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Robust method to retrieve the constitutive effective parameters of metamaterials

Robust method to retrieve the constitutive effective parameters of metamaterials Xudong Chen,Tomasz M.Grzegorczyk,Bae-Ian Wu,Joe Pacheco,Jr.,and Jin Au Kong Research Laboratory of Electronics,Massachusetts Institute of Technology,Cambridge,Massachusetts02139,USA(Received25February2004;published26July2004)We propose an improved method to retrieve the effective constitutive parameters(permittivity and perme-ability)of a slab of metamaterial from the measurement of S parameters.Improvements over existing methods include the determination of theﬁrst boundary and the thickness of the effective slab,the selection of the correct sign of effective impedance,and a mathematical method to choose the correct branch of the real part of the refractive index.The sensitivity of the effective constitutive parameters to the accuracy of the S parameters is also discussed.The method has been applied to various metamaterials and the successful retrieval results prove its effectiveness and robustness.DOI:10.1103/PhysRevE.70.016608PACS number(s):41.20.Jb,42.25.Bs,78.20.CiI.INTRODUCTIONLeft-handed(LH)structures have been realized so far asmetamaterials[1–3]and very quickly,researchers have beenworking on retrieving their effective permittivity and perme-ability to better characterize them[4–6].Known methods todate[7,8]use S parameters calculated from a wave incidentnormally on a slab of metamaterial,from which the effectiverefractive index n and impedance z areﬁrst obtained.Thepermittivity⑀and permeability␮are then directly calculated from␮=nz and⑀=n/z.It is also known that this retrieval process may fail insome instances,such as when the thickness of the effectiveslab(exhibiting bulk properties)is not accurately estimated [4]or when reﬂection͑S11͒and transmission͑S21͒data are very small in magnitude[6].Although these issues have beenaddressed to some extent in previous works,we have foundthat the retrieved results in some cases are still unsatisfac-tory.In particular,the determination of theﬁrst boundary ofthe effective homogeneous slab,the selection of the sign ofthe roots when solving for the impedance z,the determina-tion of the branch of the real part of refractive index n,andthe origin of the spikes appearing in the retrieved impedancez,are many problems that deserve further investigation.Theaforementioned issues are addressed in the next sections ofthis paper and some typical retrieval results are presented toshow the robustness and effectiveness of the method.Notethat the values of⑀,␮,and z are relative to those in free space,thus dimensionless.II.RETRIEV AL METHODA.Theoretical retrieval equationsIn order to retrieve the effective permittivity and perme-ability of a slab of metamaterial,we need to characterize it as an effective homogeneous slab.In this case,we can retrieve the permittivity and permeability from the reﬂection͑S11͒and transmission͑S21͒data.For a plane wave incident nor-mally on a homogeneous slab of thickness d with the origin coinciding with theﬁrst face of the slab,S11is equal to the reﬂection coefﬁcient,and S21is related to the transmission coefﬁcient T by S21=Te ik0d,where k0denotes the wave num-ber of the incident wave in free space.The S parameters are related to refractive index n and impedance z by[7,9,10]:S11=R01͑1−e i2nk0d͒1−R012e i2nk0d,͑1a͒S21=͑1−R012͒e ink0d1−R012e i2nk0d,͑1b͒where R01=z−1րz+1.As it has been pointed out in[4,5],the refractive index n and the impedance z are obtained by inverting Eqs.(1a)and (1b),yieldingz=±ͱ͑1+S11͒2−S212͑1−S11͒2−S212,͑2a͒e ink0d=X±iͱ1−X2,͑2b͒where X=1ր2S21͑1−S112+S212͒.Since the metamaterial un-der consideration is a passive medium,the signs in Eqs.(2a) and(2b)are determined by the requirementzЈജ0,͑3a͒nЉജ0,͑3b͒where͑·͒Јand͑·͒Љdenote the real part and imaginary part operators,respectively.The value of refractive index n can be determined from Eq.(2b)asn=1k0d͕͓͓ln͑e ink0d͔͒Љ+2m␲͔−i͓ln͑e ink0d͔͒Ј͖,͑4͒where m is an integer related to the branch index of nЈ.As mentioned above,the imaginary part of n is uniquely deter-mined,but the real part is complicated by the branches of the logarithm function.Equations(2a)and(2b)can be directly applied in the case of a homogeneous slab for which the boundaries of the slab are well deﬁned and the S parameters are accurately known. However,since a metamaterial itself is not homogeneous,the two apparently straightforward issues mentioned above need to be carefully addressed.First,the location of the twoPHYSICAL REVIEW E70,016608(2004)boundaries of the effective slab need to be determined,whichwe do here by ensuring a constant impedance for various slab thicknesses.Second,the S parameters obtained from numerical computation or measurements are noisy which can cause the retrieval method to fail,especially at those frequen-cies where z and n are sensitive to small variations of S 11and S 21.These two problems are examined in detail in the fol-lowing sections.B.Determination of the ﬁrst boundary and the thicknessof the effective slabA homogeneous slab of material can be characterized bythe fact that its impedance does not depend on its thickness.Our understanding of the physical meaning of the ﬁrst effec-tive boundary is a plane beyond which the reﬂected wave behaves like a plane wave for a plane wave incidence.When a plane wave is incident on a metamaterial,currents will be induced on the metals creating a scattered ﬁeld.The ﬁeld produced by the induced currents is not uniform:It is stron-gest around the metal and decay at a certain distance.The ﬁrst effective boundary is located where the reﬂected wave behaves like a plane wave,and it has to be determined.We use z 1and z 2to represent the impedances of two slabs ofmetamaterial of different thicknesses.The reﬂection S 11de-pends on the position of the ﬁrst boundary and the transmis-sion S 21depends on the thickness of the slab.In addition,since the impedance z is also a function of S 11and S 21,z depends on the ﬁrst boundary and the thickness of the slab as well.Taking into account the above-mentioned properties,we propose a method whereby the ﬁrst boundary and the thickness of the sample are determined by optimization so that z 1matches z 2at all frequencies.Figure 1illustrates the conﬁguration of the problem for a metamaterial made of two cells in the propagation direction (x direction ).The geometry of the metamaterial has been taken from [11,12],in which the dimensions have been slightly modiﬁed for ease of dis-cretization in ﬁnite-difference time-domain (FDTD )simula-tions.With the split-ring resonator (SRR )and rod in the cen-ter of the unit cell,the periodicity along the propagation direction is d 0.The ﬁrst boundary of the effective homoge-neous medium is located at x 1below ͑x 1ജ0͒or above ͑x 1Ͻ0͒the ﬁrst unit-cell boundary,and the thickness of the effective medium is 2d 0+x 2−x 1.The optimization model is set up to minimize the mismatch of impedances of different numbers of cells of metamaterial:min f ͑x ¯͒=1N f ͚i =1Nf͉z 1͑f i ,x ¯͒−z 2͑f i ,x ¯͉͒max ͕͉z 1͑f i ,x ¯͉͒,͉z 2͑f i ,x ¯͉͖͒,s.t.:−0.5d 0ഛx 1,x 2ഛ0.5d 0,x ¯=͑x 1,x 2͒,͑5͒where N f is the total number of sample frequencies and z j ͑f i ͒represents the impedance of slab j ͑j =1,2͒at frequency f i .In the ideal case,z 1matches z 2for all frequencies with the objective function value equal to zero.We use the differential evolution algorithm [13]to optimize the objective function,and the optimized solution is x ¯opt =͑3.8565ϫ10−4d 0,1.0479ϫ10−4d 0͒.The corresponding values of impedance are shown in Fig.2.It can be seen that the retrieved impedances for one,two,and three cells of SRR-rod metamaterial match well for most frequencies,while matching was not as satis-factory when the method in Ref.[4]was used (which corre-sponds to x 1=0.5d 0in our formulation ).We also calculated the impedance z for the case of x ¯=͑0,0͒and found that the results are almost the same as the optimized ones.We have corroborated this result with many other metamaterial thick-nesses and geometries to eventually conclude empirically that the ﬁrst effective boundary of a symmetric one-dimensional (1D )metamaterial [1,4,14]coincides with the ﬁrst unit-cell boundary and the second effective boundary coincides with the last unit-cell boundary.Fortwo-FIG.1.Illustration of the effective boundaries of a two-cellmetamaterial.The SRRs and rods are periodic along yˆand z ˆdirec-tions with periodicity a y =4mm,a z =3mm.The unit-cell thickness ͑d 0͒in the direction of wave incidence is 4mm.We choose the ﬁrst and the last unit-cell boundary as the reference plane for the param-eters x 1and x 2,respectively.The value of x 1and x 2are positive (negative )if the dashed lines are below (above )their reference planes.The thickness of the effective homogeneous medium is 2d 0+x 2−x 1͑mm ͒.FIG.2.Optimized impedance z for one,two,and three cells of SRR-rod metamaterial of Fig.1in the direction of propagation.CHEN et al.PHYSICAL REVIEW E 70,016608(2004)dimensional (2D )[11,14]and asymmetric 1D metamaterials,no such rule could be found and the effective boundaries of the slab need to be determined from optimization.C.Determination of n and z from S 11and S 21It is a common method to determine z and n from Eqs.(2a )and (2b )with the requirement of Eqs.(3a )and (3b ),where z and n are determined independently.However this method may fail in practice when z Јand n Љare close to zero:A little perturbation of S 11and S 21,easily produced in experi-mental measurements or numerical simulations,may change the sign of z Јand n Љ,making it unreliable to apply the re-quirement of Eqs.(3a )and (3b ),as discussed in Ref.[6].In fact,z and n are related and we should use their relationship to determine the signs in Eqs.(2a )and (2b ).In order to determine the correct sign of z ,we distinguish two cases.The ﬁrst is for ͉z Ј͉ജ␦z ,where ␦z is a positive number,for which we apply Eq.(3a ).In the second case,for ͉z Ј͉Ͻ␦z ,the sign of z is determined so that the corresponding refractive index n has a non-negative imaginary part,or equivalently ͉e ink 0d ͉ഛ1,where n is derived from Eqs.(1a )and (1b ):e ink 0d =S 211−S 11z −1z +1.͑6͒Note that once we obtain the value of z ,the value of e ink 0d is obtained from Eq.(6),so that we avoid the sign ambiguity in Eq.(2b )[it can be proven that only one sign of the imagi-nary part in Eq.(2b )makes it equivalent to Eq.(6)].Figure 3shows the retrieved impedance using the method presented in this paper and using only the condition of Eq.(3a ).It is noted that the discontinuities obtained when only applying the criterion z Јജ0are removed.D.Determination of the branch of n ЈWe have presented in the previous sections a method of solving for z and n Љ,but n Јremains ambiguous because ofthe branches of logarithm function as seen in Eq.(4).In order to address this problem,it has been suggested to use a slab of small thickness and applying the requirement that ⑀͑f ͒and ␮͑f ͒are continuous functions of frequency [4,5].However,no further details on the continuity argument were provided.In our method,we determine the proper branch by using the mathematical continuity of the parameters,with special attention to possible discontinuities due to reso-nances.The method is an iterative one:Assuming we have obtained the value of the refractive index n ͑f 0͒at frequency f 0,we obtain n ͑f 1͒at the next frequency sample f 1by ex-panding the function e in ͑f 1͒k 0͑f 1͒d in a Taylor series:e i n ͑f 1͒k 0͑f 1͒d Ϸe i n ͑f 0͒k 0͑f 0͒d ͩ1+⌬+12⌬2ͪ,͑7͒where ⌬=i n ͑f 1͒k 0͑f 1͒d −i n ͑f 0͒k 0͑f 0͒d and k 0͑f 0͒denotes the wave number in free space at frequency f 0.In Eq.(7),the branch index [m in Eq.(4)]of the real part of n ͑f 1͒is the only unknown.Since the left-hand side of Eq.(7)is obtained from Eq.(6),Eq.(7)is a binomial function of the unknown n ͑f 1͒.Out of the two roots,one of them is an approximation of the true solution.Since we have obtained n Љ͑f 1͒,we choose the correct root among the two by com-paring their imaginary parts with n Љ͑f 1͒.The root whose imaginary part is closest to n Љ͑f 1͒is the correct one,and we denote it as n 0.Since n 0is a good approximation of n ͑f 1͒,we choose the integer m in Eq.(4)so that n Ј͑f 1͒is as close to n 0Јas possible.The branch of n Јat the initial frequency is determined as follows:From ␮=nz and ⑀=n /z ,we have␮Љ=n Јz Љ+n Љz Ј,͑8a ͒⑀Љ=1͉z ͉2͑−n Јz Љ+n Љz Ј͒.͑8b ͒The requirements ␮Љജ0and ⑀Љജ0leadtoparison of the retrieved imped-ance z (real and imaginary parts )for one cell of metamaterial shown in Fig.1by the method pre-sented in this paper and a traditional method us-ing only the requirement z Јജ0.ROBUST METHOD TO RETRIEVE THE CONSTITUTIVE …PHYSICAL REVIEW E 70,016608(2004)͉n Јz Љ͉ഛn Љz Ј.͑9͒In particular,when n Љz Јis close to zero but z Љis not,n Јshould be close to zero.At the initial frequency,we solve for the branch integer m satisfying Eq.(9).If there is only one solution,it is the correct branch.In case of multiple solu-tions,for each of the candidate branch index m ,we deter-mine the value of n Јat all subsequent frequencies using the above-mentioned iterative method.Because the requirement of Eq.(9)applies to n Јat all frequencies,we use it to check the validity of n Јat all frequencies produced by the candi-date initial branch.Note in the special case when n Љz Јis close to zero but z Љis not,the checking process can easily be carried out.Therefore,the initial branch that satisﬁes Eq.(9)at both the initial frequency and the subsequent frequencies is the correct one.For the SRR-rod structure,we found that there is a fre-quency region at which there is no branch index m satisfying Eq.(9).We call this frequency region the resonance band.The properties of the resonance band are still disputed by researchers.Some papers [15–17]mention the existence of multiple modes in this region since the real part of n is large,yielding a wavelength comparable to or smaller than the unit size of the metamaterial thereby rendering the retrieval of the effective parameters of the metamaterials impossible.Other papers [5,18]state that retrieval is possible and the retrieved permittivity ⑀has a negative imaginary part in the resonance band.In this paper,we do not address this issue and for this reason the retrieved results presented here are interrupted in frequency by the resonance region (see,for example,Fig.4).In this case,since n ͑f ͒is not continuous through all frequen-cies,we have to determine the initial branches for two fre-quency regions:Below and above the resonance band.Note that below the resonant band,the retrieved branch index is zero,which conﬁrms the validity of the traditional method used for low-frequency retrieval.The retrieved refractive in-dexes n for one,two,and three cells in the propagation di-rection are shown in Fig.4,where the resonance band is seen to extend between 11GHz and 12GHz.We observe that thevalues of n for different cell numbers are identical above the resonant region.Below the resonant band,however,the re-trieved n for one and two cells match well,but the result for three cells differs signiﬁcantly from the previous two.This discrepancy is due to the small magnitude of S 21in this fre-quency band,as we shall discuss in the next section.E.Sensitivity analysisA close examination of the retrieved z and n for one,two,and three cells of metamaterial presented so far shows that the three results do not always match.There are two cases of discrepancies.The ﬁrst is that the retrieved refractive index n for three cells of metamaterial does not match the value for one and two cells at low frequencies (5GHz–11GHz in Fig.4).The second is that the impedance z appears to spike at some frequencies (around 12GHz,17GHz,and 19.5GHz in Fig.2).We shall show here that these discrepancies are due to the sensitivity of z and n to the accuracy of S 11and S 21.The ﬁrst case appears when ͉S 21͉is close to zero.In the region below the resonance band,the transmission is usually small,especially for thicker metamaterials.From Eq.(2b ),we see that S 21appears in the denominator,so that the values of n are very sensitive to small perturbations of S 21.Yet,a small transmission has little inﬂuence on the retrieval of z ,which can be seen by computing:ץz 2ץS 21=8S 21S 11͓͑1−S 11͒2−S 212͔2,͑10͒from which it is clear that a small ͉S 21͉makes ץz 2րץS 21small (approximately zero ).In addition,we can see from Eq.(1b )that if n Љis not small,S 21will decrease exponentially with d ,i.e.,with an increasing number of cells in the propa-gation direction.Therefore,the smaller S 21,the higher the computation and measurement relative errors,which leads to less accurate retrieval results.The second case appears when S 212is close to unity while S 11is close to zero.Similar to the ﬁrst case,the denominator in the expression of z [see Eq.(2a )]approaches zero,thus making it difﬁcult to retrieve z .However,in this case,the value of n is stable.In this situation,instead of solving fornFIG.4.Retrieved refractive index n (real and imaginary parts )for one,two,and three cells of the metamaterial structure shown in Fig.1.FIG.5.Range of z (real and imaginary parts )for tolerance ␦r =0.015and ␦t =0.0in Eqs.(11a )and (11b ).The impedance is for a three-cell metamaterial shown in Fig.1.CHEN et al.PHYSICAL REVIEW E 70,016608(2004)and z which exactly satisfy Eqs.(1a )and (1b ),we solve for the following inequalities:ͯS 11−R 01͑1−e i2nk 0d ͒1−R 012e i2nk 0dͯഛ␦r ,͑11a ͒ͯS 21−͑1−R 012͒e ink 0d 1−R 012ei 2nk 0dͯഛ␦t ,͑11b ͒where ␦r and ␦t are small positive numbers.Figure 5shows the range of z satisfying Eqs.(11a )and (11b )for ␦r =0.015and ␦t =0.0.At each frequency,all z having a real and imagi-nary parts between the bounds shown in Fig.5satisfy Eqs.(11a )and (11b ).It can be seen that the magnitude of the spikes is within the tolerance error,which implies that they are due to the noise in the S 11and S 21data.Finally,note that although the retrieved n and z for mul-tiple cells may be different from that for one cell at some speciﬁc frequencies,the calculated S 11and S 21for multiple cells using the retrieved ⑀and ␮from one cell data match well with the S 11and S 21data computed for multiple cells directly from numerical simulation,as is illustrated in Fig.6.F.ResultsThe retrieved permittivity ⑀and permeability ␮of a one cell of SRR-rod structure of Fig.1are shown in Fig.7.Notethat although the results satisfy the condition ⑀Љജ0and ␮Љജ0,the positive energy requirement ץ͑⑀␻͒/ץ␻Ͼ0[19,20]is violated in the frequency band 12GHz–12.2GHz.As a re-sult,the resonance band is extended to 11GHz–12.2GHz,as shown by the vertical dashed lines in Fig.7(a ).The value of ⑀and ␮are both negative in the frequency range 12.2GHz–12.8GHz,showing that in this band,the metamaterial exhibits a LH behavior.We also retrieved the effective parameters of four and ﬁve cells of metamaterial shown in Fig.1,and the retrieval results are close to those for one,two,and three cells.In addition,we also applied our method to retrieve the effective parameters of the structure taken from [14,21],as shown in the inset of Fig.8(a ).For a 1D structure,by match-ing the impedance z for one and two cells of the metamate-rial using the previously described method,we obtain x ¯opt=͑2.2053ϫ10−3d 0,1.1356ϫ10−3d 0͒,where d 0is the length of unit cell.Again,we ﬁnd that the two boundaries of the effective homogeneous medium are close to the outer unit-cell boundaries of the 1D metamaterial.Figure 8shows the retrieved z ,n ,⑀,and ␮for one cell of this metamaterial.It can be seen that the frequency range of 13.8GHz–14.5GHz is a LH band,which agrees with the conclusion in Ref.[14].It should be noted,however,that for a 2D version of this metamaterial,the effective boundaries should be obtained from the optimization process,as they do notnecessarilyFIG.6.S 11and S 21(real and imaginary parts )for three cells:Comparison between FDTD re-sults (dot line with *)and calculated S parameters based on the retrieved ⑀and ␮(solid line with ᮀ)for a one-cell metamaterial shown in Fig.1.FIG.7.Retrieved ⑀and ␮(real and imaginary parts )for a one-cell metamaterial shown in Fig.1.The vertical dashed lines denote the limits of the resonance band.ROBUST METHOD TO RETRIEVE THE CONSTITUTIVE …PHYSICAL REVIEW E 70,016608(2004)match the unit-cell boundaries of the metamaterial.Indeed,in this speciﬁc case,we obtain x ¯opt =͑0.33110d 0,0.30342d 0͒.III.CONCLUSIONWe have proposed an improved method to retrieve the effective parameters (index of refraction,impedance,permit-tivity,and permeability )of metamaterials from transmission and reﬂection data.The successful retrieval results for vari-ous metamaterial structures show the effectiveness of the method.Our main conclusions are as follows:(1)The ﬁrst boundary and the thickness of the effective media can be determined by matching z through all sample frequencies for different lengths of the slabs in the propaga-tion direction.For symmetric 1D metamaterials,we have drawn the empirical conclusion that the ﬁrst boundary coin-cides with the ﬁrst boundary of the unit cell facing the inci-dent wave,and the thickness of the effective medium is ap-proximately equal to the number of unit cells multiplied by the length of a unit cell.For 2D and asymmetric 1D metama-terials,the effective boundaries have to be determined by optimization.(2)The requirement z Јജ0cannot be used directly for practical retrievals when z Јis close to zero because the nu-merical or measurement errors may ﬂip the sign of z Ј,mak-ing the result unreliable.In this case,we have to determinethe sign of z by the value of its corresponding n so that n Љജ0.(3)There is a resonance band characterized by the fact that the requirement ␮Љജ0and ⑀Љജ0cannot be satisﬁed at those frequencies.On each side of the resonance,the branch of n Јcan be obtained by a Taylor expansion approach con-sidering the fact that the refractive index n is a continuous function of frequency.Since the refractive index n at the initial frequency determines the values of n Јat the subse-quent frequencies,we determine the branch of the real part of n at the initial frequency by requiring that ␮Љand ⑀Љare non-negative across all the frequency band.(4)Due to the noise contained in the S parameters,the retrieved n and z at some speciﬁc frequencies are not reli-able,especially for thicker metamaterials at lower frequen-cies.In spite of this,the fact that S 11and S 21for multiple cells of metamaterial calculated from the retrieved ⑀and ␮for a unit-cell metamaterial match the S 11and S 21computed directly from numerical simulation conﬁrms that the metamaterials can be treated as an effective homogeneous material.ACKNOWLEDGMENTSThis work was supported by DARPA (Contract No.N00014-03-1-0716)and ONR (Contact No.N00014-01-1-0713).[1]D.R.Smith,W.J.Padilla,D.C.Vier,S.C.Nemat-Nasser,and S.Schultz,Phys.Rev.Lett.84,4184(2000).[2]R.A.Shelby,D.R.Smith,and S.Schultz,Science 292,77(2001).[3]L.Ran,X.Zhang,K.Chen,T.M.Grzegorczyk,and J.A.Kong,Chin.Sci.Bull.48,1325(2003).[4]D.R.Smith,S.Schultz,P.Markoš,and C.M.Soukoulis,Phys.Rev.B 65,195104(2002).[5]P.Markošand C.M.Soukoulis,Opt.Express 11,649(2003).[6]R.W.Ziolkowshi,IEEE Trans.Antennas Propag.51,1516FIG.8.Retrieved z ,n ,⑀,and ␮(real and imaginary parts )for a one-cell metamaterial structure taken from Refs.[14,21]and shown in the inset (a ).The vertical dashed lines denote the limits of the resonance band.CHEN et al.PHYSICAL REVIEW E 70,016608(2004)(2003).[7]A.M.Nicolson and G.F.Ross,IEEE Trans.Instrum.Meas.19,377(1970).[8]J.Baker-Jarvis,E.J.Vanzura,and W.Kissick,IEEE Trans.Microwave Theory Tech.38,1096(1990).[9]J.A.Kong,Electromagnetic Wave Theory(EMW,Cambridge,MA,2000).[10]J.A.Kong,Prog.Electromagn.Res.35,1(2002).[11]D. A.Shelby, D.R.Smith,S. C.Nemat-Nasser,and S.Schultz,Appl.Phys.Lett.78,489(2001).[12]C.D.Moss,T.M.Grzegorczyk,Y.Zhang,and J.A.Kong,Prog.Electromagn.Res.35,315(2002).[13]R.Storn and K.Price,J.Global Optim.11,341(1997).[14]T.M.Grzegorczyk,C.D.Moss,J.Lu,and J.A.Kong,NewRing Resonator for the Design of Left-Handed Materials at Microwave Frequencies,Proceedings of Progress in Electro-magnetics Research Symposium,Honolulu,Hawaii,2003 (EMW,Cambridge,MA,2003),p.286.[15]C.R.Simovski,P.A.Belov,and S.He,IEEE Trans.AntennasPropag.51,2582(2003).[16]J.E.Sipe and J.V.Lranendonk,Phys.Rev.A9,1806(1974).[17]P.A.Belov,S.A.Tretyakov,and A.J.Viitanen,Phys.Rev.E66,016608(2002).[18]T.Koschny,P.Markoš,D.R.Smith,and C.M.Soukoulis,Phys.Rev.E68,065602(2003).[19]ndau,E.M.Lifshitz,and L.P.Pitaevskii,Electrody-namics of Continuous Media,2nd ed.(Pergamon,Oxford, 1984).[20]V.Veselago,p.10,509(1968).[21]C.D.Moss,Ph.D.thesis,Massachusetts Institute of Technol-ogy,2004.ROBUST METHOD TO RETRIEVE THE CONSTITUTIVE…PHYSICAL REVIEW E70,016608(2004)。

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Users are granted a nonexclusive royalty-free license to reproduce and distribute this Manual, subjectto the following limitations: (1) the work must be reproduced in its entirety, without alterations; and (2) copies of the work may not be sold.For more information on material presented in this manual, please contact your supplier.Copyright © May 2007ethylen eo xidethird editionTo the ReaderManual PreparationAs members and affiliated companies of the American Chemistry Council, we support efforts to improve the industry’s responsible managementof chemicals. To assist in this effort, the American Chemistry Council’s Ethylene Oxide/Ethylene Glycols Panel supported the creation and publication of this manual. The Panel is comprised of the following companies:Balchem Corporation/ARC Specialty ProductsBASF CorporationBayer Material Science LLCCelanese Ltd.Champion TechnologiesCroda, Inc.The Dow Chemical CompanyEastman Chemical CompanyHoneywellShell Chemical LPThe development of this manual was led by the Panel’s Ethylene Oxide Safety Task Group (EOSTG), a group comprised of producers and users of ethylene oxide. The EOSTG functions to generate, collect, evaluate and share information to support product stewardship with regard to ethylene oxide. The EOSTG formed a manual work group, chaired by Keith Vogel of Lyondell Chemical Company,to lead the development of this document. The following work group members provided significant contributions: Tom Grumbles Sasol North AmericaSusan Jackson BASF CorporationRobert Lenahan Bayer MaterialScience LLC Denis Reeser The Dow Chemical Company John Stewart BASF CorporationDon Szczepanski Huntsman PetrochemicalCorporationDavid Townsend Celanese Chemicals Ltd. Randy Viscomi Balchem Corporation/ARCSpecialty ProductsKeith Vogel Lyondell Chemical Company Mike Wagner Old World IndustriesJohn Wincek Croda, Inc.Gerald Wise Shell Chemical LPAcknowledgementsMany others contributed to the development and editing of this manual, all of whom cannot be listed here; however, the manual work group would like to thank the following individuals for their significant contributions to this publication:Ralph Gingell Shell Chemical LPWilliam Gulledge American Chemistry CouncilKarl Loos Shell Chemical LPDavid McCready The Dow Chemical Company Kristy Morrison EO STG Manager, AmericanChemistry CouncilKaryn Schmidt Assistant General Counsel,American Chemistry Councilii Ethylene Oxide Product Stewardship Guidance Manual Copyright © May 2007iiiCopyright © May 2007Ethylene Oxide Product Stewardship Guidance ManualTable of Contents6.0 Design of Facilities (39)6.1Introduction................396.2 Plant Layout and Siting ......396.3 Materials of Construction ....406.4 U nloading Facilities –Bulk Receipt of EO..........466.5 EO Storage ................496.6 Reaction Systems ..........546.7 Piping and Pumps ..........576.8 H andling of Vents andEffluent....................636.9 Miscellaneous.. (66)7.0 Personnel Exposure (68)7.1Introduction................687.2 O SHA Standard for EthyleneOxide .....................687.3 O ther Exposure Standards/Recommendations forEthylene Oxide .............687.4 Measuring Exposure ........707.5 P ersonal ProtectiveEquipment (70)8.0 Equipment Preparationand Maintenance . . . . . . . . . . . . . 828.1Introduction................828.2 P reparation for Inspection orMaintenance ...............828.3P reparation of InternalSurfaces (83)8.4 Leak Repair Clamps.........838.5 Preventive Maintenance .....848.6 Equipment Commissioning (84)9.0 Transportation andUnloading Operations (85)9.1Introduction . . . . . . . . . . . . . . . 859.2 E mergency ResponseTelephone Numbers.........859.3Ethylene Oxide Classification.851.0 Introduction (1)1.1 Purpose and Use of Manual ...12.0 Properties of Ethylene Oxide ..22.1 Introduction.................22.2Physical Properties (3)2.3 R eactive and CombustiveProperties ..................52.4 Commercial Chemistry ......142.5Uses of Ethylene Oxide (15)3.0 Health Effects ofEthylene Oxide (16)3.1 Introduction................163.2 Acute Inhalation Exposure ...163.3 Skin and Eye Contact .......163.4Chronic Exposure Hazards ..164.0 Environmental Effects ofEthylene Oxide (18)4.1 Introduction................184.2Properties in the Environment 184.3 Ecotoxicological Effects .....214.4 E nvironmental Evaluation ofEthylene Oxide Spills........214.5 Fugitive Emissions . (22)5.0 Hazards of Ethylene Oxide (23)5.1 Introduction................235.2 Contamination Incidents.. (23)5.3Formation of Ethylene Oxide Vapor Clouds...............275.4 E thylene Oxide DecompositionIncidents ..................275.5 E thylene Oxide TransportationIncidents ..................355.6Runaway Ethylene Oxide Polymerization Incidents (36)5.7 R unaway Reactions inEthoxylation Units...........365.8 I ncidents in Ethylene OxideAbatement Devices (37)9.4 Railcars (85)9.5 I M Portable Tanks(Intermodal/Iso-Containers)..949.6 N on-Bulk Packaging forHigh Purity Ethylene Oxide (94)9.7 E thylene Oxide ShippingData (98)9.8 S hipments of Ethylene Oxidebetween the U.S. andCanada (98)10.0 Emergency Response (100)10.1 Introduction . . . . . . . . . . . . . . 10010.2 Potential Hazards (100)10.3 Fire Response (101)10.4 Spill Response (102)10.5 E mergency Response toTemperature Rise (102)10.6 E mergency Response Planto Temperature Rise (103)10.7 U se of Water inEmergencies..............10411.0 Selected Regulations . (105)11.1 Introduction (105)11.2 R egulations — Numericalwith Subject Listed (105)Appendix AFigures and Tables (118)Appendix BLaboratory CompatibilityTesting of Elastomers withEthylene Oxide (137)Appendix CRailcar Repressurization (141)Appendix DReferences (145)Appendix EGlossary of SelectedTerms, Abbreviations andOrganizations (151)iv Ethylene Oxide Product Stewardship Guidance Manual Copyright © May 2007FiguresFigure 2.1 The Ethylene OxideMolecule (2)Figure 2.2 Flammable Region ofEthylene Oxide/Nitrogen/AirMixtures (7)Figure 2.3 Flammable Region ofEthylene Oxide/CarbonDioxide/Air Mixtures (7)Figure 2.4 Effects of Pressure onFlammable Region ofEthylene Oxide/Nitrogen/AirMixtures (8)Figure 2.5 Ethylene Oxide PolymerInstantaneous Drop-OutTemperatures . . . . . . . . . . . . 13 Figure 2.6 Ethylene Oxide PolymerDrop-Out Temperaturesafter 4 Days (14)Figure 4.1 Neutral EO/Water/GlycolKinetics - Isothermal Case,Initially EO/Water mixture ..19 Figure 4.2 Neutral EO/Water/GlycolKinetics - Adiabatic Case,Initially EO/Water (19)Figure 5.1 Older View of Plant BeforeExplosion Showing EO Tanksin Foreground (23)Figure 5.2 Blast Center afterExplosion – EO VesselsNo Longer Visible (23)Figure 5.3 Aerial View of the PlantShowing Overall Damage (24)Figure 5.4 EO Tank Blown Into ProcessStructure 400 Feet Away (24)Figure 5.5 Plant Laboratory AfterEO Vapor Cloud Explosion,300 Feet Away fromExplosion Center (25)Figure 5.6 Remnants of Railcar (25)Figure 5.7 Remnants of Railcar (25)Figure 5.8 Damage to Other Railcarsfrom Ethylene Oxide RailcarExplosion ................25Figure 5.9 Remnants of Railcar(after EO explosion causedby contamination withammonia) (26)Figure 5.10 High Speed CentrifugalPump “Launched” byDecomposition of 0.6 Poundsof Ethylene Oxide (29)Figure 5.11 Motor Landed on OperatingEthylene Oxide PumpDischarge Line (29)Figure 5.12 Ethylene Oxide DistillationColumn Reboiler afterExplosion (30)Figure 5.13 Aerial View of EthyleneOxide Plant after Explosion (31)Figure 5.14 Remnants of Base ofEthylene Oxide DistillationColumn after Explosion (31)Figure 5.15 Piece of Ethylene OxideDistillation Column WallTurned Inside Out byExplosion (32)Figure 5.16 Aerial View of EO UnitAfter Explosion (33)Figure 5.17 EO Plant Burningafter Explosion (33)Figure 5.18 EO Purification AfterExplosion – Two Towersare Missing (34)Figure 5.19 Ethylene Oxide Re-distillationTower Explosion (34)Figure 5.20 Resulting Damage to thePlant (34)Figure 5.21 Filter Case after RunawayPolymerization (36)Figure 5.22 Filter Case after RunawayPolymerization (36)Figure 5.23 Filter Case after RunawayPolymerization (36)Figure 5.24 Diagram of SterilizerExplosion (37)Figure 5.25 Sterilizer ExplosionDamage (38)vCopyright © May 2007 Ethylene Oxide Product Stewardship Guidance ManualFigure 5.26 Sterilization ChamberDamage (38)Figure 5.27 Damage to the buildingwall from impact of sterilizerdoor (38)Figure 6.1 Degradation of CompressedAsbestos Valve BonnetGaskets by Ethylene Oxide..41 Figure 6.2 PTFE Gasket Failures in EOService Due to Cold Flow (41)Figure 6.3 Glass Filled PTFE GasketFailure Due to EOPolymerization inPTFE-Glass Matrix (42)Figure 6.4a Deformation of a Spiral WoundStainless Steel-PTFE GasketDue to EO Permeation andPolymerization (42)Figure 6.4b Deformation of a SpiralWound Stainless Steel-PTFEGasket (42)Figure 6.5 Spiral Wound Gasket withStainless Steel Windings,Flexible Compressed GraphiteFiller, and Inner and OuterRetaining Rings . . . . . . . . . . .43 Figure 6.6 Gasket Test Showing Failureof Compressed GraphiteGasket, Laminated on FlatStainless Steel Sheet withan Adhesive (43)Figure 6.7 Laminated Gasket Made ofPolycarbon Sigraflex™BTCSS Flexible CompressedGraphite – Laminated onStainless Steel Tang Sheet .43 Figure 6.8 Laminated Gasket Made ofUCAR Grafoil GH™ E FlexibleCompressed Graphite –Laminated on StainlessSteel Tang Sheet (43)Figure 6.9 Butyl Rubber O-Ring Beforeand After Exposure to EOfor 30 days (44)Figure 6.10 Example of DegradedO-ring Attacked by EO .....44Figure 6.11 Example of SeverelyDegraded O-ring in HighTemperature EO-waterService (Chemraz® 505) (44)Figure 6.12 Example of Flange SealBand with Leak DetectionDrip Tube (45)Figure 6.13 EO Unloading Facilities (46)Figure 6.14 Representative layout ofEthylene Oxide unloadingfacilities – Pressurizedtransfer (47)Figure 6.15 Representative layout ofEthylene Oxide unloadingfacilities – Pump transfer (48)Figure 6.16 Total pressure required toinert vapor above EthyleneOxide with nitrogen diluent.51 Figure 6.17 EO Decomposable Limitsversus Molar NitrogenConcentration (56)Figure 6.18 Decomposition Limit ofMole % EO versus TotalSystem Pressure (57)Figure 6.19 Ethylene Oxide VentScrubber System (63)Figure 6.20 Schematic of TypicalFlaring System (65)Figure 6.21 EO Sampling System (67)Figure 7.1 OSHA Warning for EORegulated Areas (69)Figure 7.2 Chemical Burn Resultingfrom Low Concentrationof EO in Water (70)Figure 9.1 DOT 105-J railcar fortransporting Ethylene Oxide 86 Figure 9.2 Dome Arrangement of aDOT 105-J Railcar forEthylene Oxide Service (87)Figure 9.3 DOT “Stop—Tank CarConnected” Sign (88)Figure 9.4 Canister Mask with EthyleneOxide-Specific Canister (90)vi Ethylene Oxide Product Stewardship Guidance Manual Copyright © May 2007Figure 9.5 Positive Pressure “Hoseline”Type Respirator (90)Figure 9.6 Commonly Used Non-bulkContainers (95)Figure 9.7 Typical Drum Connections..96 Figure 10.1 Ethylene Oxide / Water(Neutral) ReactionTemperature Profile (103)Figure 1 Ethylene Oxide LiquidDensity (118)Figure 2 Ethylene Oxide VaporPressure (118)Figure 3 Ethylene Oxide LiquidHeat Capacity (119)Figure 4 Ethylene Oxide LiquidViscosity (119)Figure 5 Ethylene Oxide LiquidThermal Conductivity . . . . . 120 Figure 6 Ethylene Oxide Heat ofVaporization (120)Figure 7 Ethylene Oxide VaporHeat Capacity (121)Figure 8 Ethylene Oxide VaporViscosity (121)Figure 9 Ethylene Oxide VaporThermal Conductivity . . . . . 122 Figure 10 Freezing Points EthyleneOxide/Water Mixtures (122)Figure 11 C p/C v For SaturatedEthylene Oxide Vapor (123)Figure 12 Ethylene Oxide VaporDensity (123)Figure 13 Ethylene Oxide Coefficientof Cubic Expansion (124)Figure 14 Raoult’s Law DeviationFactors for Ethylene Oxide/Water Mixtures (126)Figure 15 Raoult’s Law DeviationFactors for Ethylene Oxide/Water Mixtures...........127Figure 16 Flammability Data on EO-AirMixtures at SubatmosphericPressures (128)Figure 17 Vapor/Liquid Equilibria ofEthylene Oxide/WaterSystems (129)Figure 18 Density vs. Composition ofEthylene Oxide/WaterSystems (130)Figure 19 Boiling points of aqueousEO concentrations (131)Figure 20 Decomposition Data (132)Figure 21 Vapor Compressibility vs.Pressure as a Function ofTemperature (133)Figure B1 Weight Change of O-ringsExposed to EO at 27°C (138)Figure B2 Volume Change of O-ringsExposed to EO at 27°C (138)Figure B3 Tensile Strength of O-ringsExposed to EO at 27°C (140)Figure B4 Maximum Deformation ofO-rings Exposed to EOat 27∞C (140)Figure C1 Unloaded RailcarRepressuring — Nitrogen —Less than 50 GallonEO Heel (142)Figure C2 Unloaded RailcarRepressuring — VaporBalancing — Less than50 Gallon Heel (144)viiCopyright © May 2007 Ethylene Oxide Product Stewardship Guidance ManualTablesTable 2.1 Physical Properties ofEthylene Oxide (3)Table 2.2 Physical Properties ofAqueous Ethylene OxideSolutions (5)Table 2.3 Heat of Reaction of VariousEthylene Oxide Reactionsat 25°C (6)Table 2.4 Physical Properties ofEthylene Oxide Polymer (12)Table 2.5 Solubility* of EthyleneOxide Polymer in VariousSolvents (13)Table 3.1 CarcinogenicityClassifications ofEthylene Oxide (17)Table 3.2 Findings of the NIOSHEthylene Oxide Studies (17)Table 4.1 Environmentally RelevantParameters of EthyleneOxide (18)Table 4.2 Biological DegradationData for Ethylene Oxide (20)Table 4.3 Aquatic Toxicity Data forEthylene Oxide* (21)Table 6.1 EO Pump Shutdown andAlarm Considerations (62)Table 7.1 AEGL Values for EthyleneOxide [ppm (mg/m3)] ......69Table 7.2 OSHA Minimum Standardsfor Respiratory Protection forAirborne Ethylene Oxide (72)Table 7.3 Ethylene Oxide PermeationData for Clothing (73)Table 7.4 Ethylene Oxide PermeationData for Gloves (79)Table 7.5 Ethylene Oxide PermeationData for Boots (81)Table 9.1 Illustration – PressuringUnloaded Railcars withPure Nitrogen (Assuming50 Gallon Ethylene Oxide LiquidHeel) (93)Table 9.2 Illustration – RepressuringUnloaded Railcars – VaporBalancing (50 Gallon EthyleneOxide Liquid Heel) (94)Table 9.3 Temperature/Density/VaporPressure for ShippingEthylene Oxide (98)Table A1 Physical PropertyEquations (134)Table A2 Conversion Factors (134)Table A3 H enry’s Law Constants(Atm/mole fraction) (135)Table A4 H enry’s Law Constants(MPa/mole fraction) (135)Table B1 O-Rings Selected forCompatibility Testing (137)viii Ethylene Oxide Product Stewardship Guidance Manual Copyright © May 20071.0 1.0 Introduction1.1 Purpose and Use of ManualThis manual has been developed for use by producers and industrial users of ethylene oxide. The purpose of this product stewardship document is to provide the reader with a better understanding of how ethylene oxide is used to produce products that play important roles in our lives. It is also our intent to address the health, safety and environmental aspects associated with manufacturing, distributing, using and disposing of ethylene oxide and the bulk of the material presented emphasizes these topics.This information is provided as a resource in the development of producers’ and users’ design, operation, maintenance, training and emergency response practices. References to applicable regulations, industry practices are made in tables and text. Contact your supplier for further information as necessary.Note that a separate, independent group of ethylene oxide producers previously produced two editions of an ethylene oxide guidance manual: Ethylene Oxide User’s Guide, First (1995) and Second (1999) Editions. It is the intention of those producers that this manual supercedes the Ethylene Oxide User’s Guide, First and Second Editions.Manual Availability and UpdatesThis document is available through your supplierin hard copy and is available on a password-protected Web site hosted by the Panel at www. . This document may beupdated. Interim updates may occur on the Website posting of this document only. Readersshould consult the Web site for the most recentversion of this manual. Readers should also stayabreast of new developments and informationabout ethylene oxide, including but not limitedto physical properties, handling technology, andregulatory requirements that occur after the dateof publication of this document.Contact your supplier to obtain the most currentversion of this manual, if you have questions orto get more information about any informationpresented in this document. We encouragecomments on the content of this document anda more in-depth dialogue concerning the issues presented.1Copyright © May 2007 Ethylene Oxide Product Stewardship Guidance Manual。

2010年中国前百所大学排名

工学类
研教1型
74
浙江工业大学
20.93
11.73
4.23
7.51
9.20
7.96
1.23
浙
2
理工
工学类
研教1型
75
江苏大学
20.62
13.11
5.00
8.11
7.51
6.66
0.85
苏
12
综合
工学类
研教2型
76
华北电力大学
20.24
12.29
4.86
7.43
7.95
7.01
0.94
京
13
理工
工学类
17.32
9.37
4.70
4.67
7.95
7.27
0.68
京
16
理工
理科类
研教2型
90
中国药科大学
17.31
8.81
4.16
4.64
8.51
8.41
0.10
苏
14
医药
医学类
研教1型
91
长安大学
17.30
11.23
4.16
7.06
6.08
5.51
0.56
陕
7
理工
工学类
研教2型
92
首都师范大学
17.24
18.62
17.66
0.97
沪
5
理工
工学类
研究2型
35
郑州大学
36.62
23.30
8.79
14.50
13.32
10.19
3.14
豫
1

山东大学工勤技能岗位首聘结果公示

山东大学工勤技能岗位首聘结果公示
根据《山东大学关于做好工勤技能岗位首聘工作的通知》( 山大人字〔2008〕86号）精神，按照工勤技能岗位任职资格条件的有关标准，经个人申报、单位资格审核推荐、学校工勤技能岗位评审委员会审核评议、学校岗位设置及聘用管理委员会评审等程序，评审通过技术工三级621人、技术工四级117人、技术工五级29人、普通工32人（威海分校评审结果由分校公示），现予以公示。

公示时间：2008年7月28日至7月31日
公示电话：88364697（监察处） 8836 4845（人事处）
公示信箱：lzsb@
特别提示：
1、由于本次岗位聘任后，工勤岗位工资不会发生调整，因此2006年7月至2008年6月已退休人员不再聘任；
2、为了能够及时核对申报人反映的情况，我们诚恳建议通过信箱书面署名反映各类问题。

对于反映问题中涉及技术等级任职时间者，请详细注明技术等级演变情况(主要是山东省人事厅发放的技术等级证书获得时间和编号)。

技术工三级：
技术工四级：
技术工五级：
普通工：。

SEI2011年设计清单

610303N 神华煤直接液化厂煤液化装置（现场服务）现场服务(设张宝海,秦有福 2004-8-1 002009-12-30 00:00:00P70547Y 中国石化青岛炼油化工有限责任公司青岛大炼油工程（总总承包宁波袁毅夫,吴雷 2005-1-1 002009-5-30 00:00:00综合管理项目管理及其它综合管理工作实施阶段赵宝军,张秀东,王毅 2005-1-1 002009-12-31 00:00:00610303Y 神华煤直接液化厂煤液化装置（E+EPCM）（总承包）总承包张宝海 2005-3-1 002009-12-30 00:00:00零星装置投产后零星处理现场问题现场服务(设计代表) 2004-1-1 002009-12-31 00:00:00270203SS 中国石油独山子石化分公司60万吨/年全密度聚乙烯装置（设计代表）现场服务(设周?ヌ？ 2007-7-1 002009-8-31 00:00:00F00701Y 陕西延长石油(集团)有限责任公司炼化公司杨庄河炼化项目六套装置EPC（总承包）总承包魏挺袁忠勋 2007-4-15 02009-3-31 00:00:00290326LS 天津100万吨乙烯及配套项目30万吨/年LLDPE装置（总承总承包骆广海 2007-6-25 02009-8-31 00:00:00290322LS 天津100万吨乙烯及配套项目45万吨/年聚丙烯装置（总承总承包苏洪 2007-6-25 02009-9-30 00:00:00080314FS-1 上海石化分公司1#乙烯异地改造项目新建38万吨/年乙二醇装置/30万吨/年PP装置/12万吨丁二烯装置（可研）前期工作朱明,祝子固曾齐家 2008-5-5 002009-2-28 00:00:00B20802C 越南云风1000万吨/年炼油项目前期工作赵清 2008-5-7 002009-12-30 00:00:00030301SA 大唐国际发电股份有限公司北京高井热电厂脱硝工程安全评价（安评）前期工作李昕 2008-4-28 02009-3-31 00:00:00090801C 齐鲁分公司乙烯三轮配套炼油技术改造工程前期工作万云,曲晓廉郭志雄 2008-5-8 002009-6-18 00:00:00310104PF 海南炼油化工有限公司100万吨/年乙烯项目（预可研）前期工作杨挺,徐惟兴 2008-5-26 02009-6-30 00:00:00091018BD 扬巴有限责任公司13万吨/年丁二烯装置（基础设计）基础设计侯霞晖丁文有 2008-6-1 002009-2-28 00:00:00190214CD 中原石化有限公司6万吨/年碳四烯烃催化裂解制丙烯项目（一段设计）一段设计安淑英李广华 2008-6-1 002009-6-30 00:00:00Q60605E 伊朗ARAK炼厂扩能及产品升级项目360万吨/年渣油加氢裂化装置（详设）详细设计(施王毅朱昌莹,叶向东 2006-12-10 2009-8-30 00:00:00Q60606E 伊朗ARAK炼厂扩能及产品升级项目480万吨/年重油催化裂化装置（详设）详细设计(施王毅吴雷,杨启业 2007-3-10 02009-8-30 00:00:00Q60607E 伊朗ARAK炼厂扩能及产品升级项目100万吨/年重整装置（详细设计(施王毅任建生,叶向东 2006-12-10 2009-8-30 00:00:00Q60610E 伊朗ARAK炼厂扩能及产品升级项目控制室（详设）详细设计(施王毅叶向东 2006-12-10 2009-8-30 00:00:00Q60611E 伊朗ARAK炼厂扩能及产品升级项目动力站（详设）详细设计(施王存智,王毅 2007-5-22 02010-6-30 00:00:00Q60612E 伊朗ARAK炼厂扩能及产品升级项目罐区（详设）详细设计(施王毅 2006-12-10 2009-8-30 00:00:00Q60613E 伊朗ARAK炼厂污水处理场（详设）详细设计(施王毅 2006-12-10 2009-8-30 00:00:00Q60614E 伊朗ARAK炼厂水系统（详设）详细设计(施王毅 2006-12-10 2009-8-30 00:00:00Q60615E 伊朗ARAK炼厂消防水系统（详设）详细设计(施王毅 2006-12-10 2009-8-30 00:00:00030401FS 中天合创能源有限责任公司内蒙古鄂尔多斯煤化工项目（可研）前期工作杨挺,祝子固余学恒,王振维 2008-6-3 002009-6-30 00:00:00190503E 辽阳石化分公司140万吨/年连续重整-歧化联合装置及配套系统工程140万吨/年连续重整-歧化联合装置（详细设计）详细设计(施曹坚,吴国有曹坚 2008-6-6 002009-10-30 00:00:00130544LS 福建炼油乙烯项目联合管理组主任部总承包郑文平 2007-1-1 002009-9-30 00:00:00130545LS 福建炼油乙烯项目联合管理组HSE部总承包胡晨 2007-1-1 002009-9-30 00:00:00270204SS 中国石油独山子石化分公司55万吨/年聚丙烯装置（设计代表）现场服务(设周涌涛,张军苏洪 2007-8-1 002009-8-31 00:00:00230701Q 扬子石油化工股份有限公司120万吨/年石脑油吸附分离装置（基础设计）基础设计朱瑜芬李广华 2007-8-6 002010-4-30 00:00:00450501E 中国石油哈尔滨石化分公司60万吨/年连续重整-80万吨/年中压加氢改质联合装置（详设）详细设计(施尉雷,刘立李浩,袁忠勋 2007-8-15 02009-1-31 00:00:00091021FS 扬子石化分公司烯烃厂废碱液处理（可研）前期工作毕铁成 2008-6-4 002009-9-30 00:00:00010802C 燕山石化分公司280万吨/年柴油加氢精制装置前期工作杨光明李浩 2009-5-20 02009-7-30 00:00:00091019BD 扬子石化分公司PTA装置节能改造项目（基础设计）基础设计于兰肖雪军 2008-7-1 002009-8-31 00:00:00080405DD 上海赛科石化股份有限公司乙烯装置扩能改造项目119万吨/年乙烯装置（详细设计）详细设计(施孙钢,苏胜利李广华,何细藕 2008-7-1 002009-5-31 00:00:00310201SA 海南省工业技术发展中心海南精细化工项目（安评）前期工作高梅 2008-6-1 002009-4-30 00:00:00014002SA 中海炼化和株式会社LG化学30万吨/年ABS项目（安评）前期工作高梅 2008-7-1 002009-6-30 00:00:00010005SA 燕化公司中日合资10万吨/年双酚A/6万吨/年聚碳装置（前期工作高梅 2008-5-15 02009-10-31 00:00:00200402SA 四川维尼纶厂安全现状评价（安评）前期工作高梅 2008-5-4 002009-4-30 00:00:00010110SA 燕山石化分公司9万吨/年溴化丁基橡胶装置（安评）前期工作高梅 2008-3-1 002009-10-31 00:00:00130546LS 福建炼油乙烯项目联合管理组质量部总承包李莉 2007-1-1 002009-9-30 00:00:00130547LS 福建炼油乙烯项目联合管理组管理控制部总承包田伟 2007-1-1 002009-9-30 00:00:00130548LS 福建炼油乙烯项目联合管理组财务部总承包张正选 2007-1-1 002009-9-30 00:00:00130549LS 福建炼油乙烯项目联合管理组设计部总承包江建,郭秀平 2007-1-1 002009-9-30 00:00:00130550LS 福建炼油乙烯项目联合管理组IT部总承包李荔宁 2007-1-1 002009-9-30 00:00:00130551LS 福建炼油乙烯项目联合管理组DCC部总承包渭？ 2007-1-1 002009-9-30 00:00:00130552LS 福建炼油乙烯项目联合管理组采购部总承包傅军 2007-1-1 002009-9-30 00:00:00130553LS 福建炼油乙烯项目联合管理组施工部总承包万锦章 2007-1-1 002009-9-30 00:00:00130554LS 福建炼油乙烯项目联合管理组行政部总承包张珍梅 2007-1-1 002009-9-30 00:00:00130558LS 福建炼油乙烯项目联合管理组IGCC项目组总承包霍宏伟 2007-1-1 002009-9-30 00:00:00130559LS 福建炼油乙烯项目联合管理组PE项目组总承包朱先捷 2007-1-1 002009-9-30 00:00:00130560LS 福建炼油乙烯项目联合管理组后处理项目组总承包张哲 2007-1-1 002009-9-30 00:00:00Q60616E伊朗ARAK炼厂扩能及产品升级项目长周期设备采购服务采购服务王毅 2007-3-10 02009-8-30 00:00:00Q60805Q~Q608伊朗HORMUZ炼厂项目（基础设计）基础设计赵向东,钟京卫 2008-8-1 002009-12-30 00:00:00E80807W海油发展惠州石化分公司加氢尾油综合利用项目40万吨/年基础油加氢装置长周期设备采购服务采购服务魏冬华 2008-7-24 02009-3-31 00:00:00700801G 神华新疆黑山300万吨/年煤直接液化项目（预可）前期工作张勇,贾辉郭志雄,戴文松 2008-7-28 02009-8-30 00:00:00290322SS天津100万吨乙烯及配套项目30万吨/年LLDPE装置（设计代表）现场服务(设骆广海 2008-8-1 002009-8-31 00:00:00130541SS 福建炼油乙烯项目C4联合装置（设计代表）现场服务(设王卫军 2008-8-1 002009-9-30 00:00:00270209BD-1中国石油独山子石化分公司乙烯工程工业废物处理装置（基础设计）基础设计姜立新安景辉 2008-8-15 02009-5-31 00:00:00011526MS 项目材料编码体系（标准系统）标准系统王建民 2006-4-1 002009-12-31 00:00:00E80501N中国海洋石油总公司惠州1200万吨/年炼油项目（现场服务）现场服务(设郑立军 2006-9-1 002009-6-30 00:00:00150414EI广州石化公司加工科威特原油南沙改扩建合资项目环境影响评价（环评）前期工作李瑾 2007-1-8 002009-5-31 00:00:00470601N 福建炼油乙烯项目800万吨/年炼油工程（现场服务）现场服务(设霍宏伟,赵向东,张英 2006-5-1 002009-6-30 00:00:00370602N乌鲁木齐石化总厂100万吨/年芳烃联合装置（现场服务）现场服务(设朱迪珠 2007-11-1 02009-11-30 00:00:00270202SS中国石油独山子石化分公司18万吨/年SSBR/SBS装置（设计代表）现场服务(设周?ヌ？ 2007-9-1 002009-8-31 00:00:00100104DD-1镇海炼化100万吨/年乙烯项目乙烯装置裂解炉（详细设计）详细设计(施杨健何细藕 2007-9-1 002009-2-28 00:00:00100104DD-2镇海炼化100万吨/年乙烯项目乙烯装置15万吨/年裂解炉（详细设计）详细设计(施杨健何细藕 2007-9-1 002009-3-31 00:00:00100104DD镇海炼化100万吨/年乙烯项目100万吨/年乙烯装置（详细设计）详细设计(施杨健 2007-9-1 002009-2-28 00:00:00100112DD镇海炼化100万吨/年乙烯项目30万吨/年聚丙烯装置（详细设计）详细设计(施李烨瑛苏洪 2007-9-1 002009-2-28 00:00:00140126EI齐鲁石化分公司常减压装置安全隐患治理及节能技术改造项目（环评）前期工作饶未欣 2007-9-10 02009-1-31 00:00:00010107BD燕化公司聚丙烯事业部第一聚丙烯装置造粒系统改造（基础设计）基础设计贾文霞 2007-9-12 02009-3-31 00:00:00F00605E陕西延长石油(集团)有限责任公司炼化公司杨庄河炼化区项目120万吨/年重整装置（详设）详细设计(施魏挺袁忠勋 2007-1-25 02009-3-30 00:00:00013803SS 北京东方石化两厂搬迁改造项目（设计代表）现场服务(设白玉强,苗济国,叶伟 2007-9-20 02009-10-31 00:00:00160652E天津石化分公司100万吨/年乙烯及配套项目炼油区外工程动力部新建污水回用设施处理（详设）详细设计(施李杰,祖超郭志雄 2007-7-1 002009-3-30 00:00:00100110DD镇海炼化100万吨/年乙烯项目16万吨/年丁二烯抽提装置（详细设计）详细设计(施杨健 2007-10-8 02009-1-31 00:00:00290331ES天津100万吨乙烯及配套项目20万吨/年丁二烯装置（设计监理）设计监理马洪波 2007-10-8 02009-2-28 00:00:00100112CD-1镇海炼化分公司30万吨/年聚丙烯装置甩头及连线项目（一段设计）一段设计李烨瑛 2007-10-8 02009-6-30 00:00:00270214PJ中国石油独山子石化分公司1000万吨/年炼油及120万吨/年乙烯改扩建工程全厂信息管理系统集成（PMC）PMC 桂宁 2007-4-1 002009-11-30 00:00:00100111DD镇海炼化100万吨/年乙烯项目70万吨/年汽油加氢装置（详细设计）详细设计(施杨健 2007-10-8 02009-1-31 00:00:00130507SS福建炼油乙烯项目800万吨/年常减压装置（设计代表）现场服务(设满堂泉,王卫军 2007-10-16 2009-5-31 00:00:00290349DD天津100万吨/年乙烯及配套项目公用工程中央化验室（详细设计）详细设计(施李蓓,白玉强 2007-10-23 2009-2-28 00:00:00430501N 武汉石化分公司炼油项目改造（现场服务）现场服务(设吴国有 2007-1-1 002009-8-15 00:00:00Q60701E 伊朗TABRIZ炼厂汽油产品升级项目（详设）详细设计(施赵铁柱任建生,黄绍明 2007-2-25 02010-3-30 00:00:00700601E神华829工程18万吨/年煤间接液化项目 ( E+Ps)（详设）详细设计(施张勇,贾辉郭志雄,戴文松 2007-11-1 02009-5-30 00:00:00100124DD镇海炼化100万吨/年乙烯项目乙烯第四循环水场中心变电所（详细设计）详细设计(施黄振铁 2007-11-1 02009-3-31 00:00:00100129DD镇海炼化100万吨/年乙烯项目化工全厂压力罐区（详细设计）详细设计(施黄振铁 2007-11-1 02009-3-31 00:00:00100130DD镇海炼化100万吨/年乙烯项目全厂工艺及供热外管（详细设计）详细设计(施黄振铁 2007-11-1 02009-5-31 00:00:00100131DD镇海炼化100万吨/年乙烯项目全厂火炬及火炬气回收系统（详细设计）详细设计(施黄振铁 2007-11-1 02009-5-31 00:00:00610703E神华直接液化148单元至829工程图幅( E+Ps)（详设）一段设计张勇,贾辉郭志雄,戴文松 2007-11-1 02009-3-30 00:00:00100132DD镇海炼化100万吨/年乙烯项目废碱液焚烧设施（详细设计）详细设计(施黄振铁 2007-11-1 02009-5-31 00:00:00B00501N 普光天然气净化厂（现场服务）现场服务(设王俊彪,郑立李浩 2006-4-1 002009-12-31 00:00:00B00501Y 中原油田分公司普光天然气净化厂（总承包）总承包王俊彪,郑立李浩,孙丽丽 2006-1-1 002009-12-31 00:00:00130521SS 福建炼油乙烯项目全厂建筑物（设计代表）现场服务(设仲耀军 2007-11-1 02009-7-31 00:00:00160710E天津石化分公司100万吨/年乙烯及配套项目炼油部分实施拿总（详设）详细设计(施李杰,祖超郭志雄 2007-11-1 02009-5-30 00:00:00080405TS上海赛科石化股份有限公司乙烯改扩建项目长周期设备采购技术服务前期工作孙钢,苏胜利 2007-11-6 02009-2-28 00:00:00100114DD镇海炼化100万吨/年乙烯项目65万吨/年乙苯装置（详细设计）详细设计(施李文光肖雪军 2007-11-8 02009-5-31 00:00:00170208PR武汉石化分公司80万吨/年乙烯及配套工程芳烃抽提装置（工艺包）工艺设计(工易建彬 2008-1-1 002009-3-31 00:00:00170211PR武汉分公司80万吨/年乙烯工程40万吨/年聚丙烯装置（工艺包）工艺设计(工苏洪 2008-1-1 002009-1-31 00:00:00320701E中石油兰州石化分公司300万吨/年重油催化裂化装置改造（详设）一段设计纪冰 2007-11-15 2009-3-30 00:00:00F00612E 陕西延长石油(集团)有限责任公司炼化公司杨庄河炼化区项目25万吨/时溶剂再生-3000吨/年-硫磺回收装置（详设）详细设计(施魏挺袁忠勋 2007-3-20 02009-3-30 00:00:00010575FS 燕山分公司化工一厂烯烃转化项目（可研）前期工作王若超李广华 2007-11-12 2009-7-31 00:00:00140127FS齐鲁石化分公司三轮乙烯技术改造工程80万吨/年乙烯装置（可研）前期工作赵剑霞,丁治李广华 2007-11-23 2009-1-31 00:00:00Q60706E 伊朗ARAK项目催化三旋成套设备EPC（详设）详细设计(施冯清晓杨启业,吴雷 2007-11-28 2009-10-30 00:00:00130504SS福建炼油乙烯项目40万吨/年聚丙烯装置（设计代表）现场服务(设满堂泉,于兰 2007-12-3 02009-7-31 00:00:00370602E 乌鲁木齐石化总厂100万吨/年芳烃联合装置（详设）详细设计(施朱迪珠罗家弼 2007-12-1 02009-7-20 00:00:00051701SS沈阳石蜡化工有限公司50万吨/年催化热裂解（CPP）制乙烯装置（设计代表）现场服务(设安淑英,盛在何细藕,李广华 2007-12-3 02009-8-31 00:00:00F00605N陕西延长石油(集团)有限责任公司炼化公司杨庄河炼化区项目（5套EPC炼油装置）（现场服务）现场服务(设魏挺袁忠勋 2007-6-1 002009-8-31 00:00:00F00608N杨庄河炼化区项目（非EPC装置及配套系统）（现场服务）现场服务(设魏挺袁忠勋 2007-6-1 002009-8-31 00:00:00160620N天津石化分公司100万吨/年乙烯及配套项目炼油装置、公用工程及辅助设施、炼油区外工程（现场服务）现场服务(设李杰,祖超 2008-1-1 002009-9-30 00:00:00510602N天津、曹妃甸、白沙湾等油库及配套系统（现场服务）现场服务(设高大兴 2007-12-1 02009-8-30 00:00:00700601N 神华829工程18万吨/年煤间接液化项目（现场服务）现场服务(设张勇,贾辉 2008-1-1 002009-12-31 00:00:00130506SS福建炼油乙烯项目70万吨/年芳烃联合装置及配套设施（设计代表）现场服务(设满堂泉,张英 2007-12-10 2009-7-31 00:00:00100109DD镇海炼化100万吨/年乙烯项目PO/SM装置（详细设计）详细设计(施李文光 2008-1-1 002009-8-31 00:00:00680801E海南炼油化工有限公司120万吨/年加氢裂化装置增产航煤改造（详设）详细设计(施秦永强 2008-1-2 002009-5-30 00:00:00D70501Y中国石化股份有限公司黄岛国家石油储备基地工程（总承包）总承包黄左坚黄左坚 2005-12-1 02009-3-30 00:00:00130527LS-1福建炼油乙烯项目40万吨/年聚丙烯装置、70万吨/年芳烃联合装置、800万吨/年常压蒸馏装置&400万吨/年减压蒸馏装置（EPC项目管理、项目控制、合同、采购、施工)总承包满堂泉,王卫军,于兰 2006-8-8 002009-7-31 00:00:00150417CD 广州石化公司聚乙烯装置排料罐改造（一段设计）一段设计贾文霞 2008-1-11 02009-1-31 00:00:00130505SS福建炼油乙烯项目公用工程及老厂改造项目（设计代表）现场服务(设张英 2008-1-21 02009-8-31 00:00:00130522SS 福建炼油乙烯项目化工罐区、火炬设施（设计代表）现场服务(设范慰颉,王云松 2008-1-21 02009-6-30 00:00:00470525N福建炼油乙烯项目鲤鱼尾油库原油罐区（一）、原油罐区（三）及泵站（现场服务）现场服务(设张英 2006-3-1 002009-3-30 00:00:00610304N神华煤直接液化厂液化项目加氢稳定装置（现场服务）现场服务(设张宝海,秦有福 2005-11-1 02009-12-30 00:00:00610305N神华煤直接液化厂液化项目加氢改质装置（现场服务）现场服务(设张宝海,秦有福 2005-11-1 02009-12-30 00:00:00610306N 神华煤直接液化项目轻烃回收装置（现场服务）现场服务(设张宝海,秦有福 2005-11-1 02009-12-30 00:00:00D70501N中国石化股份有限公司黄岛国家石油储备基地工程（现场服务）现场服务(设黄左坚 2006-3-1 002009-3-30 00:00:00080318CD上海石化分公司乙二醇循环水泵房消缺改造（一段设计）一段设计苏易 2008-2-1 002009-1-31 00:00:00100140TS镇海炼化100万吨/年乙烯项目安全设施设计专篇和职业卫生设计专篇（技术服务）前期工作孙成龙 2008-2-18 02009-3-31 00:00:00310604E上海石化股份有限公司60万吨/年芳烃联合装置及配套公用工程设施（详设）详细设计(施莫霞梅曹坚 2008-2-10 02009-3-30 00:00:00Q60605N 伊朗ARAK炼厂扩能及产品升级项目（现场服务）现场服务(设王毅 2007-1-1 002010-12-31 00:00:00170206SA武汉石化分公司80万吨/年乙烯及其配套工程安全预评价（安评）前期工作徐皓 2007-10-23 2009-7-31 00:00:00160712E天津石化分公司100万吨/年乙烯及配套项目炼油部分外包项目管理（详设）详细设计(施李杰,任玉兰祖超 2007-11-7 02009-2-28 00:00:00B20602N大连福佳？大化石油化工有限公司70万吨/年芳烃联合装置（现场服务）现场服务(设曹坚,纪冰曹坚 2008-1-1 002009-8-30 00:00:00190302EI 洛阳石化分公司聚丙烯装置扩能改造项目（环评）前期工作阚玉梅安景辉 2008-2-20 02009-2-28 00:00:00180871W 蓝星（天津）化工有限公司DCC联合装置采购服务采购服务韩洁童以豪 2008-2-25 02009-6-30 00:00:00100116DD镇海炼化100万吨/年乙烯项目PO/SM装置中间罐区和冷冻站（详细设计）详细设计(施李文光,安淑英 2008-3-10 02009-8-31 00:00:00370508E 乌鲁木齐石化分公司全厂外部火炬系统（详设）详细设计(施朱迪珠罗家弼 2008-3-11 02009-9-30 00:00:00080401CD-1上海赛科石化股份有限公司聚丙烯装置气锁器顶部脉冲反吹系统（一段设计）一段设计张军 2008-3-21 02009-3-31 00:00:00010309DD燕化股份有限公司3万吨/年卤化丁基橡胶装置（详细设计）详细设计(施胡畔丁文有 2008-4-1 002009-8-31 00:00:00130524SS 福建炼油乙烯项目80万吨/年乙烯装置（设计代表）现场服务(设孙钢 2008-4-1 002009-9-30 00:00:00290361SA天津石化分公司热电部改烧神华煤及储运系统改造工程（安评）前期工作李昕 2008-3-20 02009-4-30 00:00:00130524LS 福建炼油乙烯项目80万吨/年乙烯装置（EPC）总承包孙钢 2006-10-8 02009-9-30 00:00:00Q60605Y 伊朗ARAK炼厂扩能及产品升级项目（总承包）总承包王毅叶向东,吴雷 2006-9-1 002010-12-31 00:00:00130541LS 福建炼油乙烯项目C4联合装置（总承包）总承包王卫军 2007-5-18 02009-9-30 00:00:00280703Q锦州石化公司100万吨/年催化汽油加氢脱硫装置（基础）基础设计尉雷 2008-6-1 002009-4-30 00:00:00290332SS天津石化分公司100万吨乙烯及配套项目（设计代表）现场服务(设马洪波 2008-4-1 002009-11-30 00:00:00100103CD-1镇海炼化分公司20万吨/年聚丙烯装置操作台移位项目（一段设计）一段设计李烨瑛 2008-4-15 02009-6-30 00:00:00151401DD中石化湛江东兴石油企业有限公司14万吨/年聚丙烯装置（详细设计）详细设计(施李烨瑛苏洪 2008-5-1 002009-3-31 00:00:00100146PL镇海炼化100万吨/年乙烯裂解装置重油炉加工柴油原料项目（方案）前期工作杨健 2009-7-21 02009-10-31 00:00:00020101PR沧州东丽精细化工有限公司1万吨/年二甲基亚砜装置（工艺包深化）工艺设计(工朱先捷曾齐家 2009-7-21 02009-10-15 00:00:00P10903C大连西太平洋石油化工有限公司150万吨/年连续重整装置（可研）前期工作陈扬袁忠勋 2009-4-22 02009-6-30 00:00:00P10904C大连西太平洋石油化工有限公司120万吨/年催化汽油加氢装置（可研）前期工作陈扬袁忠勋 2009-4-22 02009-6-30 00:00:00014101SA中国石化科学技术研究中心环境和安全评价（环评和安评）前期工作黄晓梅 2009-3-16 02009-4-30 00:00:00C60901E 南充炼油化工总厂催化烟机（一段）一段设计冀江 2009-5-5 002009-6-30 00:00:00A20901E 大庆炼化公司YL15000烟机改造（一段）一段设计冀江 2009-4-20 02009-5-30 00:00:00P90802N湛江东兴石油企业有限公司120万吨/年中压加氢裂化装置吸收稳定系统利旧改造（现场服务）现场服务(设王兰华李浩 2009-5-1 002009-7-31 00:00:00230301TS中国中煤能源股份有限公司陕西靖边能源化工综合利用项目评价报告前期工作赵桂珍,杨挺 2009-4-28 02009-6-30 00:00:00013811CD北京东方石化两厂搬迁改造项目减温减压器用水设计（一段设计）一段设计叶伟 2009-5-5 002009-8-5 00:00:00350902I安庆分公司含硫原油加工适应性改造及油品质量升级工程制氢方案及新建污水处理场方案补充前期工作侯凯锋,朱瑜袁忠勋 2009-5-6 002009-6-10 00:00:00E20902C 天津原油商业储备基地工程（可研）前期工作高大兴孟庆海 2009-5-5 002009-6-30 00:00:00370902E乌鲁木齐石化分公司40万吨/年连续重整分馏系统核算改造（一段）一段设计朱迪珠 2009-4-10 02009-6-20 00:00:00E80903E 惠州炼油二期项目原油罐区（详设）详细设计(施李可梅袁忠勋 2009-5-8 002010-2-28 00:00:00200501FS 川化股份有限公司90万吨/年PTA装置（可研）前期工作安玉龙 2009-5-11 02009-7-31 00:00:00B20906R 澳大利亚制氢项目报价前期工作黎金戴文松 2009-5-11 02009-12-30 00:00:00100104CD镇海炼化100万吨/年乙烯装置新增干气脱碳、乙烯外送管线等设计项目（一段设计）一段设计杨健 2009-5-11 02009-8-31 00:00:00A10904E大港石化分公司100万吨/年加氢裂化装置伴热线改造（一段）一段设计马强 2009-5-11 02009-5-30 00:00:00B80601E克拉玛依石化分公司60万吨/年连续重整装置（详设）详细设计(施李凤霞罗家弼 2009-5-5 002010-3-30 00:00:00170211PR-1武汉分公司80万吨/年乙烯工程40万吨/年聚丙烯装置（JPP）（工艺包深化）工艺设计(工苏洪 2009-5-11 02009-10-31 00:00:00170401PL-1 武汉化工新城产业发展规划（规划设计）前期工作徐惟兴,王明尹大为 2009-5-12 02009-8-31 00:00:00B20907J 国家成品油储备深圳油库工程（规划）前期工作韩钧 2009-5-25 02009-6-30 00:00:00B80901N克拉玛依石化分公司150万吨/年延迟焦化装置改造（现场服务）现场服务(设李凤霞 2009-5-25 02009-7-30 00:00:00P70902E 青岛大炼油项目改造（一段）一段设计宁波 2009-3-9 002009-7-30 00:00:00350901F安庆分公司含硫原油加工适应性改造及油品质量升级工程（总体）总体设计朱瑜芬,尉雷袁忠勋 2009-5-26 02009-9-25 00:00:00310301FS-1中海石油炼化有限责任公司海南精细化工30万吨/年聚丙烯装置节能专篇报告（可研）前期工作杨挺,丁治新苏洪 2009-5-20 02009-7-31 00:00:00190214SS中原石化有限公司6万吨/年碳四烯烃催化裂解制丙烯项目（设计代表）现场服务(设安淑英 2009-6-1 002009-9-30 00:00:00E80903Q 惠州炼油二期项目原油罐区（基础）基础设计李可梅袁忠勋 2009-5-25 02009-8-30 00:00:00100109SS镇海炼化100万吨/年乙烯项目PO/SM、乙苯和中间罐区（设计代表）现场服务(设李文光,徐?? 2009-6-1 002010-3-31 00:00:00151503SA 中海油炼化有限责任公司惠州炼油二期2200万吨/年炼油改扩建及100万吨/年乙烯工程项目安全预评价（安评）前期工作徐皓 2009-5-1 002009-12-31 00:00:00Q60810E伊朗ESFAHAN炼厂产品升级项目450万吨/年渣油催化裂化装置外取热器包（详设）详细设计(施赵清 2009-7-16 02010-5-30 00:00:00E80702N海油发展惠州石化分公司加氢尾油综合利用项目40万吨/年基础油加氢装置（现场服务）现场服务(设魏冬华范传宏 2009-6-1 002010-12-31 00:00:00680801N海南炼油化工有限公司120万吨/年加氢裂化装置增产航煤改造（现场服务）现场服务(设秦永强 2009-5-1 002009-7-30 00:00:00110419N上海高桥分公司120万吨/年S-zorb催化汽油吸附脱硫示范装置（现场服务）现场服务(设陈扬袁忠勋 2009-5-1 002009-12-31 00:00:00380802N荆门石化分公司70万吨/年RSDS-II汽油加氢装置（现场服务）现场服务(设汤卫和袁忠勋 2009-5-1 002009-12-31 00:00:00410702N济南分公司90万吨/年S-zorb催化汽油吸附脱硫装置（现场服务）现场服务(设陈扬,曲晓廉袁忠勋 2009-6-1 002009-12-31 00:00:00680702N海南炼油化工有限公司800万吨/年常减压装置增上轻烃回收设施（现场服务）现场服务(设秦永强 2009-5-1 002009-8-30 00:00:00A20801N大庆炼化公司180万吨/年ARGG装置MIP-CGP改造（现场服务）现场服务(设高辉吴雷 2009-5-1 002009-10-30 00:00:00090701N齐鲁分公司胜利炼油厂第二套催化装置MIP-CGP技术改造（现场服务）现场服务(设曲晓廉吴雷 2009-6-1 002010-8-30 00:00:00B20902N沈阳石蜡化工有限公司催化裂解装置再生系统改造（现场服务）现场服务(设汤卫和 2009-7-1 002009-12-31 00:00:00610303V 神华煤直接液化厂煤液化装置（竣工图）终版施工图张宝海,秦有福 2009-1-10 02009-6-30 00:00:00610304V 神华煤直接液化厂液化项目加氢稳定装置（竣工图）终版施工图张宝海 2009-1-10 02009-6-30 00:00:00190216CD中原石化分公司乙烯装置BA101裂解炉改造（一段设计）一段设计刘敬坤,张磊何细藕 2009-4-13 02009-7-31 00:00:00680803E海南炼油化工有限公司800万吨/年常减压装置加热炉系统改造（一段）一段设计秦永强 2009-4-21 02009-8-30 00:00:00410801C-1济南分公司润滑油加氢质量升级工程30万吨/年润滑油加氢装置（可研修改）前期工作张英李浩 2009-4-23 02009-6-30 00:00:00110803C-1 上海高桥分公司重整氢气PSA提纯设施（可研修改）前期工作冀琳霍宏伟 2009-4-22 02009-5-30 00:00:00B20905W镇海炼化分公司1500万吨/年炼油 100万吨/年乙烯一体化项目申请报告前期工作赵向东,李杰郭志雄,孙丽丽 2009-4-23 02009-7-30 00:00:00Q60902R伊朗ESFAHAN炼厂产品升级项目450万吨/年渣油催化裂化装置三旋部分报价前期工作闫涛 2009-5-1 002009-7-30 00:00:00010901I燕山石化分公司130万吨/年中压加氢装置增产航煤方案前期工作杨光明 2009-4-15 02009-6-30 00:00:00Q60903R 伊朗ESFAHAN炼厂120万吨/年航煤碱洗预报价前期工作蒋荣兴,陈开蒋荣兴 2009-4-29 02009-8-30 00:00:00130524AB 福建炼油乙烯项目80万吨/年乙烯装置（竣工图）终版施工图孙钢 2009-4-15 02009-8-31 00:00:00020201SA石家庄炼化分公司油品质量升级和原油劣质化改造工程安全评价（安评）前期工作刘丹丹 2009-4-15 02009-9-30 00:00:00020201EI-1石家庄炼化分公司油品质量升级改造工程环境影响报告书（环评）前期工作饶未欣 2009-4-10 02009-8-31 00:00:00010804SA-1燕山分公司炼油厂80万吨/年连续重整装置扩能改造验收安全评价（安评）前期工作曾丹丹 2009-4-20 02009-9-30 00:00:00100145EI镇海炼化扩建1500万吨/年炼油项目环境影响评价阶段报告（环评）前期工作李瑾 2009-4-1 002009-5-31 00:00:00091107PL 扬巴有限责任公司乙烯裂解炉工艺方案（方案）前期工作李昌力,张磊 2009-4-22 02009-8-15 00:00:00Q60904L 伊朗SHIRAZ炼厂加氢裂化装置改造前期工作前期工作赵铁柱 2009-5-1 002009-7-30 00:00:00130541AB 福建炼油乙烯项目C4联合装置（竣工图）终版施工图王卫军 2009-5-4 002009-6-30 00:00:00230205PR陕西延长石油集团榆林能源化工有限公司30万吨/年聚丙烯装置（ST）工艺包设计（工艺包）工艺设计(工苏洪 2009-5-4 002009-11-30 00:00:00P10902C大连西太平洋石油化工有限公司42万吨/年芳烃抽提装置（可研）前期工作陈扬袁忠勋 2009-4-22 02009-6-30 00:00:00280101SA神华宁煤集团-沙索合成燃料国际有限公司煤间接液化项目安全预评价（安评）前期工作李昕 2009-5-1 002009-10-31 00:00:00140802SA胜利油田分公司石化总厂危险化学品安全评价（安评）前期工作高梅 2009-4-26 02009-9-30 00:00:00190215EI中原石化分公司乙烯原料路线改造（MTO）项目环境评价（环评）前期工作毕铁成 2009-5-1 002009-12-31 00:00:00310905E上海石化股份有限公司天然气综合利用1#制氢装置适应性改造（详设）详细设计(施莫霞梅戴文松 2009-5-25 02009-11-30 00:00:00090511CD仪征化纤分公司PTA生产中心压力过滤机改造项目（一段设计）一段设计贾文霞杨照 2009-6-1 002009-12-31 00:00:00480801N上海赛科乙烯改扩建项目芳烃抽提装置改造（现场服务）现场服务(设赵强 2009-6-1 002009-8-30 00:00:00P70903G 青岛炼化公司二期工程（预可研）前期工作宁波 2009-6-1 002009-8-31 00:00:00280901C 锦州石化公司160万吨/年延迟焦化装置（可研）前期工作尉雷袁忠勋 2009-5-7 002009-7-30 00:00:00100133CD镇海炼化100万吨/年乙烯项目全厂蒸汽系统节能设施（一段设计）一段设计黄振铁 2009-6-1 002009-9-30 00:00:00100134CD镇海炼化100万吨/年乙烯项目周遍工厂系统配套设施（一段设计）一段设计黄振铁 2009-6-1 002009-9-30 00:00:00270209DD中国石油独山子石化分公司乙烯工程工业废物处理装置（详细设计）详细设计(施姜立新安景辉 2009-6-8 002009-12-31 00:00:00150180CD茂名石化分公司2#裂解装置增加8#裂解炉甩头设计（一段设计）一段设计章践何细藕 2009-6-8 002009-6-30 00:00:00014301PL燕山分公司化工七厂利旧苯乙烯设备方案（方案设计）前期工作安淑英 2009-6-8 002009-7-31 00:00:00190904L 辽阳石化分公司100万吨/年加氢精制装置汽提塔核算前期工作刘立 2009-6-11 02009-7-20 00:00:00310906E上海石化股份有限公司2#芳烃联合装置重整装置增加重石脑油脱水设施（一段）一段设计莫霞梅曹坚 2009-6-10 02009-9-30 00:00:00Q60801E 伊朗HORMUZ炼厂520万吨/年延迟焦化装置详细设计(施钟京卫李出和 2009-6-15 02011-3-30 00:00:00110802E上海高桥分公司润滑油系统改造项目25万吨/年加氢裂化尾油减压分馏装置（详设）详细设计(施冀琳霍宏伟 2009-6-11 02009-11-30 00:00:00E20801W 曹妃甸原油商业储备基地工程安全条件论证报告前期工作高大兴孟庆海 2009-6-17 02009-8-20 00:00:00013812FS 北京东方石化有限公司火炬系统改造项目（可研）前期工作白玉强苗济国 2009-6-15 02009-8-31 00:00:00110811E上海高桥分公司润滑油系统改造项目40万吨/年2#酮苯脱蜡脱油联合装置改造（详设）详细设计(施冀琳霍宏伟 2009-6-18 02009-11-30 00:00:00B00901I 普光天然气净化厂润滑油站（方案）前期工作王俊彪,郑立李浩 2009-3-20 02009-6-30 00:00:00310908C 上海石化股份有限公司炼油改扩建工程（可研）前期工作莫霞梅曹坚 2009-6-19 02009-9-30 00:00:00B10801F-1宁夏炼化分公司260万吨/年重油催化裂化装置（总体修改）总体设计高辉 2009-6-22 02009-8-22 00:00:00B10802F-1宁夏炼化分公司80万吨/年连续重整装置(总体设计修改)总体设计高辉 2009-6-22 02009-8-22 00:00:00370903C乌鲁木齐石化公司加工1000万吨/年南疆油项目（可研）前期工作朱迪珠 2009-6-20 02009-8-15 00:00:00100103CD-2镇海炼化分公司20万吨/年聚丙烯装置操作台移位项目（一段设计）一段设计李烨瑛 2009-6-15 02009-9-30 00:00:00E80904V 惠州一期项目竣工图(系统部分)终版施工图魏冬华 2009-6-23 02009-9-30 00:00:00。

全国各大院校代码

华北电业联合职工大学
·
51837
首都联合职工大学
90001
国防大学
90020
防化指挥工程学院
,
90022
陆军航空兵学院
90025
解放军艺术学院
90026
￥
后勤指挥学院
90037
北京军医学院
90039
装备指挥技术学院
，
90041
装甲兵工程学院
90051
空军指挥学院
90203
特种警察学院
]
90204
武警北京指挥学院
张家口医学院
10093
承德医学院
10094
河北师范大学
*
10096
保定师范专科学校
10097
张家口师范专科学校
10098
]
承德民族师范高等专科学校
10099
唐山师范学院
原唐山师专升格更名
10100
廊坊师范学院
原廊坊师专教育学院师校合并新建
~
10101
衡水师范专科学校
10102
石家庄师范专科学校
10103
、
11566
山西经济管理学院
11630
山西财政税务专科学校
11928
】
山西警官高等专科学校
原公安部管干院山西警校合并新建
19110
华北工学院（分校）
41401
山西工业职业技术学院
原山西矿业职业技术学院更名
(
41402
山西建筑职业技术学院
山西建筑工程职业技术学院更名
41403
山西工程职业技术学院
41404
11964
邢台医学高等专科学校

齐鲁工业大学2020报录比(1)

齐鲁工业大学2020年报录比
学院名称
专业代码
材料科学和工程 80500
学院
85600
电气工程与自动 81100
化学院
85400
管理学院
120200
化学与制药工程 70300
学院
81700
环境科学与工程 83000
学院
85700
机械与汽车工程 80200
学院
85500
计算机科学与术学院
技
81203
金融学院
化学工程与技术
8
270/348/303
环境科学与工程
14 265/320/292
资源与环境机械工程机械
49 267/392/296 17 273/330/292 124 266/388/311
复试最低分/最高分/平均分 77/94/84 76/93/84 74/92/82 62/91/80 70/85/79 79/9-1/86 82/90/85 80/89/86
75/92/81 72/90/83 64/92/81
计算机应用技术
25 283/345/313
68/87/78
应用经济学金融
11 343/409/355 28 344与工程
马克思主义中国化研究生物学轻工技术与工程生物与医药
14 345/377/359
21 325/415/363
20 289/369/330 41 264/388/301 150 264/412/323
79/90/85
72/89/82 74/87/80 71/91/83 64/92/80
食品料学与工程
26 267/351/299
64/90/81

Particle erosion on CNF coated CF composites

Particle erosion on carbon nanoﬁber paper coated carbon ﬁber/epoxycompositesNa Zhang a ,b ,1,Fan Yang a ,1,2,Changyu Shen b ,Jose Castro c ,L.James Lee a ,⇑aDepartment of Chemical and Biomolecular Engineering,The Ohio State University,OH 43210,USA bDepartment of Materials Science and Engineering,Zhengzhou University,Zhengzhou 450052,China cDepartment of Integrative Systems Engineering,The Ohio State University,OH 43210,USAa r t i c l e i n f o Article history:Received 2October 2012Accepted 1May 2013Available online 15May 2013Keywords:A.Carbon ﬁberB.WearC.Finite element analysis (FEA)D.Electron microscopya b s t r a c tCarbon ﬁber (CF)woven fabric (52%by weight)reinforced epoxy composite and carbon nanoﬁber (CNF,12%by weight)paper coated on the surface of the CF/epoxy composite were fabricated by resin transfer molding (RTM).The surface erosion characteristics of molded CF composites were investigated by sand erosion test using silica particles with a size around 150l m as the erodent.The eroded surfaces were examined by scanning electron microscopy (SEM)and weight loss.The CNF paper was able to provide a much stronger erosion resistance compared to the CF reinforced epoxy composites,which is attributed to the high strength of CNFs and their nanoscale structure.Finite element (FE)computer simulations were used to qualitative interpret the underlying mechanisms.Ó2013Elsevier Ltd.All rights reserved.1.IntroductionPolymer composite materials often exhibit poor erosion resis-tance [1–6].Improving erosion resistance of light weight compos-ite materials is crucial for many industrial applications such as wind turbine blades [7–9].Tilly [3–5,10]presented a thorough analysis of various parameters affecting erosion,including particle properties,impact parameters,particle concentration,type of rein-forcement and temperature.For erosive wear resistance,materials can be classiﬁed into ductile and brittle categories according to their behavior with respect to the impinging angle and erosion process [12].In brittle erosion,the weight loss increases linearly with time,while in a ductile type the particles may be embedded in the target surface causing a weight gain initially,followed with a linear weight loss as a function of time by further impingement.The maximum weight loss was found at about 90°and 30°impact angles for brittle and ductile erosions,respectively [10–12].Both glass ﬁber and carbon ﬁber reinforced epoxy composites show brittle characteristics [12–15].In this study,we present a new approach for improving the erosive resistance of composites using a thin protective layer of paper made of carbon nanoﬁbers (CNFs)on the composite surface.A series of sand erosion experiments were carried out to compare the particle erosion performance of CF based composites with and without surface protection by the CNF puter simulations of ﬁnite element (FE)meth-od were used to explain the underlying mechanisms for the ob-served performance difference between the two composites made of microscale CFs and nanoscale CNFs.2.Experimental 2.1.MaterialsThe CNF used in this study was a vapor grown carbon nanoﬁber,Pyrograf Ò-III (PR-24-XT-HHT),obtained from Applied Sciences Inc.(Cedarville,OH).The length of CNFs is about 30–100l m and the average diameter is about 100nm.The carbon ﬁber woven fabric used in this work was an IM7-12k,5harness,370g/m 2fabric obtained from Textile Industries,Inc.An epoxy resin,EPIKOTETM RIM 135with an epoxy equivalent weight (EEW)of about 166–185,and a diamine curing agent,EPIKURETM RIM H 137with an amine value of about 400–600mg [KOH]/g,were provided by Hexion Specialty Chemicals (Houston,TX).This is a low tempera-ture and low viscosity resin designed for manufacturing wind tur-bine blades.Silica sand,blocky,sharp edged green particles with a size about 150l m and a hardness of 2600Knoop were selected as the erodent.A scanning electron micrograph of the silica sand is shown in Fig.1.1359-8368/$-see front matter Ó2013Elsevier Ltd.All rights reserved./10.1016/positesb.2013.05.003Corresponding author.Address:The Ohio State University,125A Koffolt Laboratories,140West 19th Avenue,Columbus,OH 43210,USA.Tel.:+16142922408;fax:+16142923769.E-mail addresses:zhangna163163@ (N.Zhang),yangyangyang99@ (F.Yang),shency@ (C.Shen),castro.38@ (J.Castro),lee.31@ (L.J.Lee).1These authors contributed equally to this work.2Present address:Department of Mechanical and Industrial Engineering,Univer-sity of Toronto,Toronto,ON,Canada M5S 3G8.2.2.Fabrication of CNF nanopaper and CNF nanopaper coated glass ﬁber/epoxy compositesA vacuum ﬁltration technique was used for preparing the nano-paper.In this set up,a 90mm diameter glass ﬁlter holder with a stainless steel screen membrane support was placed over a conical ﬂask.Once the hydrophilic polycarbonate membrane ﬁlter with a pore size of 0.4l m (Millipore Inc.)was placed plain ﬂat in the set up and clamped,it was connected to a vacuum aspirator pump.The nanoparticle solution was prepared as follows:the CNF parti-cles were dispersed in deionized (DI)water and sonicated using a Branson Digital Soniﬁer [(S450D),75%amplitude]for 30min.The resulting suspension was cooled down for 30min in a refrigerator and sonicated for 30sec again,then ﬁltered through the ﬁltration set up previously described under a pressure of $400kPa.Vacuum was applied for about 20min after all the water was ﬁltered away.The CNF nanopapers were dried overnight at room temperature.The thickness of CNF nanopapers was 0.28±0.02mm with a poros-ity of 94%.Vacuum assisted resin transfer molding (VARTM)was used to impregnate the CF and CNF nanopaper coated CF preforms,which consisted of three layers of CF fabrics with andwithout a single layer of CNF nanopaper.The performs were placed and sealed a vacuum bag.Before mold ﬁlling,vacuum was applied to force the bag to press tightly against the ﬁber stack.The epoxy mixture was degassed in a vacuum chamber for 15min,and the resin was introduced into the ﬁber preforms.The samples were cured room temperature (around 25°C)for 24hr and post-cured 80°C for an additional 15hr.The CF and CNF nanopaper contents in the composites were controlled at 52and 12wt.%,respectively,measured by a thermo-gravimetric analyzer (TGA).2.3.Particle erosion testRectangular samples of size 12.5Â80mm molded composite plaques for the erosion epoxy and CNF/epoxy composites showed brittle with the maximum erosion rate at normal impinging angle was chosen as 90°in this frame with a rectangular opening was placed the test specimens to keep the eroded area The conditions under which the erosion are listed in Table 1.A standard test procedure each erosion test.Before testing,the samples were burnished to re-move the pollutants from the sample surface.After each test,spec-imens were degreased with acetone,dried in a jet of cold air and weighted with a precision balance (Explore,ep214C).The weight loss by sand abrasion (with an accuracy of 0.1mg)was used to quantify the erosion resistance.Each data point was obtained from the average value of ﬁve measurements.Scanning electron microscopy (SEM)images were collected using a ﬁeld emission scanning electron microscope,Hitachi S-4300(Tokyo,Japan).The samples were gold-sprayed to reduce charging of the surface.3.Finite element simulationTo investigate the mechanisms of particle erosion,Finite ele-ment (FE)simulations were carried out for CF/epoxy composites with and without CNF nanopaper coating.It is difﬁcult to track the actual erosion process which involves a large number of colli-sion events.Most of the existing work simulated only one or a few particle collision events [16–20].However,the trend can still be obtained for the erosion rate as a function of various parameters such as impinging angle,velocity,and target properties [16,19].In this study,one collision event with periodically distributed par-ticles was simulated.Qualitative comparisons were made between the experiments and the simulations.This study aims at providing insights into the mechanisms underlying the particle erosion per-formance of CF and CNF reinforced epoxy composites.Three-dimensional simulations were carried out using the gen-eralized FE codes ABAQUS/EXPLICIT version 6.9.Fig.2illustrates the conﬁguration for the simulation of CF/epoxy composite.The eroding particles were simpliﬁed as spheres which were projected to the target surface in periodic arrays.The CF woven fabric has an Fig.1.Scanning electron micrograph of silica sand particles.Table 1Erosion test conditions.Impingement angle (°)90Impingement area (mm 2)600Impingement time (s)15Erodent feed rate (g/min)453.4Test temperature (°C)20Nozzle to sample distance (mm)25.4Nozzle diameter (mm)8Air pressure (MPa)0.47Fig.2.FE conﬁguration of the particle erosion on surface of CF/epoxy composite.Part B 54(2013)209–214Fig.3a.The diameter of the eroding particle is0.15mm according to the experiments.The diameter of the CFs is adjusted so that the carbon content is52%by weight,consistent with experiment mea-surements.The model contained117,153linear solid elements with reduced integration(type C3D8R).Fig.3b shows the RVE for the CNF nanopaper.The dimensions are the same as the CF/epoxy case except the coating thickness,for which a smaller value of 0.05mm was applied.Utilizing the geometric symmetry,the RVE for CNF nanopaper only needs to contain one fourth of the conﬁg-uration of that for CF/epoxy composite.The right graph in Fig.3b is a magniﬁcation of theﬁber skeleton for a small portion of the CNF nanopaper model.Since the randomly interweavedﬁber conﬁgura-tion in experiments cannot be easily constructed in meshing,a uni-formly distributed orthogonal frame of beams is used instead to represent the highly interlaced CNF network.A square cross sec-tion instead of a circular section is used for CNF for simplicity. Theﬁber diameter of CNF in simulation is chosen as0.5l m which is larger than that observed in the experiments.This is because thinner CNFs would needﬁner mesh and hence more computa-tional expense.In spite of this,a large number of elements are needed due to the huge difference between the CNF diameter and the dimension of simulation RVE which depends on the size of eroding particles.The CNF inter-space is chosen as2.82l m so that the carbon content would be12%by weight in the nanopaper, consistent with our experiments.The obtained model contains 1,060,428C3D8R elements,corresponding to more than100CPU hours for a typical run on a2.6GHz computer for3l s of simula-tion time.Although this simpliﬁed model is different from the actual composites,we expect that it can provide qualitative inter-pretation of the experimental observations.Periodic boundary conditions are applied on the lateral bound-aries by coupling the degrees of freedom of the corresponding nodes on the opposite faces using the linear equations for CF/epoxy version2.1.For all conﬁgurations the mesh is reﬁned near theimpinging location so that the eroded mass could be accuratelycaptured.The silica particles are modeled using the linear elastic constitu-tive law.While epoxy,CF and CNF are modeled using the elastic–plastic constitutive law with linear isotropic hardening.The mate-rial parameters are listed in Table2[22–25],where q is the density, E is the Young’s modulus,v is the Poisson’s ratio,r y is the yield stress,E is the Young’s modulus,E p is the hardening modulusand r s is the material strength.The physical meaning of the parameters can be revealed by the stress–strain(r–e)relation for uni-axial stretch deformation in small deformation range as in Eq.(1).e¼rE;r<r yrþrÀr yp;r P r y(ð1ÞIt can be seen from Table2that the plastic strain set is very small,reﬂecting the brittle property of these materials.In order to model the erosion of the target materials,a criterion is needed for the element removal.For the brittle erosion,the mass removal is caused by the spalling mechanism involving the evolu-tion of micro-cracks,which is very difﬁcult to model by the FE method.Some researchers used Johnson–Holmquist model and the corresponding equation of state to model the failure behavior of the brittle materials[21].However,the large amount of ele-ments and the multi-phase properties of composites would cause huge computational expense if complex models are applied.There-fore a simpliﬁed criterion based on equivalent stress is applied here for the element removal.The element is removed once the equivalent stress r at its integration point reaches the critical value r cri as in Eq.(2).Here r0is the deviatoric stress tensor, r cri is cho-sen as the material strength r s.This criterion can be simply imple-mented in the dynamic shear failure option available in ABAQUS/Computational RVEs with mesh for(a)CF/epoxy composite and(b)CNF nanopaper.The inset graph shows the enlarged view of the skeleton of CNFs in portion indicated by the square.N.Zhang et al./Composites:Part B54(2013)209–214211r ¼ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ3r 0:r 0r ¼ rcri4.Results and discussionsImages of the CF woven fabric and CNF Fig.4a and b,respectively.After uniformly stream impacting for a given time,the CF/epoxy was severely eroded while the surface protected by paper coating did not show much erosion.The inspected by SEM (Fig.4c and d).As can be seen,sists of the removal of matrix materials in the resin that the exposed ﬁbers are no longer bonded to when the epoxy matrix fails to support the ﬁbers.ﬁbers could easily break into fragments,removal during erosion.The failure mode in process involving surface matrix removing,surface micro-cracking,ﬁber/matrix debonding,ﬁber breakage and material removal [10–12].As shown in Fig.4c,many micro-cracks caused by the im-pact of erodent particles can be seen in carbon ﬁbers,and many small fragments of ﬁbers also can be seen on the eroded surface.For the surface protected by the CNF nanopaper coating,there are few exposed segments of carbon nanoﬁbers after particle ero-sion as shown in Fig.4d.many CNFs can partake the impact force and the ﬁber network be-haves as a whole shielding during particle collision.While for CF/epoxy composites,the ﬁber spacing is comparable or even larger than the size of the eroding particles,therefore,the resin matrix is not well protected.The pure epoxy plaque shows a better parti-cle erosion resistance than its CF/epoxy composite,but the resis-tance is not as good as the CNF nanopaper coating.Our FE simulation results further interpret the experimental served differences between CF/epoxy composite with and without nanopaper during particle erosion.The eroded volume is calcu-as the amount caused by the single impingement.The eroded volume for CF/epoxy is about three times as that for CNF nanopaper.addition,the erosion results are more sensitive to the impinging location for CF/epoxy composite than for CNF pares the eroded volume at different impinging positions CF/epoxy composite and CNF nanopaper.The eroded volume plotted versus a surface distance of several times of the REV range utilizing periodicity.Five representative positions A,B,C,D,and investigated for CF/epoxy composites while two positions woven fabric,(b)SEM image of CNF nanopaper,(c)SEM images of eroded CF/epoxy composite surface,composite surface.Fig.5.Mass loss of different materials after 15sec erosion test.212N.and G are investigated for CNF nanopaper as indicated in Fig.6b.For CF/epoxy composite the eroded volume at position E is nearly40% smaller than that at position A.While for CNF nanopaper the rela-tive difference for eroded volume between the two positions is below10%.The largest erosion rate occurs when particle impinges at the resin rich position in both cases.The simulation results pro-vide qualitative explanation to the fact that the eroded surface of CNF nanopaper is much smoother than that of CF/epoxy composite.Comparison of the effect of impinging positions on the eroded volume for CF/epoxy composite and CNF nanopaper.(a)The eroded volume versus curve for CNF nanopaper and right for CF/epoxy;(b)Top view of the different impinging positions,where L is the distance betweenﬁberContour plot of von Mises stress for(a)CF/epoxy and(b)CNF nanopaper at maximum erodent indentation,(c)von Mises stress versus the distance from position along the x axis on the target surface.The horizontal dash lines in(c)indicate the critical stresses for CNF/CF and epoxy,respectively.The much smaller erosion rate of CNF nanopaper can be attrib-uted to its nano-sized structure.For CF/epoxy composite theﬁber spacing is larger or comparable to the eroding particle size and the relative weak resin cannot be effectively protected.While for the nanopaper theﬁber spacing is much smaller,a large number of in-ter-connectedﬁbers can partake the impact force of the particle to-gether at the impinging position.This effect can be demonstrated by comparing the stress distribution for the two target materials. Fig.7a and b plot the contour of von Mises stress at maximum ero-dent indentation for CF/epoxy composite and CNF nanopaper, respectively.For both targets the erodent impinges at the positions corresponding to the largest erosion,i.e.position A for CF/epoxy composite and F for CNF nanopaper.It shows that for CNF nanopa-per the stress endured by the CNFs is much higher than that by the epoxy resin while for CF/epoxy composite the stresses inﬁber and resin do not differ much.In both cases,the resin is the main source for eroded volume due to its much lower strength than theﬁbers. The stress distribution can be more clearly seen in Fig.7c where the von Mises stress on the target surface is plotted against the dis-tance from the initial impinging position along the x axis.For Fig.7c the erosion criteria is switched off in the simulations for comparison convenience.The peaks and valleys on the curve of CNF nanopaper correspond to the high stresses on CNFs and low stresses on epoxy.It can be seen from Fig.7c that although the nanoﬁbers in CNF nanopaper experience very high stress near the impinge location,the epoxy resin actually experiences a lower stress than that in CF/epoxy composite because the stress is mainly endured by the CNFs for CNF nanopaper as indicated by the dark strips in Fig.7b.The intensely distributedﬁbers play an important role in partaking the impacting force,leading to smaller stress in the weak resin.While for CF/epoxy composite theﬁber may be far away from the impinge location due to the largeﬁber inter-space.The impact force is mainly endured by the weak resin. Fig.7c represents the instantaneous stress distribution for a case study.The nanopaper may not lose any weight at this time point because the endured stresses by both CNF and epoxy are lower than the critical CNF/CF and epoxy stresses marked on Fig.7c.On the other hand,some epoxy near the impinging point of the CF/ epoxy composite may be ablated away because the endured stress there reaches the critical value.Although qualitative,this simpli-ﬁed analysis provides an explanation for the observed differences of particle resistance between the two composite materials.5.ConclusionsIn this study,carbon nanoﬁber(CNF)nanopaper was prepared by theﬁltration method and used to protect the carbonﬁber (CF)/epoxy composites through vacuum assisted resin transform molding(VARTM)process.The CNF nanopaper can achieve much better particle erosion resistance than the conventional CF/epoxy composites.Ourﬁnite element simulations of the particle erosion experiments,although highly simpliﬁed,are able to provide qual-itative insight regarding the underlying mechanisms.The CNF nanopaper is indicated as a good protective coating material for wind turbine blades and other related applications in aerospace and transportation industries.AcknowledgementsTheﬁrst author would like to acknowledge the China Scholar-ship Council for theirﬁnancial support to enable the author to study at The Ohio State University.The authors would like to thank NSF and Nanomaterial Innovation Ltd.for partialﬁnancial support of this work.Carbonﬁber mats were donated by Textile Industries, Inc.and the epoxy resin was donated by Hexion.References[1]Miyazaki N,Takeda N.Solid particle erosion ofﬁber reinforced plastics.JCompos Mater1993;27(1):21–31.[2]Tsiang TH.Sand erosion ofﬁber composites:testing and evaluation.In:ChamisCC,editor.Test Methods and Design Allowables for Fibrous Composites,vol.2.ASTM STP1989:1003;55–74.[3]Tilly GP.Sand erosion of metals and plastics:a brief review.Wear1969;14:241–8.[4]Tilly GP.Erosion caused by airborne particles.Wear1969;14:63–79.[5]Tilly GP,Sage W.The interaction of particles and material behaviour in erosionprocess.Wear1970;16:447–65.[6]Miyazaki N,Hamao T.Effect of interfacial strength on erosion behavior of FRPs.J Compos Mater1996;30(1):35–50.[7]<>.Last accessed on September262012.[8]Dalili N,Edrisy A,Carriveau R.A review of surface engineering issues critical towind turbine performance.Renew Sust Energy Rev2009;13(2):428–38. [9]Barkoula NM,Karger-Kocsis J.Review processes and inﬂuencing parameters ofthe solid particle erosion of polymers and their composites.J Mater Sci 2002;37(18):3807–20.[10]Tilly GP.A two stage mechanism of ductile erosion.Wear1973;23(1):87–96.[11]Pool KV,Dharan CKH,Finnie I.Erosive wear of composite materials.Wear1986;107(1):1–12.[12]Patnaika A,Satapathyb A,Chandc N,Barkoulad NM,Biswasb S.Solid particleerosion wear characteristics ofﬁber and particulateﬁlled polymer composites:a review.Wear2010;268(1–2):249–63.[13]Zhou G,Movva S,Lee LJ.Preparation and properties of nanoparticle and long-ﬁber-reinforced unsaturated polyester composites.Polym Compos 2009;30(7):861–5.[14]Palmeri MJ,Putz KW,Ramanathan T,Brinson LC.Multi-scale reinforcement ofCFRPs using carbon nanoﬁpos Sci Technol2011;71(2):79–86. [15]Cai ZQ,Movva S,Chiou NR,Guerra D,Hioe Y,Castro JM,et al.Effect ofpolyaniline surface modiﬁcation of carbon nanoﬁbers on cure kinetics of epoxy resin.J Appl Polym Sci2010;118(4):2328–35.[16]ElTobgy MS,Ng E,Elbestawi MA.Finite element modeling of erosive wear.Int JMach Tool Manu2005;45(11):1337–46.[17]Grifﬁn D,Daadbin A,Datta S.The development of a three-dimensionalﬁniteelement model for solid particle erosion on an alumina scale/MA956substrate.Wear2004;256(9–10):900–6.[18]Takaffoli M,Papini M.Finite element analysis of single impacts of angularparticles on ductile targets.Wear2009;267(1–4):144–51.[19]Shimizu K,Noguchi T,Seitoh H,Okadab M,Matsubara Y.FEM analysis oferosive wear.Wear2001;250(1–12):779–84.[20]Bielawski M,Beres W.FE modelling of surface stresses in erosion-resistantcoatings under single particle impact.Wear2007;262(1–2):167–75.[21]Wang YF,Yang ZG.Finite element model of erosive wear on ductile and brittlematerials.Wear2008;265(5–6):871–8.[22]Martienssen W,Warlimont H.Springer handbook of condensed matter andmaterials data.Berlin:Springer;2005.[23]Low KH,Wang Y.Modeling of multi-layer circuit boards by using a model ofbi-phase and elasto-plastic plies.Circuit World2007;33:9–20.[24]Tibbetts GG,Beetz JCP.Mechanical properties of vapour-grown carbonﬁbres.JPhys D:Appl Phys1987;20(3):292–7.[25]Grace NF,Ragheb WF,Sayed GA.Development and application of innovativetriaxially braided ductile FRP fabric for strengthening concrete pos Struct2004;64(3–4):521–30.214N.Zhang et al./Composites:Part B54(2013)209–214。

数学建模案例分析--线性代数建模案例20例

线性代数建模案例汇编目录案例一. 交通网络流量分析问题1案例二. 配方问题4案例三. 投入产出问题6案例四. 平板的稳态温度分布问题7案例五. CT图像的代数重建问题11案例六. 平衡结构的梁受力计算13案例七. 化学方程式配平问题16案例八. 互付工资问题17案例九. 平衡价格问题19案例十. 电路设计问题20案例十一. 平面图形的几何变换22案例十二. 太空探测器轨道数据问题24案例十三. 应用矩阵编制Hill密码25案例十四. 显示器色彩制式转换问题27案例十五. 人员流动问题29案例十六. 金融公司支付基金的流动31案例十七. 选举问题33案例十八. 简单的种群增长问题34案例十九. 一阶常系数线性齐次微分方程组的求解36 案例二十. 最值问题38附录数学实验报告模板错误!未定义书签。

案例一. 交通网络流量分析问题城市道路网中每条道路、每个交叉路口的车流量调查，是分析、评价及改善城市交通状况的基础。

根据实际车流量信息可以设计流量控制方案，必要时设置单行线，以免大量车辆长时间拥堵。

【模型准备】某城市单行线如下图所示, 其中的数字表示该路段每小时按箭头方向行驶的车流量(单位: 辆).图3 某城市单行线车流量(1) 建立确定每条道路流量的线性方程组.(2) 为了唯一确定未知流量, 还需要增添哪几条道路的流量统计? (3) 当x 4 = 350时, 确定x 1, x 2, x 3的值.(4) 若x 4 = 200, 则单行线应该如何改动才合理?【模型假设】 (1) 每条道路都是单行线. (2) 每个交叉路口进入和离开的车辆数目相等.【模型建立】根据图3和上述假设, 在①, ②, ③, ④四个路口进出车辆数目分别满足500 = x 1 + x 2① 400 + x 1 = x 4 + 300 ② x 2 + x 3 = 100 + 200 ③ x 4 = x 3 + 300 ④ 【模型求解】根据上述等式可得如下线性方程组12142334500100300300x x x x x x x x +=⎧⎪-=-⎪⎨+=⎪⎪-+=⎩其增广矩阵(A , b ) =1100500100110001103000011300⎛⎫ ⎪--⎪ ⎪ ⎪-⎝⎭−−−−→初等行变换10011000101600001130000000--⎛⎫ ⎪⎪-- ⎪⎪⎝⎭由此可得142434100600300x x x x x x -=-⎧⎪+=⎨⎪-=-⎩ 即142434100600300x x x x x x =-⎧⎪=-+⎨⎪=-⎩. 为了唯一确定未知流量, 只要增添x 4统计的值即可. 当x 4 = 350时, 确定x 1 = 250, x 2 = 250, x 3 = 50.若x 4 = 200, 则x 1 = 100, x 2 = 400, x 3 = -100 < 0. 这表明单行线“③←④”应该改为“③→④”才合理.【模型分析】(1) 由(A , b )的行最简形可见, 上述方程组中的最后一个方程是多余的. 这意味着最后一个方程中的数据“300”可以不用统计.(2) 由142434100600300x x x x x x =-⎧⎪=-+⎨⎪=-⎩可得213141500200100x x x x x x =-+⎧⎪=-⎨⎪=+⎩, 123242500300600x x x x x x =-+⎧⎪=-+⎨⎪=-+⎩, 132343200300300x x x x x x =+⎧⎪=-+⎨⎪=+⎩, 这就是说x 1, x 2, x 3, x 4这四个未知量中, 任意一个未知量的值统计出来之后都可以确定出其他三个未知量的值.Matlab 实验题某城市有下图所示的交通图, 每条道路都是单行线, 需要调查每条道路每小时的车流量. 图中的数字表示该条路段的车流数. 如果每个交叉路口进入和离开的车数相等, 整个图中进入和离开的车数相等.图4 某城市单行线车流量(1)建立确定每条道路流量的线性方程组.(2)分析哪些流量数据是多余的.(3)为了唯一确定未知流量, 需要增添哪几条道路的流量统计.案例二. 配方问题在化工、医药、日常膳食等方面都经常涉及到配方问题. 在不考虑各种成分之间可能发生某些化学反应时, 配方问题可以用向量和线性方程组来建模. 【模型准备】一种佐料由四种原料A 、B 、C 、D 混合而成. 这种佐料现有两种规格, 这两种规格的佐料中, 四种原料的比例分别为2:3:1:1和1:2:1:2. 现在需要四种原料的比例为4:7:3:5的第三种规格的佐料. 问: 第三种规格的佐料能否由前两种规格的佐料按一定比例配制而成?【模型假设】 (1) 假设四种原料混合在一起时不发生化学变化. (2) 假设四种原料的比例是按重量计算的. (3) 假设前两种规格的佐料分装成袋, 比如说第一种规格的佐料每袋净重7克(其中A 、B 、C 、D 四种原料分别为2克, 3克, 1克, 1克), 第二种规格的佐料每袋净重6克(其中A 、B 、C 、D 四种原料分别为1克, 2克, 1克, 2克). 【模型建立】根据已知数据和上述假设, 可以进一步假设将x 袋第一种规格的佐料与y 袋第二种规格的佐料混合在一起, 得到的混合物中A 、B 、C 、D 四种原料分别为4克, 7克, 3克, 5克, 则有以下线性方程组24,327,3,2 5.x y x y x y x y +=⎧⎪+=⎨+=⎪+=⎩ 【模型求解】上述线性方程组的增广矩阵(A , b ) =214327113125⎛⎫ ⎪ ⎪ ⎪ ⎪⎝⎭−−−−→初等行变换101012000000⎛⎫ ⎪⎪ ⎪ ⎪⎝⎭,可见{1,2.x y == 又因为第一种规格的佐料每袋净重7克, 第二种规格的佐料每袋净重6克, 所以第三种规格的佐料能由前两种规格的佐料按7:12的比例配制而成. 【模型分析】(1) 若令α1 = (2, 3, 1, 1)T , α2 = (1, 2, 1, 1)T , β = (4, 7, 5, 3)T , 则原问题等价于“线性方程组Ax = b 是否有解”, 也等价于“β能否由α1, α2线性表示”.(2) 若四种原料的比例是按体积计算的, 则还要考虑混合前后体积的关系(未必是简单的叠加), 因而最好还是先根据具体情况将体积比转换为重量比, 然后再按上述方法处理.(3) 上面的模型假设中的第三个假设只是起到简化运算的作用. 如果直接设x 克第一种规格的佐料与y 克第二种规格的佐料混合得第三种规格的佐料, 则有下表因而有如下线性方程组214(),7619327(),7619113(),7619125().7619x y x y x y x y x y x y x y x y ⎧+=+⎪⎪⎪+=+⎪⎨⎪+=+⎪⎪⎪+=+⎪⎩(*) 【模型检验】把x = 7, y = 12代入上述方程组(*), 则各等式都成立. 可见模型假设中的第三个假设不影响解的正确性.Matlab 实验题蛋白质、碳水化合物和脂肪是人体每日必须的三种营养, 但过量的脂肪摄入不利于健康.人们可以通过适量的运动来消耗多余的脂肪. 设三种食物(脱脂牛奶、大豆面粉、乳清)每100克中蛋白质、碳水化合物和脂肪的含量以及慢跑5分钟消耗蛋白质、碳水化合物和脂肪的量如下表.问怎样安排饮食和运动才能实现每日的营养需求?案例三. 投入产出问题在研究多个经济部门之间的投入产出关系时, W. Leontief 提出了投入产出模型. 这为经济学研究提供了强有力的手段. W. Leontief 因此获得了1973年的Nobel 经济学奖.【模型准备】某地有一座煤矿, 一个发电厂和一条铁路. 经成本核算, 每生产价值1元钱的煤需消耗0.3元的电; 为了把这1元钱的煤运出去需花费0.2元的运费; 每生产1元的电需0.6元的煤作燃料; 为了运行电厂的辅助设备需消耗本身0.1元的电, 还需要花费0.1元的运费; 作为铁路局, 每提供1元运费的运输需消耗0.5元的煤, 辅助设备要消耗0.1元的电. 现煤矿接到外地6万元煤的订货, 电厂有10万元电的外地需求, 问: 煤矿和电厂各生产多少才能满足需求? 【模型假设】假设不考虑价格变动等其他因素.【模型建立】设煤矿, 电厂, 铁路分别产出x 元, y 元, z 元刚好满足需求. 则有下表根据需求, 应该有(0.60.5)60000(0.30.10.1)100000(0.20.1)0x y z y x y z z x y -+=⎧⎪-++=⎨⎪-+=⎩, 即0.60.5600000.30.90.11000000.20.10x y z x y z x y z --=⎧⎪-+-=⎨⎪--+=⎩ 【模型求解】在Matlab 命令窗口输入以下命令>> A = [1,-0.6,-0.5;-0.3,0.9,-0.1;-0.2,-0.1,1]; b = [60000;100000;0]; >> x = A\bMatlab 执行后得 x =1.0e+005 *1.99661.84150.5835可见煤矿要生产1.9966⨯105元的煤, 电厂要生产1.8415⨯105元的电恰好满足需求.【模型分析】令x =xyz⎛⎫⎪⎪⎝⎭, A =00.60.50.30.10.10.20.10⎛⎫⎪⎪⎝⎭, b =60000100000⎛⎫⎪⎪⎝⎭, 其中x称为总产值列向量,A称为消耗系数矩阵, b称为最终产品向量, 则Ax =00.60.50.30.10.10.20.10⎛⎫⎪⎪⎝⎭xyz⎛⎫⎪⎪⎝⎭=0.60.50.30.10.10.20.1y zx y zx y+⎛⎫⎪++⎪+⎝⎭根据需求, 应该有x-Ax = b, 即(E-A)x = b. 故x = (E-A)-1b.Matlab实验题某乡镇有甲、乙、丙三个企业. 甲企业每生产1元的产品要消耗0.25元乙企业的产品和0.25元丙企业的产品. 乙企业每生产1元的产品要消耗0.65元甲企业的产品, 0.05元自产的产品和0.05元丙企业的产品. 丙企业每生产1元的产品要消耗0.5元甲企业的产品和0.1元乙企业的产品. 在一个生产周期内, 甲、乙、丙三个企业生产的产品价值分别为100万元, 120万元, 60万元, 同时各自的固定资产折旧分别为20万元, 5万元和5万元.(1) 求一个生产周期内这三个企业扣除消耗和折旧后的新创价值.(2) 如果这三个企业接到外来订单分别为50万元, 60万元, 40万元, 那么他们各生产多少才能满足需求?案例四. 平板的稳态温度分布问题在热传导的研究中, 一个重要的问题是确定一块平板的稳态温度分布. 根据…定律, 只要测定一块矩形平板四周的温度就可以确定平板上各点的温度.图8 一块平板的温度分布图【模型准备】如图9所示的平板代表一条金属梁的截面. 已知四周8个节点处的温度(单位°C), 求中间4个点处的温度T 1, T 2, T 3, T 4.图9 一块平板的温度分布图【模型假设】假设忽略垂直于该截面方向上的热传导, 并且每个节点的温度等于与它相邻的四个节点温度的平均值.【模型建立】根据已知条件和上述假设, 有如下线性方程组1232143144231(90100)41(8060)41(8060)41(5050)4T T T T T T T T T T T T ⎧=+++⎪⎪⎪=+++⎪⎨⎪=+++⎪⎪=+++⎪⎩ 【模型求解】将上述线性方程组整理得1231241342344190414041404100T T T T T T T T T T T T --=⎧⎪-+-=⎪⎨-+-=⎪--+=⎪⎩. 在Matlab 命令窗口输入以下命令T 1T 2 T 3 T 4 10080908060506050>> A = [4,-1,-1,0;-1,4,0,-1;-1,0,4,-1;0,-1,-1,4]; b = [190;140;140;100];>> x = A\b; x’Matlab执行后得ans =82.9167 70.8333 70.8333 60.4167可见T1 = 82.9167, T2 = 70.8333, T3 = 70.8333, T4 = 60.4167.参考文献陈怀琛, 高淑萍, 杨威, 工程线性代数,: 电子工业, 2007. 页码: 15-16.Matlab实验题假定下图中的平板代表一条金属梁的截面, 并忽略垂直于该截面方向上的热传导. 已知平板内部有30个节点, 每个节点的温度近似等于与它相邻的四个节点温度的平均值. 设4条边界上的温度分别等于每位同学学号的后四位的5倍, 例如学号为16308209的同学计算本题时, 选择T l = 40, T u = 10, T r = 0, T d = 45.图10 一块平板的温度分布图(1) 建立可以确定平板内节点温度的线性方程组.(2) 用Matlab软件求解该线性方程组.(3) 用Matlab中的函数mesh绘制三维平板温度分布图.案例五. CT图像的代数重建问题X射线透视可以得到3维对象在2维平面上的投影, CT则通过不同角度的X射线得到3维对象的多个2维投影, 并以此重建对象内部的3维图像. 代数重建方法就是从这些2维投影出发, 通过求解超定线性方程组, 获得对象内部3维图像的方法.图11双层螺旋CT 图12 CT图像这里我们考虑一个更简单的模型, 从2维图像的1维投影重建原先的2维图像. 一个长方形图像可以用一个横竖均匀划分的离散网格来覆盖, 每个网格对应一个像素, 它是该网格上各点像素的均值. 这样一个图像就可以用一个矩阵表示,其元素就是图像在一点的灰度值(黑白图像). 下面我们以3⨯3图像为例来说明.3⨯3图像各点的灰度值水平方向上的叠加值x1 = 1 x2 = 0 x3 = 0 x1 + x2 + x3 = 1x4 = 0 x5 = 0.5 x6 = 0.5 x4 + x5 + x6 = 1x7 = 0.5 x8 = 0 x9 = 1 x7 + x8 + x9 = 1.5 竖直方向上的叠加值x1 + x4 + x7= 1.5x2 + x5 + x8= 0.5x3 + x6 + x9= 1.5i色. 如果我们不知道网格中的数值, 只知道沿竖直方向和水平方向的叠加值, 为了确定网格中的灰度值, 可以建立线性方程组(含有6个方程, 9个未知数)123456369111x x xx x xx x x++=⎧⎪++=⎪⎨⎪++=⎪⎩显然该方程组的解是不唯一的, 为了重建图像, 必须增加叠加值. 如我们增加从右上方到左下方的叠加值, 则方程组将增加5个方程x1 = 1,x2 + x4 = 0,x3 + x5 + x7 = 1,x 6 + x 8 = 0.5, x 9 = 1,和上面的6个方程放在一起构成一个含有11个方程, 9个未知数的线性方程组. 【模型准备】设3⨯3图像中第一行3个点的灰度值依次为x 1, x 2, x 3, 第二行3个点的灰度值依次为x 4, x 5,x 6, 第三行3个点的灰度值依次为x 7, x 8, x 9. 沿竖直方向的叠加值依次为1.5, 0.5, 1.5, 沿水平方向的叠加值依次为1, 1, 1.5, 沿右上方到左下方的叠加值依次为1, 0, 1, 0.5, 1. 确定x 1, x 2, …, x 9的值.【模型建立】由已知条件可得(含有11个方程, 9个未知数的)线性方程组1234569111x x x x x x x ++=⎧⎪++=⎪⎨⎪=⎪⎩ 【模型求解】在Matlab 命令窗口输入以下命令>> A = [1,1,1,0,0,0,0,0,0;0,0,0,1,1,1,0,0,0;0,0,0,0,0,0,1,1,1;1,0,0,1,0,0,1,0,0;0,1,0,0,1,0,0,1,0;0,0,1,0,0,1,0,0,1; 1,0,0,0,0,0,0,0,0;0,1,0,1,0,0,0,0,0;0,0,1,0,1,0,1,0,0; 0,0,0,0,0,1,0,1,0;0,0,0,0,0,0,0,0,1];>> b = [1;1;1.5;1.5;0.5;1.5;1;0;1;0.5;1]; >> x = A\b; x ’Matlab 执行后得Warning: Rank deficient, rank = 8 tol =4.2305e-015. ans =1.0000 0.0000 0 -0.0000 0.5000 0.5000 0.5000 -0.0000 1.0000 可见上述方程组的解不唯一. 其中的一个特解为x 1 = 1, x 2 = 0, x 3 = 0, x 4 = 0, x 5 = 0.5, x 6 = 0.5, x 7 = 0.5, x 8 = 0, x 9 = 1.【模型分析】上述结果表明, 仅有三个方向上的叠加值还不够.可以再增加从左上方到右下方的叠加值. 在实际情况下, 由于测量误差, 上述线性方程组可能是超定的. 这时可以将超定方程组的近似解作为重建的图像数据.Matlab 实验题给定一个3⨯3图像的2个方向上的灰度叠加值: 沿左上方到右下方的灰度叠加值依次为0.8, 1.2, 1.7, 0.2, 0.3; 沿右上方到左下方的灰度叠加值依次为0.6, 0.2, 1.6, 1.2, 0.6.(1) 建立可以确定网格数据的线性方程组, 并用Matlab 求解. (2) 将网格数据乘以256, 再取整, 用Matlab 绘制该灰度图像.案例六. 平衡结构的梁受力计算在桥梁、房顶、铁塔等建筑结构中, 涉及到各种各样的梁. 对这些梁进行受力分析是设计师、工程师经常做的事情.图14 埃菲尔铁塔局部下面以双杆系统的受力分析为例, 说明如何研究梁上各铰接点处的受力情况. 【模型准备】在图15所示的双杆系统中, 已知杆1重G1 = 200牛顿, 长L1 = 2米, 与水平方向的夹角为θ1 = π/6, 杆2重G2 = 100牛顿, 长L2 = 2米, 与水平方向的夹角为θ2 = π/4. 三个铰接点A, B, C所在平面垂直于水平面. 求杆1, 杆2在铰接点处所受到的力.图15双杆系统【模型假设】假设两杆都是均匀的. 在铰接点处的受力情况如图16所示.【模型建立】对于杆1:水平方向受到的合力为零, 故N1 = N3,竖直方向受到的合力为零, 故N2 + N4 = G1,以点A为支点的合力矩为零, 故(L1sinθ1)N3 + (L1cosθ1)N4 = (12L1cosθ1)G1.图16 两杆受力情况对于杆2类似地有AC杆1杆2CN1N2N3N5N6G1G2A B杆1杆2π/6π/4N 5 = N 7, N 6 = N 8 + G 2, (L 2sin θ2)N 7 = (L 2cos θ2)N 8 + (12L 2cos θ2)G 2.此外还有N 3 = N 7, N 4 = N 8. 于是将上述8个等式联立起来得到关于N 1, N 2, …, N 8的线性方程组:132414800N N N N G N N -=⎧⎪+=⎪⎨⎪⎪-=⎩ 【模型求解】在Matlab 命令窗口输入以下命令>> G1=200; L1=2; theta1=pi/6; G2=100; L2=sqrt(2); theta2=pi/4; >> A = [1,0,-1,0,0,0,0,0;0,1,0,1,0,0,0,0;0,0,L1*sin(theta1),L1*cos(theta1),0,0,0,0;0,0,0,0,1,0,-1,0; 0,0,0,0,0,1,0,-1;0,0,0,0,0,0,L2*sin(theta2),-L2*cos(theta2); 0,0,1,0,0,0,-1,0;0,0,0,1,0,0,0,-1];>> b = [0;G1;0.5*L1*cos(theta1)*G1;0;G2;0.5*L2*cos(theta2)*G2;0;0]; >> x = A\b; x ’ Matlab 执行后得 ans =95.0962 154.9038 95.0962 45.0962 95.0962 145.0962 95.0962 45.0962【模型分析】最后的结果没有出现负值, 说明图16中假设的各个力的方向与事实一致. 如果结果中出现负值, 则说明该力的方向与假设的方向相反. 参考文献陈怀琛, 高淑萍, 杨威, 工程线性代数,: 电子工业, 2007. 页码: 157- 158.Matlab 实验题有一个平面结构如下所示, 有13条梁(图中标号的线段)和8个铰接点(图中标号的圈)联结在一起. 其中1号铰接点完全固定, 8号铰接点竖直方向固定, 并在2号, 5号和6号铰接点上, 分别有图示的10吨, 15吨和20吨的负载. 在静平衡的条件下,任何一个铰接点上水平和竖直方向受力都是平衡的. 已知每条斜梁的角度都是45º.(1) 列出由各铰接点处受力平衡方程构成的线性方程组. (2) 用Matlab 软件求解该线性方程组, 确定每条梁受力情况.图17 一个平面结构的梁案例七. 化学方程式配平问题在用化学方法处理污水过程中, 有时会涉及到复杂的化学反应. 这些反应的化学方程式是分析计算和工艺设计的重要依据. 在定性地检测出反应物和生成物之后,可以通过求解线性方程组配平化学方程式.【模型准备】某厂废水中含K, 其浓度为650mg/L. 现用氯氧化法处理, 发生如下反应:K + 2KOH + Cl 2 = KO+ 2KCl + H 2O.投入过量液氯, 可将氰酸盐进一步氧化为氮气. 请配平下列化学方程式:KO +KOH +Cl 2 ===CO 2+N 2+KCl +H 2O.(注: 题目摘自XX 省XX 外国语学校2008-2009学年高三第三次月考化学试卷) 【模型建立】设x 1KO ＋x 2KOH ＋x 3Cl 2 === x 4CO 2 ＋x 5N 2 ＋x 6KCl ＋x 7H 2O,则1261247141527362222x x x x x x xx x x x x x x x +=⎧⎪+=+⎪⎪=⎪⎨=⎪⎪=⎪=⎪⎩, 即1261247141527360200202020x x x x x x x x x x x x x x x +-=⎧⎪+--=⎪⎪-=⎪⎨-=⎪⎪-=⎪-=⎪⎩ 【模型求解】在Matlab 命令窗口输入以下命令>> A = [1,1,0,0,0,-1,0;1,1,0,-2,0,0,-1;1,0,0,-1,0,0,0;1,0,0,0,-2,0,0;0,1,0,0,0,0,-2;0,0,2,0,0,-1,0];>> x = null(A,’r ’); format rat, x ’Matlab 执行后得 ans =1 2 3/2 1 1/2 3 1 可见上述齐次线性方程组的通解为x = k (1, 2, 3/2, 1, 1/2, 3, 1)T .取k = 2得x = (2, 4, 3, 2, 1, 6, 2)T . 可见配平后的化学方程式如下2KO + 4KOH + 3Cl 2 ===2CO 2+ N 2+ 6KCl + 2H 2O.【模型分析】利用线性方程组配平化学方程式是一种待定系数法. 关键是根据化学方程式两边所涉及到的各种元素的量相等的原则列出方程. 所得到的齐次线性方程组Ax = θ中所含方程的个数等于化学方程式中元素的种数s , 未知数的个数就是化学方程式中的项数n .当r(A ) = n -1时, Ax = θ的基础解系中含有1个(线性无关的)解向量. 这时在通解中取常数k 为各分量分母的最小公倍数即可. 例如本例中1, 2, 3/2, 1, 1/2, 3, 1分母的最小公倍数为2, 故取k = 2.当r(A ) ≤n -2时, Ax = θ的基础解系中含有2个以上的线性无关的解向量. 这时可以根据化学方程式中元素的化合价的上升与下降的情况, 在原线性方程组中添加新的方程. Matlab 实验题配平下列反应式(1) FeS + KMnO 4 + H 2SO 4—— K 2SO 4 + MnSO 4 + Fe 2(SO 4)3 + H 2O + S ↓ (2) Al 2(SO 4)3 + Na 2CO 3 + H 2O —— Al(OH)3↓+ CO 2↑+ Na 2SO 4案例八. 互付工资问题互付工资问题是多方合作相互提供劳动过程中产生的. 比如农忙季节, 多户农民组成互助组, 共同完成各户的耕、种、收等农活. 又如木工, 电工, 油漆工等组成互助组, 共同完成各家的装潢工作. 由于不同工种的劳动量有所不同, 为了均衡各方的利益, 就要计算互付工资的标准.【模型准备】现有一个木工, 电工, 油漆工. 相互装修他们的房子, 他们有如下协议:(1) 每人工作10天(包括在自己家的日子), (2) 每人的日工资一般的市价在60~80元之间, (3) 日工资数应使每人的总收入和总支出相等.求每人的日工资. 【模型假设】假设每人每天工作时间长度相同. 无论谁在谁家干活都按正常情况工作, 既不偷懒, 也不加班.【模型建立】设木工, 电工, 油漆工的日工资分别为x , y , z 元, 则由下表可得2610451044310x y z xx y z y x y z z++=⎧⎪++=⎨⎪++=⎩, 即8604504470x y z x y z x y z -++=⎧⎪-+=⎨⎪+-=⎩【模型求解】在Matlab 命令窗口输入以下命令>> A = [-8,1,6;4,-5,1;4,4,-7];>> x = null(A,’r ’); format rat, x ’ Matlab 执行后得ans =31/36 8/9 1可见上述齐次线性方程组的通解为x = k (31/36, 8/9, 1)T . 因而根据“每人的日工资一般的市价在60~80元之间”可知60 ≤3631k <98k < k ≤ 80, 即 312160≤k ≤ 80.也就是说, 木工, 电工, 油漆工的日工资分别为3631k 元, 98k 元, k 元, 其中312160≤k ≤ 80. 为了简便起见, 可取k = 72, 于是木工, 电工, 油漆工的日工资分别为62元, 64元, 72元.【模型分析】事实上各人都不必付自己工资, 这时各家应付工资和各人应得收入如下6845447y z x x z y x y z +=⎧⎪+=⎨⎪+=⎩, 即8604504470x y z x y z x y z -++=⎧⎪-+=⎨⎪+-=⎩ 可见这样得到的方程组与前面得到的方程组是一样的.Matlab 实验题甲, 乙, 丙三个农民组成互助组, 每人工作6天(包括为自己家干活的天数), 刚好完成他们三人家的农活, 其中甲在甲, 乙, 丙三家干活的天数依次为: 2, 2.5, 1.5; 乙在甲, 乙, 丙三家各干2天活, 丙在甲, 乙, 丙三家干活的天数依次为: 1.5, 2, 2.5. 根据三人干活的种类, 速度和时间, 他们确定三人不必相互支付工资刚好公平. 随后三人又合作到邻村帮忙干了2天(各人干活的种类和强度不变), 共获得工资500元.问他们应该怎样分配这500元工资才合理?案例九. 平衡价格问题为了协调多个相互依存的行业的平衡发展, 有关部门需要根据每个行业的产出在各个行业中的分配情况确定每个行业产品的指导价格, 使得每个行业的投入与产出都大致相等.【模型准备】假设一个经济系统由煤炭、电力、钢铁行业组成, 每个行业的产出在各个行业中的分配如下表所示:等的平衡价格.【模型假设】假设不考虑这个系统与外界的联系.【模型建立】把煤炭、电力、钢铁行业每年总产出的价格分别用x 1,x 2, x 3表示, 则123212331230.40.60.60.10.20.40.50.2x x x x x x x x x x x =+⎧⎪=++⎨⎪=++⎩, 即1231231230.40.600.60.90.200.40.50.80x x x x x x x x x --=⎧⎪-+-=⎨⎪--+=⎩. 【模型求解】在Matlab 命令窗口输入以下命令>> A = [1,-0.4,-0.6;-0.6,0.9,-0.2;-0.4,-0.5,0.8]; >> x = null(A,’r ’); format short, x ’ Matlab 执行后得ans =0.9394 0.8485 1.0000 可见上述齐次线性方程组的通解为x = k(0.9394, 0.8485, 1)T.这就是说, 如果煤炭、电力、钢铁行业每年总产出的价格分别0.9394亿元, 0.8485亿元, 1亿元, 那么每个行业的投入与产出都相等.【模型分析】实际上, 一个比较完整的经济系统不可能只涉及三个行业, 因此需要统计更多的行业间的分配数据.Matlab实验题假设一个经济系统由煤炭、石油、电力、钢铁、机械制造、运输行业组成, 每个行业的产出在各个行业中的分配如下表所示:产出分配购买者煤炭石油电力钢铁制造运输0 0 0.2 0.1 0.2 0.2 煤炭0 0 0.1 0.1 0.2 0.1 石油0.5 0.1 0.1 0.2 0.1 0.1 电力0.4 0.1 0.2 0 0.1 0.4 钢铁0 0.1 0.3 0.6 0 0.2 制造0.1 0.7 0.1 0 0.4 0 运输等的平衡价格.案例十. 电路设计问题电路是电子元件的神经系统. 参数的计算是电路设计的重要环节. 其依据来自两个方面: 一是客观需要, 二是物理学定律.图22 USB扩展板【模型准备】假设图23中的方框代表某类具有输入和输出终端的电路. 用11vi⎛⎫⎪⎝⎭记录输入电压和输入电流(电压v以伏特为单位, 电流i以安培为单位), 用22vi⎛⎫⎪⎝⎭记录输出电压和输入电流. 若22vi⎛⎫⎪⎝⎭= A11vi⎛⎫⎪⎝⎭,则称矩阵A为转移矩阵.图23 具有输入和输出终端的电子电路图图24给出了一个梯形网络, 左边的电路称为串联电路, 电阻为R 1(单位: 欧姆). 右边的电路是并联电路, 电路R 2. 利用欧姆定理和楚列斯基定律, 我们可以得到串联电路和并联电路的转移矩阵分别是1101R -⎛⎫ ⎪⎝⎭和2101/1R ⎛⎫ ⎪-⎝⎭串联电路并联电路图24 梯形网络设计一个梯形网络, 其转移矩阵是180.55-⎛⎫⎪-⎝⎭. 【模型假设】假设导线的电阻为零.【模型建立】设A 1和A 2分别是串联电路和并联电路的转移矩阵, 则输入向量x 先变换成A 1x , 再变换到A 2(A 1x ). 其中A 2A 1 =2101/1R ⎛⎫ ⎪-⎝⎭1101R -⎛⎫ ⎪⎝⎭=121211/1/R R R R -⎛⎫ ⎪-+⎝⎭就是图22中梯形网络的转移矩阵.于是, 原问题转化为求R 1, R 2的值使得121211/1/R R R R -⎛⎫ ⎪-+⎝⎭=180.55-⎛⎫ ⎪-⎝⎭. 【模型求解】由121211/1/R R R R -⎛⎫ ⎪-+⎝⎭=180.55-⎛⎫ ⎪-⎝⎭可得121281/0.51/5R R R R -=-⎧⎪-=-⎨⎪+=⎩. 根据其中的前两个方程可得R 1 = 8, R 2 = 2. 把R 1 = 8, R 2 = 2代入上面的第三个方程确实能使等式成立. 这就是说在图22中梯形网络中取R 1 = 8, R 2 = 2即为所求.【模型分析】若要求的转移矩阵改为180.54-⎛⎫⎪-⎝⎭, 则上面的梯形网络无法实现. 因为v 2这时对应的方程组是121281/0.51/4R R R R -=-⎧⎪-=-⎨⎪+=⎩. 根据前两个方程依然得到R 1 = 8, R 2 = 2, 但把R 1= 8, R 2 = 2代入上第三个方程却不能使等式成立.练习题根据基尔霍夫回路电路定律(各节点处流入和流出的电流强度的代数和为零, 各回路中各支路的电压降之和为零), 列出下图所示电路中电流i 1, i 2, i 3所满足的线性方程组, 并用矩阵形式表示:图25简单的回路案例十一. 平面图形的几何变换随着计算机科学技术的发展, 计算机图形学的应用领域越来越广, 如仿真设计、效果图制作、动画片制作、电子游戏开发等.图形的几何变换, 包括图形的平移、旋转、放缩等, 是计算机图形学中经常遇到的问题. 这里暂时只讨论平面图形的几何变换.【模型准备】平面图形的旋转和放缩都很容易用矩阵乘法实现, 但是图形的平移并不是线性运算, 不能直接用矩阵乘法表示. 现在要求用一种方法使平移、旋转、放缩能统一用矩阵乘法来实现. 【模型假设】设平移变换为(x , y ) → (x +a , y +b )旋转变换(绕原点逆时针旋转θ角度)为(x , y ) → (x cos θ-y sin θ, x sin θ + y cos θ)放缩变换(沿x 轴方向放大s 倍, 沿y 轴方向放大t 倍)为(x , y ) → (sx , ty )【模型求解】R 2中的每个点(x , y )可以对应于R 3中的(x , y , 1). 它在xOy 平面上方1单E 12位的平面上. 我们称(x , y , 1)是(x , y )的齐次坐标. 在齐次坐标下, 平移变换(x , y ) → (x +a , y +b )可以用齐次坐标写成(x , y , 1) → (x +a , y +b , 1).于是可以用矩阵乘积1001001a b ⎛⎫ ⎪ ⎪⎝⎭1x y ⎛⎫ ⎪ ⎪⎝⎭=1x a y b +⎛⎫⎪+ ⎪⎝⎭实现.旋转变换(x , y ) → (x cos θ-y sin θ, x sin θ + y cos θ)可以用齐次坐标写成(x , y , 1) → (x cos θ-y sin θ, x sin θ + y cos θ, 1). 于是可以用矩阵乘积cos sin 0sin cos 0001θθθθ-⎛⎫ ⎪ ⎪⎝⎭1x y ⎛⎫ ⎪ ⎪⎝⎭=cos sin sin cos 1x y x y θθθθ-⎛⎫⎪+ ⎪⎝⎭实现.放缩变换(x , y ) → (sx , ty )可以用齐次坐标写成(x , y , 1) → (sx , ty , 1).于是可以用矩阵乘积0000001s t ⎛⎫ ⎪ ⎪⎝⎭1x y ⎛⎫ ⎪ ⎪⎝⎭=1sx ty ⎛⎫⎪ ⎪⎝⎭实现.【模型分析】由上述求解可以看出, R 2中的任何线性变换都可以用分块矩阵1⎛⎫⎪⎝⎭A O O 乘以齐次坐标实现, 其中A 是2阶方阵. 这样, 只要把平面图形上点的齐次坐标写成列向量, 平面图形的每一次几何变换, 都可通过左乘一个3阶变换矩阵来实现.参考文献David C. Lay, 线性代数及其应用, 沈复兴, 傅莺莺等译,: 人民邮电, 2009. 页码: 139-141.Matlab 实验题在Matlab 命令窗口输入以下命令 >>clear all , clc,>>t=[1,3,5,11,13,15]*pi/8; >>x=sin(t); y=cos(t); >>fill(x,y,'r'); >>grid on ;>>axis([-2.4, 2.4, -2, 2])运行后得图25.图26Matlab绘制的图形(1) 写出该图形每个顶点的齐次坐标;; 最后进行横(2) 编写Matlab程序, 先将上面图形放大0.9倍; 再逆时针旋转3坐标加0.8, 纵坐标减1的图形平移. 分别绘制上述变换后的图形.案例十二. 太空探测器轨道数据问题太空航天探测器发射以后, 可能需要调整以使探测器处在精确计算的轨道里. 雷达监测到一组列向量x1, …, x k,它们给出了不同时刻探测器的实际位置与预定轨道之间的偏差的信息.图28 火星探测器【模型准备】令X k = [x1, …, x k]. 在雷达进行数据分析时需要计算出矩阵G k = X k X k T. 一旦接收到数据向量x k+1,必须计算出新矩阵G k+1. 因为数据向量到达的速度非常快, 随着k的增加, 直接计算的负担会越来越重. 现需要给出一个算法, 使得计算G k的负担不会因为k的增加而加重.【模型求解】因为G k = X k X k T=[x 1, …, x k ]T 1T k⎡⎤⎢⎥⎢⎥⎢⎥⎣⎦x x =T 1k i i i =∑x x ,G k +1 = X k +1T1k +X =[X k , x k +1]T T 1k k +⎡⎤⎢⎥⎣⎦X x = X k X k T +x k +1T 1k +x =G k +x k +1T 1k +x ,所以一旦接收到数据向量x k +1, 只要计算x k +1T1k +x , 然后把它与上一步计算得到的G k相加即可. 这样计算G k 的负担不会因为k 的增加而加重.【模型分析】计算机计算加法的时间与计算乘法的时间相比可以忽略不计. 因此在考虑计算矩阵乘积的负担时, 只要考察乘法的次数就可以了. 设x k 的维数是n , 则X k = [x 1, …, x k ]是n ⨯k 的矩阵, G k = X k X k T 是n ⨯n 的矩阵. 直接计算G k = X k X k T 需要做n 2k 次乘法. 因而计算的负担会随着k 的增加而增加. 但是对于每一个k , 计算x k Tk x 始终只要做n 2次乘法.Matlab 实验题用Matlab 编写一个程序用于处理这个问题.案例十三. 应用矩阵编制Hill 密码密码学在经济和军事方面起着极其重要的作用. 现代密码学涉及很多高深的数学知识. 这里无法展开介绍.图29 XX 通信的基本模型密码学中将信息代码称为密码, 尚未转换成密码的文字信息称为明文, 由密码表示的信息称为密文. 从明文到密文的过程称为加密, 反之为解密. 1929年, 希尔(Hill)通过线性变换对待传输信息进行加密处理, 提出了在密码史上有重要地位的希尔加密算法. 下面我们略去一些实际应用中的细节, 只介绍最基本的思想.【模型准备】若要发出信息action, 现需要利用矩阵乘法给出加密方法和加密后得到的密文, 并给出相应的解密方法.。

南京大学研究生2015拟录取名单

院系代码院系名称专业代码专业名称考生编号姓名001哲学系010101马克思主义哲学102845210115864郭子介001哲学系010101马克思主义哲学102845210107883黄艾婷001哲学系010101马克思主义哲学102845210107884李静001哲学系010101马克思主义哲学102845210107141刘翰林001哲学系010101马克思主义哲学102845210113798刘洁001哲学系010101马克思主义哲学102845102840099马宇超001哲学系010101马克思主义哲学102845210107142钱韵001哲学系010101马克思主义哲学102845103570100童晓宇001哲学系010101马克思主义哲学102845210105616王晓妍001哲学系010101马克思主义哲学102845106980101徐佳悦001哲学系010101马克思主义哲学102845107300102徐家熠001哲学系010102中国哲学102845210106209陈思吟001哲学系010102中国哲学102845210106496成逸洁001哲学系010102中国哲学102845210113397丁武刚001哲学系010102中国哲学102845210111782范琳琳001哲学系010102中国哲学102845210114182雷媛媛001哲学系010102中国哲学102845210111440梁诚001哲学系010102中国哲学102845102840103吕奇珂001哲学系010102中国哲学102845210115840潘璐001哲学系010102中国哲学102845210100014王敬源001哲学系010102中国哲学102845210100008吴梅梅001哲学系010102中国哲学102845210107886杨立军001哲学系010102中国哲学102845210107144张天治001哲学系010102中国哲学102845210100012赵印印001哲学系010102中国哲学102845210105834朱佳麒001哲学系010103外国哲学102845101410104黄晶乐001哲学系010103外国哲学102845102840105黄雨轩001哲学系010103外国哲学102845210100017金昕001哲学系010103外国哲学102845210105236倪天骄001哲学系010103外国哲学102845210106835陶佳意001哲学系010103外国哲学102845102840106汪洋001哲学系010103外国哲学102845210111052巫闽花001哲学系010103外国哲学102845102840107周菁001哲学系010104逻辑学102845100550108付梦婕001哲学系010104逻辑学102845210105696王彦杰001哲学系010104逻辑学102845102840109尹智鹤001哲学系010104逻辑学102845102840110郑梅洁001哲学系010104逻辑学102845210100026朱自展001哲学系010105伦理学102845103190111李漫玉001哲学系010105伦理学102845210105619佟瑞菲001哲学系010105伦理学102845210110031张炜炜001哲学系010107宗教学102845210106498陈天弋001哲学系010107宗教学102845210100035刘金欣001哲学系010107宗教学102845210100031庞逸001哲学系010107宗教学102845210112736王关龙001哲学系010107宗教学102845103570112王凯001哲学系010107宗教学102845210110739王正瑛001哲学系010107宗教学102845210109130吴露晞001哲学系010108科学技术哲学102845210110510艾春玲001哲学系010108科学技术哲学102845210100036范裕锋001哲学系010108科学技术哲学102845210112567葛素波001哲学系010108科学技术哲学102845103570113刘芳001哲学系030502马克思主义发展史102845210100040王楚楚002商学院020101政治经济学102845102840114范卓宇002商学院020101政治经济学102845210212151高颖颉002商学院020101政治经济学102845210200048焦琳琳002商学院020101政治经济学102845210200049李成泰002商学院020101政治经济学102845210207022刘孟002商学院020101政治经济学102845102840115刘婷002商学院020101政治经济学102845210212285马伟伟002商学院020101政治经济学102845210200059王常红002商学院020101政治经济学102845102840116王仕俊002商学院020101政治经济学102845210200065徐海洋002商学院020101政治经济学102845210205477张婉婉002商学院020101政治经济学102845210215236章懂宇002商学院020101政治经济学102845210209491赵驰宁002商学院020101政治经济学102845210200075赵润之002商学院020101政治经济学102845102840117周岐琛002商学院020101政治经济学102845210213302祝明002商学院020101政治经济学102845210211785庄绪强002商学院020104西方经济学102845210200081戴蓉002商学院020104西方经济学102845210210197方慧敏002商学院020104西方经济学102845210214747贾凯002商学院020104西方经济学102845210205275吕音002商学院020104西方经济学102845102840118汤文韬002商学院020104西方经济学102845210214832章巧玲002商学院020104西方经济学102845210200096钟婧瑶002商学院020105世界经济102845210209494戴丽琴002商学院020105世界经济102845210205328黄伟伟002商学院020105世界经济102845210200099孟鹭002商学院020105世界经济102845210214117魏泊宁002商学院020106人口、资源与环境经济学102845210200104程波002商学院020106人口、资源与环境经济学102845210215090李雨辰002商学院020106人口、资源与环境经济学102845210200109陆丽莉002商学院020106人口、资源与环境经济学102845210210649张文杰002商学院020201国民经济学102845210211445陈露002商学院020201国民经济学102845210200121冯翔002商学院020201国民经济学102845210206167郭佳赫002商学院020201国民经济学102845210208784胡梦平002商学院020201国民经济学102845102840119华东002商学院020201国民经济学102845210214464李海英002商学院020201国民经济学102845210200130李琳琳002商学院020201国民经济学102845210200131李田002商学院020201国民经济学102845102840120林晶晶002商学院020201国民经济学102845106100121凌斯凡002商学院020201国民经济学102845102840122凌晓光002商学院020201国民经济学102845210200133刘亚龙002商学院020201国民经济学102845210206174乌云002商学院020201国民经济学102845210215330杨彩姣002商学院020201国民经济学102845102840123赵文静002商学院020201国民经济学102845106970124赵雨心002商学院020201国民经济学102845102840125朱伟002商学院020201国民经济学102845210216165朱莹莹002商学院020201国民经济学102845102840126庄天慈002商学院020204金融学102845210206503包阳002商学院020204金融学102845102840127陈佳玲002商学院020204金融学102845210200160陈曦002商学院020204金融学102845102840128陈晓莹002商学院020204金融学102845102840129陈雪琴002商学院020204金融学102845210213764段雯昕002商学院020204金融学102845102840130樊小莹002商学院020204金融学102845102840131冯雪岩002商学院020204金融学102845210208349管利冬002商学院020204金融学102845210210241郭小飞002商学院020204金融学102845210200172季慧萍002商学院020204金融学102845210200179刘浩002商学院020204金融学102845210209628刘岩002商学院020204金融学102845210211790刘玉峰002商学院020204金融学102845210215294潘梦真002商学院020204金融学102845210215774蒲鑫欣002商学院020204金融学102845102840132权威002商学院020204金融学102845210205152全梦贞002商学院020204金融学102845102840133沈荻002商学院020204金融学102845102840134施一舟002商学院020204金融学102845102840135司鸿历002商学院020204金融学102845210200191屠婕002商学院020204金融学102845102840136王梓婷002商学院020204金融学102845210205385夏星创002商学院020204金融学102845102840137杨雅茹002商学院020204金融学102845102840138张楚清002商学院020204金融学102845102840139张瑾002商学院020204金融学102845210200217张夏华002商学院020204金融学102845210206508朱伟伟002商学院020204金融学102845210200222左爽002商学院020205产业经济学102845102840140陈一凡002商学院020205产业经济学102845102840141傅帅002商学院020205产业经济学102845102840142顾佳佳002商学院020205产业经济学102845102840143顾以诺002商学院020205产业经济学102845210200228黄维驰002商学院020205产业经济学102845210206509黄子耀002商学院020205产业经济学102845104870144荆晶002商学院020205产业经济学102845210200233李双002商学院020205产业经济学102845210215487陆思桦002商学院020205产业经济学102845210200239乔真紫002商学院020205产业经济学102845103350145汤家红002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