Diffusivity scaling on shear flow
|
|
- Chloe Blake
- 5 years ago
- Views:
Transcription
1 Amrcan Journal of Modrn Physcs 4; 3(5: -6 Pulshd onln Smr 3, 4 (h:// do:.648/j.ajm.435. ISSN: (Prn; ISSN: (Onln Dffusvy scalng on shar flow hong-tan Wang,, h-xong H, Ja-Q Dong, han-hu Wang, Shao-Yong Chn, Chang-Jan Tang Souhwsrn Insu of Physcs, Chngdu, Schuan, 64, Chna Collg of Physcs Scnc and Tchnology, Schuan Unvrsy, Chngdu, Schuan, 665, Chna mal addrss: wangz@sw.ac.cn (hong-tan Wang To c hs arcl: hong-tan Wang, h-xong H, Ja-Q Dong, han-hu Wang, Shao-Yong Chn, Chang-Jan Tang. Dffusvy Scalng on Shar Flow. Amrcan Journal of Modrn Physcs. Vol. 3, No. 5, 4,. -6. do:.648/j.ajm.435. Asrac: Dffusvy scalng on shar flow s nvsgad. adal lcrcal fld s h drv of h flow. Th urnng ons of h rad arcl ar no on h drf surfac, u modfd y h radal lcrcal fld. For h frs m, an analycal xrsson of h anana wdh n rsnc of shar flow s accuraly drvd. Th arcl dffusvy gvn y osnluh s rroducd u wh h shar flow modfcaon. Kywords: Tokamak Plasma, Dffusvy Scalng, Shar Flow, Trad Parcl, Gudng-Cnr. Inroducon I s gnrally clamd ha h shar flow lays an moran rol n h ons of h ranson from h L mod o H-mod. xrmnal vdnc also showd ha h lasma roas radly n h mrovd confnmn rgm, mlyng ha h radal lcrc fld s gnrad. Noclasscal on ransor n roang axsymmrc lasma has n sysmacally nvsgad y Hnon. Howvr, h nrgy loss somms n h xrmn s smallr han h sandard noclasscal rdcon. Th mrovmn s arud o h squzng facor 3 rad as h shar flow n hs ar. Thr ar rnwd nrss n h noclasscal fluxs 4-6 nsd h hrmal arrrs. Th dffusvy scalng on h shar flow rsnd y Cao 6 and Shang 5 ar dffrn. Thr ar nns argumns 6 on hs oc. I s moran caus s rlad o h rol of h shar flow n h hrmal arrr. Physcss should gv a dfn answr. Th dscrancy wn Cao 6 and Shang 5 coms from h rad arcl dynamcs whch s mhaszd n hs ar. Accura anana wdh, ounc frquncy, and h urnng on oson n h rsnc of h shar flow ar rsnd. Drf knc quaon s solvd wh a arcl-consrvd Krook collson oraor. osnluh s rsul 7 s rroducd u wh h shar flow modfcaon. Th fracon of h rad arcls smad hr s h sam as Shang s 5, howvr, dffusvy scalng on shar flow s dffrn. In scon, a s of canoncal gudng-cnr varals s drvd y ara-consrvd ransformaon. Dynamcs for h rad arcls s gvn n scon 3. Th drf knc quaon s solvd and h dffusvy scalng s drvd n scon 4. Summary s rsnd n h las scon.. Canoncal Gudng-Cnr Varals For a okamak confguraon, h Hamlonan of a chargd arcl can xrssd as: H + ( P [( P M A A + ( P / ] + Φ A, ( whr A, A, and A ar h vcor onal comonns of h magnc fld, Φ h lcrcal onal assumd o a funcon of h olodal magnc flux Ψ, M h mass of h chargd arcl s qual o uny for smlcy, and h charg. P, P, and P ar h canoncal momnum n h cylndrcal coordnas,, and, rscvly, whch ar as followng: P + A, ( P + A, (3 P + A. (4
2 Amrcan Journal of Modrn Physcs 4; 3(5: -6 3 Th magnc fld n okamaks can xrssd as: Ψ + I, (5 whr I s rlad o h olodal currn. Th vcor onal comonns ar A Ψ, A Iln, A. (6 As sady Lljohn,hr has n a gradual voluon ovr h yars away from h avragng aroach and owards h ransformaon aroach 8. W nroduc a gnrang funcon 9 o chang h cylndrcal varals o gudng-cnr varals: Ω X X F x( (ln gα X (7 Ω Ω whr C X Ωln, (8 Ω s h orodal gyrofrquncy a h magnc axs, ρ h Larmor radus, α h gyrohas, and h suscrs o and c rfr o h valus a h magnc axs and h gudng cnr, rscvly. X and α ar h nw coordnas conjuga o h nw momna: ρ P X + ρsnα + snα, (9 4 P α C ΩC ρ, ( whr P X s h gudng cnr of h coordna, c. Th momnum s ofn ransformd no h coordna durng ara-consrvd canoncal ransformaon 9. Th Hamlonan s rwrn as: H Ω [( C CPα sn α + cos α ] + [ P + Ψ ] + Φ. ( ϕ Th canoncal ransformaon maks h Hamlonan xac n h nw coordnas. Th canoncal gudng-cnr varals, Pα, P, PX, α,, X, ar drvd and sasfy h Hamlonan quaons: H Pɺ, ( q H qɺ, (3 P whr h P and q ar known as h gnralzd momna and coordnas. Th Jacoan s uny for h ara-consrvd ransformaon 9, ha s, J dpα dpx dpd αdxd. (4 For h okamaks, h ordrng s δ ~ ρ / r~ r/ /, (5 whr r and ar h mnor and major rad rscvly and + rcos. To h frs ordr, h gyro-avragd Hamlonan n q. ( s aroxmaly xrssd as: H P Ω + ( + Ψ α c P + Φ ξ c c. (6 W hav a s of quaons of moon n h gudng-cnr sysm: d Ψ, (7 ( + z d, (8 ϕ whr ϕ ( P + Ψ c /, Φ, and Ψ, d ( Ω C µ + Ψ s n h radal drcon whras s Ω n h olodal drcon. quaons (7 and (8 ar h gnralzd vrsons of h quaons of moon oand y alscu. 3. Dynamcs for h Trad Parcls For h rad arcls, h orodal vlocy s smallr han h rndcular vlocy, / /( Ω P c α δ. (9 In h roaon fram, w can consruc a Hamlonan n h dvlod canoncal varals, Pα, P, PX, α,, X, H Ω P + P + Ψ u + u X X X Ω Ω Ω α ϕ os, ( " P + Ψ ρφ ( r whr u, u, S +, T S S ρ s h olodal Larmor radus, / s h ordr of δ, T/ M s h arcl hrmal vlocy, S s h squzng facor, h shar flow. Th dffrn forms of h Hamlonan dscr h sam moon. qs.(7 and (8 can rroducd from q.(. Wh h small nvrs asc rao aroxmaon, w hav
3 4 hong-tan Wang al.: Dffusvy Scalng on Shar Flow u u sn k, ( [ α ( ], ( u H Ω P r εu u k (. (3 Th r should anana cnr oson. Th urnng ons of h anana or ar dcdd y h followng formula, k sn. (4 Onc w hav k and umax ( ε u for h rad arcls. W s Ψ as h anana cnr surfac whr urnng ons ar valuad and hn w xand Ψ and nar Ψ. Th anana wdh and h oson of anana cnr surfac ar oand afr h xanson, u whr + Ψ + Ω P S P + Ψ S s h anana wdh, u u S S, (5 k sn, (6 Ω S Ω Ψ Ψ + /, (7 whr Ψ P / s drf surfac and s h valu of on h anana cnr surfac. W can s ha h urnng ons of h rad arcl ar no on h drf surfac u shfd o anana cnr surfac du o h radal lcrcal fld. W form an nvaran 9 varal, Ω Ω P dx d r d, (8 Π X c c c whch s acually h flux nclosd y anana or. Now w nroduc a nw angl whch sasfs h quaon, hn, β, (9 sn k sn 4 ( sn k sn d k sn S Ω S Ω ru Π q u k β dβ β,(3 Ω α 8 q ( P [ ( k ( k K ( k ] S whr k k, K and ar coml llc funcons. Th ounc frquncy of h rad arcl s H Π ( εs (. (3 q K( k qs. (-3 gv, for h frs m, a so clar cur of h rad arcl moon dndn on h shar flow. I s ral moon no ohr choc. For a Maxwllan dsruon funcon, h fracon of h rad arcls can asly calculad va xmax xmax y x F yd y dx, (3 whr y /, x /, and S max S u max ( ε. For h rad arcls, x s small, hus lads y F 4 dy y ( εs ( ε S, (33 whch agrs wh Shang s 5 and dsagrs wh Cao s 6. Snc h rad arcl ch angl s lmd, h cv collson frquncy ν hr should ν/( /. Thus, h dffusvy s dffrn wh Shang s 5. u ν / νρ( ε/ 4. Noclasscal Transor F u S whch s To llusra h sgnfcanc of h rad-arcl dynamcs, h arcl dffusvy s calculad. Insad of canoncal gyroknc varals, Pα, P, PX, α,, X, w us xndd has sac varals, Pα, P, r, H, α,, β,, n h drf knc quaon, f dβ f dr f + + C( f. (34 d β d W dfn an avragd angl vlocy, d β d β < > d d T, (35 d T
4 Amrcan Journal of Modrn Physcs 4; 3(5: -6 5 whr T s h ounc rod. W can s ha h avragd angl vlocy s h ounc frquncy n q. (3. To llusra flow shar cs on h noclasscal ransor, w ak f f + g f + g + g sn β + g cos β, (36 s c whr f s qulrum dsruon funcon n a Maxwllan form wh H a h lac of nrgy and P a h lac of oson, ( [ lnn f ] Fm r, (37 Ω r f. (38 To cach h ky ons and avod h comlxy w only consdr dnsy gradn. Tmraur gradn can chang h xrsson of dffusvy, u can no chang h scalng on h shar flow. q. (34 s rwrn as and β g sn g d C( g gm f β, (39 g m To mak q. (39 racal, w ak lnn Fm. (4 Ω r dβ dβ < >, (4 d d C( g g ν ( g g. (4 m m Furhrmor, s assumd ha k and ar small, whch mans dly rad arcls domna. In q. (36 g s and g c ar on ordr smallr han g. From q. (9 and g kν q. (39 w oan g g m, gs, g + ν. c ν Wh q. (37 and q. (38 h drf quaon of q. (39 afr h ounc avrag urns o f ν k. (43 d Fm + ν In h anana rgm, w hav ν δ. (44 Afr ngrang q. (43 ovr vlocy sac, w g h connuy quaon whr n Γ D, xmax n + Γ, (45 xmax ν k D ydy dx.75 / S d y x ν ε ρ, (46 εs whr x, y, xmax εsy. From q.(46 w can s ha osnluh s rsul 9 s rroducd u wh h shar flow modfcaon. 5. Summary Th ara-consrvd ransformaon roosd y Lchnrg and Lrman9 s mloyd. A coml s of canoncal gudng-cnr varals, Pα, P, PX, α,, X, ar drvd. Th accura rlaon wn h arcl moon and h shar flow for h rad arcls s also drvd, u u ncludng h anana wdh k sn, S Ω S Ω h oson of anana cnr surfac Ψ Ψ + / and h ounc frquncy H ( εs (. For Π q K( k a Maxwllan dsruon funcon, h fracon of h rad arcls s calculad as y 4 ( ( F dy y εs ε S whch agrs wh Shang s5 and dsagrs wh Cao s6. Snc h rad arcl ch angl s lmd, h cv collson frquncy ν hr should ν/( u /, hrfor, h / ( / dffusvy s F ν u νρ ε S whch s dffrn wh Shang s5. Drf knc quaon s solvd wh arcl-consrvd Krook collson oraor. osnluh s rsul7 s rroducd u wh shar flow modfcaon n hs ar. Acknowldgmns I s arcad ha Dr.. D. Hazln and Dr. P. Morrson chckd and vrfd h gnrang funcon whn auhor. T. Wang workd a IFS of h Unvrsy of Txas. Ths work was suord y Naural Scnc Fund No. 6437, No.553, No.535, No.546 and Th Naonal Magnc Confnmn Fuson Scnc Program (Gran No. 3G7.
5 6 hong-tan Wang al.: Dffusvy Scalng on Shar Flow frncs [].J.Doyl,.J. Gronr, K.M.urrll, P. Gohl, T. Lhcka, N. C. Luhmann Jr., H. Masumoo, T. H. Osorn, W. A. Pls, and. Phlona, Modfcaon n urulnc and dg lcrc fld a h L-H ranson n Dlll-D okamak, Phys. Fluds 3, 3(99. [] F.L.Hnon and S.K.Wong, Noclasscal on ransor n roang axsymmrcal lasmas, Phys. Fluds 8, 38(985. [3].D.Hazln, Slf-conssn radal shah, Phys.Fluds, 3(989. [4] G. Kagan and P. J. Cao, Phys. v. L. 5, 45(. [5] K. C. Shang and C. T. Hsu, Phys. Plasmas 9, 5(. [6] P. J. Cao, F. I. Parra, G. Kagan, J.. Parkr, I. Pusza, and M. Landrman, Plasma Phys. Conrol. Fuson, 55, 459(3. [7] M. N. osnluh,. D. Hazln, F. L. Hnon, Phys. Fluds, 5, 6(97. [8]. G. Lljohn, J. Plasma hyscs 9, (983. [9] A. J. Lchnrg and Lrman, gular and Sochasc Moon, Ald Scncs 38, (Srngr-Vrlag Nw York Inc []. alscu, n Transor Procsss n Plasma, (Norh-Holland, Amsrdam Oxford Nw York Tokyo, 988, Vol., P.393.
Frequency Response. Response of an LTI System to Eigenfunction
Frquncy Rsons Las m w Rvsd formal dfnons of lnary and m-nvaranc Found an gnfuncon for lnar m-nvaran sysms Found h frquncy rsons of a lnar sysm o gnfuncon nu Found h frquncy rsons for cascad, fdbac, dffrnc
More informationConsider a system of 2 simultaneous first order linear equations
Soluon of sysms of frs ordr lnar quaons onsdr a sysm of smulanous frs ordr lnar quaons a b c d I has h alrna mar-vcor rprsnaon a b c d Or, n shorhand A, f A s alrady known from con W know ha h abov sysm
More informationSummary: Solving a Homogeneous System of Two Linear First Order Equations in Two Unknowns
Summary: Solvng a Homognous Sysm of Two Lnar Frs Ordr Equaons n Two Unknowns Gvn: A Frs fnd h wo gnvalus, r, and hr rspcv corrspondng gnvcors, k, of h coffcn mar A Dpndng on h gnvalus and gnvcors, h gnral
More informationSupplementary Figure 1. Experiment and simulation with finite qudit. anharmonicity. (a), Experimental data taken after a 60 ns three-tone pulse.
Supplmnar Fgur. Eprmn and smulaon wh fn qud anharmonc. a, Eprmnal daa akn afr a 6 ns hr-on puls. b, Smulaon usng h amlonan. Supplmnar Fgur. Phagoran dnamcs n h m doman. a, Eprmnal daa. Th hr-on puls s
More informationSIMEON BALL AND AART BLOKHUIS
A BOUND FOR THE MAXIMUM WEIGHT OF A LINEAR CODE SIMEON BALL AND AART BLOKHUIS Absrac. I s shown ha h paramrs of a lnar cod ovr F q of lngh n, dmnson k, mnmum wgh d and maxmum wgh m sasfy a cran congrunc
More informationAdvanced Queueing Theory. M/G/1 Queueing Systems
Advand Quung Thory Ths slds ar rad by Dr. Yh Huang of Gorg Mason Unvrsy. Sudns rgsrd n Dr. Huang's ourss a GMU an ma a sngl mahn-radabl opy and prn a sngl opy of ah sld for hr own rfrn, so long as ah sld
More informationWave Superposition Principle
Physcs 36: Was Lcur 5 /7/8 Wa Suroson Prncl I s qu a common suaon for wo or mor was o arr a h sam on n sac or o xs oghr along h sam drcon. W wll consdr oday sral moran cass of h combnd ffcs of wo or mor
More informationUNIT #5 EXPONENTIAL AND LOGARITHMIC FUNCTIONS
Answr Ky Nam: Da: UNIT # EXPONENTIAL AND LOGARITHMIC FUNCTIONS Par I Qusions. Th prssion is quivaln o () () 6 6 6. Th ponnial funcion y 6 could rwrin as y () y y 6 () y y (). Th prssion a is quivaln o
More informationt=0 t>0: + vr - i dvc Continuation
hapr Ga Dlay and rcus onnuaon s rcu Equaon >: S S Ths dffrnal quaon, oghr wh h nal condon, fully spcfs bhaor of crcu afr swch closs Our n challng: larn how o sol such quaons TUE/EE 57 nwrk analys 4/5 NdM
More informationELEN E4830 Digital Image Processing
ELEN E48 Dgal Imag Procssng Mrm Eamnaon Sprng Soluon Problm Quanzaon and Human Encodng r k u P u P u r r 6 6 6 6 5 6 4 8 8 4 P r 6 6 P r 4 8 8 6 8 4 r 8 4 8 4 7 8 r 6 6 6 6 P r 8 4 8 P r 6 6 8 5 P r /
More informationEE243 Advanced Electromagnetic Theory Lec # 10: Poynting s Theorem, Time- Harmonic EM Fields
Appl M Fall 6 Nuruhr Lcur # r 9/6/6 4 Avanc lcromagnc Thory Lc # : Poynng s Thorm Tm- armonc M Fls Poynng s Thorm Consrvaon o nrgy an momnum Poynng s Thorm or Lnar sprsv Ma Poynng s Thorm or Tm-armonc
More informationOne dimensional steady state heat transfer of composite slabs
BUILDING PHYSICS On dmnsonal sady sa a ransfr of compos slas Par 2 Ass. Prof. Dr. Norr Harmay Budaps Unvrsy of Tcnology and Economcs Dparmn of Buldng Enrgcs and Buldng Srvc Engnrng Inroducon - Buldng Pyscs
More informationState Observer Design
Sa Obsrvr Dsgn A. Khak Sdgh Conrol Sysms Group Faculy of Elcrcal and Compur Engnrng K. N. Toos Unvrsy of Tchnology Fbruary 2009 1 Problm Formulaon A ky assumpon n gnvalu assgnmn and sablzng sysms usng
More informationConventional Hot-Wire Anemometer
Convnonal Ho-Wr Anmomr cro Ho Wr Avanag much mallr prob z mm o µm br paal roluon array o h nor hghr rquncy rpon lowr co prormanc/co abrcaon roc I µm lghly op p layr 8µm havly boron op ch op layr abrcaon
More informationGauge Theories. Elementary Particle Physics Strong Interaction Fenomenology. Diego Bettoni Academic year
Gau Thors Elmary Parcl Physcs Sro Iraco Fomoloy o Bo cadmc yar - Gau Ivarac Gau Ivarac Whr do Laraas or Hamloas com from? How do w kow ha a cra raco should dscrb a acual hyscal sysm? Why s h lcromac raco
More informationHomework: Introduction to Motion
Homwork: Inroducon o Moon Dsanc vs. Tm Graphs Nam Prod Drcons: Answr h foowng qusons n h spacs provdd. 1. Wha do you do o cra a horzona n on a dsancm graph? 2. How do you wak o cra a sragh n ha sops up?
More informationa dt a dt a dt dt If 1, then the poles in the transfer function are complex conjugates. Let s look at f t H t f s / s. So, for a 2 nd order system:
Undrdamd Sysms Undrdamd Sysms nd Ordr Sysms Ouu modld wih a nd ordr ODE: d y dy a a1 a0 y b f If a 0 0, hn: whr: a d y a1 dy b d y dy y f y f a a a 0 0 0 is h naural riod of oscillaion. is h daming facor.
More informationTheoretical Seismology
Thorcal Ssmology Lcur 9 Sgnal Procssng Fourr analyss Fourr sudd a h Écol Normal n Pars, augh by Lagrang, who Fourr dscrbd as h frs among Europan mn of scnc, Laplac, who Fourr rad lss hghly, and by Mong.
More informationThermodynamic Properties of the Harmonic Oscillator and a Four Level System
www.ccsn.org/apr Appld Physcs Rsarch Vol. 3, No. ; May Thrmodynamc Proprs of h Harmonc Oscllaor and a Four Lvl Sysm Oladunjoy A. Awoga Thorcal Physcs Group, Dparmn of Physcs, Unvrsy of Uyo, Uyo, Ngra E-mal:
More informationBlack-Scholes Partial Differential Equation In The Mellin Transform Domain
INTRNATIONAL JOURNAL OF SCINTIFIC & TCHNOLOGY RSARCH VOLUM 3, ISSU, Dcmbr 4 ISSN 77-866 Blac-Schols Paral Dffrnal qaon In Th Mlln Transform Doman Fadgba Snday mmanl, Ognrnd Rosln Bosd Absrac: Ths ar rsns
More informationTwo-Dimensional Quantum Harmonic Oscillator
D Qa Haroc Oscllaor Two-Dsoal Qa Haroc Oscllaor 6 Qa Mchacs Prof. Y. F. Ch D Qa Haroc Oscllaor D Qa Haroc Oscllaor ch5 Schrödgr cosrcd h cohr sa of h D H.O. o dscrb a classcal arcl wh a wav ack whos cr
More information10.5 Linear Viscoelasticity and the Laplace Transform
Scn.5.5 Lnar Vclacy and h Lalac ranfrm h Lalac ranfrm vry uful n cnrucng and analyng lnar vclac mdl..5. h Lalac ranfrm h frmula fr h Lalac ranfrm f h drvav f a funcn : L f f L f f f f f c..5. whr h ranfrm
More information(heat loss divided by total enthalpy flux) is of the order of 8-16 times
16.51, Rok Prolson Prof. Manl Marnz-Sanhz r 8: Convv Ha ransfr: Ohr Effs Ovrall Ha oss and Prforman Effs of Ha oss (1) Ovrall Ha oss h loal ha loss r n ara s q = ρ ( ) ngrad ha loss s a S, and sng m =
More informationRELATIONSHIPS BETWEEN SPECTRAL PEAK FREQUENCIES OF A CAUSAL AR(P) PROCESS AND ARGUMENTS OF ROOTS OF THE ASSOCIATED AR POLYNOMIAL.
RELATIONSHIPS BETWEEN SPECTRAL PEAK FREQUENCIES OF A CAUSAL AR(P) PROCESS AND ARGUMENTS OF ROOTS OF THE ASSOCIATED AR POLYNOMIAL A Wrng Proc Prsnd o T Faculy of Darmn of Mamacs San Jos Sa Unvrsy In Paral
More informationOUTLINE FOR Chapter 2-2. Basic Laws
0//8 OUTLINE FOR Chapr - AERODYNAMIC W-- Basc Laws Analss of an problm n fld mchancs ncssarl nclds samn of h basc laws gornng h fld moon. Th basc laws, whch applcabl o an fld, ar: Consraon of mass Conn
More informationChapter 13 Laplace Transform Analysis
Chapr aplac Tranorm naly Chapr : Ouln aplac ranorm aplac Tranorm -doman phaor analy: x X σ m co ω φ x X X m φ x aplac ranorm: [ o ] d o d < aplac Tranorm Thr condon Unlaral on-dd aplac ranorm: aplac ranorm
More informationNeutron electric dipole moment on the lattice
ron lcrc dol on on h lac go Shnan Unv. of Tkba 3/6/006 ron lcrc dol on fro lac QCD Inrodcon arar Boh h ha of CKM arx and QCD vac ffc conrb o CP volaon P and T volaon arar. CP odd QCD 4 L arg d CKM f f
More informationWave 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
More informationControl System Engineering (EE301T) Assignment: 2
Conrol Sysm Enginring (EE0T) Assignmn: PART-A (Tim Domain Analysis: Transin Rspons Analysis). Oain h rspons of a uniy fdack sysm whos opn-loop ransfr funcion is (s) s ( s 4) for a uni sp inpu and also
More informationInstitute of Actuaries of India
Insiu of Acuaris of India ubjc CT3 Probabiliy and Mahmaical aisics Novmbr Examinaions INDICATIVE OLUTION Pag of IAI CT3 Novmbr ol. a sampl man = 35 sampl sandard dviaion = 36.6 b for = uppr bound = 35+*36.6
More informationFI 3103 Quantum Physics
/9/4 FI 33 Quanum Physcs Aleander A. Iskandar Physcs of Magnesm and Phooncs Research Grou Insu Teknolog Bandung Basc Conces n Quanum Physcs Probably and Eecaon Value Hesenberg Uncerany Prncle Wave Funcon
More informationLecture 1: Numerical Integration The Trapezoidal and Simpson s Rule
Lcur : Numrical ngraion Th Trapzoidal and Simpson s Rul A problm Th probabiliy of a normally disribud (man µ and sandard dviaion σ ) vn occurring bwn h valus a and b is B A P( a x b) d () π whr a µ b -
More informationinnovations shocks white noise
Innovaons Tm-srs modls ar consrucd as lnar funcons of fundamnal forcasng rrors, also calld nnovaons or shocks Ths basc buldng blocks sasf var σ Srall uncorrlad Ths rrors ar calld wh nos In gnral, f ou
More informationPhysics of Very High Frequency (VHF) Capacitively Coupled Plasma Discharges
Physcs of Vry Hgh Frquncy (VHF) Capactvly Coupld Plasma Dschargs Shahd Rauf, Kallol Bra, Stv Shannon, and Kn Collns Appld Matrals, Inc., Sunnyval, CA AVS 54 th Intrnatonal Symposum Sattl, WA Octobr 15-19,
More informationChapter 9 Transient Response
har 9 Transn sons har 9: Ouln N F n F Frs-Ordr Transns Frs-Ordr rcus Frs ordr crcus: rcus conan onl on nducor or on caacor gornd b frs-ordr dffrnal quaons. Zro-nu rsons: h crcu has no ald sourc afr a cran
More informationA Note on Estimability in Linear Models
Intrnatonal Journal of Statstcs and Applcatons 2014, 4(4): 212-216 DOI: 10.5923/j.statstcs.20140404.06 A Not on Estmablty n Lnar Modls S. O. Adymo 1,*, F. N. Nwob 2 1 Dpartmnt of Mathmatcs and Statstcs,
More informationLecture 1: Growth and decay of current in RL circuit. Growth of current in LR Circuit. D.K.Pandey
cur : Growh and dcay of currn in circui Growh of currn in Circui us considr an inducor of slf inducanc is conncd o a DC sourc of.m.f. E hrough a rsisr of rsisanc and a ky K in sris. Whn h ky K is swichd
More informationEAcos θ, where θ is the angle between the electric field and
8.4. Modl: Th lctric flux flows out of a closd surfac around a rgion of spac containing a nt positiv charg and into a closd surfac surrounding a nt ngativ charg. Visualiz: Plas rfr to Figur EX8.4. Lt A
More informationSun and Geosphere, 2008; 3(1): ISSN
Sun Gosphr, 8; 3(): 5-56 ISSN 89-839 h Imporanc of Ha Conducon scos n Solar Corona Comparson of Magnohdrodnamc Equaons of On-Flud wo-flud Srucur n Currn Sh Um Dn Gor Asronom Spac Scncs Dparmn, Scnc Facul,
More informationMechanics 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
More informationSearching for pairing interactions with coherent charge fluctuations spectroscopy
Sarchng for parng nracons wh cohrn charg flucuaons spcroscopy J. Lornzana ISC-CNR, Sapnza, Unvrsy of Rom B. Mansar, A. Mann, A. Odh, M. Scaronglla, M. Chrgu, F. Carbon EPFL, Lausann Ouln Raman scarng Cohrn
More informationThe Variance-Covariance Matrix
Th Varanc-Covaranc Marx Our bggs a so-ar has bn ng a lnar uncon o a s o daa by mnmzng h las squars drncs rom h o h daa wh mnsarch. Whn analyzng non-lnar daa you hav o us a program l Malab as many yps o
More informationNAME: ANSWER KEY DATE: PERIOD. DIRECTIONS: MULTIPLE CHOICE. Choose the letter of the correct answer.
R A T T L E R S S L U G S NAME: ANSWER KEY DATE: PERIOD PREAP PHYSICS REIEW TWO KINEMATICS / GRAPHING FORM A DIRECTIONS: MULTIPLE CHOICE. Chs h r f h rr answr. Us h fgur bw answr qusns 1 and 2. 0 10 20
More informationEngineering 323 Beautiful HW #13 Page 1 of 6 Brown Problem 5-12
Enginring Bautiful HW #1 Pag 1 of 6 5.1 Two componnts of a minicomputr hav th following joint pdf for thir usful liftims X and Y: = x(1+ x and y othrwis a. What is th probability that th liftim X of th
More informationThe Hyperelastic material is examined in this section.
4. Hyprlastcty h Hyprlastc matral s xad n ths scton. 4..1 Consttutv Equatons h rat of chang of ntrnal nrgy W pr unt rfrnc volum s gvn by th strss powr, whch can b xprssd n a numbr of dffrnt ways (s 3.7.6):
More informationGrand Canonical Ensemble
Th nsmbl of systms mmrsd n a partcl-hat rsrvor at constant tmpratur T, prssur P, and chmcal potntal. Consdr an nsmbl of M dntcal systms (M =,, 3,...M).. Thy ar mutually sharng th total numbr of partcls
More informationLecture 12: Introduction to nonlinear optics II.
Lcur : Iroduco o olar opcs II r Kužl ropagao of srog opc sgals propr olar ffcs Scod ordr ffcs! Thr-wav mxg has machg codo! Scod harmoc grao! Sum frqucy grao! aramrc grao Thrd ordr ffcs! Four-wav mxg! Opcal
More informationOn the Speed of Heat Wave. Mihály Makai
On h Spd of Ha Wa Mihály Maai maai@ra.bm.hu Conns Formulaion of h problm: infini spd? Local hrmal qulibrium (LTE hypohsis Balanc quaion Phnomnological balanc Spd of ha wa Applicaion in plasma ranspor 1.
More informationFAULT TOLERANT SYSTEMS
FAULT TOLERANT SYSTEMS hp://www.cs.umass.du/c/orn/faultolransysms ar 4 Analyss Mhods Chapr HW Faul Tolranc ar.4.1 Duplx Sysms Boh procssors xcu h sam as If oupus ar n agrmn - rsul s assumd o b corrc If
More informationCIVL 8/ D Boundary Value Problems - Triangular Elements (T6) 1/8
CIVL 8/7 -D Boundar Valu Problm - rangular Elmn () /8 SI-ODE RIAGULAR ELEMES () A quadracall nrpolad rangular lmn dfnd b nod, hr a h vrc and hr a h mddl a ach d. h mddl nod, dpndng on locaon, ma dfn a
More informationLectures 9-11: Fourier Transforms
Lcurs 9-: ourr Transforms Rfrncs Jordan & Smh Ch7, Boas Ch5 scon 4, Kryszg Ch Wb s hp://wwwjhudu/sgnals/: go o Connuous Tm ourr Transform Proprs PHY6 Inroducon o ourr Transforms W hav sn ha any prodc funcon
More informationNDC Dynamic Equilibrium model with financial and
9 July 009 NDC Dynamc Equlbrum modl wh fnancal and dmograhc rsks rr DEVOLDER, Inmaculada DOMÍNGUEZ-FABIÁN, Aurél MILLER ABSTRACT Classcal socal scury nson schms, combnng a dfnd bnf hlosohy and a ay as
More informationSurface Impedance of Superconductors and Normal Conductors in EM Simulators 1
hp://wwwmmanraodu/mmos/hml-mmos/mma45/mmo45pdf MMA Mmo No 45 Surfac Impdanc of Suprconducors and Normal Conducors n EM Smulaors 1 A R Krr January 7, 1999 (Rvsd Augus 9, 1999) Th concp of surfac mpdanc
More information8. Queueing systems. Contents. Simple teletraffic model. Pure queueing system
8. Quug sysms Cos 8. Quug sysms Rfrshr: Sml lraffc modl Quug dscl M/M/ srvr wag lacs Alcao o ack lvl modllg of daa raffc M/M/ srvrs wag lacs lc8. S-38.45 Iroduco o Tlraffc Thory Srg 5 8. Quug sysms 8.
More informationEngineering Circuit Analysis 8th Edition Chapter Nine Exercise Solutions
Engnrng rcu naly 8h Eon hapr Nn Exrc Soluon. = KΩ, = µf, an uch ha h crcu rpon oramp. a For Sourc-fr paralll crcu: For oramp or b H 9V, V / hoo = H.7.8 ra / 5..7..9 9V 9..9..9 5.75,.5 5.75.5..9 . = nh,
More information( r) E (r) Phasor. Function of space only. Fourier series Synthesis equations. Sinusoidal EM Waves. For complex periodic signals
Inoducon Snusodal M Was.MB D Yan Pllo Snusodal M.3MB 3. Snusodal M.3MB 3. Inoducon Inoducon o o dsgn h communcaons sd of a sall? Fqunc? Oms oagaon? Oms daa a? Annnas? Dc? Gan? Wa quaons Sgnal analss Wa
More informationKlein-Gordon Equation
Inroducon o lnar Parcl Phscs. Lcur 5 Pag of 5 Kln-Gordon quaon 96 Schrodngr: Quanu chancal quaon for non-rlavsc chancs: V,, V V 96 Kln Rlavsc chancs (fr arcl):,, Soluons ar: ( r), whr ( r), whr ) Soluons
More informationPart I: Short Answer [50 points] For each of the following, give a short answer (2-3 sentences, or a formula). [5 points each]
Soluions o Midrm Exam Nam: Paricl Physics Fall 0 Ocobr 6 0 Par I: Shor Answr [50 poins] For ach of h following giv a shor answr (- snncs or a formula) [5 poins ach] Explain qualiaivly (a) how w acclra
More informationThe Finite Element Method for the Analysis of Non-Linear and Dynamic Systems
Swss Federal Insue of Page 1 The Fne Elemen Mehod for he Analyss of Non-Lnear and Dynamc Sysems Prof. Dr. Mchael Havbro Faber Dr. Nebojsa Mojslovc Swss Federal Insue of ETH Zurch, Swzerland Mehod of Fne
More information9. Simple Rules for Monetary Policy
9. Smpl Ruls for Monar Polc John B. Talor, Ma 0, 03 Woodford, AR 00 ovrvw papr Purpos s o consdr o wha xn hs prscrpon rsmbls h sor of polc ha conomc hor would rcommnd Bu frs, l s rvw how hs sor of polc
More information1997 AP Calculus AB: Section I, Part A
997 AP Calculus AB: Sction I, Part A 50 Minuts No Calculator Not: Unlss othrwis spcifid, th domain of a function f is assumd to b th st of all ral numbrs for which f () is a ral numbr.. (4 6 ) d= 4 6 6
More informationCharging of capacitor through inductor and resistor
cur 4&: R circui harging of capacior hrough inducor and rsisor us considr a capacior of capacianc is conncd o a D sourc of.m.f. E hrough a rsisr of rsisanc R, an inducor of inducanc and a y K in sris.
More informationThe 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
More informationAdvances in the study of intrinsic rotation with flux tube gyrokinetics
Adans n th study o ntrns rotaton wth lux tub gyroknts F.I. Parra and M. arns Unrsty o Oxord Wolgang Paul Insttut, Vnna, Aprl 0 Introduton In th absn o obous momntum nput (apart rom th dg), tokamak plasmas
More informationLecture 4 : Backpropagation Algorithm. Prof. Seul Jung ( Intelligent Systems and Emotional Engineering Laboratory) Chungnam National University
Lcur 4 : Bacpropagaon Algorhm Pro. Sul Jung Inllgn Sm and moonal ngnrng Laboraor Chungnam Naonal Unvr Inroducon o Bacpropagaon algorhm 969 Mn and Papr aac. 980 Parr and Wrbo dcovrd bac propagaon algorhm.
More information22/ Breakdown of the Born-Oppenheimer approximation. Selection rules for rotational-vibrational transitions. P, R branches.
Subjct Chmistry Papr No and Titl Modul No and Titl Modul Tag 8/ Physical Spctroscopy / Brakdown of th Born-Oppnhimr approximation. Slction ruls for rotational-vibrational transitions. P, R branchs. CHE_P8_M
More informationVertical Sound Waves
Vral Sond Wavs On an drv h formla for hs avs by onsdrn drly h vral omonn of momnm qaon hrmodynam qaon and h onny qaon from 5 and hn follon h rrbaon mhod and assmn h snsodal solons. Effvly h frs ro and
More information1997 AP Calculus AB: Section I, Part A
997 AP Calculus AB: Sction I, Part A 50 Minuts No Calculator Not: Unlss othrwis spcifid, th domain of a function f is assumd to b th st of all ral numbrs x for which f (x) is a ral numbr.. (4x 6 x) dx=
More informationEXERCISE - 01 CHECK YOUR GRASP
DIFFERENTIAL EQUATION EXERCISE - CHECK YOUR GRASP 7. m hn D() m m, D () m m. hn givn D () m m D D D + m m m m m m + m m m m + ( m ) (m ) (m ) (m + ) m,, Hnc numbr of valus of mn will b. n ( ) + c sinc
More informationPhys463.nb Conductivity. Another equivalent definition of the Fermi velocity is
39 Anohr quival dfiniion of h Fri vlociy is pf vf (6.4) If h rgy is a quadraic funcion of k H k L, hs wo dfiniions ar idical. If is NOT a quadraic funcion of k (which could happ as will b discussd in h
More informationFor massive neutrinos one could introduce in analogy to the quark mixing a mixing matrix describing the relation between mass and flavor states:
Advancd Parcl Physcs: IX. Flavor Oscllaon and CP Volaon. wr 4. Nurno Oscllaons τ τ τ τ For assv nurnos on could nroduc n analogy o h quark xng a xng arx dscrbng h rlaon bwn ass and flavor sas: Consan for
More information:2;$-$(01*%<*=,-./-*=0;"%/;"-*
!"#$%'()%"*#%*+,-./-*+01.2(.*3+456789*!"#$%"'()'*+,-."/0.%+1'23"45'46'7.89:89'/' ;8-,"$4351415,8:+#9' Dr. Ptr T. Gallaghr Astrphyscs Rsarch Grup Trnty Cllg Dubln :2;$-$(01*%
More informationSCALING OF SYNCHROTRON RADIATION WITH MULTIPOLE ORDER. J. C. Sprott
SCALING OF SYNCHROTRON RADIATION WITH MULTIPOLE ORDER J. C. Sprott PLP 821 Novmbr 1979 Plasma Studis Univrsity of Wisconsin Ths PLP Rports ar informal and prliminary and as such may contain rrors not yt
More informationPages 2-33 of this pdf file are Tycko's lecture slides from January 8, Pages are notes about quantum mechanics, NMR, homonuclear
Pags -33 of hs pdf fl ar Tycko's lcur slds from January 8, 8. Pags 34-74 ar nos abou quanum mchancs, NM, homonuclar rcouplng, and rlad hngs, prpard orgnally n 8 and subsqunly corrcd/amndd. nroducon o h
More informationJournal of Theoretical and Applied Information Technology 10 th January Vol. 47 No JATIT & LLS. All rights reserved.
Journal o Thortcal and Appld Inormaton Tchnology th January 3. Vol. 47 No. 5-3 JATIT & LLS. All rghts rsrvd. ISSN: 99-8645 www.att.org E-ISSN: 87-395 RESEARCH ON PROPERTIES OF E-PARTIAL DERIVATIVE OF LOGIC
More informationChapter 7 Stead St y- ate Errors
Char 7 Say-Sa rror Inroucon Conrol ym analy an gn cfcaon a. rann ron b. Sably c. Say-a rror fnon of ay-a rror : u c a whr u : nu, c: ouu Val only for abl ym chck ym ably fr! nu for ay-a a nu analy U o
More informationMotion of Wavepackets in Non-Hermitian. Quantum Mechanics
Moon of Wavepaces n Non-Herman Quanum Mechancs Nmrod Moseyev Deparmen of Chemsry and Mnerva Cener for Non-lnear Physcs of Complex Sysems, Technon-Israel Insue of Technology www.echnon echnon.ac..ac.l\~nmrod
More information9.5 Complex variables
9.5 Cmpl varabls. Cnsdr th funtn u v f( ) whr ( ) ( ), f( ), fr ths funtn tw statmnts ar as fllws: Statmnt : f( ) satsf Cauh mann quatn at th rgn. Statmnt : f ( ) ds nt st Th rrt statmnt ar (A) nl (B)
More informationBethe-Salpeter Equation Green s Function and the Bethe-Salpeter Equation for Effective Interaction in the Ladder Approximation
Bh-Salp Equaon n s Funcon and h Bh-Salp Equaon fo Effcv Inacon n h Ladd Appoxmaon Csa A. Z. Vasconcllos Insuo d Físca-UFRS - upo: Físca d Hadons Sngl-Pacl Popagao. Dagam xpanson of popagao. W consd as
More informationHeisenberg Model. Sayed Mohammad Mahdi Sadrnezhaad. Supervisor: Prof. Abdollah Langari
snbrg Modl Sad Mohammad Mahd Sadrnhaad Survsor: Prof. bdollah Langar bstract: n ths rsarch w tr to calculat analtcall gnvalus and gnvctors of fnt chan wth ½-sn artcls snbrg modl. W drov gnfuctons for closd
More informationImplementation of the Extended Conjugate Gradient Method for the Two- Dimensional Energized Wave Equation
Lonardo Elcronc Jornal of raccs and Tchnolos ISSN 58-078 Iss 9 Jl-Dcmbr 006 p. -4 Implmnaon of h Endd Cona Gradn Mhod for h Two- Dmnsonal Enrd Wav Eqaon Vcor Onoma WAZIRI * Snda Ass REJU Mahmacs/Compr
More informationMechanics Physics 151
Mechancs Physcs 5 Lecure 9 Hamlonan Equaons of Moon (Chaper 8) Wha We Dd Las Tme Consruced Hamlonan formalsm H ( q, p, ) = q p L( q, q, ) H p = q H q = p H = L Equvalen o Lagrangan formalsm Smpler, bu
More informationChapter 7: Plane Electromagnetic Waves and Wave Propagation
Chapr 7: Plan lcromagnc Wavs and Wav Propagaon An Hsorcal Prspcv: Faraday:Tm-varyng magnc fld gnras lcrc fld. Mawll:Tm-varyng lcrc fld gnras magnc fld. Hr dscovrd rado wavs; nsn's spcal hory Mawll's hory
More informationOscillations of Hyperbolic Systems with Functional Arguments *
Avll ://vmd/gs/9/s Vol Iss Dcmr 6 95 Prvosly Vol No Alcons nd Ald mcs AA: An Inrnonl Jornl Asrc Oscllons of Hyrolc Sysms w Fnconl Argmns * Y So Fcly of Engnrng nzw Unvrsy Isw 9-9 Jn E-ml: so@nzw-c Noro
More informationCHAPTER 33: PARTICLE PHYSICS
Collg Physcs Studnt s Manual Chaptr 33 CHAPTER 33: PARTICLE PHYSICS 33. THE FOUR BASIC FORCES 4. (a) Fnd th rato of th strngths of th wak and lctromagntc forcs undr ordnary crcumstancs. (b) What dos that
More informationMechanics Physics 151
Mechancs Physcs 5 Lecure 9 Hamlonan Equaons of Moon (Chaper 8) Wha We Dd Las Tme Consruced Hamlonan formalsm Hqp (,,) = qp Lqq (,,) H p = q H q = p H L = Equvalen o Lagrangan formalsm Smpler, bu wce as
More informationEE"232"Lightwave"Devices Lecture"16:"p7i7n"Photodiodes"and" Photoconductors"
EE"232"Lgwav"Dvcs Lcur"16:"p77n"Pooos"an" Pooconucors" Rang:"Cuang,"Cap."15"(2 n E) Insrucor:"Mng"C."Wu Unvrsy"of"Calforna,"Brkly Elcrcal"Engnrng"an"Compur"Scncs"Dp. EE232$Lcur$16-1 Rvrs"bas%p""n%juncon
More informationGuaranteed Cost Control for a Class of Uncertain Delay Systems with Actuator Failures Based on Switching Method
49 Inrnaonal Journal of Conrol, Ru Wang Auomaon, and Jun and Zhao Sysms, vol. 5, no. 5, pp. 49-5, Ocobr 7 Guarand Cos Conrol for a Class of Uncran Dlay Sysms wh Acuaor Falurs Basd on Swchng Mhod Ru Wang
More informationPartition Functions for independent and distinguishable particles
0.0J /.77J / 5.60J hrodynacs of oolcular Syss Insrucors: Lnda G. Grffh, Kbrly Haad-Schffrl, Moung G. awnd, Robr W. Fld Lcur 5 5.60/0.0/.77 vs. q for dsngushabl vs ndsngushabl syss Drvaon of hrodynac Proprs
More informationA New Generalized Gronwall-Bellman Type Inequality
22 Inernaonal Conference on Image, Vson and Comung (ICIVC 22) IPCSIT vol. 5 (22) (22) IACSIT Press, Sngaore DOI:.7763/IPCSIT.22.V5.46 A New Generalzed Gronwall-Bellman Tye Ineualy Qnghua Feng School of
More informationNUMERICAL MODEL BASED ON A BERNOULLI INTEGRAL EXTENSION FOR PRESSURE ANALYZE ON A MILLIMETER DEVICE IN A TURBULENT FLOW
591 TECHNICAL UNIVERSITY OF CLUJ-NAPOCA ACTA TECHNICA NAPOCENSIS Srs: Ald Mahmacs, Mchancs, and Engnrng Vol. 6, Issu IV, Novmbr, 17 NUMERICAL MODEL BASED ON A BERNOULLI INTEGRAL EXTENSION FOR PRESSURE
More informationDynamic modeling, simulation and control of a hybrid driven press mechanism
INTERNTIONL JOURNL OF MECHNICS Volum 1 16 Dynamc modlng smulaon and conrol of a hybrd drvn prss mchansm Mhm Erkan Küük Lal Canan Dülgr bsrac Hybrd drvn mchansm combns h moon of a larg consan vlocy moor
More informationCONTINUOUS TIME DYNAMIC PROGRAMMING
Eon. 511b Sprng 1993 C. Sms I. Th Opmaon Problm CONTINUOUS TIME DYNAMIC PROGRAMMING W onsdr h problm of maxmng subj o and EU(C, ) d (1) j ^ d = (C, ) d + σ (C, ) dw () h(c, ), (3) whr () and (3) hold for
More informationA MATHEMATICAL MODEL FOR NATURAL COOLING OF A CUP OF TEA
MTHEMTICL MODEL FOR NTURL COOLING OF CUP OF TE 1 Mrs.D.Kalpana, 2 Mr.S.Dhvarajan 1 Snior Lcurr, Dparmn of Chmisry, PSB Polychnic Collg, Chnnai, India. 2 ssisan Profssor, Dparmn of Mahmaics, Dr.M.G.R Educaional
More informationA THREE COMPARTMENT MATHEMATICAL MODEL OF LIVER
A THREE COPARTENT ATHEATICAL ODEL OF LIVER V. An N. Ch. Paabhi Ramacharyulu Faculy of ahmaics, R D collgs, Hanamonda, Warangal, India Dparmn of ahmaics, Naional Insiu of Tchnology, Warangal, India E-ail:
More informationSouthern Taiwan University
Chaptr Ordinar Diffrntial Equations of th First Ordr and First Dgr Gnral form:., d +, d 0.a. f,.b I. Sparabl Diffrntial quations Form: d + d 0 C d d E 9 + 4 0 Solution: 9d + 4d 0 9 + 4 C E + d Solution:
More informationLecture 9: Dynamic Properties
Shor Course on Molecular Dynamcs Smulaon Lecure 9: Dynamc Properes Professor A. Marn Purdue Unversy Hgh Level Course Oulne 1. MD Bascs. Poenal Energy Funcons 3. Inegraon Algorhms 4. Temperaure Conrol 5.
More informationEDGE PEDESTAL STRUCTURE AND TRANSPORT INTERPRETATION (In the absence of or in between ELMs)
I. EDGE PEDESTAL STRUCTURE AND TRANSPORT INTERPRETATION (In th absnc of or n btwn ELMs) Abstract W. M. Stacy (Gorga Tch) and R. J. Grobnr (Gnral Atomcs) A constrant on th on prssur gradnt s mposd by momntum
More informationMajor: All Engineering Majors. Authors: Autar Kaw, Luke Snyder
Nolr Rgrsso Mjor: All Egrg Mjors Auhors: Aur Kw, Luk Sydr hp://urclhodsgusfdu Trsforg Nurcl Mhods Educo for STEM Udrgrdus 3/9/5 hp://urclhodsgusfdu Nolr Rgrsso hp://urclhodsgusfdu Nolr Rgrsso So populr
More informationTransient Analysis of Two-dimensional State M/G/1 Queueing Model with Multiple Vacations and Bernoulli Schedule
Inrnaonal Journal of Compur Applcaons (975 8887) Volum 4 No.3, Fbruary 22 Transn Analyss of Two-dmnsonal Sa M/G/ Quung Modl wh Mulpl Vacaons and Brnoull Schdul Indra Assoca rofssor Dparmn of Sascs and
More information