to the record sections of shots ZIZ,HYA and LUD(the eastern branch).After picking the arrival times of various phases on the record section of each shot,we applied topographic corrections to them for a reference elevation of3000m.The corrected traveltimes were used to calculate the mean velocity of the reflection phases and apparent velocity of the refraction phases[Giese and Prodehl,1976;Sheriff and Geldart,1995].The topo-graphic correction is calculated byD t¼ÀH sþH oðÞÂﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃU2rÀU2aqwhere H s=H spÀH r,H o=H stÀH r,H sp is the elevation of shot point,H st is the elevation of station,and H r is the reference elevation;U r=1/V r,U a=1/V a,V r is the average velocity of the layer above reference elevation,and V a is the horizontal apparent velocity of the phase at the station,as evaluated from the traveltime curve of the phase.Record sections used in the analysis are shown in Figures4–10and the auxiliary material Figures S1to S4,with dashed lines delineating interpreted phases.3.2.1.Line AA’3.2.1.1.Shot ZBL(Zhubalong)[17]Shot ZBL was a2500kg underwater explosion fired in the Jinshajiang River.On the record section(Figure4),P g has an apparent velocity of5.90km/s at distances from30 to60km.Phase P1is weak.P2is a fairly strong phase, traceable from60to140km and a mean velocity of 5.98km/s.P3is a distinct phase at distances from140to 200km with a mean velocity of6.18km/s.P4is traceable from160to210km.Phase P m P is weak and P n is not clearly observable.3.2.1.2.Shot LIT(Litang)[18]Shot LIT was a borehole3000kg explosion near the town of Litang.In the western branch(Figure5a),P g has a low apparent velocity of5.85km/s at distances less than 50km.P1can be traced at distances from40to85km.P2isTable1.Location of Shot Points and Their Shot ChargesLine Shot Name Code Latitude N Longitude E Altitude,m Charge,kg AA’Zhubalong ZBL29°52.15099°02.22025002500 AA’Litang LIT29°57.680100°17.38039403000 AA’Yajiang YJ130°10.560101°00.84026302500 AA’Luding LUD29°50.570102°12.34012702000 AA’Hongya HYA29°55.970103°07.4005302500 AA’Zizhong ZIZ29°53.070104°45.0903102500 BB’Benzilan BZL28°09.38099°23.76020302500 BB’Yajiang YJ230°07.340100°59.81026302500 BB’Daofu DFU30°47.080101°05.51029902000 BB’Maerkang MEK32°06.540102°01.04024902500 BB’Tangke TKE33°24.430102°23.85034504000to 122km.Because of the limited observation distances (less than 122km),P 4,P m P and P n are not observed.[19]In the eastern branch (Figure 5b),P g has an apparent velocity of 5.85km/s at distances from 30to 80km.P 1can be traced from 60to 120km,with a mean velocity of 5.90km/s.P 2is a dominant phase traceable from 80to 150km with a mean velocity of 5.93km/s.P 3is distinct at distances from 120to 200km and has a mean velocity of 6.15km/s.P m P is distinct from 165to 250km with a mean velocity of 6.30km/s.P 4is weak and P n is not clearly observable.3.2.1.3.Shot YJ1(Yajiang 1)[20]Shot YJ1was a 2500kg underwater explosion in the Yalongjiang River.In the western branch,P g has an apparent velocity of 6.00km/s at distances from 25to 60km.P 1is weak but traceable from 50to 100km.P 2is a distinct phase from 60to 120km and has a mean velocity of 5.90km/s.P 3can be traced at distances from 120to 180kmwith a mean velocity of 6.08km/s.P 4is weak and P m P and P n are not observed.[21]In the eastern branch,there exists large background noise beyond 90km.However,besides P g ,which is distinct for distances up to 70km and has an apparent velocity of 5.95km/s,P 1and P 2can be traced from 70to 130km and 100to 170km with mean velocities of 6.12km/s and 6.10km/s,respectively.P 3is traceable from 120to 185km.P m P is weak,but can be traced from 160to 240km,maintaining a mean velocity of 6.36km/s.P 4is weak and P n is not clearly observable.3.2.1.4.Shot LUD (Luding)[22]Shot LUD was a 2000kg underwater explosion in the Daduhe River.In the western branch (Figure 6a),P g has an apparent velocity of 5.95km/s at distances up to 80km.P 1has a mean velocity of 5.95km/s at distances from 60to 110km.P 2is distinct from 70to 140km with ameanFigure 4.Trace-normalized low-pass-filtered (8Hz)record section of shot ZBL with reduced velocity 6.0km/s.For this and all other record sections (Figures 5to 10),the interpretive phase lines are described in the maintext.Figure 5.(a)Trace-normalized low-pass-filtered (8Hz)record section of shot LIT (the western branch).velocity of6.02km/s.P3is traceable at distances from120 to180km,with a mean velocity of6.20km/s.P4can be traced from150to190km.A strong seismic phase P a with low frequency(1.0to1.5Hz)and high apparent velocity (13.0to15.0km/s)appears beyond160km.P m P is weak and P n is not observed.[23]The appearance of seismic phases along the eastern branch(Figure6b)is quite different from that along the western branch.Along the eastern branch,P g has an apparent velocity of6.05km/s at distances up to60km. P1and P3can be traced from70to140km and110to 170km with mean velocities of6.05km/s and6.15km/s, respectively.P2is not observed.P4is distinct at distances from130to190km,with a mean velocity of6.35km/s. P m P can be traced at distances from140to250km,with a mean velocity of6.50km/s.P n is distinct beyond200km, with an apparent velocity of8.12km/s.3.2.1.5.Shot HYA(Hongya)[24]Shot HYA was a2500kg underwater explosion in the Minjiang River.Except for P g,the traceable distances of all other phases are obviously shorter than they are on the record sections of other shots in this survey.This difference was probably caused by a unique geological environment or by an incomplete explosion.In the western branch,P g is the first arrival at distances less than60km.P1is traceable at distances from50to90km and has a mean velocity of 6.01km/s.P2is traceable at distances from70to110km, and has a mean velocity of6.05km/s.P3is distinct from 100to160km,with a mean velocity of6.13km/s.P4is weak,but can be traced from135to185km.P m P and P n[25]In the eastern branch,P g has a lower apparent velocity of5.75km/s at distances up to60km.P1is not clear and P2is not observed.P3can be traced from70to 130km,and has a mean velocity of6.05km/s.P4is distinct from85to140km,with a mean velocity of6.18km/s.P m P is traceable from105to160km,with a mean velocity of 6.48km/s.3.2.1.6.Shot ZIZ(Zizhong)[26]Shot ZIZ was a2500kg underwater explosion in a local river.On the record section(Figure7),P g has a low apparent velocity of 5.85km/s at distances less than 100km.P1,P3and P4can be traced with mean velocities of 6.05, 6.16,and 6.40km/s,respectively.P2is not observed.P m P is a dominant phase with strong amplitude from130to240km,and has a high mean velocity (6.50km/s).P n appears beyond180km and has high apparent velocity of8.15km/s.3.2.2.Line BB’3.2.2.1.Shot BZL(Benzilan)[27]Shot BZL was a2500kg underwater explosion in the Jinshajiang River.On the record section(Figure8),P g has a high apparent velocity of about6.18km/s from20to80km. P1and P2can be traced at distance from50to110km and from60to130km,and has mean velocities of6.10and 6.12km/s,respectively.P3is distinct from100to160km and has a mean velocity of6.25km/s.P4is weak.P m P can be traced from140to230km,with a mean velocity of 6.35km/s.P n is not clearly observable.3.2.2.2.Shot YJ2(Yajiang2)[28]Shot YJ2was a2500kg underwater explosion in theFigure6.(a)Trace-normalized low-pass-filtered(8Hz)record section of shot LUD(the western branch).(b)Trace-normalized low-pass-filtered(8Hz)record section of shot LUD(the eastern branch).70km.P1and P2can be traced with mean velocities of6.05 and6.08km/s at distances from40to80km and from60to 130km,respectively.P3and P4can be traced and have mean velocities of6.15and6.25km/s,respectively.P m P and P n are not clearly observable.[29]In the northern branch,P g has an apparent velocity of 6.08km/s at distances from20to80km.P1and P2have mean velocities of6.08and6.03km/s,respectively.P3is distinct from100to170km,with a mean velocity of 6.15km/s.P4is traceable from120to200km,with a mean velocity of6.25km/s.P m P and P n are not clearly observable.3.2.2.3.Shot DFU(Daofu)[30]Shot DFU was a2000kg underwater explosion in the Xianshuihe River.In the southern branch,P g has an apparent velocity of6.05km/s at distances from20to 80km.P1and P2can be traced with low mean velocities of 6.05and6.07km/s,respectively.P3and P4have mean velocities of 6.15and 6.25km/s,respectively.P m P is traceable from140to210km,with a mean velocity of 6.30km/s.P n is not clearly observed.[31]In the northern branch,P g has an apparent velocity of 6.05km/s at distances from20to70km.The reduced time-distance curve of phase P g has an arc shape,which implies the presence of a low-velocity zone with small local extent close to the Xianshuihe fault belt.P1is weak.P2and P3 have mean velocities of 6.05km/s and 6.15km/s at distances from60to90km and from80to150km, respectively.P4is weak.P m P is distinct at distances from 150to220km with a mean velocity of6.36km/s.P n is not clearly observable.3.2.2.4.Shot MEK(Ma’erkang)[32]Shot MEK was a2500kg underwater explosion in the Daduhe River.In the southern branch(Figure9a),P g has an apparent velocity of5.90km/s at distances from20 to70km.P1and P2can be traced from70to125km, respectively,with the same mean velocity of6.05km/s.P3 is distinct at distances from110to150km,with a mean velocity of6.20km/s.P4has a mean velocity of6.25km/s. P m P is traceable at distances from150to260km,with a mean velocity of6.30km/s.P n is not clear.A distinct seismic phase P b with low apparent velocity(5.20km/s) and relatively high energy appears at distances from125to 170km.[33]In the northern branch(Figure9b),P g has a low apparent velocity(5.65km/s)at distances up to80km.P1 can be traced from60to120km with a mean velocity of 5.95km/s.P2is distinct at distances from80to150km and has a mean velocity of5.90km/s.P3is traceable from80to 150km with a mean velocity of6.15km/s.Because of limited distance(150km),phases P4,P m P and P n were not observed.3.2.2.5.Shot TKE(Tangke)[34]Shot TKE was a4000kg underwater explosion in the Yellow River.On the record section(Figure10),P g has a low apparent velocity(5.60km/s),which is consistent with the northern branch of shot MEK.P1has a low mean velocity of5.85km/s.P2is weak.P3is distinct at distances from120to180km with a mean velocity of6.15km/s.P4 has a mean velocity of6.20km/s.P m P is traceable from170 to280km,with a mean velocity of6.25km/s.P n is not clearly observable.4.The2-D Velocity and Density Structure4.1.Interpretation Methods of DSS Data[35]The2-D interpretation of seismic wide-angle reflec-tion/refraction data generally consists of two steps,iterative Figure7.Trace-normalized low-pass-filtered(8Hz)record section of shotZIZ.。

mongolian-chinese_dictionary_web_user_guide_chines

Web版《蒙汉词典》使用说明2020.10.20 目录1.概要1-1.前言1-2.主要特点1-3.操作系统要求1-4.使用要求■字体的安装方法2.《蒙汉词典》词条细目的构成3.使用方法3-1.开始3-2.页面内容3-2-1.检索画面3-2-2.按键3-2-3.检索结果画面显示3-2-4.原文画面显示3-3.检索方法3-3-1.检索对象3-3-1-1.“蒙文词条”（针对蒙古文字检索）3-3-1-2. “转写字母”（针对罗马字转写检索）3-3-1-3. 《全文》（指定全文检索）■全文检索的功能3-3-2. 检索方法的种类3-3-3. 检索选项3-3-3-1.模糊查询■模糊查询的功能3-3-3-2. 不分大小写3-3-3-3. 不包括副条（限定主条检索）3-4.检索结果显示3-4-1. 检索结果显示画面3-4-2. 检索结果中出现的词条总数3-4-3. 检索结果不在一个页面上的情况3-4-4.页面上所显示的词条行数3-4-5. 原文图像显示3-4-6. 检索结果的复制、打印■补充说明补充内容(一) 关于《蒙汉词典》补充内容(二) 按键与蒙古文字母、罗马字转写对应实例补充内容(三) 蒙古文字检索中的注意事项1.概要1-1.前言Web版《蒙汉词典》是内蒙古大学蒙古学研究院（现内蒙古大学蒙古学学院）、蒙古语文研究所编撰的《蒙汉词典（增订本）》（内蒙古大学出版社，1999年）经过数据电子化，通过互联网可以进行检索、利用的网络界面。

《蒙汉词典（增订本）》的电子化利用项目是由东北大学东北亚研究中心与内蒙古大学蒙古学学院共同研发的研究成果，并得到了ALMAS（ALMAS Inc）公司的技术支持。

1-2.主要特点●Web版《蒙汉词典》中使用传统的蒙古文字来进行单词检索，可显示蒙古文字。

检索字符串输入栏中，尤其在没有启动输入法(IME)的情况下，可以直接使用键盘输入蒙古语文字，进行蒙古文字检索。

传统蒙古文字是根据Unicode的规格录入的。

网页设计师必备：Web版设计色彩速查表

网页设计师必备：Web版设计色彩速查表对于网页设计师来说色彩的把握在设计中起到很大作用，熟知一些具体的颜色代码与含义可以更好的为我们的设计服务，这篇文章总结了Web版设计色彩速查表，对于日常的使用和查找都很有帮助，而且其中大多都是网页安全色，可以放心使用。

████粉红(#ffb3a7)，即浅红色。

别称：妃色杨妃色湘妃色妃红色████妃色妃红色(#ed5736)：古同“绯”，粉红色。

杨妃色湘妃色粉红皆同义。

████品红(#f00056)：比大红浅的红色（quester注：这里的“品红”估计是指的“一品红”，是基于大红色系的，和现在我们印刷用色的“品红M100”不是一个概念）████桃红(#f47983)，桃花的颜色，比粉红略鲜润的颜色。

（quester注：不大于M70的色彩，有时可加入适量黄色）████海棠红(#db5a6b)，淡紫红色、较桃红色深一些，是非常妩媚娇艳的颜色。

████石榴红(#f20c00)：石榴花的颜色，高色度和纯度的红色。

████樱桃色(#c93756)：鲜红色████银红(#f05654)：银朱和粉红色颜料配成的颜色。

多用来形容有光泽的各种红色，尤指有光泽浅红。

████大红(#ff2121)：正红色，三原色中的红，传统的中国红，又称绛色（quester注：RGB 色中的 R255 系列明度）████绛紫(#8c4356)：紫中略带红的颜色████绯红(#c83c23)：艳丽的深红████胭脂(#9d2933)：1，女子装扮时用的胭脂的颜色。

2，国画暗红色颜料████朱红(#ff4c00)：朱砂的颜色，比大红活泼，也称铅朱朱色丹色（quester注：在YM对等的情况下，适量减少红色的成分就是该色的色彩系列感觉）████丹(#ff4e20)：丹砂的鲜艳红色████彤(#f35336)：赤色████茜色(#cb3a56)：茜草染的色彩，呈深红色████火红(#ff2d51)：火焰的红色，赤色████赫赤(#c91f37)：深红，火红。

化学科研数据库工具集合

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Marc Loudon教授/~loudonm/美国威斯康星大学麦迪逊分校化学系：化学概念测试题/~concept/mainpage.html美国亚利桑那大学生物项目：化学品与人类健康/chh/default.html美国亚利桑那大学生物项目：生物化学教材/bioc...ochemistry.html美国耶鲁大学：结构生物学中心(Center Structural Biology: Programs and Tools) /牛津大学化学系在线网络实践与课程牛津大学化学系在线演讲：化学信息学与化学教育/it/lectures.html牙买加西印度大学Mona分校化学系所开发的免费软件.jm:1104/chemsoft.html(免费)英国帝国理工学院化学系列举的Java在化学中应用实例/java/英国桑德兰大学药学与化学学院的化学网络测试题/~hs0dad/student.htm#acids英国约克大学：化学工业教育中心/ciec_home.htm英国制药行业协会的教育网站/default.asp犹他大学：生物化学在线教程NetBiochem/NetBiochem/NetWelco.htm课程材料：物理化学实验(美国新墨西哥州立大学开设)/studntres/chem435/课程材料：物理化学与分析科学(英国谢费尔德哈莱姆大学)/schools/sci/chem/tutorials/课程材料：物质与能量守恒，美国赖斯大学化工系/~ceng301/toc.html课程材料：仪器分析原理(Harry Finklea讲授)/chem210/课程材料：有机和生物分子的计算机模拟(美国宾夕法尼亚大学化学系) /shsgroup/chem647/课程材料：有机化学补充材料(Organic Chemistry Supplementary Materials) /courses.../tutorials.html课程材料：有机化学分子建模(Henry Rzepa讲授)课程材料：有机化学实验(Dr Donald Robertson讲授)/home/dlr/211exp.htm课程材料：有机化学实验(美国科罗拉多大学化学与生物化学系提供) /courses/lab.html课程材料：有机化学在线(Organic Chemistry On-Line)/IEMDL.HTM课程材料：有机与生物化学(Barry Ganong 讲授)/bganong/102.html课程材料：蛋白质结构原理(Birkbeck College)/PPS2/课程材料：地球物质(Stephen A. 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An intuitive color-selection tool

An intuitive color-selection toolPM Henry, S Westland and TLV Cheung, Centre for Colour Design Technology, University of Leeds (UK)AbstractA color-picker or color-selection tool is part of a GUI that allows users to select colors for use in software applications. There is a widespread belief that some color spaces or models are more “natural” than others. However, this intuitively appealing idea that a color space based on the nature of color perception (such as HSL) may be preferable to one that is driven by the nature of the technology (such as RGB) has not been confirmed by all studies. In this paper we argue that it is not the color space per se that is the most important factor underlying the usability of a color-selection tool but rather the color-mixing algorithm. An experiment was conducted to determine matching performance in a color-selection tool where the sliders interacted with the on-screen color using either a direct additive model or an indirect subtractive model to control the RGB values of the on-screen color. When observers were given a limited amount of time to use the sliders to match target colors their performance was statistically superior when they used the subtractive CMY sliders than when they used the additive RGB sliders. This is consistent with some previous work that suggests that observers possess better internal models of subtractive mixing than additive mixing and that the design of color-selection tools could exploit this. It should be noted that this work differs from some related work that has looked at the influence of color space on the usability of color-selection tools. Our hypothesis is that it is the color-mixing model that relates the slider bars to the on-screen color that is important rather than the choice of color space itself.IntroductionA color-picker or color-selection tool is part of a GUI that allows users to select colors for use in software applications. A number of studies have considered whether the choice of color space affects the usability of such tools1-4. There is a widespread belief2 that some color spaces or models are more “natural” than others. For example, one established text5 claims that “The RGB, CMY, and YIQ models are hardware oriented. By contrast, … HSV … is user-oriented, being based on the intuitive appeal of the artist’s tint, shade and tone”. However, this intuitively appealing idea that a color space based on the nature of color perception (such as HSL) may be preferable to one that is driven by the nature of the technology (such as RGB) has not been confirmed by all studies. For example, Douglas and Kirkpatrick concluded that choice of color space (specifically, in this case, comparing RGB and HSL) was not an important factor in the usability of a color-selection interface2. In this paper we argue that it is not the color space per se that is the most important factor underlying the usability of a color-selection tool but rather the color-mixing algorithm. The use of RGB sliders as part of a color-selection tool is essentially a color-matching task (where the user is additively combining primaries to match a target color) and therefore the user must have knowledge about the additive-mixing properties of the primaries controlled by the sliders. In a previous study we showed that users are better able to predict the results of subtractive color mixing than they are additive color mixing6. Users may possess well-developed internal models of subtractive color-mixing processes that developed in childhood as they experimented with inks and paints. A typical user, for example, would not be surprised to be informed that yellow and blue inks mixed together make green but may not be so familiar with the fact that red and green lights can be added together to make yellow. In this work, user performance in color-selection tasks is measured and compared for color-selection tools that are based upon additive and subtractive color mixing.MethodA graphical-user interface (GUI) was created in MATLAB that enabled observers to adjust a color by adjusting each of three slider bars (see Figure 1). Users were instructed to adjust a sample color so that it was a visual match for a target color and were given a fixed amount of time to complete the task. Two time limits were employed: 120 seconds and 30 seconds. A total of nineteen observers were recruited to take part in the experiments but three were discarded because they displayed abnormal color vision. Six observers (3 male, 3 female) with normal color vision took part in the 120-second experiment. A different set of 10 observers (5 male, 5 female) with normal color vision took part in the 30-second experiment.Figure 1: MATLAB GUI for color selection. The left-hand color is adjusted by the sliders to match the right-hand one. The bar at the bottom indicates the time remaining for the task.In the experiments, a total of 12 target colors were presented in turn in the right-hand part of the display (see Figure 1). The RGB values of the target colors are given in Table 1. The first three of these were for training purposes only to allow users to getused to the slider bars. The accuracy of the matching task for thefirst three colors in Table 1 was therefore not considered and results were calculated for the remaining nine target colors.Table 1: sRGB specifications of color targets used in the experiment. target R G B1 (training) 180 180 1802 (training) 140 80 903 (training) 255 255 2554 244 207 545 91 188 1806 244 161 777 94 141 698 220 103 759 170 97 18010 122 111 17711 115 180 12712 236 142 70The experiment was conducted for two types of slider bars.The first type, RGB, controlled the RGB values of the samplepatch directly and enabled the full gamut of the display (RGB ∈ {0… 255}) to be displayed. The second type, CMY, controlled theamounts of three arbitrary theoretical subtractive primaries. A simple Kubelka-Munk model was used to convert the amounts ofthe primaries into spectral reflectance factors for the subtractivemixture denoted by the sliders at any one time.F igure 2: Reflectance factors for CMY primaries. These curves wereobtained by measurement from a Xerox Phaser 7300 printer.Figure 2 shows the spectral reflectance factors of the CMYprimaries at unit concentration. At each wavelength the reflectancefactors were converted to K/S values using the equation K/S = (1-R)2/2R. The slider bar values were mapped onto colorant concentration (in the range 0-1) for each of the CMY primariesand the K/S of the mixture calculated by summing the K/S valuesat unit-concentration each weighted by the concentration denotedby the slider bar. The inverse Kubelka-Munk equation was thenused to predict reflectance at each wavelength, thus R = 1 + K/S –((1+K/S)2 - 1)0.5. The predicted spectral reflectance was thenconverted to CIE XYZ under illuminant D65 for the 1964 CIE observer and finally the XYZ values were converted into sRGB values. In this way, the CMY sliders indirectly controlled the RGBvalues of the sample patch via a subtractive model of which the user was unaware. We feel that the choice of the primaries andeven the nature of the Kubelka-Munk model are relatively unimportant for this experiment. The important difference between the RGB and CMY sliders is that the former is based on additive mixing whereas the latter is based on subtractive mixing. Thus, whereas increasing the intensities of the RGB sliders would increase the brightness of the sample patch, increasing the intensities of the CMY sliders would decrease the brightness of the sample patch. Another example would be that increasing both the red and green sliders in the RGB case would create a yellow sample patch, increasing the cyan and magenta sliders in the CMY case would create a dark blue. Our hypothesis is that is users do indeed possess a more intuitive understanding of subtractive mixing than they do of additive mixing then their performance in the CMY case would be better than in the RGB case. In preliminary experiments the values (in the range 0 - 1) from the CMY sliders bars were directly mapped to CMY concentrations in the range 0 - 1. However, the non-linear relationship between concentration and XYZ resulted in several undesirable properties. Specifically, moving the CMY sliders hadalmost no visible effect on the colour on screen until they reached almost the half-way mark of their full range. Therefore, for the slider bar values were mapped to CMY concentrations using power functions with exponents 2.7, 1.8 and 3.4 for the C, M and Y respectively. These exponents were chosen so that when all three sliders were at the 0.5 position a mid-grey resulted on the screen which was close to R=G=B = 128. It should be noted that the use of the Kubelka-Munk model in the CMY sliders did not allow the full gamut of the monitor to be explored. Therefore, the 12 target color samples (see Table 1) were selected partly so as to be within both the monitor gamut and the subtractive-primary gamut. Performance was assessed by computing the CIE XYZ values of the target and final sample patches and then computing CIELAB and CIEDE2000 color differences. The RGB values of the target and sample patches were converted to XYZ values using a monitor characterization model. Results The accuracy of matching in the 120-second experiment is shown in Table 2. It can be seen that in terms of CIELAB color differences observers were achieved an average performance of 4.45 and 4.49 for the RGB and CMY sliders respectively. The differences were statistically not significant at the 5% level using a Wilcoxon signed-rank non-parametric test. The accuracy of matching in the 30-second experiment is shown in Table 3. It can be seen that in terms of CIELAB colordifferences observers achieved an average performance of 24.88 and 11.34 for the RGB and CMY sliders respectively. The differences were statistically significant using a Wilcoxon signed-rank non-parametric test at the 5% level (and even at the 10%level).Table 2: Results of color matching in 120-second experiment.CIELAB ∆E CIEDE2000observersRGB CMY RGB CMYa 4.47 4.38 2.34 1.93b 4.07 4.79 2.25 2.09c 3.48 4.39 1.78 1.94d 5.32 4.13 2.22 1.82e 5.19 4.70 2.44 2.33f 4.18 4.54 1.93 1.94 average 4.45 4.49 2.16 2.01 p > 0.05 > 0.05Table 3: Results of color matching in 30-second experiment.CIELAB ∆E CIEDE2000observersRGB CMY RGB CMY1 20.21 9.32 8.90 3.882 36.18 11.23 18.30 7.373 21.02 10.38 7.93 5.204 26.92 14.83 10.17 6.655 15.21 8.23 7.01 4.306 8.50 12.67 3.64 5.707 54.22 13.09 23.46 5.858 28.75 15.30 13.46 7.659 10.62 7.23 4.53 3.5310 27.18 11.17 9.43 6.80 average 24.88 11.34 10.68 5.69 p < 0.05 < 0.05Note that of the 10 observers that took part in the 30-second experiment, only 1 performed better using the RGB sliders whereas 9 performed better using the CMY sliders. In the 120-second experiment the matching performance is similar for the RGB and CMY sliders. This is because, given enough time observers will eventually achieve good matches whether they find the sliders particularly easy to use or not. The time-restricted task– at 30 seconds – is necessary to differentiate between the two setsof sliders. We therefore conclude that performance is better using the CMY sliders than using the RGB sliders and this supports the notion that observers have a better internal model for subtractive color mixing and that the design of color-selection tools could exploit this. We note that the same conclusions are reached whether the results are analysed in terms of CIELAB or CIEDE2000 color differences.However, it is clear that the experiment did not isolate the effect of additive and subtractive mixing since the primaries usedin the additive and subtractive system were very different. This makes it hard to argue that a color-selection tool based upon subtractive mixing is superior to one based on additive mixing since the effect of choice of primary may be dominant. The experiment was therefore repeated using a different set of subtractive primaries. Figure 3 is a chromaticity diagram that shows the sRGB gamut (red line) and the CMY gamut (magenta line). We devised a new set of subtractive primaries that were red, green and blue. Their gamut is illustrated in Figure 3 by the blue line. The reflectance factors of the subtractive RGB primaries were obtained by measurement from samples printed using the Xerox Phaser 7300 printer. F igure 3: CIE chromaticity diagram showing the gamuts for the sRGB primaries (red line), the CMY primaries of the Xerox Phaser 7300 printer (magenta line) and the subtractive RGB primaries (blue line).The experiment was repeated using the RGB additive sliderbars as before but replacing the CMY subtractive slider bars withRGB subtractive primaries. Six observers took part in this experiment and the results can be seen in Table 4.Table 4: Results of color matching in 30-second experiment.CIELAB ∆CI D2000 observersRGB RGB_S RGB RGB_Si 23.9415.08 15.93 9.66ii 16.65 12.13 9.59 7.62iii 11.99 12.02 6.83 7.44iv 23.02 14.29 12.75 8.97v 24.02 9.92 14.50 6.44vi 9.76 10.58 5.59 7.85average 18.23 12.34 10.86 8.00 p < 0.05 < 0.05Again, statistically better performance was obtained using the subtractive system (denoted as RGB_S in Table 4) than using the additive system (denoted as RGB). It is disappointing, however,that the agreement between the additive RGB primaries and the subtractive RGB primaries (see Figure 3) was not closer since itcould still be argued that it is the choice of primaries (and their resultant gamuts) that determines performance rather than the additive or subtractive nature of the mixing model. Nevertheless,there is strong evidence that users make more accurate matches intime-restricted tasks when using slider bars that control a subtractive-mixing system than when using slider bars that controlan additive-mixing system. Further work is required to confirmthe hypothesis that the more intuitive nature of subtractive mixingis a critical component of color-selection GUI design.xyConclusionsAn experiment was conducted to determine matching performance in a color-selection tool where the sliders interacted with the on-screen color using either a direct additive model or an indirect subtractive model to control the RGB values of the on-screen color. When observers were given a limited amount of time to use the sliders to match target colors their performance was statistically superior when they used the subtractive CMY sliders than when they used the additive RGB sliders. This is consistent with some previous work6 that suggests that observers possess better internal models of subtractive mixing than additive mixing and that the design of color-selection tools could exploit this. We note that in practical terms it is probably not especially important whether a user can achieve a match in a color-selection tool in 3 seconds or 5 seconds. However, we argue that creative workers will prefer to work with tools with which they feel comfortable and that the use of such tools will complement rather than hinder the creative process. The accuracy to which an observer can make a match given a limited amount of time can reasonably be used as an indicator as to whether a particular tool is likely to be comfortable for a designer working in the digital domain.It should be noted that this work differs from some related work that has looked at the influence of color space on the usability of color-selection tools. Our hypothesis is that it is the color-mixing model that relates the slider bars to the on-screen color that is important rather than the choice of color space itself. In other to further support this hypothesis, an additional experiment was carried out to compare an additive RGB slider bar model with a subtractive RGB slider bar model. Performance in the 30-second task was better in the subtractive case than the additive case even though both were based on RGB systems. References[1] J.M. Taylor, Color spaces: language and framework for color,Proceedings of the 9th Color Imaging Conference, 6 (1993).[2] S.A Douglas and A.E. Kirkpatrick, Model and representation: theeffect of visual feedback on human performance in a color picker interface, ACM Transactions on Graphics, 18 (2), 96 (1999).[3] H. Yaguchi, Color categories in various color spaces, Proceedings ofthe 9th Color Imaging Conference, 6 (2001).[4] H. Zhang and E.D. Montag, How well can people use different colorattributes, Proceedings of the 12th Color Imaging Conference, 10 (2004).[5] J. Foley A. van Dam, S. Feiner and J. Hughes, Computer graphics:principles and practice, 2nd edition, Addison-Wesley (1990).[6] P.M. Henry, S. Westland, S.M. Burkinshaw and T.L.V. Cheung, Howwell can people predict subtractive mixing, Proceedings of the 13th Color Imaging Conference, 85 (2005).Author BiographyPhil Henry is a Teaching Fellow at the University of Leeds. He is currently working towards a PhD in the Centre for Colour D esign Technology at Leeds University.。

配色辞典及各种颜色十六进制代码表（全图）

配⾊辞典及各种颜⾊⼗六进制代码表（全图）柔和的、明亮的、温和的R　255 G　255 B　204 #FFFFCCR　204G　255B　255#CCFFFFR　255G　204B　204#FFCCCCR　255G　204B　204#FFCCCCR　255G　255B　153#FFFF99R　204G　204B　255#CCCCFFR　255G　153B　102#FF9966R　255G　102B　102#FF6666R　255G　204B　204#FFCCCCR　255G　204B　153#FFCC99R　204G　255B　153#CCFF99R　204G　204B　204#CCCCCCR　255G　204B　204#FFCCCCR　255G　255B　255#FFFFFFR　204G　255B　204#CCFFCCR　204 G　255 B　255 #CCFFFFR　204G　204B　204#CCCCCCR　204G　255B　153#CCFF99R　255G　204B　204#FFCCCCR　255G　255B　255#FFFFFFR　153G　204B　153#99CC99R　153G　204B　204#99CCCCR　255G　204B　153#FFCC99R　255G　204B　204#FFCCCCR　204G　204B　255#CCCCFFR　255G　255B　204#FFFFCCR　204G　255B　255#CCFFFFR　255G　204B　153#FFCC99R　255G　255B　204#FFFFCCR　153G　204B　204#99CCCC柔和的、洁净的、爽朗的R　204 G　255 B　153 #CCFF99R　255G　255B　255#FFFFFFR　153G　204B　255#99CCFFR　153G　204B　204#99CCCCR　255G　255B　255#FFFFFFR　204G　255B　153#CCFF99R　153G　204B　255#99CCFFR　255G　255B　255#FFFFFFR　102G　204B　204#66CCCCR　204G　204B　255#CCCCFFR　255G　255B　255#FFFFFFR　153G　204B　204#99CCCCR　153G　204B　255#99CCFFR　153G　204B　204#99CCCCR　255G　255B　204#FFFFCCR　204 G　255 B　255 #CCFFFFR　255G　255B　255#FFFFFFR　204G　204B　255#CCCCFFR　204G　255B　255#CCFFFFR　255G　255B　255#FFFFFFR　153G　204B　255#99CCFFR　102G　204B　153#66CC99R　255G　255B　255#FFFFFFR　204G　255B　255#CCFFFFR　102G　253B　204#6699CCR　255G　255B　255#FFFFFFR　153G　204B　255#99CCFFR　204G　204B　255#CCCCFFR　255G　255B　255#FFFFFFR　153G　204B　255#99CCFF可爱的、快乐的、有趣的R　102 G　204 B　204 #66CCCCR　204G　255B　102#CCFF66R　255G　153B　204#FF99CC　R　255G　153B　153#FF9999R　255G　255B　255#FFFFFFR　255G　204B　153#FFCC99　R　255G　102B　102#FF6666R　255G　255B　102#FFFF66R　153G　204B　102#99CC66　R　102G　102B　153#666699R　255G　255B　255#FFFFFFR　255G　153B　153#FF9999　R　153G　204B　51#99CC33R　255G　153B　0#FF9900R　255G　204B　00#FFCC00R　255 G　0 B　51 #FF0033R　255G　255B　255#FFFFFFR　255G　153B　102#FF9966　R　255G　153B　0#FF9900R　204G　255B　0#CCFF00R　204G　51B　153#CC3399　R　153G　204B　51#99CC33R　255G　255B　255#FFFFFFR　255G　102B　0#FF6600　R　153G　51B　120#993366R　204G　204B　51#333399R　102G　102B　51#666633　R　102G　204B　204#66CCCCR　255G　255B　255#FFFFFFR　102G　102B　153#666699活泼的、快乐的、有趣的R　204 G　153 B　153 #CC9999R　255G　255B　153#FFFF99R　102G　102B　153#666699　R　255G　153B　0#FF9900R　255G　255B　0#FFFF00R　0G　153B　204#0099CC　R　204G　204B　153#CCCC99R　204G　51B　153#CC3399R　153G　204B　0#99CC00　R　255G　102B　102#FF6666R　255G　255B　0#FFFF00R　51G　153B　204#3399CC　R　204G　102B　0#CC6600R　153G　153B　153#999999R　204G　204B　51#CCCC33R　255 G　153 B　51 #FF9933R　255G　255B　204#FFFFCCR　0G　153B　51#009933　R　0G　153B　204#0099CCR　204G　204B　204#CCCCCCR　255G　102B　102#FF6666　R　255G　102B　0#FF6600R　255G　255B　102#FFFF66R　9G　153B　102#009966　R　204G　102B　51#CC6633R　255G　204B　153#FFCC99R　204G　102B　0#CC6600　R　204G　0B　102#CC0066R　0G　153B　153#009999R　255G　204B　51#FFCC33运动型的、轻快的R　255 G　102 B　102 #FF6666R　255G　255B　0#FFFF00R　0G　102B　153#006699R　255G　153B　102#FF9966R　255G　255B　204#FFFFCCR　0G　102B　204#0066CCR　51G　153B　51#339933R　255G　204B　51#FFCC33R　51G　102B　153#336699R　255G　153B　0#FF9900R　255G　255B　204#FFFFCCR　51G　102B　153#336699R　255G　102B　0#FF6600R　204G　204B　51#CCCC33R　51G　102B　153#336699R　153 G　204 B　51 #99CC33R　255G　255B　255#FFFFFFR　0G　153B　204#0099CC　R　153G　204B　51#99CC33R　255G　102B　102#FF6666R　51G　102B　153#336699　R　51G　102B　153#336699R　255G　255B　255#FFFFFFR　153G　204B　204#99CCCC　R　255G　0B　51#FF0033R　51G　51B　153#333399R　204G　204B　0#CCCC00　R　51G　204B　153#33FF99R　255G　255B　0#FFFF00R　51G　102B　153#336699轻快的、华丽的、动感的R　153 G　0 B　102 #990066R　255G　204B　0#FFCC00R　204G　0B　51#CC0033　R　255G　204B　51#FFCC33R　51G　51B　153#333399R　255G　0B　51#FF0033　R　102G　102B　153#666699R　255G　255B　0#FFFF00R　255G　0B　51#FF0033　R　255G　0B　51#FF0033R　0G　102B　153#006699R　255G　255B　51#FFFF33　R　255G　204B　0#FFCC00R　0G　153B　153#009999R　204G　51B　102#CC3366R　255 G　0 B　51 #FF0033R　204G　204B　0#CCCC00R　0G　102B　153#006699　R　204G　204B　0#CCCC00R　255G　153B　51#FF9933R　102G　51B　153#663399　R　255G　153B　51#FF9933R　255G　255B　0#FFFF00R　51G　102B　153#336699　R　204G　51B　51#CC3333R　255G　204B　204#FFCCCCR　153G　204B　0#99CC00　R　0G　51B　153#003399R　255G　255B　0#FFFF00R　255G　102B　0#FF6600狂野的、充沛的、动感的R　153 G　0 B　102 #990066R　255G　255B　0#FFFF00R　0G　51B　153#003399　R　204G　0B　51#CC0033R　0G　0B　0#000000R　0G　51B　153#003399　R　0G　51B　153#003399R　255G　255B　0#FFFF00R　0G　0B　0#000000　R　204G　51B　51#CC3333R　204G　204B　204#CCCCCCR　204G　51B　102#CC3366　R　204G　0B　51#CC0033R　51G　51B　51#333333R　204G　204B　0#CCCC00R　0 G　0 B　0 #000000R　153G　204B　0#99CC00R　204G　0B　51#CC0033　R　204G　0B　51#FF0033R　51G　51B　51#333333R　255G　153B　0#FF9900　R　153G　0B　102#990066R　0G　0B　0#000000R　0G　153B　102#009966　R　102G　102B　102#666666R　255G　102B　0#FF6600R　51G　51B　51#333333　R　153G　51B　51#993333R　204G　204B　0#CCCC00R　102G　51B　102#663366华丽的、花哨的、⼥性化的R　255 G　255 B　153 #FFFF99R　153G　51B　153#993399R　255G　153B　204#FF99CC　R　255G　102B　102#FF6666R　255G　255B　255#FFFFFFR　51G　153B　153#339999　R　255G　153B　204#FF99CCR　0G　51B　204#003399R　204G　255B　0#CCFF00　R　102G　204B　153#66CC99R　255G　255B　255#FFFFFFR　204G　102B　153#CC6699　R　204G　51B　153#CC3399R　255G　204B　153#FFCC99R　255G　102B　102#FF6666R　255 G　204 B　204 #FFCCCCR　255G　255B　255#FFFFFFR　255G　102B　102#FF6666　R　204G　102B　153#CC6699R　204G　102B　153#CC6699R　102G　102B　153#666699　R　204G　51B　153#CC3399R　255G　204B　153#FFCC99R　255G　102B　102#FF6666　R　204G　102B　153#CC6699R　153G　204B　102#99CC66R　102G　51B　102#663366　R　255G　51B　204#FF33CCR　204G　204B　153#CCCC99R　102G　51B　102#663366回味的、⼥性化的、优雅的R　204 G　204 B　204 #CCCCCCR　204G　153B　204#CC99CCR　204G　51B　153#CC3399　R　255G　204B　204#FFCCCCR　255G　153B　204#FF99CCR　204G　204B　255#CCCCFF　R　204G　51B　153#CC3399R　153G　51B　204#9933CCR　204G　153B　204#CC99CC　R　153G　153B　204#9999CCR　255G　255B　204#FFFFCCR　255G　204B　204#FFCCCC　R　102G　51B　102#663366R　204G　204B　204#CCCCCCR　204G　153B　204#CC99CCR　255 G　153 B　153 #FF9999R　255G　204B　204#FFCCCCR　255G　153B　204#FF99CC　R　153G　102B　102#996666R　204G　153B　204#CC99CCR　255G　204B　204#FFCCCC　R　204G　153B　153#CC9999R　204G　204B　204#CCCCCCR　255G　204B　204#FFCCCC　R　255G　153B　153#FF9999R　153G　102B　153#996699R　255G　204B　204#FFCCCC　R　153G　102B　153#996699R　255G　204B　204#FFCCCCR　204G　153B　204#CC99CC⾼尚的、⾃然的、安稳的R　204 G　204 B　51 #CCCC33R　255G　255B　153#FFFF99R　204G　153B　51#CC9933　R　204G　153B　102#CC9966R　204G　204B　102#CCCC66R　102G　153B　153#666699　R　255G　153B　102#FF9966R　153G　102B　0#996600R　204G　204B　0#CCCC00　R　204G　204B　102#CCCC66R　102G　0B　51#660033R　204G　102B　0#CC6600　R　204G　204B　0#CCCC00R　102G　102B　0#666600R　204G　204B　255#CCCCFFR　204 G　153 B　51 #CC9933R　0G　153B　153#009999R　255G　204B　51#FFCC33　R　153G　153B　102#999966R　204G　204B　153#CCCC99R　51G　153B　153#339999　R　153G　204B　153#99CC99R　102G　153B　51#669933R　51G　102B　51#336633　R　102G　102B　51#666633R　153G　153B　51#999933R　204G　153B　102#CC9966　R　102G　0B　0#660000R　204G　153B　0#CC9900R　204G　204B　153#CCCC99冷静的、⾃然的R　255 G　255 B　153 #FFFF99R　153G　204B　153#99CC99R　102G　102B　0#666600　R　153G　102B　51#996633R　255G　255B　153#FFFF99R　153G　204B　102#99CC66　R　0G　102B　0#006600R　102G　204B　102#66CC66R　204G　255B　153#CCFF99　R　102G　102B　0#666600R　204G　204B　102#CCCC66R　204G　255B　204#CCFFCC　R　102G　153B　51#669933R　204G　204B　51#CCCC33R　102G　51B　0#663300R　102 G　102 B　51 #666633R　153G　153B　51#999933R　204G　153B　102#CC9966　R　0G　51B　0#003300R　102G　153B　51#669933R　204G　204B　153#CCCC99　R　0G　102B　51#006633R　102G　51B　0#663300R　204G　204B　102#CCCC66　R　102G　102B　0#666600R　255G　255B　204#FFFFCCR　153G　153B　153#999999　R　0G　102B　51#006633R　51G　51B　0#333300R　204G　204B　153#CCCC99传统的、⾼雅的、优雅的R　153 G　153 B　51 #999933R　255G　255B　204#FFFFCCR　204G　153B　204#CC99CC　R　204G　153B　102#CC9966R　102G　102B　102#666666R　204G　153B　153#CC9999　R　204G　204B　153#CCCC99R　51G　51B　51#333333R　153G　102B　204#9966CC　R　204G　204B　153#CCCC99R　102G　102B　102#666666R　204G　153B　153#CC9999　R　153G　102B　153#996699R　204G　204B　153#CCCC99R　102G　153B　153#669999R　204 G　153 B　102 #CC9966R　153G　153B　153#999999R　102G　102B　102#666666　R　51G　153B　102#339966R　204G　204B　204#CCCCCCR　153G　102B　153#996699　R　102G　51B　102#663366R　153G　153B　153#999999R　204G　204B　255#CCCCFF　R　153G　102B　153#996699R　153G　153B　204#9999CCR　204G　204B　255#CCCCFF　R　204G　204B　153#CCCC99R　153G　153B　153#999999R　102G　51B　0#663300传统的、稳重的、古典的R　102 G　153 B　204 #6699CC R　102G　51B　102#663366R　204G　204B　153#CCCC99　R　153G　0B　51#990033R　204G　255B　102#CCFF66R　255G　153B　0#FF9900　R　102G　102B　153#666699R　102G　0B　51#660033R　153G　204B　153#99CC99　R　102G　51B　0#663300R　255G　153B　51#FF9933R　255G　255B　102#FFFF66　R　153G　0B　51#990033R　0G　102B　51#006633R　204G　204B　0#CCCC00R　204 G　0 B　51 #CC0033R　153G　153B　51#999933R　102G　0B　153#660099　R　153G　51B　102#993366R　204G　204B　51#CCCC33R　102G　102B　51#666633　R　153G　102B　0#996600R　204G　204B　102#CCCC66R　102G　102B　0#666600　R　0G　153B　51#009933R　204G　153B　0#CC9900R　102G　102B　102#666666　R　102G　102B　51#666633R　204G　204B　51#CCCC33R　204G　51B　102#CC3366忠厚的、稳重的、有品位的R　255 G　255 B　204 #FFFFCCR　204G　153B　51#CC9933R　51G　102B　102#336666　R　51G　102B　102#336666R　153G　102B　51#996633R　204G　204B　51#CCCC33　R　51G　102B　51#336633R　153G　0B　51#990033R　255G　204B　153#FFCC99　R　51G　51B　102#333366R　102G　153B　153#669999R　102G　153B　0#669900　R　153G　51B　51#993333R　204G　153B　102#CC9966R　0G　51B　0#003300R　51 G　102 B　51 #336633R　204G　204B　153#CCCC99R　51G　51B　102#333366　R　102G　51B　0#663300R　153G　153B　51#999933R　51G　51B　51#333333　R　102G　51B　102#663366R　102G　102B　102#666666R　51G　51B　102#333366　R　153G　153B　0#999900R　153G　0B　51#990033R　204G　153B　204#CC99CC　R　51G　51B　102#333366R　153G　0B　51#990033R　204G　204B　204#CCCCCC简单的、洁净的、进步的R　204 G　204 B　204 #CCCCCCR　255G　255B　255#FFFFFFR　102G　102B　153#666699　R　204G　255B　102#CCFF66R　255G　255B　255#FFFFFFR　0G　51B　102#003366　R　153G　204B　255#99CCFFR　255G　255B　255#FFFFFFR　51G　51B　153#333399　R　204G　204B　51#CCCC33R　255G　255B　255#FFFFFFR　51G　102B　153#336699　R　0G　153B　255#0099FFR　255G　255B　204#FFFFCCR　102G　102B　153#666699R　153 G　204 B　51 #99CC33R　204G　204B　204#CCCCCCR　0G　0B　0#000000　R　204G　204B　204#CCCCCCR　0G　51B　102#003366R　153G　204B　255#99CCFF　R　0G　153B　204#0099CCR　204G　255B　102#CCFF66R　102G　102B　102#666666　R　51G　153B　204#3399CCR　0G　51B　102#003366R　204G　204B　204#CCCCCC　R　51G　102B　153#336699R　255G　255B　102#FFFF66R　102G　153B　255#6699FF简单的、时尚的、⾼雅的R　153 G　204 B　255 #99CCFFR　255G　255B　255#FFFFFFR　102G　102B　102#666666　R　51G　102B　102#336666R　255G　255B　255#FFFFFFR　153G　153B　153#999999　R　0G　153B　204#0099CCR　255G　255B　255#FFFFFFR　102G　102B　102#666666　R　153G　153B　153#999999R　204G　204B　204#CCCCCCR　51G　102B　102#336666　R　204G　204B　204#CCCCCCR　153G　153B　153#999999R　102G　51B　102#663366R　102 G　102 B　102 #666666R　204G　204B　204#CCCCCCR　102G　153B　204#6699CC　R　153G　153B　153#999999R　255G　255B　255#FFFFFFR　51G　51B　102#333366　R　102G　153B　153#669999R　204G　204B　204#CCCCCCR　102G　102B　102#666666　R　153G　153B　153#999999R　204G　204B　204#CCCCCCR　51G　51B　51#333333　R　51G　102B　153#336699R　0G　153B　204#0099CCR　102G　102B　102#666666简单的、进步的、时尚的R　51 G　51 B　102 #333366R　153G　204B　51#99CC33R　51G　102B　153#336699　R　153G　153B　153#999999R　0G　51B　102#003366R　102G　153B　153#669999　R　0G　51B　153#003399R　204G　255B　153#CCFF99R　51G　51B　51#333333　R　153G　153B　51#999933R　51G　102B　153#336699R　51G　51B　51#333333　R　102G　102B　102#666666R　153G　204B　51#99CC33R　0G　51B　102#003366R　153 G　153 B　153 #999999R　51G　102B　153#336699R　51G　51B　51#333333　R　51G　102B　0#336600R　204G　204B　102#CCCC66R　51G　51B　0#333300　R　102G　153B　204#6699CCR　00G　102B　153#006699R　0G　0B　0#000000　R　0G　51B　102#003366R　204G　204B　204#CCCCCCR　00G　102B　153#006699　R　0G　0B　0#000000R　153G　153B　153#999999R　0G　51B　102#003366各种颜⾊⼗六进制代码表【其⼀】红⾊和粉红⾊，以及它们的16进制代码。

2002 V216 N6 Part I J Sys and Ctrl Eng IMechE

467 A pole placement controller for non-linear dynamic plantsQ M Zhu*and L Z GuoFaculty of Computing,Engineering and Mathematical Sciences,University of the West of England,Bristol,UKAbstract:In this study a control-oriented model is proposed to represent a wide range of non-linear discrete-time dynamic plants.As a testimony to the e ciency of the model structure forcontrol system design,a pole placement controller is designed for non-linear discrete-time plants.Mathematically the solution of the controller output is converted into resolving a polynomial equationin the current control term u(t),which signi cantly reduces the di culties encountered in non-linearcontrol system synthesis and computational complexities.The integrated procedure provides astraightforward methodology to use in linear control system design techniques when designing non-linear control systems.For a demonstration of the e ectiveness of the proposed methodology usedto deal with practical problems,pole placement controllers are designed for three non-linear plants,including the Hammerstein model,a laboratory-scale liquid level system and a continuous stirredtank reactor.The simulation results are presented with graphical illustrations.Keywords:non-linear control systems,control oriented plant models,pole placement control1INTRODUCTION ler for a non-linear dynamic plant is based on a locallinearization model of the plant around an operatingpoint,and linear design methods are employed in order Pole placement is one of the most useful and popularto obtain the placement of poles of the linearized plant control techniques used to solve a variety of control[3–5].However,it is well known that this method su ers problems in many di erent engineering elds.from its local applicability,which might result in an Particularly for linear systems,synthesis of the poleunacceptable performance of the closed-loop system in placement controllers,where the closed-loop eigenvaluesthe presence of severe non-linearities.To overcome the are placed in some speci ed position in a complex planelimitations arising from the application of linear control in order to meet a set of performance speci cations,hastechniques and methods to non-linear control problems, been very popular due to its intuitive appeal andmany non-linear feedback control approaches have been straightforward algorithmic structure[1,2].However,proposed,including the exact input/output feedback lin-control problems arising in a wide variety of engineeringearization method[4,6,7]and the non-linear coordinate elds are characterized by essential non-linearities.Intransformation approach[8,9].In the case of non-linear the case of non-linear dynamic plants,the pole place-discrete-time systems,the feedback linearization prob-ment approach cannot generally be directly appliedlem with pole placement received a lot of attention as because the dynamic behaviour of non-linear plantswell[10,11].However,those approaches are either only cannot be easily determined according to the position ofapplicable to a limited class of non-linear plants,i.e. zeros and poles.It is obvious that applying pole place-feedback linearizable plants,or based on a set of very ment to non-linear plants synthesizes a control systemrestrictive conditions[4].in such a way that the non-linearities of the non-linearIt should be mentioned that the main di culty for plant should be removed,resulting in a closed-loopnon-linear control system design lies in the lack of a system that behaves linearly.To this end,many di erentgeneral modelling framework for non-linear plants, approaches have been proposed.A popular and tra-which allows the synthesis of control input for the plant ditional approach to designing a pole placement control-to be performed analytically and e ectively.Thereforethere is a need for some kind of non-linear dynamic The MS was recei v ed on16July2002and was accepted after re v isionfor publication on27September2002.model that is general enough to describe a wide range *Corresponding author:Faculty of Computing,Engineering and of non-linear plants and provides a concise basis for con-Mathematical Sciences,Uni v ersity of the West of England,FrenchayCampus,Coldharbour Lane,Bristol BS161QY,UK.troller design.Motivated by some previous theoretical468Q M ZHU AND L Z GUOresults [12,13],in this study a control-oriented model cedure is applicable for arbitrary known plant delay as well.Leontarities and Billings [15]have shown that such structure is proposed to represent a class of non-linear discrete-time plants.Accordingly,a pole placement con-a NARMAX model can represent a broad class of non-linear systems.Furthermore,the Hammerstein,Wiener,trol design procedure is presented to provide a straight-forward methodology to design non-linear control bilinear and several other well-known linear and non-linear model sets can be shown to be special classes systems by using linear control system design techniques.The proposed model can be explained as an expansion of the NARMAX model.With its generality,the di -culty occurs when controlling a plant based on the of the plant output according to its current control term u (t )and therefore the input /output behaviour of the NARMAX model is considered because of the lack of a manoeuvrable structure.Therefore various possibilities plant is described by a power series of u (t ).This is a quite general modelling framework because many non-for parameterizing f (·)exist,including the extended model set NARMAX models [16].In this paper a newly linear systems can be represented by this model.In particular,the sampled-data representation of any parameterized control-oriented model is proposed.The control-oriented model can be obtained by continuous-time feedback linearization system can be of such a format [14].With this modelling framework,expanding the non-linear function f (·)as a polynomial with respect to u (t 1)as follows:those controller design methodologies derived from linear plants can be conveniently extended to design non-linear discrete-time systems.Furthermore,since the y (t )=Mj =0a j (t )u j (t 1)(2)model structure exhibits a polynomial structure in the current control u (t ),there is only a need to solve a poly-where M is the degree of model input u (t 1),parameter a j(t )is a function of past inputs and outputs nomial equation to obtain a pole placement controller output.u (t 2),...,u (t n ),y (t 1),...,y (t n )and errors e (t ),...,e (t n ).By this arrangement,the control-The main contents of this paper are divided into three sections.In Section 2a control-oriented U-model is pro-oriented model can be treated as a pure power series of input u (t 1)with associated time-varying parameters posed to represent a wide range of non-linear plants.In Section 3a general pole placement controller is designed a j(t ).Such an example is shown below:with the U-model framework,and the corresponding y (t )=0.1y (t 1)y (t 2)0.5y (t 1)u 2(t 1)root solver,the Newton–Raphson algorithm,is intro-duced to obtain the controller output.In Section 4three +0.8u (t 1)u (t 2)(3)typical non-linear plants,i.e.the Hammerstein model,a which can be rewritten in the notation of equation (2)laboratory-scale liquid level system and a continuous asstirred tank reactor,are selected to demonstrate the pole placement controller design procedure and the corre-y (t )=a 0(t )+a 1(t )u (t 1)+a 2(t )u 2(t 1)(4)sponding simulation results are presented with graphical where a 0(t )=0.1y (t 1)y (t 2),a 1(t )=0.8u (t 2)andillustrations.a 2(t )=0.5y (t 1).Note that the parameter a j(t )is a function of past inputs and outputs u (t 2),...,u (t n ),y (t 1),...,y (t n )and errors e (t ),...,e (t n )and,in 2CONTROL-ORIENTED NON-LINEAR PLANT particular,e (t )is an unknown quantity,which hence is MODELSunpredictable.Although equation (1)is a more realistic representation for real non-linear plants,the following Consider single-input single-output (SISO)non-linear representation is mathematically simple and can be used dynamic plants with a NARMAX (non-linear auto-to represent a wide class of non-linear plants in practice regressive moving average with exogenous inputs)as well:representation of the form y (t )=Mj =0a j (t )u j (t 1)+e (t )(5)y (t )=f [y (t 1),...,y (t n ),u (t 1),...,u (t n ),e (t ),...,e (t n )](1)where a j(t )is a function of u (t 2),...,u (t n ),y (t 1),...,y (t n ),e (t 1),...,e (t n )[note that the where y (t )and u (t )are the output and input signals of same notations are used as in equation (2)but this the plant respectively at the discrete-time instant t ,n is should not cause any confusion].In this paper,a pole the plant order,f (·)is a non-linear function and the placement controller will be designed under the model modelling error term e (t )could be induced from structure of equation (5).measurement noise,disturbance,plant variation,uncer-There are several advantages of the proposed control-tain dynamics,modelling inaccuracy and imperfect or oriented model over many other parameterizing partial knowledge of plants.Note that here the plant approaches:delay has been assumed to be one for the sake of brevity.Without losing generality,the proposed control pro- 1.The control-oriented model has a more general appeal469A POLE PLACEMENT CONTROLLER FOR NON-LINEAR DYNAMIC PLANTSthan many other parameterizing approaches,such as where q is the forward operator and n,m and l are theorders of the polynomials R,T and S respectively.A the polynomial NARMAX model[17,18],theHammerstein model,etc.designed controller must satisfy the following causalitycondition:2.The sampled-data representation of many non-linearcontinuous-time systems can be of the form oforder(S)<order(R),order(T)order(R)(10) equation(2)[14].3.Since the control-oriented model exhibits a poly-i.e.l<n and m n.nomial structure in the current control u(t1),the The control law of equation(8)represents a negativenon-linear algebraic equations,which need to be feedback with the transfer function S/R and a feedfor-solved to obtain the output value of the pole place-ward with the transfer function T/R.It thus has2degrees ment controller,are polynomials in u(t1).This of freedom.A block diagram of the closed-loop control is a clear advantage of the proposed modelling system is shown in Fig.1.The output y(t)can be linked approach,since many other methods,in general,lead to the reference w(t)asto complex non-linear algebraic equations such astranscendental algebraic equations.y(s)=TR+Sw(t)=TA cw(t)(11)In order to apply linear control system design method-ologies to the non-linear model,a further transform is where polynomial Ac is the closed-loop characteristic presented as follows:equation speci ed by designers in advance,i.e.y(t)=U(t)(6)R+S=A c(12) whereTo cancel the possible output o set in the steady state,U(t)=W[u(t1)]+e(t)=Mj=0a j(t)u j(t1)+e(t)i.e.to make the steady state error equal to zero at thecontrolled output,polynomial T is speci ed with(7)T=A c(1)(13)The expression of equation(6)is de ned as a U-model.In other words,this is a pseudo-input-only polynomialThe key idea of the design is to specify the desired closed-non-linear model.loop characteristic polynomial A c and then to resolvethe polynomials R and S through a Diophantine equa-tion.An algorithm solving the Diophantine equation is 3DESIGN OF THE POLE PLACEMENTpresented in the Appendix.The signal U(t)can be CONTROLLERobtained by equation(8)as long as polynomials R,Sand T are determined.A standard reference[19]is used to develop the follow-With U(t)as a root solver,the Newton–Raphson ing formulations for designing a pole placement control-algorithm[20]can be used to nd the controller output ler.Considering the U-model of equation(6),a generalu(t1).The recursive computation can be described by controller can be described byRU(t)=Tw(t)Sy(t)(8)u k+1(t1)=u k(t1)W[U k (t1)]U(t)d W[u(t1)]d u(t1) where w(t)is the reference for the output target and R,S and T are the polynomials of the forward shift oper-ator q,which are described by=u k(t1)åM j=0a j(t)u j k(t1)U(t)d[åM j=0a j(t)u j(t1)]/d u(t1)u j(t1)=u jk(t1)(14)R=q n+r1q n1+···+r nT=t0q m+t1q m1+···+t m S=s0q l+s1q l1+···+s lwhere the subscript k is the iteration index,such that the(k+1)th iteration is obtained from the k th iteration,k0.(9)Fig.1A general closed-loop non-linear control system470Q M ZHU AND L Z GUORemarksy (t )=T R +S w (t )+RR +S ¢(t )1.Actually,there will be a future unknown term e (t )contained in U (t )that is unpredictable.This value is =T A c w (t )+RA c¢(t )(19)set to zero,its conditional mean during the period of recursive computation.Furthermore,other terms wheree (t 1),...,e (t n )are unknown,but may be esti-mated at each sampling instant.From equation (5),¢(t )=Mj =0[a j (t )a ˆj (t )]u ¯j (t 1)+e (t )an estimate may be found at each sampling instant for those terms as follows:which can be regarded as an additional disturbance signal.Obviously,this additional signal does not e ˆ(t )=Mj =0a ˆj (t )u j (t 1)y (t )(15)change the location of the poles of the closed-loop system.The rst term in ¢(t )is caused by the esti-where a ˆj (t )is the estimate of a j (t ),which is calculated mation,which can diminish when a ˆj(t )converges to using eˆ(t 1),...,e ˆ(t n ).Therefore,substituting its true value a j(t ).To suppress the e ect of theequation (15)into equation (14)yields a new iterative second term of ¢(t ),polynomials R and A cmay beformula for computing the controller output:chosen to form a lter according to the spectral characteristics of e (t )if its statistics are available u k +1(t 1)=u k(t 1)earlier.3.There are two problems that may occur when using åM j =0a ˆj(t )u j (t 1)U (t )d[åj =0a ˆj (t )u j (t 1)]d u (t 1)Ku j (t 1)=u j k (t 1)the root solver of equation (16).The rst one is(16)d[åM j =0a ˆj(t )u j (t 1)]d u (t 1)#02.If the root solver (16)converges to a real root in each sampling interval and is performing satisfactorily,in the neighbourhood of a solution.This is a critical then the output of the closed-loop system should be point because in practice it cannot be guaranteed that close to the desired value,but with some discrepancy the derivative of the function will not approximately due to the modelling error terms.Considering theequate to zero after any particular recursion due to estimated terms a ˆj(t )and neglected term e (t )in the plant variation,computation error and even an root solver (16),the actual closed-loop dynamics unsuitable initial value.The second one is the pos-could be derived as follows.sibility that no real root of the polynomial exists,thus Assume that u¯(t 1)is a root of equation (16),causing a breakdown of the algorithm.To deal with which obviously satis es equation (8).Substituting the problems,Zhu et al.[12]proposed an improved u ¯(t 1)into equation (7)and then equation (6)gives computation for the traditional Newton–Raphson algorithm.y (t )=Mj =0a j (t )u ¯j (t 1)+e (t )4.If the system output is linear with respect to the cur-rent control u (t 1)then the proposed controller has the following simpli ed form from equation (16):=M j =0a ˆj (t )u ¯j (t 1)u (t 1)=U (t )a ˆ0(t )a ˆ1(t )(20)+Mj =0[a j (t )a ˆj (t )]u ¯j (t 1)+e (t )(17)which can be viewed as a kind of feedback lineariz-Multiplying both sides of equation (17)by R and ation control.More particularly,consider an SISO considering equation (8)yield linear discrete-time plant as follows:A (q )y (t )=B (q )u (t 1)+e (t )(21)Ry (t )=R Mj =0a ˆj (t )u ¯j (t 1)with+R Mj =0[a j (t )a ˆj (t )]u ¯j (t 1)+Re (t )A (q )=1+a 1q 1+···+a nq nB (q )=b 0+b 1q 1+···+b n 1q n +1=Tw (t )Sy (t )(22)+R Mj =0[a j (t )a ˆj(t )]u ¯j (t 1)+Re (t )An equivalent U-model for such a linear plant (21)(18)can be obtained readily as y (t )=U (t )=a 0(t )+a 1(t )u (t 1)+e (t )(23)Then the actual closed-loop dynamics is471A POLE PLACEMENT CONTROLLER FOR NON-LINEAR DYNAMIC PLANTS wherefollows:a 0(t )=[A 1(q )y (t )+B 1(q )u (t 1)]and a 1(t )=b 0withy (t )=BTRBA +B (S +RA 1)w (t )+RBRBA +B (S +RA 1)e (t )=BT B (S +R )w (t )+RB B (S +R )e (t )=T S +R w (t )+RS +Re (t )u (t 1)=ATRBA +B (S +RA 1)w (t )+S +RA1RBA +B (S +RA 1)e (t )=AT B (S +R )w (t )+S +R RA B (S +R )e (t )A 1(q )=(a 1q 1+···+a nq n )B 1(q )=b 1q 1+···+b n 1q n +1(24)Based on the linear model (21),a standard pole assignment design Ru (t 1)=Tw (t )Sy (t )(25)(29)leads to the following characteristics of the closed-loop system:From equation (29),if polynomial B is stable,i.e.equa-tion (21)is a minimum-phase system,the stability of thecontroller can be guaranteed.y (t )=BT RA +BS w (t )+RRA +BSe (t )u (t 1)=AT RA +BS w (t )+SRA +BSe (t )4CASE STUDIESA Hammerstein model,a laboratory-scale liquid level (26)system and a continuous stirred tank reactor are selected to test the design methodology.The same closed-loop On the other hand,obviously as long as b 00,aspeci cations are assigned for these models to demon-solution always exists for the U-model based pole strate that the proposed method is generally suitable for placement design.From equations (8)and (20)andcontrolling di erent dynamics.considering that a ˆj (t )is equal to its true value a j(t ),The closed-loop characteristic equation is speci ed by j =0,1,the solution yields A c=q 2 1.3205q +0.4966(30)Rb 0u (t 1)=RU (t )R [A 1y (t )+B 1u (t 1)]Therefore the closed-loop poles are 1and 0.61.This =Tw (t )Sy (t )RA 1y (t )design speci cation corresponds to a natural frequency of 1rad /s and a damping ratio of 0.7.To achieve zero RB 1u (t 1)(27)steady state error,specifyand then T =A c(1)=1 1.3205+0.4966=0.1761(31)For the polynomials R and S ,specify RBu (t 1)=Tw (t )(S +RA 1)y (t )(28)R =q 2+r 1q +r2S =s 0q +s1Comparing the controllers of equations (25)and (28),it can be seen that for linear plants the proposed (32)U-model based pole placement design is an extension Substituting the speci cations of equations (30)and (32)of the conventional one in the sense that a set of into the Diophantine equation of (12),the coe cients special controller parameters is used in equation (28).in polynomials R and S can be expressed by Generally the standard pole placement controller of equation (25)requires the polynomials A and B to r 2+s 1=0.4966r 1+s 0= 1.3205be relatively prime,but the U-model based controller of equation (28)does not.Similar to equation (26)(33)the closed-loop characteristics for plant (21)under the U-model based controller can be derived asTo guarantee the computation convergence of the472Q M ZHU AND L Z GUOsequence U (t ),i.e.to keep the di erence equation with 4.2Control of a laboratory-scale liquid level system stable dynamics,let r 1=0.9and r 2=0.009.ThisIn this simulation example,the developed control assignment corresponds to the characteristic equation of approach is applied to the height control of a laboratory-U (t )as (q 0.89)(q 0.01)=0.Then the coe cients in scale liquid level system [17].The system described by polynomial S can be determined from the Diophantine Sales and Billings [17]consists of a d.c.water pump feed-equation of (33)as ing a conical ask which in turn feeds a square tank.The control input is the voltage to the pump motor and the s 0=0.4205s 1=0.4876system output is the height of the water in the conical ask.Following Sales and Billings [17],the plant model was (34)constructed to be Substituting the coe cients of the polynomials R and S y (t )=0.9722y (t 1)+0.3578u (t 1)0.1295u (t 2)into the controller of equation (8)gives rise to 0.3103y (t 1)u (t 1)0.04228y 2(t 2)U (t +1)=0.9U (t )0.009U (t 1)+0.1761w (t 1)+0.1663y (t 2)u (t 2)+0.4205y (t )0.4876y (t 1)(35)+0.2573y (t 2)e (t 1)Therefore the controller output u (t )can be determined 0.03259y 2(t 1)y (t 2)by solving the root in terms of equation (16).0.3513y 2(t 1)u (t 2)+0.3084y (t 1)y (t 2)u (t 2)4.1Control of the Hammerstein model +0.2939y 2(t 2)e (t 1)+0.1087y (t 2)u (t 1)u (t 2)Consider the following Hammerstein model:+0.4770y (t 2)u (t 1)e (t 1)y (t )=0.5y (t 1)+x (t 1)+0.1x (t 2)x (t )=1+u (t )u 2(t )+0.2u 3(t )+0.6389u 2(t 2)e (t 1)+e (t )(41)(36)The noise sequence e (t )was Gaussian and given as N (0.0,0.05).The corresponding control-oriented model The corresponding control-oriented model is obtained is obtained from equation (6)as follows:from formulation (6):y (t )=a 0(t )+a 1(t )u (t 1)+e (t )(42)y (t )=a 0(t )+a 1(t )u (t 1)+a 2(t )u 2(t 1)which is linear with respect to u (t 1)and +a 3(t )u 3(t 1)(37)a 0(t )=0.9722y (t 1)0.04288y 2(t 2)where+0.1663y (t 2)u (t 2)a 0(t )=0.5y (t 1)+1+0.3x (t 2),a 1(t )1a 2(t )=1,a 3(t )=0.2+0.2573y (t 2)e (t 1)0.03259y 2(t 1)y (t 2)(38)0.3513y 2(t 1)u (t 2)The controller output u (t )is determined by solving +0.3084y (t 1)y (t 2)u (t 2)a 3(t +1)u 3(t )u 2(t )+u (t )+a 0(t +1)U (t +1)+0.2939y 2(t 2)e (t 1)0.1295u (t 2)=0(39)+0.6389u 2(t 2)e (t 1)(43)The derivative of U (t +1)against u (t )is required in the andNewton–Raphson root solving algorithm,which is given bya 1(t )=0.35780.3103y (t 1)+0.1087y (t 2)u (t 2)d[U (t +1)]d u (t )=3a 3(t +1)u 2(t )2u (t )+1(40)+0.4770y (t 2)e (t 1)(44)Figure 2gives the system response under the proposedBecause the output of the plant is linear with respect to pole placement control.It can be seen from the simu-the control u (t 1),the controller output can be simply lation result that the resultant closed-loop system obtained from behaves similarly to that of a linear system,which is due to cancellation of the non-linearity by the proposed u (t )=U (t +1)a ˆ0(t +1)a ˆ1(t +1)(45)control-oriented model and controller design approach.A POLE PLACEMENT CONTROLLER FOR NON-LINEAR DYNAMIC PLANTS473Fig.2System response of the Hammerstein modelIn this simulation,a periodic triangular wave was selec- 4.3Control of a continuous stirred tank reactor(CSTR) ted to be the reference signal,to be followed by theThe dynamics of a perfectly mixed,continuous stirred system output.The simulation results are shown intank reactor may be written in dimensionless variables Figs3and4,where Fig.3gives the system response andas follows[14]:Fig.4the controller output.The simulation results showthat the proposed control strategy provides a stable y b=(1+2a)y+au uy ay2(46) system performance even in the presence of randomnoise.It should be mentioned that,because the output where y is the dimensionless representation of the con-of the system is linear with respect to the current controlcentration of some species in the reactor,which is the input,the proposed method is equivalent to the feedback measured output of the plant,and u is the dimensionless linearization control approach.However,compared torepresentation of the owrate,which is the control input the feedback linearization approach,the approach pro-of the plant.posed in this paper is applicable to more general dynamicIf a zero holder is considered between the control-systems,as shown in the other two simulation examples.ler and the plant,an approximate sampled dataFig.3System output of the liquid level control474Q M ZHU AND L Z GUOFig.4Controller output of the liquid level control systemrepresentation of equation (46)resulting from a third-the reference signal to be tracked by the system output.The simulation results are shown in Fig.5.For the pur-order truncation of the Taylor expansion can be expressed aspose of comparison,two linear models were also con-sidered based on the controllers developed and tested.y (t +1)=y (t )+T s {3y (t )y 2(t )+[1y (t )]u (t )}The rst linear model was obtained using Euler’s discret-ization method for the plant (46),which resulted in the +T 2s 2{9y (t )+9y 2(t )+2y 3(t )following sampled data representation:+[3+4y (t )+3y 2(t )]u (t )y (t +1)=0.85y (t )0.05y 2(t )+[0.050.05y (t )]u (t )(49)+[1+y (t )]u 2(t )}Using the feedback linearization controller design based +T 3s 6{27y (t )63y 2(t )36y 3(t )6y 4(t )upon equation (49)to control the plant model (48)resulted in the estimation blowing up around 100+[92y (t )18y 2(t )12y 3(t )]u (t )samples during the period of simulation.The reason is +[4y (t )7y 2(t )]u 2(t )the denominator,0.050.05y (t ),of the controller became close to zero,which means that model (49)+[1y (t )]u 3(t )}(47)cannot match the dynamics of the plant well enough.If it is assumed that the sampling period of T s=0.05The second linear model of the stirred tank reactor was was set,then this model becomes identi ed using the least squares algorithm with a sinus-oidal exciting signal.The linear model obtained is as y (t +1)=0.8606y (t )0.0401y 2(t )+0.0017y 3(t )follows:0.000125y 4(t )y (t +1)=0.1673y (t )0.1673y (t 1)+[0.04640.045y (t )+0.0034y 2(t )+0.9997y (t 2)0.0476u (t )0.00025y 3(t )]u (t )0.066u (t 1)0.03u (t 2)(50)+[0.0012+0.0013y (t )0.0001458y 2(t )]u 2(t )Based on equation (50),a linear controller was designed and applied to control the stirred tank reactor model +[0.000020830.00002083y (t )]u 3(t )(48)(48).The system response under this linear control is shown in Fig.6.It can be observed that the linear con-As discussed in the paper by Kazantzis and Kravaris [14],a third-order truncation is accurate enough to rep-troller results in the loss of control of the overall system.Therefore the proposed methods are superior to the resent the original plant dynamics.Again,in this simu-lation the periodic triangular wave was selected to beother two linear model based approaches.A POLE PLACEMENT CONTROLLER FOR NON-LINEAR DYNAMIC PLANTS475Fig.5System response of the stirred tank reactorFig.6System response of the stirred tank reactor under linear control5CONCLUSIONS controller is investigated,but it is strongly believed thatthe principles are straightforward for other linear con-trollers.Further studies on the developed methodology, A general control-oriented U-model and the correspond-such as stability,robustness,expansion to other format ing pole placement controller design formulations havecontrollers,and so on,will be conducted to provide been derived to enhance non-linear control systema comprehensive prospectus in designing non-linear design.The U-model transforms non-linear dynamiccontrol systems by using linear control system design models into a class of pseudo-input-only non-linear poly-techniques.nomials with time-varying parameters.With modulariz-ation,the procedure of non-linear control system designcan be conducted as a linear control system design,ACKNOWLEDGEMENTwhere the only di erence is in obtaining a root as thecontroller output from a polynomial equation.Also,the U-model structure signi cantly simpli es linear con-The authors are grateful for the support from GrantGR/M84305of the Engineering and Physical Sciences troller design procedures and the routine to resolve theDiophantine equation.Here only the pole placement Research Council(EPSRC),UK.。

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1.送信发送2.電子メールで电子邮件页面3.リンクを電子メールで电子邮件链接4.ショートカットをデスクトップへ桌面快捷方式5.このページの検索查找（在当前页）6.ツールバー工具栏7.ステータスバー状态栏8.エクスプローラーバー浏览器栏9.移動转到10.中止停止11.最新の情報に更新刷新12.文字のサ゗ズ文字大小13.エンコード编码14.ソース源文件15.プラ゗バシーレポート隐私报告16.全画面表示全屏显示17.標準のボタン标准按钮18.ゕドレスバー地址栏19.リンク链接20.ツールバーを固定する锁定工具栏21.オンラ゗ン作業联机工作22.検索搜索23.お気に入り收藏夹24.メデゖゕ媒体25.履歴历史记录26.フォルダ文件夹27.ヒント提示28.コメント讨论29.前に戻る后退30.次へ進む前进31.ホームページ主页32.最大最大33.最小最小34.自動選択自动选择35.お気に入りに追加添加到收藏夹36.お気に入りの整理整理收藏夹37.メールとニュース邮件和新闻38.同期同步39.関連したリンクの表示显示相关站点40.゗ンターネットオプションInternet选项41.メールを読む阅读邮件42.メッセージの作成新建邮件43.リンクの送信发送链接44.ページの送信发送网页45.ニュースを読む阅读新闻46.目次とキーワード目录和关键字scapeユーザーNetscape用户48.オンラ゗ンサポート联机支持49.フゖードバック送信发送反馈意见50.全般常规51.セキュリテゖ安全52.プラ゗バシー隐私53.コンテンツ内容54.接続连接55.プログラム程序56.ゕドレス地址57.現在のページを使用使用当前页58.標準設定使用默认页59.空白を使用使用空白页60.゗ンターネット一時フゔ゗ルInternet临时文件61.Cooksの削除删除Cooks62.フゔ゗ルの削除删除文件63.ページ履歴を保存する日数网页保存在历史记录中的天数64.履歴のクリゕ清除历史记录65.色颜色66.フォント字体67.言語语言68.信頼済みサ゗ト受信任的站点69.制限付きサ゗ト受限制的站点70.レベルのカスタマ゗ズ自定义级别71.既定のレベル默认级别72.゗ンポート导入73.Webサ゗ト网站74.コンテンツゕドバ゗ザ分级审查75.有効にする启用76.証明書证书77.ＳＳＬの状態のクリゕ清除SSL状态78.発行元发行商79.個人情報个人信息80.オートコンプリート自动完成81.ダ゗ヤルゕップ拨号连接82.仮想プラ゗ベートネットワーク虚拟专用网络83.追加添加84.ダ゗ヤルしない从不进行拨号连接85.現在の既定値当前默认连接86.既定に設定设置默认值Nの設定局域网设置88.゗ンターネットプログラムInternet程序89.HTMLエデゖタHTML编辑器90.ニュースグループ新闻组91.゗ンターネット電話Internet呼叫92.カレンダー日历93.連絡先一覧联系人列表94.Web設定のリセット恢复Web设置95.フゔ゗ル文件96.編集编辑97.表示视图98.挿入插入99.書式格式100.ツール工具101.罫線表格102.ウ゗ンドウ窗口103.ヘルプ帮助104.新規作成新建105.開く打开106.閉じる关闭107.上書き保存保存108.名前を付けて保存另保存109.Ｗｅｂページとして保存另存为Web页110.検索搜索111.版の管理版本112.プラウザでプレビューWeb页预览113.ページの設定页面设定114.印刷プレビュー打印预览115.印刷打印116.プロパテゖ属性117.メールの宛先邮件收件人118.メールの宛先（検閲用）邮件收件人（审阅）119.メールの宛先（添付フゔ゗ル）邮件收件人（以附件形式）120.回覧传送收件人121.ExchangeフォルダExchange文件夹122.オンラ゗ン会議の参加者联机会议参加人123.Faxの宛先传真收件人124.元に戻せません无法撒消125.繰り返しできません无法重复126.切り取り剪切127.コピー复制128.クリップボード剪贴板129.貼り付け粘贴130.形式を選択して貼り付け选择性粘贴131.ハ゗パーリンク超连接132.クリゕ消除133.書式格式134.すべて選択全选135.検索查找136.置換替换137.ジャンプ定位138.日本語入力辞書への単語登録更新输入法词典139.リンクの設定链接140.オブジェクト对象141.下書き普通142.Webレ゗ゕウトWeb版本143.印刷レ゗ゕウト页面144.作業ウゖンドウ任务窗格145.ルーラー标尺146.段落記号显示段落标记147.グリッド線网络线148.見出しマップ文档结构图149.ヘッダー页眉150.フッター页脚151.脚注脚注152.変更履歴标记153.全画面表示全屏显示154.ズーム显示比例155.標準常用156.書式設定格式157.WebツールWeb工具箱158.あいさつ文问候语159.ゕウトラ゗ン大纲160.コントロールボックス控件工具箱161.チェック／コメント审阅162.データベース数字库163.フゔンクションキーの表示功能键表示164.フォーム窗体165.フレーム框架集166.ワードゕート艺术字167.拡張書式設定其他格式168.罫線表格和边框169.図图片170.図形描画绘图171.定型句自动图文集172.文字カウント字数统计173.ユーザー設定自定义174.記号と特殊文字符号175.コメント批注176.番号数字177.参照引用178.WebコンポーネントWeb组件179.テキストボックス文本框180.ブックマーク书签181.ハ゗パーリンク超链接182.相互参照交叉引用183.索引と目次索引和目录184.クリップゕート剪贴画185.テキストから来自文件186.スキャナまたはカメラから来自扫描仪或照相机187.組織図组织结构图188.新しい描画とオブジェクト绘制新图形189.グラフ图表190.横書き横排191.縦書き竖排192.フォント字体193.箇条書きと段落記号项目符号和编号194.段組み分栏195.タブとリーダー制表位196.ギャップ首字下沉197.変換更改大小写198.均等割り付け调整宽度199.オートフォーマット自动套用格式200.スタ゗ルと書式样式和格式201.書式の詳細設定显示格式202.ルビ拼音指南203.囲い文字带圈字符204.縦中横纵横混排205.組み文字合并字符206.その他の色其它颜色207.塗りつぶし効果填充效果208.透かし水印209.破損したテキストの修復修复损坏文本210.要約の作成自动编写摘要211.音声语音212.文字の保護保护文档213.オンラ゗ングループの作業联机协作214.はがきの差し込み印刷信函和邮件215.Web上のツール网上工具216.テンプレートとゕド゗ン模板和加载项217.オートコレクションのオプション自动更正选项218.会議の開始现在开会219.会議のスケジュール安排会议220.WebデゖスカッションWeb讨论221.マクロ宏222.新しいマクロの記録录制新宏223.セキュリテゖ安全性224.罫線を引く绘制表格225.セル单元格226.削除删除227.選択选择228.セルの結合合并单元格229.セルの分割拆分单元格230.表の分割拆分表格231.表のオートフォーマット表格自动套用格式232.自動調整自动调整233.タ゗トル行の繰り返し标题行重复234.変換转换235.並び替え排序236.計算式公式237.表のグルッド線を表示しない隐藏虚框238.表のプロパテゖ表格属性239.文字列の幅に合わせる根据内容调整表格240.ウ゗ンドウサ゗ズに合わせる根据窗口调整表格241.列の幅を固定する固定列宽242.行の高さを揃える平均分布各行243.列の幅を揃える平均分布各列244.文字列を表にする文本转换成表格245.表の解除表格转换成文本246.新しいウ゗ンドウを開く新建窗口247.並べて表示拆分248.ゕシスタントを表示する显示帮助249.翻訳翻译250.類義語辞典同义词库251.ハ゗フネーション段字252.作業状態の保存保存工作区253.印刷の範囲打印区域254.印刷の範囲の設定设置打印区域255.印刷の範囲のクリゕ取消打印区域256.シートの削除删除工作表257.シートの移動またはコピー移动或复制工作表258.関数函数259.名前名称260.コメント批注261.定義定义262.条件つき書式条件格式263.幅列宽264.高さ行高265.自動調整最合适的行高266.表示しない隐藏267.再表示取消隐藏268.標準の幅标准列宽269.名前の変更重命名270.シートの見出しの色工作表标检颜色271.エラーチェック错误检查272.ブックの共有共享工作簿273.変更履歴の記録修订274.ブック工作簿275.ゴールシーク单变量求解276.シナリオ方案277.ワークシートの分析公式审核278.ゕド゗ン加载宏279.変更箇所の表示突出显示修订280.変更箇所の確認接受或拒绝修订281.シートの保護保护工作表282.範囲の編集と許可允许用户编辑区域283.ブックの保護と共有化保护并共享工作簿284.参照元のトレース追踪引用单元格285.参照先のトレース追踪从属单元格286.エラーのトレース追踪错误287.すべてのトレース矢印を削除取消所有追踪箭头288.[ウォッチ]ウ゗ンドウの表示显示监视窗口289.ワークシートの分析モード公式审核模式290.[ワークシートの分析]ツールバーの表示显示“公式审核”工具栏291.データ数据292.並び替え排序293.フゖルタ筛选294.フォーム记录单295.集計分类汇总296.統合合并计算297.ピボットテーブルとピボットグラフレポート数据透视表和数字透视表298.外部データの取り込み导入外部数据299.データの更新更新数据300.オートフゖルタ自动筛选301.すべて表示全部显示302.フゖルタオプションの設定高级筛选303.詳細を表示しない隐藏明细数据304.詳細データの表示显示明细数据305.グループ化组合306.グループ解除取消组合307.ゕウトラ゗ンの自動作成自动建立分级显示308.ゕウトラ゗ンのクリゕ清除分级显示309.データの取り込み导入数据310.新しいウェブクエリ新建Web查询311.新しいデータベースクエリ新建数据库查询312.クエリの編集编辑查询313.データ範囲のプロパテゖ数据区域属性314.パラメータ参数315.ウ゗ンドウの固定冻结窗格316.分割位置の移動移动拆分317.プレゼンテーションパック打包318.複製复制319.スラ゗ドの削除删除幻灯片320.検索查找321.置換替换322.プロパテゖへ移動定位至属性323.リンクの設定链接324.オブジェクト对象325.スラ゗ド一覧幻灯片浏览326.スラ゗ドショー幻灯片放映327.ルーラー标尺328.マスタ母版329.スラ゗ドマスタ幻灯片母版330.ノートマスタ备注母版331.新しいスラ゗ド新幻灯片332.スラ゗ドの複製幻灯片副本333.スラ゗ド番号幻灯片编号334.フゔ゗ルからスラ゗ド幻灯片（从文件）335.ゕウトラ゗ンからスラ゗ド幻灯片（从大纲）336.ビデオとサウンド影片和声音337.ギャラリーからビデオ剪辑管理器中的影片338.ギャラリーからサウンド剪辑管理器中的声音339.フゔ゗ルからサウンド文件中的声音340.ＣＤオーデゖオトラックの再生播放CD乐曲341.サウンドの録音录制声音342.配置对齐方式343.左揃え左对齐344.中央揃え居中345.右揃え右对齐346.両端揃え两端对齐347.均等割り付け分散对齐348.フォントの配置字体对齐方式349.上揃え顶端对齐350.英字下揃え罗马方式对齐351.下揃え底端对齐352.行間行距353.改行分行354.フォントの置換更改大小写355.実行观看放映356.ナレーションの録音录制旁白357.オンラ゗ンブロードキャスト联机广播358.スラ゗ドショーの設定设置放映方式359.動作設定ボタン动作按钮360.オブジェクトの動作設定动作设定361.ゕニメーションの設定自定义动画362.画面切り換え幻灯片切换363.非表示スラ゗ドに設定隐藏幻灯片364.重ねて表示层叠365.ゕプリケーションの自動修復检测并修复366.゗ンポート导入367.テーブルのリンク链接表368.データベースプロパテゖ数字库属性369.データベースオブジェクト数字库对象370.テーブル表371.クエリ查询372.フォーム窗体373.レポート报表374.ページ页375.マクロ宏376.モジュール模块377.大きいゕ゗コン大图标378.小さいゕ゗コン小图标379.一覧列表380.詳細详细信息381.名前順按名称382.種類順按类型383.作成順按创建日期384.更新順按修改时间385.ゕ゗コンの自動整列自动排列386.等間隔に整列对齐图表387.コード代码388.クラス类模块389.オートフォーム自动窗体390.オートレポート自动报表391.リレーションシップ关系392.解析分析393.パフォーマンスの最適化性能394.データベースの変換转换数据库395.リンクテーブルマネージャ链接表管理器396.ゕップサ゗ジングウゖザード升迁向导397.MDEフゔ゗ルの作成生成MDE文件398.データベースのパスワードの設定设置数字库密码399.ユーザー/グループの権限用户与组权限400.ユーザー/グループゕカウント用户与组帐户401.セキュリテゖウゖザード设置安全机制向导402.暗号化/解読加密/解密数字库403.同期立即同步404.レプリカの作成创建副本405.部分レプリカウゖザード部分副本向导406.デザ゗ンマスタの修復恢复设计母版407.競合の解決解决冲突408.ゕド゗ン加载项409.ゕド゗ンマネージャ加载项管理器410.デザ゗ン设计411.メデゖゕラ゗ブラリに追加添加到媒体库中412.再生リストをメデゖゕラ゗ブラリに読み込む将播放列表导入到媒体库中413.再生リストをフゔ゗ルに書き出す将播放列表导出到文件414.現在再生中のトラックを追加添加当前播放的曲目415.トラブルシューテゖング疑难解答416.ＵＲＬを追加添加URL417.オーデゖオＣＤからコピー从音频CD复制418.オーデゖオＣＤにコピー复制到音频CD419.ポータブルデバ゗スにコピー复制到便携设备420.フルモード完整模式421.スキンモード外观模式422.フルモードオプション完全模式选项423.プレ゗ビューツール正在播放工具424.タスクバー任务栏425.フゔ゗ルマーカー文件标记426.統計情報统计信息427.拡大/縮小缩放428.メニューバーを表示显示菜单栏429.メニューバーを隠す隐藏菜单栏430.メニューバーを自動的に隠す自动隐藏菜单栏431.タスクバーを隠す隐藏任务栏432.再生リストの表示显示播放列表433.視覚エフェクトの表示显示可视化效果434.゗コラ゗ザおよび設定の表示显示均衡器及设置435.グラフゖック゗コラ゗ザ图形均衡器436.ビデオ設定视频设置437.メデゖゕ情報媒体信息438.キャプション字幕439.歌詞歌词440.サ゗ズ変更バーの表示显示调整大小栏441.プレ゗ビュー正在播放442.メデゖゕガ゗ド媒体指南443.メデゖゕラ゗ブラリ媒体库444.ラジオチューナー收音机调谐器445.スキンセクタ外观选择器446.ウ゗ンドウの大きさに合わせる适应窗口447.再生播放448.再生/一時停止播放/暂停449.停止停止450.前のトラックへ上一个451.次のトラックへ下一个452.巻き戻し倒带453.早送り快进454.シャッフル无序播放455.連続再生重复456.音量音量457.取り出し弹出458.上げる增大459.下げる减少460.ミュート静音461.視覚エフェクトのダウンロード下载可观化效果462.メデゖゕフゔ゗ルの検索搜索媒体文件463.ラ゗センス管理许可证管理464.タ゗トルの表示显示标题465.すべてのプログラム所有程序466.スタート开始467.ゕクセサリ附件468.エンターテ゗メント娱乐469.ボリュームコントロール音量控制470.システムツール系统工具471.システムの復元系统还原472.システムの情報系统信息473.タスク任务计划474.デゖスククリーンゕップ磁盘清理475.デゖスクデフラグ磁盘碎片整理程序476.フゔ゗ルの設定の転送ウゖザード文件和设置转移向导477.文字コード表字符映射表478.スクリーンキーボード屏幕键盘479.ユーザー補助の設定ウゖザード辅助功能向导480.拡大鏡放大镜481.通信通讯482.ネットワークセットゕップウゖザード网络安装向导483.ネットワーク接続网络连接484.ハ゗パーターミナル超级终端485.リモートデスクトップ接続远程桌面连接486.新しい接続ウゖザード新建连接向导487.Windows XPツゕー漫游Windows XP 488.ゕドレス帳通讯簿489.エクスプローラ资源管理器490.コマンドプロンプト命令提示符491.プログラム変換性ウゖザード程序兼容性向导492.ペ゗ント画图493.メモ帳记事本494.電卓计算器495.ゲーム游戏496.スタートゕップ启动497.ごみ箱回收站498.マ゗コンピュータ我的电脑499.システムのタスク系统任务500.システム情報を表示する查看系统信息501.プログラムの追加と削除添加/删除程序502.設定を変更する更改一个设置503.マ゗ネットワーク网上邻居504.マ゗ドキュメント我的文档505.共有ドキュメント共享文档506.コントロールパネル控制面板507.システムフォルダ系统文件夹508.゗ンターネットオプションInternet选项509.キーボード键盘510.ゲームコントローラ游戏控制器511.サウンドとオーデゖオデバ゗ス声音和音频设备512.システム系统513.スキャナとカメラ扫描仪和照相机514.タスクバーと[スタート]メニュー任务栏和[开始]菜单515.ネットワーク接続网络连接516.ハードウェゕの追加添加硬件517.フォルダオプション文件夹选项518.フォント字体519.プリンタとFAX 打印机和传真520.プログラムの追加と削除添加或删除程序521.マウス鼠标522.ユーザーゕカウント用户帐户523.ユーザー補助のオプション辅助功能选项524.音声認識语音525.管理ツール管理工具526.地域と言語オプション区域和语言选项527.電源オプション电源选项528.電話とモデムのオプション电话和调制解调器选项529.日付と時刻日期和时间530.システム系统531.コンピュータ名计算机名532.ハードウェゕ硬件533.デバ゗スマネージャ设备管理器534.バスホストコントローラ总线主控制器535.DVD/CD-ROMドラ゗ブDVD/CD-ROM驱动器Bコントローラ通用串行总线控制器537.サウンド、ビデオおよびコントローラ声音、视频和游戏控制器538.システムデバ゗ス系统设备539.デゖスクドラ゗ブ硬盘驱动器540.ネットワークゕダプタ网络适配器541.バッテリ电池542.プロセッサ处理器543.モデム调制解调器544.記憶領域リューム存储卷545.ショートカット快捷方式546.ゕ゗コンの整列排列图表547.ショートカットの貼り付け粘贴快捷方式548.ブリーフケース公文包549.゗メージ图像550.テキストドキュメント文本文档551.テーマ主题552.デスクトップ桌面553.スクリーンセーバー屏幕保护程序554.デザ゗ン外观555.ゕクテゖブウゖンドウ活动窗口556.デスクトップのカスタマ゗ズ自定义桌面557.参照浏览558.プレビュー预览559.メッセージボックス消息框560.ウゖンドウとボタン窗口和按钮561.画面の解析度屏幕分辨率562.ピクセル像素563.画面の色颜色质量564.ログオフ注销565.終了关闭计算机566.スタンバ゗待机567.電源を切る关闭568.再起動重新启动569.フゔ゗ルを追加添加文件。

goldendict帮助手册要点

Goldendict是一款功能强大的跨评台词典及翻译软件，无论是在学习、工作还是生活中，它都能为用户提供便利。

在本文中，我将会对Goldendict的使用技巧、功能特点和个人见解进行全面的探讨，以便读者能深入了解这款软件，并从中受益。

一、Goldendict的基本介绍Goldendict是一款基于开源项目的跨评台词典软件，支持多种主流操作系统，如Windows、Linux、macOS和Android等。

用户可以通过Goldendict轻松地查找词汇释义、进行翻译或学习语言，它的功能强大且使用简便，是众多词典软件中的佼佼者。

二、Goldendict的主要功能特点1. 多语言支持：Goldendict支持多种语言的辞典及翻译资源，并且能够进行多语言互译，满足用户在语言学习及翻译方面的各种需求。

2. 离线词典：用户可以下载并使用各种离线词典资源，无需依赖网络，使用更加便捷。

3. 自定义设置：Goldendict允许用户自定义词典资源及外观设置，个性化定制，满足个人需求。

4. 词典管理：用户可以通过Goldendict管理自己所需的词典资源，实现快速查找及切换。

三、关于Goldendict的使用技巧1. 安装与配置：在使用Goldendict之前，用户需要下载并安装软件，并配置好所需的词典资源。

在配置过程中，用户可以根据自己的需求进行个性化设置，以便更好地使用该软件。

2. 查词及翻译：在Goldendict中，用户可以通过输入关键词或语句来查找对应的释义或翻译，软件会自动匹配相应的词典资源，并呈现给用户。

3. 自定义设置：Goldendict允许用户根据需要自定义外观风格、添加或删除词典资源等操作，以实现个性化定制。

4. 划词翻译：在使用Goldendict时，用户可以通过划词操作来快速查找对应的释义或翻译，这种操作方式非常便捷且高效。

四、对Goldendict的个人见解作为一款功能丰富且使用便捷的词典软件，Goldendict在语言学习、翻译及工作中具有重要的应用价值。

The Mott metal-insulator transition in the 1D Hubbard model in an external magnetic field

The Mott metal-insulator transition in the 1D Hubbard model in an external magnetic ﬁeld
Holger Frahm1 and Temo Vekua2
1
Institut f¨ ur Theoretische Physik, Leibniz Universit¨ at Hannover, Appelstraße 2, 30167 Hannover, Germany

INTRODUCTION
Exact solutions play an invaluable role in our understanding of the behavior of electron systems in one dimension, especially for eﬀective ﬁeld theory approaches in regimes when strong coupling develops. Here eﬀective theories have to be assisted with a non-perturbative, unbiased analysis. Strong coupling regimes can develop when the initial interactions between electrons are strong, but also in certain situations when the bare couplings are arbitrarily weak. One well known example of the latter case is provided by the so called commensurateincommensurate phase transition [1, 2], in which a single bosonic mode is involved. By comparing with a free fermions picture the universal physics at long wavelengths across the transition was established [1]. A physical system realizing such transition is e.g. the repulsive Hubbard model at half ﬁlling, where Mott metal-insulator transition takes place upon variation of the chemical potential in the absence of an external magnetic ﬁeld. In this case the charge mode undergoes a commensurate-incommensurate phase transition, while the spin sector is decoupled. In the absence of special symmetries such as time reversal symmetry, however, there is no reason for the decoupling of spin and charge modes. This is well known for the Hubbard model away of half ﬁlling in ﬁnite magnetic ﬁeld [3]. At half-ﬁlling, on the other hand, spin and charge modes are strictly decoupled even in an external magnetic ﬁeld and the low energy sector is equivalent to the Heisenberg antiferromagnet. Here one might be led to think that the admixture between spin and charge modes will die out gradually approaching the half ﬁlling. If this expection would be correct, the Mott metal-insulator transition in the presence of an external magnetic ﬁeld would look pretty similar to that at zero ﬁeld: all relevant changes aﬀect only the charge sector, while the spin sector remains practically undisturbed. Thus the phase transition would fall in the the single mode commensurate-incommensurate universality class even in the presence of magnetic ﬁeld. In the following we will show that the above expectation is misleading. Any small coupling between the spin and charge modes increases under the renormalization and qualitatively inﬂuences the critical properties of the system.

网页色彩名称与色值

下表由w3c提供，色彩名称可以等同色值使用，并可以被所有主要浏览器识别。

注：尽管如此，若要页面色彩通过html或css标准认证，w3c仅提供16个可用的色彩名称：aqua, black, blue, fuchsia, gray, green, lime, maroon, navy, olive, purple, red, silver, teal, white, yellow. 其它的颜色则必须给出rgb或hex值。

点击一个颜色名（或数值）作为背景色，可以查看其它颜色作为文本正文的效果：Color HEX ColorColor Name ArrayAliceBlue#F0F8FFAntiqueWhite#FAEBD7Aqua#00FFFFAquamarine#7FFFD4Azure#F0FFFFBeige#F5F5DCBisque#FFE4C4Black#000000BlanchedAlmond#FFEBCDBlue#0000FFBlueViolet#8A2BE2Brown#A52A2ABurlyWood#DEB887CadetBlue#5F9EA0Chartreuse#7FFF00Chocolate#D2691ECoral#FF7F50CornflowerBlue#6495EDCornsilk#FFF8DCCrimson#DC143CCyan#00FFFFDarkBlue#00008BDarkCyan#008B8BDarkGoldenRod#B8860BDarkGray#A9A9A9DarkGrey#A9A9A9DarkGreen#006400DarkKhaki#BDB76BDarkMagenta#8B008BDarkOliveGreen#556B2FDarkorange#FF8C00DarkOrchid#9932CCDarkRed#8B0000DarkSalmon#E9967ADarkSeaGreen#8FBC8FDarkSlateBlue#483D8BDarkSlateGray#2F4F4FDarkSlateGrey#2F4F4FDarkTurquoise#00CED1DeepPink#FF1493DeepSkyBlue#00BFFFDimGray#696969DimGrey#696969DodgerBlue#1E90FFFireBrick#B22222FloralWhite#FFFAF0ForestGreen#228B22Fuchsia#FF00FFGainsboro#DCDCDCGhostWhite#F8F8FFGold#FFD700GoldenRod#DAA520Gray#808080Grey#808080Green#008000GreenYellow#ADFF2FHoneyDew#F0FFF0HotPink#FF69B4IndianRed#CD5C5CIndigo#4B0082Ivory#FFFFF0Khaki#F0E68CLavender#E6E6FALavenderBlush#FFF0F5LawnGreen#7CFC00LemonChiffon#FFFACDLightBlue#ADD8E6LightCoral#F08080LightCyan#E0FFFFLightGoldenRodYellow#FAFAD2LightGray#D3D3D3LightGrey#D3D3D3LightGreen#90EE90LightPink#FFB6C1LightSalmon#FFA07ALightSeaGreen#20B2AALightSkyBlue#87CEFALightSlateGray#778899LightSlateGrey#778899LightSteelBlue#B0C4DELightYellow#FFFFE0Lime#00FF00LimeGreen#32CD32Linen#FAF0E6Magenta#FF00FFMediumAquaMarine#66CDAAMediumBlue#0000CDMediumOrchid#BA55D3MediumPurple#9370D8MediumSeaGreen#3CB371MediumSlateBlue#7B68EEMediumSpringGreen#00FA9AMediumTurquoise#48D1CCMediumVioletRed#C71585MidnightBlue#191970MintCream#F5FFFAMistyRose#FFE4E1Moccasin#FFE4B5NavajoWhite#FFDEADNavy#000080OldLace#FDF5E6Olive#808000OliveDrab#6B8E23Orange#FFA500OrangeRed#FF4500Orchid#DA70D6PaleGoldenRod#EEE8AAPaleGreen#98FB98PaleTurquoise#AFEEEEPaleVioletRed#D87093PapayaWhip#FFEFD5PeachPuff#FFDAB9Peru#CD853FPink#FFC0CBPlum#DDA0DDPowderBlue#B0E0E6Purple#800080Red#FF0000RosyBrown#BC8F8FRoyalBlue#4169E1SaddleBrown#8B4513Salmon#FA8072SandyBrown#F4A460SeaGreen#2E8B57SeaShell#FFF5EESienna#A0522DSilver#C0C0C0SkyBlue#87CEEBSlateBlue#6A5ACDSlateGray#708090SlateGrey#708090Snow#FFFAFASpringGreen#00FF7FSteelBlue#4682B4Tan#D2B48CTeal#008080Thistle#D8BFD8Tomato#FF6347Turquoise#40E0D0Violet#EE82EEWheat#F5DEB3White#FFFFFFWhiteSmoke#F5F5F5Yellow#FFFF00YellowGreen#9ACD32另外一个有价值的色表来自蓝色理想经典论坛ColorKey配色软件参考色板，在此引用的是其中的色调列表，色标由背景色名称与数值两种表示，另一个引用理由也许就是其中的中文色彩名称了吧。

【精品】web颜色对照表

【关键字】精品《WEB颜色对照表》■■Web■■【颜色值】#000000【中文】黑色【英文】black■■Web■■【颜色值】#000080【中文】海军色【英文】navy■■颜色■■【颜色值】#00008B【中文】暗蓝色【英文】darkblue■■颜色■■【颜色值】#0000CD【中文】间兰色【英文】mediumblue■■颜色■■【颜色值】#0000FF【中文】蓝色【英文】blue■■Web■■【颜色值】#006400【中文】暗绿色【英文】darkgreen■■Web■■【颜色值】#008000【中文】绿色【英文】green■■颜色■■【颜色值】#008080【中文】水鸭色【英文】teal■■颜色■■【颜色值】#008B8B【中文】暗青色【英文】darkcyan■■颜色■■【颜色值】#00BFFF【中文】深天蓝色【英文】deepskyblue■■Web■■【颜色值】#00CED1【中文】暗宝石绿【英文】darkturquoise■■Web■■【颜色值】#00FA【中文】间春绿色【英文】mediumspringgreen ■■颜色■■【颜色值】#00FF00【中文】酸橙色【英文】lime■■颜色■■【颜色值】#00FF【中文】春绿色【英文】springgreen■■颜色■■【颜色值】#00FFFF【中文】青色【英文】cyan■■Web■■【颜色值】#191970【中文】中灰兰色【英文】midnightblue■■Web■■【颜色值】#1E90FF【中文】闪兰色【英文】dodgerblue■■颜色■■【颜色值】#20B2AA【中文】亮海蓝色【英文】lightseagreen■■颜色■■【颜色值】#228B22【中文】森林绿【英文】forestgreen■■颜色■■【颜色值】#2E8B57【中文】海绿色【英文】seagreen■■Web■■【颜色值】#【中文】墨绿色【英文】darkslategray■■Web■■【颜色值】#32CD32【中文】橙绿色【英文】limegreen■■颜色■■【颜色值】#3CB371【中文】间海蓝【英文】mediumseagreen■■颜色■■【颜色值】#40E0D0【中文】青绿色【英文】turquoise■■颜色■■【颜色值】#4169E1【中文】皇家蓝【英文】royalblue■■Web■■【颜色值】#4682B4【中文】钢兰色【英文】steelblue■■Web■■【颜色值】#483D8B【中文】暗灰蓝色【英文】darkslateblue■■颜色■■【颜色值】#48D1CC【中文】间绿宝石【英文】mediumturquoise ■■颜色■■【颜色值】#4B0082【中文】靛青色【英文】indigo■■颜色■■【颜色值】#556B【中文】暗橄榄绿【英文】darkolivegreen■■Web■■【颜色值】#9EA0【中文】军兰色【英文】cadetblue■■Web■■【颜色值】#6495ED【中文】菊兰色【英文】cornflowerblue■■颜色■■【颜色值】#66CDAA【中文】间绿色【英文】mediumaquamarine ■■颜色■■【颜色值】#696969【中文】暗灰色【英文】dimgray■■颜色■■【颜色值】#5ACD【中文】石蓝色【英文】slateblue■■Web■■【颜色值】#6B8E23【中文】深绿褐色【英文】olivedrab■■Web■■【颜色值】#708090【中文】灰石色【英文】slategray■■颜色■■【颜色值】#778899【中文】亮蓝灰【英文】lightslategray■■颜色■■【颜色值】#7B68EE【中文】间暗蓝色【英文】mediumslateblue 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字典的用法

[分享] 常见字典用法集锦及代码详解[复制链接]前言凡是上过学校的人都使用过字典，从新华字典、成语词典，到英汉字典以及各种各样数不胜数的专业字典，字典是上学必备的、经常查阅的工具书。

有了它们，我们可以很方便的通过查找某个关键字，进而查到这个关键字的种种解释，非常快捷实用。

凡是上过EH论坛的想学习VBA里面字典用法的，几乎都看过研究过northwolves狼版主、oobird版主的有关字典的精华贴和经典代码。

我也是从这里接触到和学习到字典的，在此，对他们表示深深的谢意，同时也对很多把字典用得出神入化的高手们致敬，从他们那里我们也学到了很多，也得到了提高。

字典对象只有4个属性和6个方法，相对其它的对象要简洁得多，而且容易理解使用方便，功能强大，运行速度非常快，效率极高。

深受大家的喜爱。

本文希望通过对一些字典应用的典型实例的代码的详细解释来给初次接触字典和想要进一步了解字典用法的朋友提供一点备查的参考资料，希望大家能喜欢。

给代码注释估计是大家都怕做的，因为往往是出力不讨好的，稍不留神或者自己确实理解得不对，还会贻误他人。

所以下面的这些注释如果有不对或者不妥当的地方，请大家跟帖时指正批评，及时改正。

字典的简介字典（Dictionary）对象是微软Windows脚本语言中的一个很有用的对象。

附带提一下，有名的正则表达式（RegExp）对象和能方便处理驱动器、文件夹和文件的（FileSystemObject ）对象也是微软Windows脚本语言中的一份子。

字典对象相当于一种联合数组，它是由具有唯一性的关键字（Key）和它的项（Item）联合组成。

就好像一本字典书一样，是由很多生字和对它们对应的注解所组成。

比如字典的“典”字的解释是这样的：“典”字就是具有唯一性的关键字，后面的解释就是它的项，和“典”字联合组成一对数据。

常用关键字英汉对照：Dictionary 字典Key 关键字Item 项，或者译为条目字典对象的方法有6个：Add方法、Keys方法、Items方法、Exists方法、Remove方法、RemoveAll方法。

calibri 的16 进制 -回复

calibri 的16 进制-回复【calibri 的16 进制】在计算机领域中，字体是一种非常重要的元素。

在文字处理软件、网页设计和图像处理中，选择合适的字体可以极大地影响内容的可读性和视觉效果。

其中，Calibri 是一款备受欢迎的字体之一，它在2004年由卡尔·思恩（Lucas de Groot）设计并发布。

这款字体在微软Office软件中广泛使用，并因其简洁而优雅的外观而受到许多人的钟爱。

Calibri 字体是一种众所周知的无衬线字体，也被称为grotesque sans serif（古北风格无衬线）字体。

它具有现代感和流线型的特点，每个字母都被设计成清晰可辨，并且在各种大小和分辨率的显示屏上都能保持良好的可读性。

而该字体的16进制颜色码则表示了它的字体颜色。

首先，我们需要了解颜色在计算机中是如何以16进制表示的。

16进制由0-9和字母A-F组成，它是在RGB色彩空间中对颜色进行编码的一种方式。

在这种编码方式中，每个颜色通道都用2位16进制数字表示，一共有三个颜色通道。

例如，如果我们想要表示红色的最大亮度，我们可以使用#FF0000 ，其中FF表示红色通道的最大值。

以Calibri 字体的16进制颜色码为主题，我们可以深入探讨这种字体的设计和可视化特点。

字体的颜色对于整个设计方案的完成度和视觉吸引力起着至关重要的作用。

Calibri 字体的16进制颜色码是#000000 ，这表示了字体的黑色。

黑色是一种经典和常用的字体颜色，它与白色或其他浅色背景形成鲜明的对比。

使用黑色字体可以使文本内容更加突出，便于阅读，并提供了一种专业和现代的感觉。

在设计中，黑色字体通常与其他亮色或鲜明的配色方案结合使用，以创造出视觉冲击力和吸引力。

例如，在网页设计中，黑色字体可以与醒目的彩色背景相结合，以突出文字内容并吸引用户的注意力。

此外，黑色字体也可以与白色背景搭配使用，使页面看起来更加干净整洁，保持视觉平衡。

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