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(1)Reactor Numerical Analysis and Design Spring 2010. How to use the MCNP May 11, 2010 Prof. Joo Han-gyu Department of Nuclear Engineering. 1 / 55. SNURPL. (2) Contents. 1. C ode overview. 2. Input overview. 3. Input C ard specification. 4. E xecution. 2 / 55. SNURPL. (3) Code overview  M CNP : a general purpose Monte Carlo N -Particle code by Los Alamos Nat'l Lab. (ver. 4C2).  Monte Carlo simulates individual part icles and recording results (tallies) of thei r average behav ior.. < Example of neutron behavior >.  Averaging particle behavior represents solving integrated Transport eq.. ̂. R. Q r. r. R  r  r  [cm ].  g ( r , ˆ ) . 3 / 55. . Q g ( r ) s. 4 R. 2. e.  t R. dr . SNURPL. (4) Code overview  Consists of three part : Input, Nuclear-data, and Output  Input file contains 1. geom etry specification 2. description of m aterials 3. location and characteristics of (neut ron) sources 4. types of answ ers or tallies desired INPUT Geometry Composition Tally spec. OUTPUT. read MCNP.exe. OUTPUT file (Keff, tally). DATA Cross-section files. 4 / 55. SNURPL. (5) Input overview  Compose of 4 cards. Message Block (Optional) Blank Line Delimiter (Optional).  The message block ends with a blank line delimiter. One Line Problem Title Card Cell Cards … … Blank Line Delimiter.  T he colum ns of line : 1~80  C om m ent : c. Surface Cards … … Blank Line Delimiter.  Termination of data entry on a line : $. Data Cards … … Blank Line Terminator (Optional). 5 / 55. SNURPL. (6) Input overview  Facilitation of Input Card Preparation  The FIDO (Flexible Input Deterministic Output ) system. nR : Repeat the preceding entry n times One Line 2 4R : 2 2 2 2 2 nl : Insert n linear interpolates between the entries preceding and following 1.5 2I 3.0 : 1.5 2.0 2.5 3.0 xM : Multiply the previous entry by x 1 1 2M 2M 2M 4M 2M = 1 1 2 4 8 32 64 nJ : Jump over n items and use the default value 1 2 J 0.5. 6 / 55. SNURPL. (7) Input Example c Godiva 1 1 0.047984 -1 $ sphere 2 0. C ell card. +1 B lank line delim iter. 1 so 8.7407. S urface card B lank line delim iter. mode n imp:n 1 0 ksrc 0. 0. 0. kcode 10000 1.0 100 1000 D ata card. totnu print c material m1 92234.70c 4.9184e-4 92235.70c 4.4994e-2. 7 / 55. SNURPL. (8) Cell card (1)  C ell cards.  Cell cards describe the cells - geometry, material, density, cell parameter.  Form cell number. cell material number. cell material density. geometry. cell parameter (optional).  cell num ber cell number. cell material number. cell material density. geometry. cell parameter (optional). The first entry and must begin in the first five columns 1  cell num ber  99999.  Example 1) 1 2) 4. 1 6.72E-2 0. 3) 99998.  7 9  10 u=1 imp:n=1. 1 :-2 :3 :-4 :5 :-6 :-9 :10 3 6.63E-02 -1 2 -3 4 -5 6 12 imp:n=1 vol=1.336. 8 / 55. SNURPL. (9) Cell card  cell m aterial num ber cell number. cell material number. cell material density. geometry. cell parameter (optional).  0 if the cell is a void.  m aterial num ber if the cell is not a vo id..  Material number is corresponding to the number, which is specified on the M m card. (Data cards) 1 21 -10.0 -7 9 -10 2 22 0.0429 7 -8 9 -10 3 23 -0.9961 -1 2 -3 4 -5 6 8 9 -10 4 0 1 :-2 :3 :-4 :5 :-6 :-9 :10 *1 *2 *3 *4 *5 *6 7 8 *9 *10. p 1.732050807569 -1 0 1.611854897735 p 1.732050807569 -1 0 -1.611854897735 p 1.732050807569 1 0 1.611854897735 p 1.732050807569 1 0 -1.611854897735 py 0.8059274488677 py -0.8059274488677 cz 0.44 cz 0.5 pz -0.75 pz 0.75. mode n kcode 10000 1.0 50 1050 20000 0 13000 m21 92235.60c -0.02468 92238.60c -0.8568 8016.60c -0.1185 $Fuel Region m22 40000.60c 1 $ Zr m23 1001.60c -0.1119 8016.60c -0.8881 $ H2o. 9 / 55. SNURPL. (10) Cell card  cell material density cell number. cell material number. cell material density. geometry. cell parameter (optional).  A bsent if the cell is a void. .  postive value : atom ic density unit : 1 0. . 24. negative value : m ass density unit: g/cm. atom s/cm 3. 3.  or 1 atom s/barn  cm . . Mass density Atomic density Mass density. 1 2 3 4. 21 -10.0 -7 9 -10 22 0.0429 7 -8 9 -10 23 -0.9961 -1 2 -3 4 -5 6 8 9 -10 0 1 :-2 :3 :-4 :5 :-6 :-9 :10 Absent(void). 10 / 55. SNURPL. (11) Cell card  g eo m etry cell number. cell material number. cell material density. geometry. cell parameter (optional).  Consist of signed surface number and boolean operator  Surface number is corresponding to the number that is in the surface cards  A surface divide space into positive & negative sides  T he regions are com bined by boolean ope rator 1) intersection.  no sym bol. 2) union. . : (colon). 3) com plem ent . # (sharp). -5. +5. +7. +9 surface 7. surface 5. -9. surface 9. -7. 11 / 55. SNURPL. (12) Cell card  g eo m etry cell number. cell material number. cell material density. geometry. cell parameter (optional). 1) intersection  no symbol. +7 +5. 7 -5. 95 -9 5. surface 7. -7 -5. -9 -5 9 -5. -7 5. surface 9. surface 5. surface 5. 1 0. 9 5. 7 5. 2 0. 9 5. 12 0. 7 5. 5 0. 9 5. 13 0. 7 5. 7 0. 9 5. 10 0. 7. 11 0. 5. 12 / 55. SNURPL. (13) Cell card  g eo m etry cell number. cell material number. cell material density. geometry. cell parameter (optional). 2) union  : (colon). -9 : 5. 7 :5. surface 9. surface 7. -7 -5. 9 -5. surface 5. surface 5. 1 0. 7:5. 5 0 9 :5. 7 0. 7 5. 9 0 9 5. 13 / 55. SNURPL. (14) Cell card  g eo m etry cell number. cell material number. cell material density. geometry. cell parameter (optional). 3) complement  # (sharp) The number immediately after a #, without parentheses, is interpreted as a cell number.. #(9 -5). 5 :7. surface 9. surface 7. #(5 :7). 9 -5. surface 5. surface 5. 10 0 5 7 20 0 #(5 7). . 10 0 5 7. 1 0 9 -5. 20 0 #1. 2 0 #(9 -5). 14 / 55. . 1 0 9 -5 2 0 #1. SNURPL. (15) Cell card  g eo m etry cell number. cell material number. 2. cell material density. geometry. Yellow part. 3. 1 0 3. 1. 1. 2. cell parameter (optional). 3. 1:  2 .  1 0.   3 1 :   1.  1 0.   3 1. Blue part Yellow part.  2  3. :  3  2 . 1 0 1 :  2 :  3. 2 0 #1  2 0 1 2 3. 15 / 55. SNURPL. (16) Cell card  cell parameter cell number. cell material number. cell material density. geometry. cell parameter (optional).  Form : keyword  value  cell parameter related with Data cards.  A llow ed keyw ord : IM P , V O L , P W T , FC L , W W N , D X C , N O N U , P D , T M P U , T R C L , L A T , FIL L.  example 8. 3 6.63E-02 -1 2 -3 4 -5 6 12 im p:n=1 vol=1.336. 16 / 55. SNURPL. (17) Surface card  Form surface number. eqaution mnemonic. entry.  surface num ber 1  surface num ber  99999. the surface number with asterisk ('*'): for a reflecting surface.  equation mnemonic  en try. T he surface type, equations, m nem onics are given. T o specify a surface by this m ethod, find the surface and determ ine the co efficients for the equation..  example *1. p 1.7  1 0 1.6. 7. cz 0.6225. 21. so 0.0175. 17 / 55. SNURPL. (18) Surface card. 18 / 55. SNURPL. (19) Surface card. 19 / 55. SNURPL. (20) Surface card  defining the sign of surface  substitute a point ( v ) w hich is not on the surface into the equation f ( x )  0  the value f ( v ) represents the sign of surface regard to the point. (x1, y1,z1) (A,B,C). This side is represented by ‘+’ If Ax1+By1+Cz1-D>0. Ax+By+Cz-D=0. 20 / 55. SNURPL. (21) Data card  Categories 1) P roblem type C ard 2) G eom etry C ards 3) V ariance R eduction 4) S ource S pecification 5) T ally S pecification 6) M aterial S pecification 7) E nergy and T herm al T reatm ent S pecification 8) P roblem C utoff C ards 9) U ser D ata A rrays 10) P eripheral C ards. 21 / 55. SNURPL. (22) Problem type Card  Form. MODE. particle designator. particle designator.  default . N. : neutron transport. P. : photon transport. E. : electron transport. N P. : neutron and neutron-induced p hoton transport. P E. : photon and electron transport. N P E : neutron, neutron-induced photon and electron transport.  example MODE N. 22 / 55. SNURPL. (23) Geometry Cards a) V O L. (optional) : C ell volum e. b) A R E A (optional) : S urface A rea. c) U. (optional) : U niverse. d) T R C L (optional) : C ell T ransform ation. e) LA T. (optional) : Lattice. f) FILL (optional) : Fill. g) T R n (optional) : C oordinate T ransform a tion. 23 / 55. SNURPL. (24) Geometry Cards  V O L : C ell volum e. Form : V O L x1 x 2 or. VOL NO. xi x1 x 2. xi.  can write in cell cards (cell parameter)  MCNP attempts to calculate the volume of all cells unless "NO" appears on the V OL cards.  If no value is entered for a cell on th e V O L card, the calculated volum e is use d ..  M C N P calculate the volum e basically. H ow ever M C N P cannot calculate the volum e of com plicated region.  V olum es of cells are required for tallies. So w e w rite the volum e m anually, w hen M C N P cannot calculate it.. 24 / 55. SNURPL. (25) Geometry Cards  Repeated Structures Cards U : U niverse FILL : Fill.  example. 10 20 30 40 50. 1 -2 -3 4 -5 6 fill=1 -7 1 -3 8 u=1 fill=2 lat=1 -11 u=2 11 u=2 -1:2:3:-4:5:-6. 1 px 0 2 px 50 3 py 10 4 py -10 5 pz 5 6 pz -5 7 px 10 8 py 0 11 s 5 5 0 4. 25 / 55. SNURPL. (26) Variance Reduction. a) IM P. (required) : C ell im portances. b) E S P LT (optional) : E nergy splitting a nd roulette. c) P W T. (optional) : P hoton production w eights. d) E X T. (optional) : E xponential tran sform. e) V E C T (op tional) : V ector input. f) B B R E M (optional) : B rem sstrahlung bia sing. 26 / 55. SNURPL. (27) Variance Reduction  Cell importances  Form. IM P:n x1 x 2. xI. n : N for neutrons, P for photons, E for electrons xi : importance for cell i. I : number of cells in the problem  The importance of a cell is used to terminate the particle's history if the importance is zeros.  can write in the cell parameter in the cell cards.  example 1 1 0.5 1 -2 -3 4 -5 6 fill=1 2 1 0.5 -7 1 -3 8 u=1 fill=2 lat=1 3 4 0.5 -11 u=2 4 1 0.5 11 u=2 5 0 -1:2:3:-4:5:-6. 1 1 0.5 1 -2 -3 4 -5 6 fill=1 imp:n=1 2 1 0.5 -7 1 -3 8 u=1 fill=2 lat=1 imp:n=1 3 4 0.5 -11 u=2 imp:n=1 4 1 0.5 11 u=2 imp:n=1 5 0 -1:2:3:-4:5:-6 imp:n=0. 1 px 0 2 px 50 . . 11 s 5 5 0 4 mode n kcode 10000 1.000000 100 500 imp:n 1 1 1 1 0 m1 8016.60c 0.035432 $MAT 6000.60c 0.011811 92235.60c m4 6000.60c 0.048081 $MAT sdef pos=20 0 0 cel=1. 1 px 0 2 px 50 . . 11 s 5 5 0 4 mode n kcode 10000 1.000000 100 500 m1 8016.60c 0.035432 $MAT 6000.60c 0.011811 92235.60c m4 6000.60c 0.048081 $MAT sdef pos=20 0 0 cel=1. 0.0024754. 27 / 55. 0.0024754. SNURPL. (28) Source Specification a) S D E F : G en eral so u rce. b ) S In. : S o u rce in fo rm atio n. c) S P n. : S o u rce p ro b ab ility. d) SBn. : S o u rce b ias. e) D S n. : D ep en d en t so u rce. f) S C n. : S o u rce co m m en t. g ) K C O D E : C riticality so u rce. h) K SR C. : S o u rce p o in ts. 28 / 55. SNURPL. (29) Source Specification  Criticality source Form : K C O D E N S R C K R K K IK Z K C T M S R K K N R M M R K P K C 8 A LP H A. N S R C K = num ber of source histories per cycle R K K = initial guess for keff IK Z = num ber of cycles to be skipped before beginning tally accum ulation K C T = num ber of cycles to be done M S R K = num ber of source points to allocate storage for K N R M = norm alize tallies by 0= w eight / 1 = histories M R K P = m axim um num ber of cycle values on M C T A L or R U N T P E K C 8 = sum m ary and tally inform ation averaged over: 0 = all cycles 1 = active cycles only. D efaults: N S R C K = 1000; R K K = 1.0; IK Z= 30; K C T = IK Z+ 100; M S R K = 4500 or 2* N S R C K ; K N R M = 0; M R K P = 6500;K C 8= 1;. The KCODE card specifies the MCNP criticality source that is used for determining. 29 / 55. SNURPL. (30) Source Specification  Source points Form : KSRC x1 y1 z1. x2 y 2 z 2. xi y i z i : location of initial source points. At least one point m ust be in a cell con taining fissile m aterial and points m ust be aw ay from cell bo undaries. T he energy of each particle in the initial source is sam pled from a W att fission spectrum hardw ired into M C N P If this card is absent, an SR C T P source file or SD EF card m ust be supplied to provide initial source points for a criticality calculation. 30 / 55. SNURPL. (31) Source Specification  G eneral source. S D E F : G eneral source S In. : S ource inform ation. SPn. : S ource probability. P O S : R eference point for position sam p ling C E L : S tarting cell num ber E R G : S tarting energy W G T : S tarting w eight T M E : T im e (S hakes) R A D : R adial distance of the position SUR. : S urface. V E C : R eference vector for D IR. 31 / 55. SNURPL. (32) Tally Specification a) Fna : T ally type. b) FC n : T ally com m ent. c) E n. : T ally energies. d) FQ n : T ally print hierarchy. e) FM n : T ally m ultiplier. f) D E n/D Fn : D ose energy/D ose function. g) E M n. h) S D n. : E nergy m ultiplier. : S egm ented volum e/area. 32 / 55. SNURPL. (33) Tally Specification  Tally type Fna : Tally type. 33 / 55. SNURPL. (34) Tally Specification  Surface and Cell tallies (tally types 1, 2, 4, 6 and 7)  Form. F n :pl S1 S 2. Sk. n  tally number pl  N or P or N,P or E S i  problem number of surface or cell for tallying.  example. f104:n 1 fc104 Flux averaged over a cell 1 fm104 1. f104:n ( 1 2 3 ) fc104 Flux averaged over a cell 1 2 3 fm104 1. 34 / 55. SNURPL. (35) Tally Specification  Tally energies  Form. E n E1 E 2. Ek. n = tally num ber. E i = upper bound (in M eV ) of the i-th ene rgy bin for tally n..  the order of increasing magnitude  An E0 card can be used to set up a default energy bin structure for all tallies.  A specific En card will override the default structure for tally n..  example. E 11 .1 1 20 0.1 MeV. 35 / 55. 1 MeV. 20 MeV. SNURPL. (36) Material Specification a) M m. b) D R X S. : M aterial. : D iscrete reactio n. c) T O T N U : T o tal fissio n . d) N O N U. : F issio n tu rn o ff. e) A W T A B : A to m ic w eig h t. f) X S n. : C ro ss-sectio n files. g ) V O ID. : N eg ates m aterial s. h ) M G O P T : M u ltig ro u p card. 36 / 55. SNURPL. (37) Material Specification  M aterial  Form. M n ZAID 1 fraction 1 ZAID 2 fraction 2 n. : corresponds to the m aterial num b er on the cell cards. ZA ID i = either a full ZZZA A A .nnX w here ZZZ is the atom ic nu m ber, A A A is the atom ic m ass, nn is the l ibrary identifier and X is the class of data fraction i = atom ic fraction (or w eight fr action if entered as a negativenum ber)..  example. m1. 92235.60c 1.649991E-02 92238.60c 3.168330E-01 8016.60c 6.666671E-01 $Fuel Region m2 40000.60c 1 $ Zr m3 1001.60c 6.666667E-01 8016.60c 3.333333E-01. 37 / 55. $ H2o. SNURPL. (38) Energy and Thermal Treatment Specification a) P H Y S : E nergy physics cutoff. b) T M P. : Free-gas therm al tem perature. c) T H T M E : T herm al tim es. d) M T m. : S (  ,  ) m aterial. 38 / 55. SNURPL. (39) Energy and Thermal Treatment Specification  S( , ) material  Form. MTm. X1. X2. m : m aterial num ber on M m card X i : S(  ,  ) identifier corresponding to a particular com ponent on the M m card  W hen therm al treatm ents are needed, this card is used..  example. m3 1001.60c 6.666667E-01 8016.60c 3.333333E-01 mt3 lwtr.01t. 39 / 55. $ H2o. SNURPL. (40) Execution  basic execution com m and. mcnp i=[input file name] o=[output file name]  input file name and output file name don't have to over 8 character.  T he treatm ent for ascii file of input file follow the treatm ent in the LIN U X . (LF[Line Feed] only) so input file m ust not include the C R [C arriage R eturn]..  when there is same output file name, MCNP generates output file with another name.  "xsdir" file must need to determine the xs data directory..  plot geometry mcnp ip i=[input file name]. 40 / 55. SNURPL. (41) Contents  M C N P execution  C 5G 7 benchm ark  S ource definition  T ally definition  P ractice. 41 / 55. SNURPL. (42) Required files for MCNP  Executable file : mcnp.exe  C ross-section data file : xsdir T his data file specifies the location an d name of xsec files of each material ID  cross-section files : cross-section files located in ./xs/* for default.  input file INPUT Geometry Composition Tally spec. OUTPUT. read MCNP.exe. Cross-section Data file (xsdir). OUTPUT file (Keff, tally). Cross-section files. 42 / 55. SNURPL. (43) Execution  basic execution com m and. mcnp i=[input file name] o=[output file name]  input file name and output file name don't have to over 8 character.  T he treatm ent for ascii file of input file follow the treatm ent in the LIN U X . (LF[Line Feed] only) so input file m ust not include the C R [C arriage R eturn]..  when there is same output file name, MCNP generates output file with another name.  "xsdir" file must need to determine the xs data directory.. 43 / 55. SNURPL. (44) Test Execution  test file in your practice package contains a simple arbitrary pincell.  run mcnp for test input. use the 'test' file in your mcnp folder as the input file.  open the output file and confirm that e stimated keff is near 0.63 use searching option for finding "keff ='. R=0.45.  cylindrical pincell is consisted of low enriched UO2  Pincell is barreled in w ater m oderator.. 6 cm. See that therm al treatm ent xsec is specified in data card.. 1 cm 44 / 55. SNURPL. (45) C5G7 benchmark problem  try C5 Mox fuel assembly problem..  Before calculation >  Open the 'c5g7' input file and figure out the configuration of geometry.  See that flux tally is specified in data card.  A s 7-group xsec is used for the m ateria ls, copy the cross section files into the folder m cnp file located. the xsec files for C 5G 7 is under C 5G 7 sub-folder. (m astab1~ 7).  A documentation for C5G7 is prepared in pdf format..  After calculation >  C onfirm that keff is near the calculation reference. (see page 4 in docum ent).  find the output for flux tally. < Quarter core configuration of C5G7 >. 45 / 55. SNURPL. (46) Practice  C alculation keff 2D pincell dim ension : radius 6cm 3. hexagonal m oderator m aterial : w ater (1g/cm ) critical calculation in all reflective boundary. 46 / 55. SNURPL. (47) Source Specification  Four source type S D E F : G eneral source K C O D E : C riticality source S S R : S urface source S O U R C E , S R C D X : U ser-supplied source. 47 / 55. SNURPL. (48) Source Specification  S I card. Ex). S In optio n val ues. SDEF ERG=D1. options : B lank. S I1 H 0.01 0.1 1 5 14. H - histogram bin boundaries (default) L - D iscrete values. SDEF POS=D5. A - points w here pro bability d ens ity distribution is defined. S I5 L 0 0 0 0 5 0. S : distribution num bers Ex).  S P card. SDEF ERG=D1. S P n optio n values. S I1 H. options D - bin probabilities. 0 .0 1 0 .1 1 5 1 4. SP1 D 0 2 1 1 6. C - cum ulative bin probability. o r S P 1 C 0 0 .2 0 .3 0 .4. 1. V - probability propo r tional t o volum e. SDEF ERG=D5 S I5 -2 1 $ m ax w ellian d istrib u tio n. 48 / 55. SNURPL. (49) Source Specification  S ource C ard E xam ples ( S In L ) S D E F E R G = D 3 P O S= 1 1 1 S I3 L 0.1 0.5 1 2. 5. S P 3 D 0.0 0.1 0.2 0.3. 0.4.  S ource C ard E xam ples ( S In H ) S D E F E R G = D 3 P O S= 1 1 1 S I3 H. 0.1 0.5 1 2. 5. S P 3 D 0.0 0.1 0.2 0.3 0.4  S ource C ard E xam p les 2 S D E F C E L D 4 S I4 L. 1 10 20. SP4 V S C 4 C ellS ource :proportional t o cell vol u m e. 49 / 55. SNURPL. (50) Source Specification  S ource C ard E xam ples ( S In L ) S D E F E R G = D 3 P O S= 1 1 1 S I3 L 0.1 0.5 1 2. 5. S P 3 D 0.0 0.1 0.2 0.3. 0.4.  S ource C ard E xam ples ( S In H ) S D E F E R G = D 3 P O S= 1 1 1 S I3 H. 0.1 0.5 1 2. 5. S P 3 D 0.0 0.1 0.2 0.3 0.4  S ource C ard E xam p les 2 S D E F C E L D 4 S I4 L. 1 10 20. SP4 V S C 4 C ellS ource :proportional t o cell vol u m e. 50 / 55. SNURPL. (51) Tally Type and Estimator (F4)  T rack-length E stim ator : F4 tally (S tandard T ally) Fluence :.  i. wi V. 2  i  particle / cm . λ1. V. λ2. λn.  concept of track length estimator >. 51 / 55. SNURPL. (52) Tally Type and Estimator (F2)  S urface E stim ator : F2 tall y Fluence :.  i. wi V. i =. wi.   A| i. =. .  i. i. |. wi.  particle / cm 2   A | i |  A. λi. μ. δ.  concept of surface estimator >. 52 / 55. SNURPL. (53) Tally Card  Fn card Fn:pl S1 S 2 S 3 . ...  Ex) F4: N 2 F14:N 1 (2 3) (4 5 6). n: tally num ber pl: N , P , or E S : tally surf ace, cell n um be r.  FC C ard tally com m ent card : the title heading of the tally in output file FC n com m ent.  E x) F2:p 5 FC 2 surface detector #1.  FM C ard tally m ultiplier car d FM n C m R C. .  ( E ) R m ( E ) dE. 53 / 55. SNURPL. (54) Tally Card  FS C ard.  E x) F4: N 1. FS n S1 S 2 S 3 .... FS 4 -3 -4. n: tally num ber S : signed problem num ber of a seg m enting surface. 3. 4. Cell1. 54 / 55. SNURPL. (55) Practice 2cm.  C alculation of neutron flux. 3. m aterial : w ater (1g/cm ). Point isotropic src. isotropic point source of 1M ev 1 cm aw ay from the left surface. 40cm. slab dim ension : W 2cm L 20cm H 40 cm.  Calculate the flux at the right end surface of the slab using f2 tally. 55 / 55. SNURPL. (56)

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Therefore, the objectives of the present study were to 1 examine the changes in the trajectories of cognitive function and identify the risk factors that influence these changes, 2 to

Pipeline Route Selection • When layout the field architecture, several considerations should be accounted for: : Compliance with regulation authorities and design codes : Future field

Design analysis • Wall thickness analysis : The wall-thickness level for pipelines should be able to withstand pressure and pressure effect hoop and burst strength : A difference of

ii rotor should operate at lowest feasible 𝑉𝑡𝑖𝑝 𝐶𝑇 ~ 𝑉𝑡𝑖𝑝2 and 𝐶𝑃~ 𝑉𝑡𝑖𝑝3 → for a given thrust, smallest profile-drag power loss is obtained at the smallest 𝑉𝑡𝑖𝑝 Thrust also ∝ 𝐶𝐿 →

Culture Modes Production of recombinant protein in CHO cells Culture Modes High level expression Low level expression β-IFN Recombinant EPO β Hydrophobicity Factor VIII FSH