Chapter 6. Isoparametric Formulation
|
|
|
- Franklin Wilkins
- 5 years ago
- Views:
Transcription
1 ME 78 FIIE ELEME MEHOD Chper. Ioprerc Forlon Se fncon h ed o defne he eleen geoer ed o defne he dplceen whn he eleen ode r Eleen Lner geoer Lner dplceen ode Be Eleen Qdrc geoer Qdrc dplceen We gn he e locl coordne e o ech eleen. h coordne e clled he nrl coordne e. he dvnge of choong h coordne e eer o defne he hpe fncon nd he negron over he rfce of he eleen eer (we wll e nercl negron whch ch pler n he nrl coordne e nd cn e cled o he cl re he ep n dervng he eleenl ffne rce re he e: Sep Selec eleen pe Sep Selec dplceen fncon Sep Defne rn/dplceen re/rn relon Sep Derve eleen ffne r nd eqon.
2 -D r Eleen For -D lner r eleen he nrl coordne e for n eleen : - he nrl coordne re reled o he glol coordne hrogh whchwecnolveforhe : [( ( ] or n r for : [ ] where ow followng he render of he ep ecoe ch pler. Sep Selec dplceen fncon [ ] Sep Defne / nd /σ relon Recll h we hd he followng relon: ( d d hen pplng he chn rle of dfferenon we hve.
3 ( d d d d h B L L he re/rn relon epreed : h: σ D where D E σ EB Sep. Derve he eleen ffne r nd eqon he ffne r e K ( L AE B B d whch h n negrl over whch we hve o conver o n negrl over. h done hrogh he rnforon: L f ( d f ( J d where J he Jcon nd for he ple r eleen : And Vol!! K ( e d J d AE L L L L / L d L AE L.
4 . CS Eleen we chooe nrl coordne e hown nd defne he geoer n er of he nrl coordne e : whchwecnwrenrfor: Whch cn e olved : A β α β α β α..
5 . In h ce hee re he hpe fncon he of he hpe fncon nwhere on he eleen dd o oe h n h ce he re pl nd. Sep : Chooe he dplceen fncon we cn pl wre he eleen dplceen fncon of nodl dof n he e for ed o decre he geoer:
6 . ( ( or Ψ Sep : Srn/dplceen nd re/rn relon In -D he rn dplceen relon re: nd or n r for : B In -D he re/rn relon re: DB D σ Where D depend on wheher plne re or plne rn condon prevl(ee Chper for del
7 .7 Snce he hpe fncon re fncon of he nrl coordne nd no nd we ppl he chn rle : Le conder he followng B o hen for he dervve of he hpe fncon wh repec o he glol coordne e we pl hve: β β β And he rn re wren : A β β β β β β Sep. Derve he eleen ffne r nd eqon Ll we e he PMPE o on he ffne eqon : V S rc od V ds dv dv X P B DB Snce ll he er n B re conn nd ng he hckne nd erl propere re conn over he eleen we hve: f K where DB B K A
8 .8 Lner Srn rngle (LS Eleen Agn we chooe he e nrl coordne e for he CS we defne he geoer n er of he nrl coordne e hrogh he hpe fncon : Whch we cn olve for he hpe fncon n er of he nrl coordne follow: Le e qdrc fncon of nd ( we cn epre fncon of nd : - - o whch en h here re nknown coeffcen o e deerned for ech hpe fncon...
9 .9 Ung he followng nforon h node we wn nd ll oher hen we ge eqon for ech hpe fncon nd we cn olve for he coeffcen nd we hve: ( ( ( or recognzng h hen we hve ( ( (( ( ( ( In h ce hee look lke he of he hpe fncon nwhere on he eleen dd o
10 . Incdenll he hpe fncon n he glol coordne e for nce eleen wh de lgned wh he nd e wold look oehng lke h: / /( / / /( / /( / / / / / /( / / / h h h h h h h h h h h h wh we e he Ioprerc forlon!!! Sep : Chooe he dplceen fncon We cn pl wre he eleen dplceen fncon of nodl dof n he e for ed o decre he geoer: ( ( or Ψ
11 . Sep : Srn/dplceen nd re/rn relon In -D he rn/dplceen relon re: nd or n r for : In -D he re/rn relon re: DB D σ Where D depend on wheher plne re or plne rn condon prevl(ee Chper for del So how do we conrc he B r? Le defne he followng r 8 8 B o nd le he Jcon r e (noe h
12 . J hen he er n he B r re pl erced fro he prodc o B J Sep. Derve he eleen ffne r nd eqon Ll we e he PMPE o on he ffne eqon : V S rc od V ds dv dv X P B DB We e Gn qdrre o perfor he negron over he eleen (oe h B nd n he ove re fncon of he nrl coordne nd
13 Gn Qdrre (ercl Inegron A we w he dervon of he ffne reqre h we perfor n negron over he eleen (h coe fro he defnon of he nernl rn energ nd when we ele he force vecor. Ofen h dffcl o do eplcl nle o re ng Mhec o we rn o nercl negron echnqe. oe h n he eleen forlon we re choong he fncon for of he dplceen (hence ndrecl he for of he rn nd re whch pper n he nernl rn energ he prncple ehnd Gn Qdrre h f we know he fnconl for of wh we re rng o negre hen here cern ner of pon where we need o evle he fncon whch wll gve n ec repreenon of he negrl. G Forl: I f ( di n n W f ( We evle n negrl evlng he fncon we wn o negre dcree pon n n nd lpl h n ppropre wegh Rle: n n negron pon rle n n order ccrc Eple: negron pon wll negre order polnol ecl - n n W.
14 negron pon wll negre rd order polnol ecl - n n / ± W W G Forl n -Denon: I / / W f ( dd W f ( W f ( d W W f ( Eple: CS (conn rn rngle Here we ed lner dplceen fncon whch en h he rn feld (nd he re feld conn over he eleen. he fnd he negrl of conn.e. he re nder he crve we need onl evle h fncon one pon. For CS h pon loced n he cener of he rngle n he nrl coordne e h pon loced. nd he correpondng wegh. -node ver -node rnglr eleen.
15 . Rernng o he node LS eleen we hd B nd whch were epreed n er of he nrl coordne. For hee eleen we hve G pon wh locon nd wegh : W gp W gp W gp h gve degree of precon of (negre nd order polnol ecl o we now hve for he ffne r ( ( ( (... gp gp gp n plne plne e W da da DB J B DB J B DB J B J DB B J DB B DB B k where he Jcon h lred een conrced (when we fored he B r : de J Slrl we cn perfor he negrl pperng n he force vecor oe: he fcor of ½ coe fro he re of he rngle n pce
16 -D Brck Eleen rl coordne e For ech eleen we gn locl coordne e repreened nd whch oh pn he rnge fro o over he re of he eleen Lner dplceen fncon Qdrc dplceen fncon ( noded (8 noded ode Brck BLner Qd - we chooe nrl coordne e hown nd defne he geoer n er of he nrl coordne e : -.
17 .7 or rher n er of he hpe fncon nd he nodl coordne : whchwecnwrenrfor: Here he hpe fncon re ( ( ( ( ( ( ( ( h we hve he of he hpe fncon nwhere on he eleen dd o
18 .8 Sep : Chooe he dplceen fncon we cn pl wre he eleen dplceen fncon of nodl dof n he e for ed o decre he geoer: ( ( or Ψ Sep : Srn/dplceen nd re/rn relon Agn he -D rn dplceen relon re: nd or n r for :
19 .9 A B In -D he re/rn relon re: DB D σ Where D depend on wheher plne re or plne rn condon prevl (gn ee Chper for del B re fncon of nd nd no nd o we hve o ppl he chn rle of dfferenon gn. h e we hve: d Or n r for : nd re dffcl o evle nd re no o we cn wre:
20 . J nd J where he deernn of he Jcon J : J de So we ge new B whch eql B now fncon of nd. Sep. Derve he eleen ffne r nd eqon Ll we e he PMPE o on he ffne eqon : V S rc od A ds dv da X P DB B n whch we rnfor he negrl n he - plne o negrl over he - plne fro o hrogh he rnforon nd e Gn Qdrre o perfor he negron ( n A W dd J f dd f J DB B ( (
21 . 8-ode Brck Eleen rl coordne e For ech eleen we gn locl coordne e repreened nd whch oh pn he rnge fro o over he re of he eleen Qdrc dplceen fncon he hpe fncon re: ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( 8 7 lernvel we chooe nrl coordne e hown nd defne he geoer n er of he nrl coordne e : oe h h n ncoplee qdrc polnol. 7 8
22 G pon node nd 8 node rck eleen Recll h we hd ed he for of he dplceen : h lner pproon no lner n ever drecon nd o perhp pon no ffcen Qd end o eh nle. he followng ode hve no rn herefore we e ore pon
23 PACH ES Vld of Ioprerc Eleen Crcl e for vld he pch e Serve necer nd ffcen condon for he correc convergence of fne eleen forlon Bc de o ele ll ner of eleen o h le one node whn he pch hred ore hn wo eleen. he ondr node of he odel re loded e of conenl derved nodl lod correpondng o e of conn re. Eple A pch e for σ for -node eleen F F F F A pch e e perfored for ll conn re e dended of he eleen A ccefl pch e revel h he eleen - wll dpl e of conn rn - wll no rn when eced o rgd od oon - cople wh dcen eleen when eced o e of conn rn.
24 ercl eple of LS Specf he nodl coordne ccord 88. < 8 < 8 < 8.< 8.7 < 8.7.<<; Merl propere nd pln re D r plnre; E.; ν.; D E ν ν :8 ν < 8ν < : >>; Specf he hpe fncon ; n H L; n H L; n H L; n ; n ; n ; For he Bno r nd deerne he Jcon MrFor@ Bno 88D@n D D@n D D@n D D@n D D@n D D@n D< 8D@n D D@n D D@n D D@n D D@n D D@n D<<D H L H L J H L H L MrFor@J Splf@Bno.ccordDêêChopD J.. MrFor@Bno Splf@Invere@JD.BnoDD J For he B r MrFor@ B 88Bno@@ DD Bno@@ DD Bno@@ DD Bno@@ DD Bno@@ DD Bno@@ DD < 8 Bno@@ DD Bno@@ DD Bno@@ DD Bno@@ DD Bno@@ DD Bno@@ DD< 8Bno@@ DD Bno@@ DD Bno@@ DD Bno@@ DD Bno@@ DD Bno@@ DD Bno@@ DD Bno@@ DD Bno@@ DD Bno@@ DD Bno@@ DD Bno@@ DD<<D k Sr forng he ffne r MrFor@K@ D De@JD Splf@rnpoe@BD.D.BDD Perfor nercl negron(evle he g pon MrFor@ Kloc ê.ê HK@..D K@..D K@..DLD k { {.
25 Appl he ondr condon R ; R ; R ; R ; R.; R ; R ; R.; R ; ; ; ; ; MrFor@ fvec 88R< 8R< 8R< 8R< 8R< 8R< 8R< 8R< 8R< 8R< 8R< 8R<<D MrFor@ vec 88< 8< 8< 8< 8< 8< 8< 8< 8< 8< 8< 8<<D Solve@Kloc.vec fvecd R. R. R.9 7 R.99<< MrFor@ fvec 88R< 8R< 8R< 8R< 8R< 8R< 8R< 8R< 8R< 8R< 8R< 8R<<D MrFor@ vec 88< 8< 8< 8< 8< 8< 8< 8< 8< 8< 8< 8<<D k { k.98 { MrFor@revec@ D Splf@D.B.vecDD.8.. k Deerne he ree he G pon MrFor@revec@..DD MrFor@revec@..DD MrFor@revec@..DD k.99 { k.79 { nd k.887 { {.
1.B Appendix to Chapter 1
Secon.B.B Append o Chper.B. The Ordnr Clcl Here re led ome mporn concep rom he ordnr clcl. The Dervve Conder ncon o one ndependen vrble. The dervve o dened b d d lm lm.b. where he ncremen n de o n ncremen
Introduction. Section 9: HIGHER ORDER TWO DIMENSIONAL SHAPE FUNCTIONS
Secon 9: HIGHER ORDER TWO DIMESIO SHPE FUCTIOS Inroducon We ne conder hpe funcon for hgher order eleen. To do h n n orderl fhon we nroduce he concep of re coordne. Conder ere of rngulr eleen depced n he
PHY2053 Summer C 2013 Exam 1 Solutions
PHY053 Sue C 03 E Soluon. The foce G on o G G The onl cobnon h e '/ = doubln.. The peed of lh le 8fulon c 86,8 le 60 n 60n h 4h d 4d fonh.80 fulon/ fonh 3. The dnce eled fo he ene p,, 36 (75n h 45 The
Review: Transformations. Transformations - Viewing. Transformations - Modeling. world CAMERA OBJECT WORLD CSE 681 CSE 681 CSE 681 CSE 681
Revew: Trnsforons Trnsforons Modelng rnsforons buld cople odels b posonng (rnsforng sple coponens relve o ech oher ewng rnsforons plcng vrul cer n he world rnsforon fro world coordnes o cer coordnes Perspecve
Recap Shape Functions
Seon : ISOPARAMETRIC FORMULATIO Whkewz College o Engneerng Rep Shpe Fnon Th good ple o op nd remnd orele where we re n he proe o ormlng nmerl olon ng ne elemen mehod. For omponen we re olng he glol ore
Supporting information How to concatenate the local attractors of subnetworks in the HPFP
n Effcen lgorh for Idenfyng Prry Phenoype rcors of Lrge-Scle Boolen Newor Sng-Mo Choo nd Kwng-Hyun Cho Depren of Mhecs Unversy of Ulsn Ulsn 446 Republc of Kore Depren of Bo nd Brn Engneerng Kore dvnced
II The Z Transform. Topics to be covered. 1. Introduction. 2. The Z transform. 3. Z transforms of elementary functions
II The Z Trnsfor Tocs o e covered. Inroducon. The Z rnsfor 3. Z rnsfors of eleenry funcons 4. Proeres nd Theory of rnsfor 5. The nverse rnsfor 6. Z rnsfor for solvng dfference equons II. Inroducon The
Calculus 241, section 12.2 Limits/Continuity & 12.3 Derivatives/Integrals notes by Tim Pilachowski r r r =, with a domain of real ( )
Clculu 4, econ Lm/Connuy & Devve/Inel noe y Tm Plchow, wh domn o el Wh we hve o : veco-vlued uncon, ( ) ( ) ( ) j ( ) nume nd ne o veco The uncon, nd A w done wh eul uncon ( x) nd connuy e he componen
Laplace Transform. Definition of Laplace Transform: f(t) that satisfies The Laplace transform of f(t) is defined as.
Lplce Trfor The Lplce Trfor oe of he hecl ool for olvg ordry ler dfferel equo. - The hoogeeou equo d he prculr Iegrl re olved oe opero. - The Lplce rfor cover he ODE o lgerc eq. σ j ple do. I he pole o
Response of MDOF systems
Response of MDOF syses Degree of freedo DOF: he nu nuber of ndependen coordnaes requred o deerne copleely he posons of all pars of a syse a any nsan of e. wo DOF syses hree DOF syses he noral ode analyss
Stochastic Programming handling CVAR in objective and constraint
Sochasc Programmng handlng CVAR n obecve and consran Leondas Sakalaskas VU Inse of Mahemacs and Informacs Lhana ICSP XIII Jly 8-2 23 Bergamo Ialy Olne Inrodcon Lagrangan & KKT condons Mone-Carlo samplng
Go over vector and vector algebra Displacement and position in 2-D Average and instantaneous velocity in 2-D Average and instantaneous acceleration
Mh Csquee Go oe eco nd eco lgeb Dsplcemen nd poson n -D Aege nd nsnneous eloc n -D Aege nd nsnneous cceleon n -D Poecle moon Unfom ccle moon Rele eloc* The componens e he legs of he gh ngle whose hpoenuse
ESS 265 Spring Quarter 2005 Kinetic Simulations
SS 65 Spng Quae 5 Knec Sulaon Lecue une 9 5 An aple of an lecoagnec Pacle Code A an eaple of a knec ulaon we wll ue a one denonal elecoagnec ulaon code called KMPO deeloped b Yohhau Oua and Hoh Mauoo.
Chapter 6 Plane Motion of Rigid Bodies
Chpe 6 Pne oon of Rd ode 6. Equon of oon fo Rd bod. 6., 6., 6.3 Conde d bod ced upon b ee een foce,, 3,. We cn ume h he bod mde of e numbe n of pce of m Δm (,,, n). Conden f he moon of he m cene of he
THEORETICAL AUTOCORRELATIONS. ) if often denoted by γ. Note that
THEORETICAL AUTOCORRELATIONS Cov( y, y ) E( y E( y))( y E( y)) ρ = = Var( y) E( y E( y)) =,, L ρ = and Cov( y, y ) s ofen denoed by whle Var( y ) f ofen denoed by γ. Noe ha γ = γ and ρ = ρ and because
1. Find a basis for the row space of each of the following matrices. Your basis should consist of rows of the original matrix.
Mh 7 Exm - Prcice Prolem Solions. Find sis for he row spce of ech of he following mrices. Yor sis shold consis of rows of he originl mrix. 4 () 7 7 8 () Since we wn sis for he row spce consising of rows
Background and Motivation: Importance of Pressure Measurements
Imornce of Pressre Mesremens: Pressre s rmry concern for mny engneerng lcons e.g. lf nd form drg. Cvon : Pressre s of fndmenl mornce n ndersndng nd modelng cvon. Trblence: Velocy-Pressre-Grden ensor whch
8. INVERSE Z-TRANSFORM
8. INVERSE Z-TRANSFORM The proce by whch Z-trnform of tme ere, nmely X(), returned to the tme domn clled the nvere Z-trnform. The nvere Z-trnform defned by: Computer tudy Z X M-fle trn.m ued to fnd nvere
UNIVERSAL BOUNDS FOR EIGENVALUES OF FOURTH-ORDER WEIGHTED POLYNOMIAL OPERATOR ON DOMAINS IN COMPLEX PROJECTIVE SPACES
wwwrresscom/volmes/vol7isse/ijrras_7 df UNIVERSAL BOUNDS FOR EIGENVALUES OF FOURTH-ORDER WEIGHTED POLYNOIAL OPERATOR ON DOAINS IN COPLEX PROJECTIVE SPACES D Feng & L Ynl * Scool of emcs nd Pyscs Scence
Chapter 6 DETECTION AND ESTIMATION: Model of digital communication system. Fundamental issues in digital communications are
Chaper 6 DCIO AD IMAIO: Fndaenal sses n dgal concaons are. Deecon and. saon Deecon heory: I deals wh he desgn and evalaon of decson ang processor ha observes he receved sgnal and gesses whch parclar sybol
Notes on the stability of dynamic systems and the use of Eigen Values.
Noes on he sabl of dnamc ssems and he use of Egen Values. Source: Macro II course noes, Dr. Davd Bessler s Tme Seres course noes, zarads (999) Ineremporal Macroeconomcs chaper 4 & Techncal ppend, and Hamlon
ANOTHER CATEGORY OF THE STOCHASTIC DEPENDENCE FOR ECONOMETRIC MODELING OF TIME SERIES DATA
Tn Corn DOSESCU Ph D Dre Cner Chrsn Unversy Buchres Consnn RAISCHI PhD Depren of Mhecs The Buchres Acdey of Econoc Sudes ANOTHER CATEGORY OF THE STOCHASTIC DEPENDENCE FOR ECONOMETRIC MODELING OF TIME SERIES
OH BOY! Story. N a r r a t iv e a n d o bj e c t s th ea t e r Fo r a l l a g e s, fr o m th e a ge of 9
OH BOY! O h Boy!, was or igin a lly cr eat ed in F r en ch an d was a m a jor s u cc ess on t h e Fr en ch st a ge f or young au di enc es. It h a s b een s een by ap pr ox i ma t ely 175,000 sp ect at
T h e C S E T I P r o j e c t
T h e P r o j e c t T H E P R O J E C T T A B L E O F C O N T E N T S A r t i c l e P a g e C o m p r e h e n s i v e A s s es s m e n t o f t h e U F O / E T I P h e n o m e n o n M a y 1 9 9 1 1 E T
Physics 120 Spring 2007 Exam #1 April 20, Name
Phc 0 Spng 007 E # pl 0, 007 Ne P Mulple Choce / 0 Poble # / 0 Poble # / 0 Poble # / 0 ol / 00 In eepng wh he Unon College polc on cdec hone, ued h ou wll nehe ccep no pode unuhozed nce n he copleon o
_ J.. C C A 551NED. - n R ' ' t i :. t ; . b c c : : I I .., I AS IEC. r '2 5? 9
C C A 55NED n R 5 0 9 b c c \ { s AS EC 2 5? 9 Con 0 \ 0265 o + s ^! 4 y!! {! w Y n < R > s s = ~ C c [ + * c n j R c C / e A / = + j ) d /! Y 6 ] s v * ^ / ) v } > { ± n S = S w c s y c C { ~! > R = n
CAT. NO /irtl,417~ S- ~ I ';, A RIDER PUBLICATION BY H. A. MIDDLETON
CAT. NO. 139-3 THIRD SUPPLEMENT I /irtl,417~ S- ~ I ';,... 0 f? BY H. A. MIDDLETON.. A RIDER PUBLICATION B36 B65 B152 B309 B319 B329 B719 D63 D77 D152 DA90 DAC32 DAF96 DC70 DC80 DCC90 DD6 DD7 DF62 DF91
1.2. Paths, Cycles, and Trails
2301-670 Grph heory 1.2 Ph, Cyle, n Trl 1 emeer 2550 1 1.2. Ph, Cyle, n Trl 1.2.2. Defnon. Le G e grph. A lk l 0, e 1, 1,, e k, k of ere n ege h h, for 1 k, he ege e h en pon -1 n. A rl lk h no repee ege.
Physics 15 Second Hour Exam
hc 5 Second Hou e nwe e Mulle hoce / ole / ole /6 ole / ------------------------------- ol / I ee eone ole lee how ll wo n ode o ecee l ced. I ou oluon e llegle no ced wll e gen.. onde he collon o wo 7.
An analytical solution versus half space BEM formulation for acoustic radiation and scattering from a rigid sphere
Journl of Phyc: Conference Sere PAPER OPEN ACCESS An nlycl oluon veru hlf pce forulon for couc rdon nd cerng fro rgd phere To ce h rcle: B. Soenrko nd D. Sedkrun 06 J. Phy.: Conf. Ser. 776 0065 Reled conen
Integral Equations and their Relationship to Differential Equations with Initial Conditions
Scece Refleco SR Vol 6 wwwscecereflecocom Geerl Leers Mhemcs GLM 6 3-3 Geerl Leers Mhemcs GLM Wese: hp://wwwscecereflecocom/geerl-leers--mhemcs/ Geerl Leers Mhemcs Scece Refleco Iegrl Equos d her Reloshp
Multivariate Time Series Analysis
Mulvre me Sere Anl Le { : } be Mulvre me ere. Denon: () = men vlue uncon o { : } = E[ ] or. (,) = Lgged covrnce mr o { : } = E{[ - ()][ - ()]'} or, Denon: e me ere { : } onr e jon drbuon o,,, e me e jon
Science & Technologies GENERAL BIRTH-DEATH PROCESS AND SOME OF THEIR EM (EXPETATION- MAXIMATION) ALGORITHM
GEERAL BIRH-EAH ROCESS A SOME OF HEIR EM EXEAIO- MAXIMAIO) ALGORIHM Il Hl, Lz Ker, Ylldr Seer Se ery o eoo,, eoo Mcedo l.hl@e.ed.; lz.er@e.ed.; ylldr_@hol.co ABSRAC Brh d deh roce coo-e Mrco ch, h odel
Control Systems. Mathematical Modeling of Control Systems.
Conrol Syem Mahemacal Modelng of Conrol Syem chbum@eoulech.ac.kr Oulne Mahemacal model and model ype. Tranfer funcon model Syem pole and zero Chbum Lee -Seoulech Conrol Syem Mahemacal Model Model are key
E-Companion: Mathematical Proofs
E-omnon: Mthemtcl Poo Poo o emm : Pt DS Sytem y denton o t ey to vey tht t ncee n wth d ncee n We dene } ] : [ { M whee / We let the ttegy et o ech etle n DS e ]} [ ] [ : { M w whee M lge otve nume oth
ONE APPROACH FOR THE OPTIMIZATION OF ESTIMATES CALCULATING ALGORITHMS A.A. Dokukin
Iero Jor "Iforo Theore & co" Vo 463 ONE PPROH FOR THE OPTIIZTION OF ETITE UTING GORITH Do rc: I h rce he ew roch for ozo of eo ccg gorh ggeed I c e ed for fdg he correc gorh of coexy he coex of gerc roch
Numerical Study of Large-area Anti-Resonant Reflecting Optical Waveguide (ARROW) Vertical-Cavity Semiconductor Optical Amplifiers (VCSOAs)
USOD 005 uecal Sudy of Lage-aea An-Reonan Reflecng Opcal Wavegude (ARROW Vecal-Cavy Seconduco Opcal Aplfe (VCSOA anhu Chen Su Fung Yu School of Eleccal and Eleconc Engneeng Conen Inoducon Vecal Cavy Seconduco
( ) ( ) ( ) ( ) ( ) ( ) j ( ) A. b) Theorem
b) Theoe The u of he eco pojecon of eco n ll uull pependcul (n he ene of he cl poduc) decon equl o he eco. ( ) n e e o The pojecon conue he eco coponen of he eco. poof. n e ( ) ( ) ( ) e e e e e e e e
(,,, ) (,,, ). In addition, there are three other consumers, -2, -1, and 0. Consumer -2 has the utility function
MACROECONOMIC THEORY T J KEHOE ECON 87 SPRING 5 PROBLEM SET # Conder an overlappng generaon economy le ha n queon 5 on problem e n whch conumer lve for perod The uly funcon of he conumer born n perod,
, t 1. Transitions - this one was easy, but in general the hardest part is choosing the which variables are state and control variables
Opmal Conrol Why Use I - verss calcls of varaons, opmal conrol More generaly More convenen wh consrans (e.g., can p consrans on he dervaves More nsghs no problem (a leas more apparen han hrogh calcls of
Decompression diagram sampler_src (source files and makefiles) bin (binary files) --- sh (sample shells) --- input (sample input files)
. Iroduco Probblsc oe-moh forecs gudce s mde b 50 esemble members mproved b Model Oupu scs (MO). scl equo s mde b usg hdcs d d observo d. We selec some prmeers for modfg forecs o use mulple regresso formul.
CONSISTENT EARTHQUAKE ACCELERATION AND DISPLACEMENT RECORDS
APPENDX J CONSSTENT EARTHQUAKE ACCEERATON AND DSPACEMENT RECORDS Earhqake Acceleraons can be Measred. However, Srcres are Sbjeced o Earhqake Dsplacemens J. NTRODUCTON { XE "Acceleraon Records" }A he presen
ERASMUS Application form for entry Please use BLOCK CAPITAL letters.
ERSMUS ppl fr fr 2018-19 ery Plee e BLOCK CPITL leer. Plee re ll he fr he he re reflly efre pleg h fr. Frher fr he ppl pre vlle hp://f.le..k/rre-e/erve/er/fr-fr-g-e I el 1. He 2. H epre LSE 3. e f prgre
P a g e 5 1 of R e p o r t P B 4 / 0 9
P a g e 5 1 of R e p o r t P B 4 / 0 9 J A R T a l s o c o n c l u d e d t h a t a l t h o u g h t h e i n t e n t o f N e l s o n s r e h a b i l i t a t i o n p l a n i s t o e n h a n c e c o n n e
THIS PAGE DECLASSIFIED IAW EO IRIS u blic Record. Key I fo mation. Ma n: AIR MATERIEL COMM ND. Adm ni trative Mar ings.
T H S PA G E D E CLA SSFED AW E O 2958 RS u blc Recod Key fo maon Ma n AR MATEREL COMM ND D cumen Type Call N u b e 03 V 7 Rcvd Rel 98 / 0 ndexe D 38 Eneed Dae RS l umbe 0 0 4 2 3 5 6 C D QC d Dac A cesson
by Lauren DeDieu Advisor: George Chen
b Laren DeDe Advsor: George Chen Are one of he mos powerfl mehods o nmercall solve me dependen paral dfferenal eqaons PDE wh some knd of snglar shock waves & blow-p problems. Fed nmber of mesh pons Moves
Chapter 2 Linear Mo on
Chper Lner M n .1 Aerge Velcy The erge elcy prcle s dened s The erge elcy depends nly n he nl nd he nl psns he prcle. Ths mens h prcle srs rm pn nd reurn bck he sme pn, s dsplcemen, nd s s erge elcy s
P-Convexity Property in Musielak-Orlicz Function Space of Bohner Type
J N Sce & Mh Res Vol 3 No (7) -7 Alble ole h://orlwlsogocd/deh/sr P-Coey Proery Msel-Orlcz Fco Sce o Boher ye Yl Rodsr Mhecs Edco Deree Fcly o Ss d echology Uerss sl Neger Wlsogo Cerl Jdoes Absrcs Corresodg
-HYBRID LAPLACE TRANSFORM AND APPLICATIONS TO MULTIDIMENSIONAL HYBRID SYSTEMS. PART II: DETERMINING THE ORIGINAL
UPB Sc B See A Vo 72 I 3 2 ISSN 223-727 MUTIPE -HYBRID APACE TRANSORM AND APPICATIONS TO MUTIDIMENSIONA HYBRID SYSTEMS PART II: DETERMININ THE ORIINA Ve PREPEIŢĂ Te VASIACHE 2 Ace co copeeă oă - pce he
Scattering at an Interface: Oblique Incidence
Course Insrucor Dr. Raymond C. Rumpf Offce: A 337 Phone: (915) 747 6958 E Mal: rcrumpf@uep.edu EE 4347 Appled Elecromagnecs Topc 3g Scaerng a an Inerface: Oblque Incdence Scaerng These Oblque noes may
LAPLACE TRANSFORMS. 1. Basic transforms
LAPLACE TRANSFORMS. Bic rnform In hi coure, Lplce Trnform will be inroduced nd heir properie exmined; ble of common rnform will be buil up; nd rnform will be ued o olve ome dierenil equion by rnforming
Parts Manual. EPIC II Critical Care Bed REF 2031
EPIC II Critical Care Bed REF 2031 Parts Manual For parts or technical assistance call: USA: 1-800-327-0770 2013/05 B.0 2031-109-006 REV B www.stryker.com Table of Contents English Product Labels... 4
THE PREDICTION OF COMPETITIVE ENVIRONMENT IN BUSINESS
THE PREICTION OF COMPETITIVE ENVIRONMENT IN BUSINESS INTROUCTION The wo dmensonal paral dfferenal equaons of second order can be used for he smulaon of compeve envronmen n busness The arcle presens he
An Ising model on 2-D image
School o Coputer Scence Approte Inerence: Loopy Bele Propgton nd vrnts Prolstc Grphcl Models 0-708 Lecture 4, ov 7, 007 Receptor A Knse C Gene G Receptor B Knse D Knse E 3 4 5 TF F 6 Gene H 7 8 Hetunndn
( )a = "t = 1 E =" B E = 5016 V. E = BHv # 3. 2 %r. c.) direction of induced current in the loop for : i.) "t < 1
99 3 c dr b a µ r.? d b µ d d cdr a r & b d & µ c µ c b dr µ c µ c b & ' ln' a +*+* b ln r ln a a r a ' µ c b 'b* µ c ln' * & ln, &a a+ ncreang no he page o nduced curren wll creae a - feldou of he page
J i-1 i. J i i+1. Numerical integration of the diffusion equation (I) Finite difference method. Spatial Discretization. Internal nodes.
umercal negraon of he dffuson equaon (I) Fne dfference mehod. Spaal screaon. Inernal nodes. R L V For hermal conducon le s dscree he spaal doman no small fne spans, =,,: Balance of parcles for an nernal
EE 410/510: Electromechanical Systems Chapter 3
EE 4/5: Eleomehnl Syem hpe 3 hpe 3. Inoon o Powe Eleon Moelng n Applon of Op. Amp. Powe Amplfe Powe onvee Powe Amp n Anlog onolle Swhng onvee Boo onvee onvee Flyb n Fow onvee eonn n Swhng onvee 5// All
HEAT CONDUCTION PROBLEM IN A TWO-LAYERED HOLLOW CYLINDER BY USING THE GREEN S FUNCTION METHOD
Journal of Appled Mahemacs and Compuaonal Mechancs 3, (), 45-5 HEAT CONDUCTION PROBLEM IN A TWO-LAYERED HOLLOW CYLINDER BY USING THE GREEN S FUNCTION METHOD Sansław Kukla, Urszula Sedlecka Insue of Mahemacs,
IX.1.1 The Laplace Transform Definition 700. IX.1.2 Properties 701. IX.1.3 Examples 702. IX.1.4 Solution of IVP for ODEs 704
Chper IX The Inegrl Trnform Mehod IX. The plce Trnform November 6, 8 699 IX. THE APACE TRANSFORM IX.. The plce Trnform Definiion 7 IX.. Properie 7 IX..3 Emple 7 IX..4 Soluion of IVP for ODE 74 IX..5 Soluion
Lecture 36. Finite Element Methods
CE 60: Numercl Methods Lecture 36 Fnte Element Methods Course Coordntor: Dr. Suresh A. Krth, Assocte Professor, Deprtment of Cvl Engneerng, IIT Guwht. In the lst clss, we dscussed on the ppromte methods
ELEC 6041 LECTURE NOTES WEEK 3 Dr. Amir G. Aghdam Concordia University
ecre Noe Prepared b r G. ghda EE 64 ETUE NTE WEE r. r G. ghda ocorda Uer eceraled orol e - Whe corol heor appled o a e ha co of geographcall eparaed copoe or a e cog of a large ber of p-op ao ofe dered
Quick Visit to Bernoulli Land
Although we have een the Bernoull equaton and een t derved before, th next note how t dervaton for an uncopreble & nvcd flow. The dervaton follow that of Kuethe &Chow ot cloely (I lke t better than Anderon).
Laplace Examples, Inverse, Rational Form
Lecure 3 Ouline: Lplce Exple, Invere, Rionl For Announceen: Rein: 6: Lplce Trnfor pp. 3-33, 55.5-56.5, 7 HW 8 poe, ue nex We. Free -y exenion OcenOne Roo Tour will e fer cl y 7 (:3-:) Lunch provie ferwr.
Flow Networks Alon Efrat Slides courtesy of Charles Leiserson with small changes by Carola Wenk. Flow networks. Flow networks CS 445
CS 445 Flow Nework lon Efr Slide corey of Chrle Leieron wih mll chnge by Crol Wenk Flow nework Definiion. flow nework i direced grph G = (V, E) wih wo diingihed erice: orce nd ink. Ech edge (, ) E h nonnegie
F-Tests and Analysis of Variance (ANOVA) in the Simple Linear Regression Model. 1. Introduction
ECOOMICS 35* -- OTE 9 ECO 35* -- OTE 9 F-Tess and Analyss of Varance (AOVA n he Smple Lnear Regresson Model Inroducon The smple lnear regresson model s gven by he followng populaon regresson equaon, or
Maximum likelihood estimate of phylogeny. BIOL 495S/ CS 490B/ MATH 490B/ STAT 490B Introduction to Bioinformatics April 24, 2002
Mmm lkelhood eme of phylogey BIO 9S/ S 90B/ MH 90B/ S 90B Iodco o Bofomc pl 00 Ovevew of he pobblc ppoch o phylogey o k ee ccodg o he lkelhood d ee whee d e e of eqece d ee by ee wh leve fo he eqece. he
when t = 2 s. Sketch the path for the first 2 seconds of motion and show the velocity and acceleration vectors for t = 2 s.(2/63)
. The -coordine of pricle in curiliner oion i gien b where i in eer nd i in econd. The -coponen of ccelerion in eer per econd ured i gien b =. If he pricle h -coponen = nd when = find he gniude of he eloci
v v at 1 2 d vit at v v 2a d
SPH3UW Unt. Accelerton n One Denon Pge o 9 Note Phyc Inventory Accelerton the rte o chnge o velocty. Averge ccelerton, ve the chnge n velocty dvded by the te ntervl, v v v ve. t t v dv Intntneou ccelerton
Chapter 2. Review of Hydrodynamics and Vector Analysis
her. Ree o Hdrodmcs d Vecor Alss. Tlor seres L L L L ' ' L L " " " M L L! " ' L " ' I s o he c e romed he Tlor seres. O he oher hd ' " L . osero o mss -dreco: L L IN ] OUT [mss l [mss l] mss ccmled h me
IX.1.1 The Laplace Transform Definition 700. IX.1.2 Properties 701. IX.1.3 Examples 702. IX.1.4 Solution of IVP for ODEs 704
Chper IX The Inegrl Trnform Mehod IX. The plce Trnform November 4, 7 699 IX. THE APACE TRANSFORM IX.. The plce Trnform Definiion 7 IX.. Properie 7 IX..3 Emple 7 IX..4 Soluion of IVP for ODE 74 IX..5 Soluion
- Double consonant - Wordsearch 3
Wh 3 Kn, Kn. Wh' h? Hpp. Hpp h? Hpp hy yu, Hpp hy yu! A h f h pg f. Th hn n h pu. Th h n p hny (ng ) y (ng n). Whn yu fn, n un. p n q q h y f h u g h q g u g u n g n g n q x p g h u n g u n y p f f n u
Rotations.
oons j.lbb@phscs.o.c.uk To s summ Fmes of efeence Invnce une nsfomons oon of wve funcon: -funcons Eule s ngles Emple: e e - - Angul momenum s oon geneo Genec nslons n Noehe s heoem Fmes of efeence Conse
A L A BA M A L A W R E V IE W
A L A BA M A L A W R E V IE W Volume 52 Fall 2000 Number 1 B E F O R E D I S A B I L I T Y C I V I L R I G HT S : C I V I L W A R P E N S I O N S A N D TH E P O L I T I C S O F D I S A B I L I T Y I N
P a g e 3 6 of R e p o r t P B 4 / 0 9
P a g e 3 6 of R e p o r t P B 4 / 0 9 p r o t e c t h um a n h e a l t h a n d p r o p e r t y fr om t h e d a n g e rs i n h e r e n t i n m i n i n g o p e r a t i o n s s u c h a s a q u a r r y. J
Physics 240: Worksheet 16 Name
Phyic 4: Workhee 16 Nae Non-unifor circular oion Each of hee proble involve non-unifor circular oion wih a conan α. (1) Obain each of he equaion of oion for non-unifor circular oion under a conan acceleraion,
A modified new Homotopy Perturbation Method for solving linear integral equations differential
Amercn Jornl of Appled Mhemc 4; 3: 79-84 Plhed onlne Jne 4 hp://www.cenceplhnrop.com/j/jm do:.648/j.jm.43. A modfed new Homoop Perron Mehod for olvn lner nerl eqon dfferenl An Khojeh * Mhmod Prpor M. A.
( ) ( ) ( ) ( ) ( ) ( y )
8. Lengh of Plne Curve The mos fmous heorem in ll of mhemics is he Pyhgoren Theorem. I s formulion s he disnce formul is used o find he lenghs of line segmens in he coordine plne. In his secion you ll
X-Ray Notes, Part III
oll 6 X-y oe 3: Pe X-Ry oe, P III oe Deeo Coe oupu o x-y ye h look lke h: We efe ue of que lhly ffee efo h ue y ovk: Co: C ΔS S Sl o oe Ro: SR S Co o oe Ro: CR ΔS C SR Pevouly, we ee he SR fo ye hv pxel
CHAPTER 11 PARAMETRIC EQUATIONS AND POLAR COORDINATES
CHAPTER PARAMETRIC EQUATIONS AND POLAR COORDINATES. PARAMETRIZATIONS OF PLANE CURVES., 9, _ _ Ê.,, Ê or, Ÿ. 5, 7, _ _.,, Ÿ Ÿ Ê Ê 5 Ê ( 5) Ê ˆ Ê 6 Ê ( 5) 7 Ê Ê, Ÿ Ÿ $ 5. cos, sin, Ÿ Ÿ 6. cos ( ), sin (
! -., THIS PAGE DECLASSIFIED IAW EQ t Fr ra _ ce, _., I B T 1CC33ti3HI QI L '14 D? 0. l d! .; ' D. o.. r l y. - - PR Pi B nt 8, HZ5 0 QL
H PAGE DECAFED AW E0 2958 UAF HORCA UD & D m \ Z c PREMNAR D FGHER BOMBER ARC o v N C o m p R C DECEMBER 956 PREPARED B HE UAF HORCA DVO N HRO UGH HE COOPERAON O F HE HORCA DVON HEADQUARER UAREUR DEPARMEN
The sphere of radius a has the geographical form. r (,)=(acoscos,acossin,asin) T =(p(u)cos v, p(u)sin v,q(u) ) T.
Che 5. Dieeil Geome o Sces 5. Sce i meic om I 3D sce c be eeseed b. Elici om z =. Imlici om z = 3. Veco om = o moe geel =z deedig o wo mees. Emle. he shee o dis hs he geoghicl om =coscoscossisi Emle. he
Geometric Correction or Georeferencing
Geoetrc Correcton or Georeferencng GEOREFERENCING: fro ge to p Coordntes on erth: (λ, φ) ge: (, ) p: (, ) rel nteger Trnsfortons (nvolvng deforton): erth-to-ge: χ erth-to-p: ψ (crtogrphc proecton) ge-to-p:
Modeling and Predicting Sequences: HMM and (may be) CRF. Amr Ahmed Feb 25
Modelg d redcg Sequeces: HMM d m be CRF Amr Ahmed 070 Feb 25 Bg cure redcg Sgle Lbel Ipu : A se of feures: - Bg of words docume - Oupu : Clss lbel - Topc of he docume - redcg Sequece of Lbels Noo Noe:
A NEW INTERPRETATION OF INTERVAL-VALUED FUZZY INTERIOR IDEALS OF ORDERED SEMIGROUPS
ScInLhore),7),9-37,4 ISSN 3-536; CODEN: SINTE 8 9 A NEW INTERPRETATION O INTERVAL-VALUED UZZY INTERIOR IDEALS O ORDERED SEMIGROUPS Hdy Ullh Khn, b, Nor Hnz Srmn, Asghr Khn c nd z Muhmmd Khn d Deprmen of
The Mathematics of Harmonic Oscillators
Th Mhcs of Hronc Oscllors Spl Hronc Moon In h cs of on-nsonl spl hronc oon (SHM nvolvng sprng wh sprng consn n wh no frcon, you rv h quon of oon usng Nwon's scon lw: con wh gvs: 0 Ths s sos wrn usng h
[ ] 2. [ ]3 + (Δx i + Δx i 1 ) / 2. Δx i-1 Δx i Δx i+1. TPG4160 Reservoir Simulation 2018 Lecture note 3. page 1 of 5
![[ ] 2. [ ]3 + (Δx i + Δx i 1 ) / 2. Δx i-1 Δx i Δx i+1. TPG4160 Reservoir Simulation 2018 Lecture note 3. page 1 of 5](/thumbs/85/92299540.jpg "[ ] 2. [ ]3 + (Δx i + Δx i 1 ) / 2. Δx i-1 Δx i Δx i+1. TPG4160 Reservoir Simulation 2018 Lecture note 3. page 1 of 5")
TPG460 Reservor Smulaon 08 page of 5 DISCRETIZATIO OF THE FOW EQUATIOS As we already have seen, fne dfference appromaons of he paral dervaves appearng n he flow equaons may be obaned from Taylor seres
THIS PAGE DECLASSIFIED IAW EO 12958
THIS PAGE DECLASSIFIED IAW EO 2958 THIS PAGE DECLASSIFIED IAW EO 2958 THIS PAGE DECLASSIFIED IAW E0 2958 S T T T I R F R S T Exhb e 3 9 ( 66 h Bm dn ) c f o 6 8 b o d o L) B C = 6 h oup C L) TO d 8 f f
PHYS 1443 Section 001 Lecture #4
PHYS 1443 Secon 001 Lecure #4 Monda, June 5, 006 Moon n Two Dmensons Moon under consan acceleraon Projecle Moon Mamum ranges and heghs Reerence Frames and relae moon Newon s Laws o Moon Force Newon s Law
ASSESSMENT OF STOCHASTIC FATIGUE FAILURES BASED ON DETERMINISTIC FUNCTIONS
h Inernonl Conference on Prolsc Sfe Assessen nd Mngeen (PSAM ) ~7 Ocoer, 6 Sheron Grnde Wlkerhll Seoul, Kore www.ps.org ASSESSMENT OF STOCHASTIC FATIGUE FAILURES BASED ON DETERMINISTIC FUNCTIONS Hossen
Wave Phenomena Physics 15c
Wv hnon hyscs 5c cur 4 Coupl Oscllors! H& con 4. Wh W D s T " u forc oscllon " olv h quon of oon wh frcon n foun h sy-s soluon " Oscllon bcos lr nr h rsonnc frquncy " hs chns fro 0 π/ π s h frquncy ncrss
STATISTICAL MECHANICS OF THE INVERSE ISING MODEL
STATISTICAL MECHANICS OF THE INVESE ISING MODEL Muro Cro Supervsors: rof. Mchele Cselle rof. ccrdo Zecchn uly 2009 INTODUCTION SUMMAY OF THE ESENTATION Defnton of the drect nd nverse prole Approton ethods
Main questions Motivation: Recognition
Tod Algnen & Wrpng Thursd, Oc 9 Algnen & wrpng d rnsforons Forwrd nd nverse ge wrpng Consrucng oscs Hoogrphes Rous fng wh RANSAC Krsen Grun UT-Ausn Mn quesons Movon: Recognon T Wrpng: Gven source ge nd
Mechanics Physics 151
Mechancs Physcs 5 Lecure 0 Canoncal Transformaons (Chaper 9) Wha We Dd Las Tme Hamlon s Prncple n he Hamlonan formalsm Dervaon was smple δi δ Addonal end-pon consrans pq H( q, p, ) d 0 δ q ( ) δq ( ) δ
H STO RY OF TH E SA NT
O RY OF E N G L R R VER ritten for the entennial of th e Foundin g of t lair oun t y on ay 8 82 Y EEL N E JEN K RP O N! R ENJ F ] jun E 3 1 92! Ph in t ed b y h e t l a i r R ep u b l i c a n O 4 1922
CHAPTER 10: LINEAR DISCRIMINATION
CHAPER : LINEAR DISCRIMINAION Dscrmnan-based Classfcaon 3 In classfcaon h K classes (C,C,, C k ) We defned dscrmnan funcon g j (), j=,,,k hen gven an es eample, e chose (predced) s class label as C f g
Physics 201 Lecture 15
Phscs 0 Lecue 5 l Goals Lecue 5 v Elo consevaon of oenu n D & D v Inouce oenu an Iulse Coens on oenu Consevaon l oe geneal han consevaon of echancal eneg l oenu Consevaon occus n sses wh no ne eenal foces
Chapter 3: Vectors and Two-Dimensional Motion
Chape 3: Vecos and Two-Dmensonal Moon Vecos: magnude and decon Negae o a eco: eese s decon Mulplng o ddng a eco b a scala Vecos n he same decon (eaed lke numbes) Geneal Veco Addon: Tangle mehod o addon
2015 Sectional Physics Exam Solution Set
. Crrec answer: D Ne: [quan] denes: uns quan WYSE cadec Challenge 05 Secnal Phscs Ea SOLUTION SET / / / / rce lengh lengh rce enu ass lengh e a) / ass ass b) energ c) wrk lengh e pwer energ e d) (crrec
4.8 Improper Integrals
4.8 Improper Inegrls Well you ve mde i hrough ll he inegrion echniques. Congrs! Unforunely for us, we sill need o cover one more inegrl. They re clled Improper Inegrls. A his poin, we ve only del wih inegrls
Epistemic Game Theory: Online Appendix
Epsemc Game Theory: Onlne Appendx Edde Dekel Lucano Pomao Marcano Snscalch July 18, 2014 Prelmnares Fx a fne ype srucure T I, S, T, β I and a probably µ S T. Le T µ I, S, T µ, βµ I be a ype srucure ha