NXO a Spatially High Order Finite Volume Numerical Method for Compressible Flows
|
|
- Bernadette Terry
- 5 years ago
- Views:
Transcription
1 NXO Spty Hgh Ode Fnte Voume Nume Method fo Compebe Fow Jen-Me e Gouez One CFD Deptment Fouth HO CFD Wohop Heon June 4th
2 B of the NXO heme Eue o Nve-Stoe fo pefet g w of tte dof pe e nd pe equton Voume vege wde ten Coe pttonng of the gd : one ptton pe node hed memoy hybd pogmmng MPI / OpenMP o Cud Poynom eontuton gothm fo the onevtve vbe o fux denty fed Pepoeo phe : Weghted et-sque poynom degee dpt to the quty of the ten Gve the ntepoton oeffent of onevtve vbe fed fom voume vege to ufe vege Fo the Eue fuxe : e-enteed ten n ed ep. geen fo the ded eontuton poeton on one of the fe of th e ufe nteg of the poynom Fo the dffuve fuxe : Tget ntefe Intefe-enteed ten unon ed-geen Poeton of the gdent of the poynom Sme poynom eontuton ued fo the oveet gd poeton method NextFow : Spty Hgh-Ode Fnte Voume method fo ANS / ES Fouth HO CFD Wohop Heon June 4th
3 Addeng the gothm effeny be : uy veu numbe of dof Hghft Peue NextFow : Spty Hgh-Ode Fnte Voume method fo ANS / ES oe pttonng wde ho Fouth HO CFD Wohop Heon June 4th
4 Ptpton to the HO Wohop - Chengng the DG? Wohop Wohop 2 Wohop 3 mn / DNS Tyo-Geen Votex omputed on egu gd of teted Untedy mn : du o tme teppng Hevng N2 n the untedy we of ynde omputton of the fequeny o-n of the votex heddng Gd nd ode onvegene fo the oveet gd e Eue Ientop votex tnpot ght fgue eut mpoved eenty by ung the fux eontuton method Compon n the ondton of the HO wohop : 50 t Untey mn Hevng nd pthng n2 t eynod numbe 000 nd 5000 demontton of the gd onvegene fo both e modete omputton ot Eue Hgh ode geomety ngeb Fow wth nove fomuton of the method on Fnte Voume of H.O. geomety. Convegene dffute on the fnet gd but good eut n the oe one even wth ow ount of dof ute C-BC on uved w Wohop 3 Untey mn B3 Hevng nd pthng N2 3 dffeent moton of the wng Gd / tme tep / poynom ode onvegene to be onfmed modete omputton ot Fouth HO CFD Wohop Heon June 4th
5 HO Wohop 4 : Ce B3 Enegy exttng Gd nd ode onvegene fo the oveet gd e Compon n the ondton of the Nme HO / wohop dt ode : 50 Cot t Ndof/ Y- Wo extent TBu eqn Mometum Gd / 60 2./ Gd2 / 60 2./ Gd3 / 60 2./ Gd4 / 60 2./ Gd / 60 2./ Gd / 60 2./ Gd / 60 2./ Fouth HO CFD Wohop Heon June 4th
6 Hgh Ode CFD Wohop Ce 3.5 Tyo-Geen Votex Compon of tme devtve of entophy nd ed Dpton of net enegy Ouene of n out phenomenon Hgh Ode CFD Wohop Nhve Jn. 202
7 GPU mpementton of the NextFow ove Pefomne on eh K20Xm GPU : n 3 8e-8 pe HS 0.36 fo e n 4 25e-8 pe HS 0.50 fo e Tyo-Geen Votex ey 600 Computton on wedge Tyo Geen votex 256**3 - w-o 2 hou on 6 IVY-Bdge poeo tot 28 oe : 600 hou CPU Inte oe 25 mnute on 6 Te K20M GPU By ompon t the t HO CFD wohop th e equeted between 00 nd Inte oe Cpu hou dependng on the nume method. Tyo Geen votex 52**3 - w-o : 4 hou on 6 Te K20M GPU 7 GTC 206 Ap 7th Sn Joé Cfon
8 H.O. Fu 3D Voume to fe ntepoton : eontuton nd poeton XY C { } Y X Y X 2 Ω Ω n dv Y X ϖ ψ { } { } { } { } { } Ω n ϖ ψ Ω dv Y X : Voume moment of ode eontuton eo funton n Sten ze : nb of monom + 50% n λ ˆ n µ ˆ { } { } { } { } { } { } ' ' ' 0 P κ > + Μ / eontuton n eft ten ented on
9 FV NXO method : eontuton nd poeton ˆ ˆ Μ + Α 0 { } { } { ' ' '} { } S S Ω κ X Y ds Ω X Y ds ˆ ˆ { } { } 2/ Poeton on the ntefe ν { } { } { } { } η Ω X Y S ν ds η κ { } { } { } ν { } e X + ν { } e Y + ν { } e { } η { } { } g κ { } { } { } { } g ν C XY λ µ n ˆ λ n ˆ µ
10 FV NXO method : Invd fuxe opton : Voume vege ˆ : ufe vege ˆ : NXO heme n Ω W + S Fˆ Fˆ 0 t n n v n 2 opton fo the nvd fuxe Chtet Upwnd o ented Fˆ F W W W W Upwnd heme : one vege fux evuton fom the eft nd ght extpoted vege onevtve vbe htet pttng tte upwnd Fˆ F F τθ mx W W W W Cented heme : ntepoton of the e-vege fux denty teno n e of the ten to the ntefe + tbzton tem Mn nuy oue : F ˆ F Wˆ Upwnd heme F F W Cented heme
Neural Network Introduction. Hung-yi Lee
Neu Neto Intoducton Hung- ee Reve: Supevsed enng Mode Hpothess Functon Set f, f : : (e) Tnng: Pc the est Functon f * Best Functon f * Testng: f Tnng Dt : functon nput : functon output, ˆ,, ˆ, Neu Neto
More informationSurface x(u, v) and curve α(t) on it given by u(t) & v(t). Math 4140/5530: Differential Geometry
Surface x(u, v) and curve α(t) on it given by u(t) & v(t). α du dv (t) x u dt + x v dt Surface x(u, v) and curve α(t) on it given by u(t) & v(t). α du dv (t) x u dt + x v dt ( ds dt )2 Surface x(u, v)
More information_ 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
More informationChapter I Vector Analysis
. Chpte I Vecto nlss . Vecto lgeb j It s well-nown tht n vecto cn be wtten s Vectos obe the followng lgebc ules: scl s ) ( j v v cos ) ( e Commuttv ) ( ssoctve C C ) ( ) ( v j ) ( ) ( ) ( ) ( (v) he lw
More informationRotational Kinematics. Rigid Object about a Fixed Axis Western HS AP Physics 1
Rotatonal Knematcs Rgd Object about a Fxed Axs Westen HS AP Physcs 1 Leanng Objectes What we know Unfom Ccula Moton q s Centpetal Acceleaton : Centpetal Foce: Non-unfom a F c c m F F F t m ma t What we
More informationCOMP 465: Data Mining More on PageRank
COMP 465: Dt Mnng Moe on PgeRnk Sldes Adpted Fo: www.ds.og (Mnng Mssve Dtsets) Powe Iteton: Set = 1/ 1: = 2: = Goto 1 Exple: d 1/3 1/3 5/12 9/24 6/15 = 1/3 3/6 1/3 11/24 6/15 1/3 1/6 3/12 1/6 3/15 Iteton
More information6.6 The Marquardt Algorithm
6.6 The Mqudt Algothm lmttons of the gdent nd Tylo expnson methods ecstng the Tylo expnson n tems of ch-sque devtves ecstng the gdent sech nto n tetve mtx fomlsm Mqudt's lgothm utomtclly combnes the gdent
More informationTutorial Chemical Reaction Engineering:
Dpl.-Ing. ndeas Jöke Tutoal Chemal eaton Engneeng:. eal eatos, esdene tme dstbuton and seletvty / yeld fo eaton netwoks Insttute of Poess Engneeng, G5-7, andeas.joeke@ovgu.de 8-Jun-6 Tutoal CE: esdene
More informationV. Principles of Irreversible Thermodynamics. s = S - S 0 (7.3) s = = - g i, k. "Flux": = da i. "Force": = -Â g a ik k = X i. Â J i X i (7.
Themodynamcs and Knetcs of Solds 71 V. Pncples of Ievesble Themodynamcs 5. Onsage s Teatment s = S - S 0 = s( a 1, a 2,...) a n = A g - A n (7.6) Equlbum themodynamcs detemnes the paametes of an equlbum
More informationDynamically Equivalent Systems. Dynamically Equivalent Systems. Dynamically Equivalent Systems. ME 201 Mechanics of Machines
ME 0 Mechnics of Mchines 8//006 Dynmicy Equivent Systems Ex: Connecting od G Dynmicy Equivent Systems. If the mss of the connecting od m G m m B m m m. Moment out cente of gvity shoud e zeo m G m B Theefoe;
More informationVECTORS VECTORS VECTORS VECTORS. 2. Vector Representation. 1. Definition. 3. Types of Vectors. 5. Vector Operations I. 4. Equal and Opposite Vectors
1. Defnton A vetor s n entt tht m represent phsl quntt tht hs mgntude nd dreton s opposed to slr tht ls dreton.. Vetor Representton A vetor n e represented grphll n rrow. The length of the rrow s the mgntude
More informationUniform Circular Motion
Unfom Ccul Moton Unfom ccul Moton An object mong t constnt sped n ccle The ntude of the eloct emns constnt The decton of the eloct chnges contnuousl!!!! Snce cceleton s te of chnge of eloct:!! Δ Δt The
More informationON THE EXTENSION OF WEAK ARMENDARIZ RINGS RELATIVE TO A MONOID
wwweo/voue/vo9iue/ijas_9 9f ON THE EXTENSION OF WEAK AENDAIZ INGS ELATIVE TO A ONOID Eye A & Ayou Eoy Dee of e Nowe No Uvey Lzou 77 C Dee of e Uvey of Kou Ou Su E-: eye76@o; you975@yooo ABSTACT Fo oo we
More informationCHAPTER (6) Biot-Savart law Ampere s Circuital Law Magnetic Field Density Magnetic Flux
CAPTE 6 Biot-Svt w Ampee s Ciuit w Mgneti Fied Densit Mgneti Fu Soues of mgneti fied: - Pemnent mgnet - Fow of uent in ondutos -Time ving of eeti fied induing mgneti fied Cuent onfigutions: - Fiment uent
More informationE-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
More informationT 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
More informationCOLLEGE OF FOUNDATION AND GENERAL STUDIES PUTRAJAYA CAMPUS FINAL EXAMINATION TRIMESTER /2017
COLLEGE OF FOUNDATION AND GENERAL STUDIES PUTRAJAYA CAMPUS FINAL EXAMINATION TRIMESTER 1 016/017 PROGRAMME SUBJECT CODE : Foundaton n Engneeng : PHYF115 SUBJECT : Phscs 1 DATE : Septembe 016 DURATION :
More informationX-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
More informationLecture 9-3/8/10-14 Spatial Description and Transformation
Letue 9-8- tl Deton nd nfomton Homewo No. Due 9. Fme ngement onl. Do not lulte...8..7.8 Otonl et edt hot oof tht = - Homewo No. egned due 9 tud eton.-.. olve oblem:.....7.8. ee lde 6 7. e Mtlb on. f oble.
More informationVEKTORANALYS FLUX INTEGRAL LINE INTEGRAL. and. Kursvecka 2. Kapitel 4 5. Sidor 29 50
VEKTORANAYS Ksecka INE INTEGRA and UX INTEGRA Kaptel 4 5 Sdo 9 5 A wnd TARGET PROBEM We want to psh a mne cat along a path fom A to B. Bt the wnd s blowng. How mch enegy s needed? (.e. how mch s the wok?
More informationCh.9. Electromagnetic Induction
PART Ch.9. Eectomgnetic nuction F. Mutu nuctnce between the Two Cicuits G. Exmpes of nuctnce Ccution H. Enegy Stoe in the Coi. Wok by Eectomgnetic Foce J. Ey Cuent n Skin Effect Yong-Jin Shin, Pofesso
More informationRotary motion
ectue 8 RTARY TN F THE RGD BDY Notes: ectue 8 - Rgd bod Rgd bod: j const numbe of degees of feedom 6 3 tanslatonal + 3 ota motons m j m j Constants educe numbe of degees of feedom non-fee object: 6-p
More informationQuestion 1. Typical Cellular System. Some geometry TELE4353. About cellular system. About cellular system (2)
TELE4353 Moble a atellte Commucato ystems Tutoal 1 (week 3-4 4 Questo 1 ove that fo a hexagoal geomety, the co-chael euse ato s gve by: Q (3 N Whee N + j + j 1/ 1 Typcal Cellula ystem j cells up cells
More informationis the instantaneous position vector of any grid point or fluid
Absolute inetial, elative inetial and non-inetial coodinates fo a moving but non-defoming contol volume Tao Xing, Pablo Caica, and Fed Sten bjective Deive and coelate the govening equations of motion in
More informationNONLINEAR CONTINUUM FORMULATIONS CONTENTS
NONLINEAR CONTINUUM FORMULATIONS CONTENTS Introduction to nonlinear continuum mechanics Descriptions of motion Measures of stresses and strains Updated and Total Lagrangian formulations Continuum shell
More informationdu(l) 5 dl = U(0) = 1 and 1.) Substitute for U an unspecified trial function into governing equation, i.e. dx + = =
Consider an ODE of te form: Finite Element Metod du fu g d + wit te following Boundary Conditions: U(0) and du(l) 5 dl.) Substitute for U an unspecified trial function into governing equation, i.e. ^ U
More informationEE 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
More informationWinnie flies again. Winnie s Song. hat. A big tall hat Ten long toes A black magic wand A long red nose. nose. She s Winnie Winnie the Witch.
Wnn f gn ht Wnn Song A g t ht Tn ong to A k g wnd A ong d no. no Sh Wnn Wnn th Wth. y t d to A ong k t Bg gn y H go wth Wnn Whn h f. wnd ootk H Wu Wu th t. Ptu Dtony oo hopt oon okt hng gd ho y ktod nh
More informationChapter 5: Your Program Asks for Advice.
Chte 5: You Pogm Asks fo Advce. Pge 63 Chte 5: You Pogm Asks fo Advce. Ths chte ntoduces new tye of ves (stng ves) nd how to get text nd numec esonses fom the use. Anothe Tye of Ve The Stng Ve: In Chte
More informationBaltimore County ARML Team Formula Sheet, v2.1 (08 Apr 2008) By Raymond Cheong. Difference of squares Difference of cubes Sum of cubes.
Bltimoe Couty ARML Tem Fomul Seet, v. (08 Ap 008) By Rymo Ceog POLYNOMIALS Ftoig Diffeee of sques Diffeee of ues Sum of ues Ay itege O iteges ( )( ) 3 3 ( )( ) 3 3 ( )( ) ( )(... ) ( )(... ) Biomil expsio
More informationParametric Methods. Autoregressive (AR) Moving Average (MA) Autoregressive - Moving Average (ARMA) LO-2.5, P-13.3 to 13.4 (skip
Pmeti Methods Autoegessive AR) Movig Avege MA) Autoegessive - Movig Avege ARMA) LO-.5, P-3.3 to 3.4 si 3.4.3 3.4.5) / Time Seies Modes Time Seies DT Rdom Sig / Motivtio fo Time Seies Modes Re the esut
More information(A) 6.32 (B) 9.49 (C) (D) (E) 18.97
Univesity of Bhin Physics 10 Finl Exm Key Fll 004 Deptment of Physics 13/1/005 8:30 10:30 e =1.610 19 C, m e =9.1110 31 Kg, m p =1.6710 7 Kg k=910 9 Nm /C, ε 0 =8.8410 1 C /Nm, µ 0 =4π10 7 T.m/A Pt : 10
More informationChapter 11 Exercise 11A. Exercise 11B. Q. 1. (i) = 2 rads (ii) = 5 rads (iii) 15 = 0.75 rads. Q. 1. T = mv2 r = 8(25) (iv) 11 = 0.
Chpte Execise A Q.. (i) 0 0 = ds (ii) 00 0 = ds (iii) = 0.7 ds 0 (iv) = 0. ds 0 Q.. (i) = cm (ii) 0.8 = cm (iii). = 6 cm (iv).7 = 8. cm Q.. =. = cm Q.. =.07 =. cm.8 Q.. Angu speed = 8 =.8 ds/sec 0 Q. 6.
More informationChapter Linear Regression
Chpte 6.3 Le Regesso Afte edg ths chpte, ou should be ble to. defe egesso,. use sevel mmzg of esdul cte to choose the ght cteo, 3. deve the costts of le egesso model bsed o lest sques method cteo,. use
More informationSound Radiation of Circularly Oscillating Spherical and Cylindrical Shells. John Wang and Hongan Xu Volvo Group 4/30/2013
Sound Radaton of Culaly Osllatng Spheal and Cylndal Shells John Wang and Hongan Xu Volvo Goup /0/0 Abstat Closed-fom expesson fo sound adaton of ulaly osllatng spheal shells s deved. Sound adaton of ulaly
More informationMagnetic Materials. The inductor Φ B = LI (Q = CV) = L I = N Φ. Power = VI = LI. Energy = Power dt = LIdI = 1 LI 2 = 1 NΦ B capacitor CV 2
Magnetic Materials The inductor Φ B = LI (Q = CV) Φ B 1 B = L I E = (CGS) t t c t EdS = 1 ( BdS )= 1 Φ V EMF = N Φ B = L I t t c t B c t I V Φ B magnetic flux density V = L (recall I = C for the capacitor)
More informationPLEASE DO NOT TURN THIS PAGE UNTIL INSTRUCTED TO DO SO THEN ENSURE THAT YOU HAVE THE CORRECT EXAM PAPER
OLLSCOIL NA ÉIREANN, CORCAIGH THE NATIONAL UNIVERSITY OF IRELAND, CORK COLÁISTE NA OLLSCOILE, CORCAIGH UNIVERSITY COLLEGE, CORK 4/5 Autumn Suppement 5 MS Integ Ccuus nd Diffeenti Equtions Pof. P.J. Rippon
More informationModule 3: Element Properties Lecture 5: Solid Elements
Modue : Eement Propertes eture 5: Sod Eements There re two s fmes of three-dmenson eements smr to two-dmenson se. Etenson of trngur eements w produe tetrhedrons n three dmensons. Smr retngur preeppeds
More information( ) D x ( s) if r s (3) ( ) (6) ( r) = d dr D x
SIO 22B, Rudnick dpted fom Dvis III. Single vile sttistics The next few lectues e intended s eview of fundmentl sttistics. The gol is to hve us ll speking the sme lnguge s we move to moe dvnced topics.
More informationGCE AS and A Level MATHEMATICS FORMULA BOOKLET. From September Issued WJEC CBAC Ltd.
GCE AS d A Level MATHEMATICS FORMULA BOOKLET Fom Septeme 07 Issued 07 Pue Mthemtcs Mesuto Suce e o sphee = 4 Ae o cuved suce o coe = heght slt Athmetc Sees S = + l = [ + d] Geometc Sees S = S = o < Summtos
More informationPart 2: CM3110 Transport Processes and Unit Operations I. Professor Faith Morrison. CM2110/CM Review. Concerned now with rates of heat transfer
CM30 anspot Pocesses and Unit Opeations I Pat : Pofesso Fait Moison Depatment of Cemical Engineeing Micigan ecnological Uniesity CM30 - Momentum and Heat anspot CM30 Heat and Mass anspot www.cem.mtu.edu/~fmoiso/cm30/cm30.tml
More informationInspiration and formalism
Inspirtion n formlism Answers Skills hek P(, ) Q(, ) PQ + ( ) PQ A(, ) (, ) grient ( ) + Eerise A opposite sies of regulr hegon re equl n prllel A ED i FC n ED ii AD, DA, E, E n FC No, sies of pentgon
More informationOH 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
More informationChapter 13 - Universal Gravitation
Chapte 3 - Unesal Gataton In Chapte 5 we studed Newton s thee laws of moton. In addton to these laws, Newton fomulated the law of unesal gataton. Ths law states that two masses ae attacted by a foce gen
More informationOutline. Basics of interference Types of interferometers. Finite impulse response Infinite impulse response Conservation of energy in beam splitters
ntefeometes lectue C 566 Adv. Optics Lab Outline Basics of intefeence Tpes of intefeometes Amplitude division Finite impulse esponse nfinite impulse esponse Consevation of eneg in beam splittes Wavefont
More informationMATHEMATICS II PUC VECTOR ALGEBRA QUESTIONS & ANSWER
MATHEMATICS II PUC VECTOR ALGEBRA QUESTIONS & ANSWER I One M Queston Fnd the unt veto n the deton of Let ˆ ˆ 9 Let & If Ae the vetos & equl? But vetos e not equl sne the oespondng omponents e dstnt e detons
More informationGCE AS/A Level MATHEMATICS GCE AS/A Level FURTHER MATHEMATICS
GCE AS/A Level MATHEMATICS GCE AS/A Level FURTHER MATHEMATICS FORMULA BOOKLET Fom Septembe 07 Issued 07 Mesuto Pue Mthemtcs Sufce e of sphee = 4 Ae of cuved sufce of coe = slt heght Athmetc Sees S l d
More informationBroadband Noise Predictions Based on a New Aeroacoustic Formulation
Boadband Noise Pedictions Based on a New Aeoacoustic Fomulation J. Caspe and F. Faassat NASA Langley Reseach Cente Hampton, Viginia AIAA Pape -8 Aifame Noise Session 4 th AIAA Aeospace Sciences Meeting
More information3. Perturbation of Kerr BH
3. Petubation of Ke BH hoizon at Δ = 0 ( = ± ) Unfotunately, it i technically fomidable to deal with the metic petubation of Ke BH becaue of coupling between and θ Nevethele, thee exit a fomalim (Newman-Penoe
More informationMachine Learning. Spectral Clustering. Lecture 23, April 14, Reading: Eric Xing 1
Machne Leanng -7/5 7/5-78, 78, Spng 8 Spectal Clusteng Ec Xng Lectue 3, pl 4, 8 Readng: Ec Xng Data Clusteng wo dffeent ctea Compactness, e.g., k-means, mxtue models Connectvty, e.g., spectal clusteng
More information2. Elementary Linear Algebra Problems
. Eleety e lge Pole. BS: B e lge Suoute (Pog pge wth PCK) Su of veto opoet:. Coputto y f- poe: () () () (3) N 3 4 5 3 6 4 7 8 Full y tee Depth te tep log()n Veto updte the f- poe wth N : ) ( ) ( ) ( )
More informationphysicsandmathstutor.com
physicsadmathstuto.com physicsadmathstuto.com Jue 005. A cuve has equatio blak x + xy 3y + 16 = 0. dy Fid the coodiates of the poits o the cuve whee 0. dx = (7) Q (Total 7 maks) *N03B034* 3 Tu ove physicsadmathstuto.com
More informationLecture 5 Single factor design and analysis
Lectue 5 Sngle fcto desgn nd nlss Completel ndomzed desgn (CRD Completel ndomzed desgn In the desgn of expements, completel ndomzed desgns e fo studng the effects of one pm fcto wthout the need to tke
More informationt r ès s r â 2s ré t s r té s s s s r é é ér t s 2 ï s t 1 s à r
P P r t r t tr t r ès s rs té P rr t r r t t é t q s q é s Prés té t s t r r â 2s ré t s r té s s s s r é é ér t s 2 ï s t 1 s à r ès r é r r t ît P rt ré ré t à r P r s q rt s t t r r2 s rtí 3 Pr ss r
More informationThe Area of a Triangle
The e of Tingle tkhlid June 1, 015 1 Intodution In this tile we will e disussing the vious methods used fo detemining the e of tingle. Let [X] denote the e of X. Using se nd Height To stt off, the simplest
More information1.050 Engineering Mechanics I. Summary of variables/concepts. Lecture 27-37
.5 Engneeng Mechancs I Summa of vaabes/concepts Lectue 7-37 Vaabe Defnton Notes & ments f secant f tangent f a b a f b f a Convet of a functon a b W v W F v R Etena wok N N δ δ N Fee eneg an pementa fee
More informationANSWER KEY WITH SOLUTION MATHEMATICS 1. C 2. A 3. A 4. A 5. D 6. A 7. D 8. A 9. C 10. D 11. D 12. A 13. C 14. C
ONLINE TEST PAPER JEE MAIN - 6 DATE : --6 ANSWER KEY WITH SOLUTION MATHEMATICS. C. A. A. A. D 6. A 7. D 8. A 9. C. D. D. A. C. C. D 6. D 7. A 8. A 9. A. D. B. A. D. A. B 6. B 7. C 8. D 9. D. B PHYSICS....
More informationAbhilasha Classes Class- XII Date: SOLUTION (Chap - 9,10,12) MM 50 Mob no
hlsh Clsses Clss- XII Dte: 0- - SOLUTION Chp - 9,0, MM 50 Mo no-996 If nd re poston vets of nd B respetvel, fnd the poston vet of pont C n B produed suh tht C B vet r C B = where = hs length nd dreton
More information7.5-Determinants in Two Variables
7.-eteminnts in Two Vibles efinition of eteminnt The deteminnt of sque mti is el numbe ssocited with the mti. Eve sque mti hs deteminnt. The deteminnt of mti is the single ent of the mti. The deteminnt
More informationF í s. i c HARMONIC MOTION. A p l. i c a U C L M
HRONI OTION 070311 1 Hooke w hrterzton of Sme Hrmon oton (SH) Veoty n eerton n hrmon moton. Exeme. Horzont n vert rng Sme enuum Phy enuum Energy n hrmon moton Dme hrmon moton Hooke w Srng ontnt The fore
More informationharmonic oscillator in quantum mechanics
Physics 400 Spring 016 harmonic oscillator in quantum mechanics lecture notes, spring semester 017 http://www.phys.uconn.edu/ rozman/ourses/p400_17s/ Last modified: May 19, 017 Dimensionless Schrödinger
More information10/15/2013. PHY 113 C General Physics I 11 AM-12:15 PM MWF Olin 101
10/15/01 PHY 11 C Geneal Physcs I 11 AM-1:15 PM MWF Oln 101 Plan fo Lectue 14: Chapte 1 Statc equlbu 1. Balancng foces and toques; stablty. Cente of gavty. Wll dscuss elastcty n Lectue 15 (Chapte 15) 10/14/01
More informationQuestion Bank. Section A. is skew-hermitian matrix. is diagonalizable. (, ) , Evaluate (, ) 12 about = 1 and = Find, if
Subject: Mathematics-I Question Bank Section A T T. Find the value of fo which the matix A = T T has ank one. T T i. Is the matix A = i is skew-hemitian matix. i. alculate the invese of the matix = 5 7
More informationReference. Reference. Properties of Equality. Properties of Segment and Angle Congruence. Other Properties. Triangle Inequalities
Refeene opeties opeties of qulity ddition opety of qulity If =, ten + = +. Multiplition opety of qulity If =, ten =, 0. Reflexive opety of qulity = Tnsitive opety of qulity If = nd =, ten =. Suttion opety
More informationAN ALGEBRAIC APPROACH TO M-BAND WAVELETS CONSTRUCTION
AN ALGEBRAIC APPROACH TO -BAN WAELETS CONSTRUCTION Toy L Qy S Pewe Ho Ntol Lotoy o e Peeto Pe Uety Be 8 P. R. C Att T e eet le o to ott - otool welet e. A yte of ott eto ote fo - otool flte te olto e o
More informationThe formulae in this booklet have been arranged according to the unit in which they are first
Fomule Booklet Fomule Booklet The fomule ths ooklet hve ee ge og to the ut whh the e fst toue. Thus te sttg ut m e eque to use the fomule tht wee toue peeg ut e.g. tes sttg C mght e epete to use fomule
More information1.2 Differential cross section
.2. DIFFERENTIAL CROSS SECTION Febuay 9, 205 Lectue VIII.2 Diffeential coss section We found that the solution to the Schodinge equation has the fom e ik x ψ 2π 3/2 fk, k + e ik x and that fk, k = 2 m
More informationThe Shape of the Pair Distribution Function.
The Shpe of the P Dstbuton Functon. Vlentn Levshov nd.f. Thope Deptment of Phscs & stonom nd Cente fo Fundmentl tels Resech chgn Stte Unvest Sgnfcnt pogess n hgh-esoluton dffcton epements on powde smples
More informationRemark: Positive work is done on an object when the point of application of the force moves in the direction of the force.
Unt 5 Work and Energy 5. Work and knetc energy 5. Work - energy theore 5.3 Potenta energy 5.4 Tota energy 5.5 Energy dagra o a ass-sprng syste 5.6 A genera study o the potenta energy curve 5. Work and
More informationP 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
More informationInternet Appendix for A Bayesian Approach to Real Options: The Case of Distinguishing Between Temporary and Permanent Shocks
Intenet Appendix fo A Bayesian Appoach to Real Options: The Case of Distinguishing Between Tempoay and Pemanent Shocks Steven R. Genadie Gaduate School of Business, Stanfod Univesity Andey Malenko Gaduate
More informationChapter Introduction to Finite Element Methods
Chapte 1.4 Intoduction to Finite Element Methods Afte eading this chapte, you should e ale to: 1. Undestand the asics of finite element methods using a one-dimensional polem. In the last fifty yeas, the
More informationMath 324 Advanced Financial Mathematics Spring 2008 Final Exam Solutions May 2, 2008
Mat 324 Advanced Fnancal Matematcs Sprng 28 Fnal Exam Solutons May 2, 28 Ts s an open book take-ome exam. You may work wt textbooks and notes but do not consult any oter person. Sow all of your work and
More informationMark Scheme (Results) January 2008
Mk Scheme (Results) Jnuy 00 GCE GCE Mthemtics (6679/0) Edecel Limited. Registeed in Englnd nd Wles No. 4496750 Registeed Office: One90 High Holbon, London WCV 7BH Jnuy 00 6679 Mechnics M Mk Scheme Question
More informationSB4223E00 Nov Schematic. Lift Trucks Electric System D110S-5, D130S-5, D160S-5
E00 Nov.00 chematic ift Trucks Electric ystem D0, D0, D0 ETIEE for Engine tart & harging ystem / IITION WIT / 0 / / / / Warning amp GE / 0 FUE OX / X ED D D D D EP EP EP F N INTEOK EY 0 a / / D X D D IUIT
More informationReview of Vector Algebra and Vector Calculus Operations
Revew of Vecto Algeba and Vecto Calculus Opeatons Tpes of vaables n Flud Mechancs Repesentaton of vectos Dffeent coodnate sstems Base vecto elatons Scala and vecto poducts Stess Newton s law of vscost
More informationJim Lambers MAT 280 Summer Semester Practice Final Exam Solution. dy + xz dz = x(t)y(t) dt. t 3 (4t 3 ) + e t2 (2t) + t 7 (3t 2 ) dt
Jim Lambers MAT 28 ummer emester 212-1 Practice Final Exam olution 1. Evaluate the line integral xy dx + e y dy + xz dz, where is given by r(t) t 4, t 2, t, t 1. olution From r (t) 4t, 2t, t 2, we obtain
More informationQuality control. Final exam: 2012/1/12 (Thur), 9:00-12:00 Q1 Q2 Q3 Q4 Q5 YOUR NAME
Qulity contol Finl exm: // (Thu), 9:-: Q Q Q3 Q4 Q5 YOUR NAME NOTE: Plese wite down the deivtion of you nswe vey clely fo ll questions. The scoe will be educed when you only wite nswe. Also, the scoe will
More information1D2G - Numerical solution of the neutron diffusion equation
DG - Numeical solution of the neuton diffusion equation Y. Danon Daft: /6/09 Oveview A simple numeical solution of the neuton diffusion equation in one dimension and two enegy goups was implemented. Both
More informationAP Calculus AB Exam Review Sheet B - Session 1
AP Clcls AB Em Review Sheet B - Session Nme: AP 998 # Let e the nction given y e.. Find lim nd lim.. Find the solte minimm vle o. Jstiy tht yo nswe is n solte minimm. c. Wht is the nge o? d. Conside the
More informationChapter 4. Interaction of Many-Electron Atoms with Electromagnetic Radiation
Cpte 4. Intecton o ny-ecton Atos wt ectognetc Rdton Redng: Bnsden & ocn Cpte 9 ny-ecton Atos n n Fed Htonn V t A e p t A e p V t ea p H H Te-ndependent Htonn nt t H Intecton o te to wt te dton ed Te dependent
More informationExercise 4: Adimensional form and Rankine vortex. Example 1: adimensional form of governing equations
Fluid Mechanics, SG4, HT9 Septembe, 9 Execise 4: Adimensional fom and Rankine votex Example : adimensional fom of govening equations Calculating the two-dimensional flow aound a cylinde (adius a, located
More informationA Study on Root Properties of Super Hyperbolic GKM algebra
Stuy on Root Popetes o Supe Hypebol GKM lgeb G.Uth n M.Pyn Deptment o Mthemts Phypp s College Chenn Tmlnu In. bstt: In ths ppe the Supe hypebol genelze K-Mooy lgebs o nente type s ene n the mly s lso elte.
More informationGeneral momentum equation
PY4A4 Senio Sophiste Physics of the Intestella and Integalactic Medium Lectue 11: Collapsing Clouds D Gaham M. Hape School of Physics, TCD Geneal momentum equation Du u P Dt uu t 1 B 4 B 1 B 8 Lagangian
More informationProblem 1. Part b. Part a. Wayne Witzke ProblemSet #1 PHY 361. Calculate x, the expected value of x, defined by
Poblem Pat a The nomal distibution Gaussian distibution o bell cuve has the fom f Ce µ Calculate the nomalization facto C by equiing the distibution to be nomalized f Substituting in f, defined above,
More informationPHY126 Summer Session I, 2008
PHY6 Summe Sesson I, 8 Most of nfomaton s avalable at: http://nngoup.phscs.sunsb.edu/~chak/phy6-8 ncludng the sllabus and lectue sldes. Read sllabus and watch fo mpotant announcements. Homewok assgnment
More informationCalculate the electric potential at B d2=4 m Calculate the electric potential at A d1=3 m 3 m 3 m
MTE : Ch 13 5:3-7pm on Oct 31 ltenate Exams: Wed Ch 13 6:3pm-8:pm (people attending the altenate exam will not be allowed to go out of the oom while othes fom pevious exam ae still aound) Thu @ 9:-1:3
More informationInstantaneous velocity field of a round jet
Fee shea flows Instantaneos velocty feld of a ond et 3 Aveage velocty feld of a ond et 4 Vtal ogn nozzle coe Developng egon elf smla egon 5 elf smlaty caled vaables: ~ Q ξ ( ξ, ) y δ ( ) Q Q (, y) ( )
More informationSOLUTIONS ( ) ( )! ( ) ( ) ( ) ( )! ( ) ( ) ( ) ( ) n r. r ( Pascal s equation ). n 1. Stepanov Dalpiaz
STAT UIU Pctice Poblems # SOLUTIONS Stepov Dlpiz The followig e umbe of pctice poblems tht my be helpful fo completig the homewo, d will liely be vey useful fo studyig fo ems...-.-.- Pove (show) tht. (
More informationCAREER POINT TARGET IIT JEE CHEMISTRY, MATHEMATICS & PHYSICS HINTS & SOLUTION (B*) (C*) (D) MeMgBr 9. [A, D]
CAREER PINT TARGET IIT JEE CEMISTRY, MATEMATICS & PYSICS RS -- I -A INTS & SLUTIN CEMISTRY Section I n +. [B] C n n + n + nc + (n + ) V 7 n + (n + ) / 7 n VC 4 n 4 alkane is C 6 a.[a] P + (v b) RT V at
More informationP 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
More information= ρ. Since this equation is applied to an arbitrary point in space, we can use it to determine the charge density once we know the field.
Gauss s Law In diffeentia fom D = ρ. ince this equation is appied to an abita point in space, we can use it to detemine the chage densit once we know the fied. (We can use this equation to ve fo the fied
More informationSuppose the medium is not homogeneous (gravity waves impinging on a beach,
Slowly vaying media: Ray theoy Suppose the medium is not homogeneous (gavity waves impinging on a beach, i.e. a vaying depth). Then a pue plane wave whose popeties ae constant in space and time is not
More informationConquering kings their titles take ANTHEM FOR CONGREGATION AND CHOIR
Coquerg gs her es e NTHEM FOR CONGREGTION ND CHOIR I oucg hs hm-hem, whch m be cuded Servce eher s Hm or s hem, he Cogrego m be referred o he No. of he Hm whch he words pper, d ved o o sgg he 1 s, 4 h,
More informationTHIS 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
More informationLecture 2 - Thermodynamics Overview
2.625 - Electochemical Systems Fall 2013 Lectue 2 - Themodynamics Oveview D.Yang Shao-Hon Reading: Chapte 1 & 2 of Newman, Chapte 1 & 2 of Bad & Faulkne, Chaptes 9 & 10 of Physical Chemisty I. Lectue Topics:
More information19 The Born-Oppenheimer Approximation
9 The Bon-Oppenheme Appoxmaton The full nonelatvstc Hamltonan fo a molecule s gven by (n a.u.) Ĥ = A M A A A, Z A + A + >j j (883) Lets ewte the Hamltonan to emphasze the goal as Ĥ = + A A A, >j j M A
More informationH 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
More informationDoublet structure of Alkali spectra:
Doublet stuctue of : Caeful examination of the specta of alkali metals shows that each membe of some of the seies ae closed doublets. Fo example, sodium yellow line, coesponding to 3p 3s tansition, is
More informationLarge scale magnetic field generation by accelerated particles in galactic medium
Lage scale magnetc feld geneaton by acceleated patcles n galactc medum I.N.Toptygn Sant Petesbug State Polytechncal Unvesty, depatment of Theoetcal Physcs, Sant Petesbug, Russa 2.Reason explonatons The
More information