11/11/2017. Randal W. Samstag, MS, PE, BCEE Civil and Sanitary Engineer Bainbridge Island, WA US

Size: px
Start display at page:

Download "11/11/2017. Randal W. Samstag, MS, PE, BCEE Civil and Sanitary Engineer Bainbridge Island, WA US"

Transcription

1 11/11/017 Randal W. Samsag, MS, PE, BCEE Cl and Sanary Engneer Banbrdge Island, WA S To gan some ndersandng of how compaonal fld dynamcs (CFD) can help s o beer ndersand waer resorce recoery facles sng an open sorce ool. 1

2 11/11/017 If we know wha s happenng whn he essel, hen we are able o predc he behaor of he essel as a reacor. Thogh fne n prncple, he aendan complees make mpraccal o se hs approach. Ocae Leenspel (197) Compaonal fld dynamcs (CFD) changes hs pcre. sng CFD, we can compe hree-dmensonal elocy felds and follow neracons of reacans and prodcs hrogh a ank. We can se hs nformaon o opmze ank geomery and o mproe desgns and operaon. TIME TOPIC INSTRCTOR AND AFFILIATION 8:30 o 9:15 Welcome and Inrodcon o CFD for WRRF Randal Samsag, Cl and Sanary Engneer 9:15 o 10:00 Good Modelng Pracce for CFD Edward Wcklen, Carollo Engneers 10:00 o 10:30 Break 10:30 o 1:00 Inrodcon o CFD sng Open FOAM Nelson Marqes, blecape 1:00 o 1:30 Lnch 1:30 o 3:00 Geng Sared wh OpenFOAM: Eample Case (Parshall flme) - Sep, Meshng, Pre Processng, Smlaon and Pos Processng 3:00 o 3:30 Break Nelson Marqes, blecape 3:30 o 4:00 CFD for flow splng Edward Wcklen, Carollo Engneers 4:00 o 5:00 OpenFOAM case: Flow Splng Nelson Marqes, blecape

3 11/11/017 TIME TOPIC INSTRCTOR AND AFFILIATION 8:30 o 9:00 Welcome and Bref Inrodcon o CFD for WRRF and nsallaon of sofware for parcpans who cold no aend Day One Randal Samsag, Cl and Sanary Engneer Nelson Marqes, blecape 9:00 o 9:30 CFD for mng Edward Wcklen, Carollo Engneers Sephen Sanders, IBIS Grop CFD 9:30 o 10:00 OpenFOAM case sdy: Mng Nelson Marqes, blecape 10:00 o 10:30 Break 10:30 o 11:00 CFD for Sedmenaon: Calbraon Modelng Alonso Grboro, Hazen and Sawyer and Verfcaon 11:00 o 1:00 OpenFOAM case sdy: Sedmenaon Nelson Marqes, blecape 1:00 o 1:30 Lnch 1:30 o :00 CFD of Dsnfecon Facles Edward Wcklen and Sephen Sanders :00 o 3:00 OpenFOAM case sdy: lraole Nelson Marqes, blecape Dsnfecon 3:00 o 3:30 Break 3:30 o 4:45 OpenFOAM adanced opcs: Makng yor Nelson Marqes, blecape own cases 4:45 o 5:00 Wrap-p and Adorn Randal Samsag, Cl and Sanary Engneer IWA CFD Workng Grop The WG nends o sole shorcomngs arsng from lack of knowledge of CFD n he waer and wasewaer commny n he shor erm by prodcng papers and books as well as hands-on ranng for he IWA MIA members (and beyond). Frhermore, a book dedcaed for ranng new people n he waer/wasewaer feld wll be prodced. 3

4 11/11/017 Pblshed Papers Good Modellng Pracce n Applyng Compaonal Fld Dynamcs for WWTP Modellng, WEFTEC 01 A proocol for he se of compaonal fld dynamcs as a sppore ool for wasewaer reamen plan modellng, WST Compaonal Fld Dynamcs: an mporan modellng ool for he waer secor, IWC Conference Good Modellng Pracce n Applyng Compaonal Fld Dynamcs for WWTP Modellng, WST (016) CFD for Wasewaer: An Oerew, WST (016) Workshops WEFTEC 01 (Flen) WWTMod 01 Waermae 015 (OpenFOAM) WEFTEC 016 (Flow-3D) WEFTEC 017 (OpenFOAM) Book Proecs IWA Scenfc and Techncal Repor CFD for Waer Book for Sdens and Praconers 4

5 11/11/017 Web: hp://rsamsag.com/ Phone: +1 (06) Emal: 5

6 11/11/017 Randal W. Samsag, MS, PE, BCEE Cl and Sanary Engneer Banbrdge Island, WA S Wha s CFD? How s done? Wha s good for? Conclsons 6

7 11/11/017 Wha s CFD (compaonal fld dynamcs)?... flows and relaed phenomena can be descrbed by paral dfferenal eqaons, whch canno be soled analycally ecep n specal cases. To oban an appromae solon nmercally, we hae o se a dscrezaon mehod whch appromaes he dfferenal eqaons by a sysem of algebrac eqaons, whch can hen be soled on he comper. - Ferzger and Perc (00) Compaonal Technqes for Fld Dynamcs, 3 rd Edon, Sprnger. Compaonal fld dynamcs, hen, s a separae dscplne, dsnc from and spplemenng boh epermenal and heorecal fld dynamcs, wh s own echnqes, s own dffcles, and s own realm of ly, offerng new perspeces n he sdy of physcal processes. - Roach, P.J. (198) Compaonal Fld Dynamcs, Hermosa Pblshers. Naer-Sokes Eqaons Generalzed Transpor Eqaon Trblence Reynolds Aeragng Prandl mng lengh model k-epslon model Large Eddy Smlaon Dscrezaon Fne Dfference Fne Elemen Fne Volme Grdless Mehods 7

8 11/11/017 Solon echnqes Vorcy / sream fncon mehod SIMPLE algorhm sng 3D ranspor models for solds ranspor Volme of Fld Mehod for open waer srface modellng sng 3D ranspor for boknecs Ml-phase models for waer and ar Drf fl model for sedmenaon Wcklen e al. (016) Good modellng pracce n applyng compaonal fld dynamcs for WWTP modellng, WST, 73 (5)

9 11/11/017 Wcklen e al. (016) Wcklen e al. (016) 9

10 11/11/017 Wcklen e al. (016) Wcklen e al. (016) 10

11 11/11/017 Hand Coded Forran C++ Commercal plaforms (Eamples) ANSYS (Flen and CFX) Cd-adapco (STAR-CCM+ and STAR-CD) FLOW Scence (FLOW-3D) COMSOL Mlphyscs CHAM (PHOENICS) Open sorce plaforms OpenFOAM 11

12 11/11/017 1

13 11/11/017 Wha can be done wh CFD? Wasewaer Treamen Eamples Samsag e al. (016) CFD for Wasewaer: An Oerew, Waer Scence and Technology, 74 (3),

14 11/11/017 Parshall Flme (Day 1) Spler Bo (Day 1) Mng Tank (Day ) Clarfer (Day ) V Dsnfecon (Day ) 14

15 11/11/017 Opmze ank geomery Ealaon of he mpacs of reacor geomery on performance Ealaon of locaon for conrol sensors Improe flow and solds splng n dsrbon channels Ealae he mpacs of mng on performance Verfy smpler models Improe basc ndersandng of process behaor 15

16 11/11/017 Web: hp://rsamsag.com/ Phone: +1 (06) Emal: 16

17 11/11/ CFD Soles he Naer-Sokes Eqaons by nmercal schemes. Conny Eqaon: Law of Mass Conseraon Momenm Eqaons: Newon s Second Law (ncompressble lamnar flow) 0 F P 1 r r r g P ) ( 1 nseady Term Adece Term Pressre Term Dffson Term Sorce Term (gray force)

18 11/11/017 S nseady Adecon Dffson Sorce Wha abo rblence? One way o model s o se he Reynolds Aeraged Naer-Sokes Eqaons (RANS). All flow n WRRF s rblen. Trblen flow s arable n space and me Osborne Reynolds sggesed ha rblen flow cold be consdered as a compose of an aerage par and a flcang par. See Henze, J. O. (1975) Trblence, nd Ed, McGraw-Hll. 18

19 11/11/ r r g P 1 S Rod (1980) Trblence Models and Ther Applcaon n Hydralcs: A sae-of-he ar reew, IAHR / AIRH. Rod (1980) Trblence Models and Ther Applcaon n Hydralcs: A sae-of-he ar reew, IAHR / AIRH.

20 11/11/017 0 Smples model: Prandl s Mng Lengh Hypohess (Plane mng layer, wdh δ) Two Eqaon Models: k epslon y l m G P k g k k k S k C R c G P k C f ) ( k C 0.07 l m Rod (1980) Trblence Models and Ther Applcaon n Hydralcs: A sae-of-he ar reew, IAHR / AIRH. RANS Smlaon (Seady Sae) LES Smlaon (Transen)

21 11/11/017 Fne dfference Mehod of weghed resdals (fne elemen) Fne olme formlaon Grd-less mehods All of hese hae been sed n CFD for wasewaer. Fne dfference was he frs echnqe sed. Fne elemen has been sed for clarfer modelng. Fne olme formlaon s he mos common commercal CFD sofware approach. Grd-less mehods hae no been mch sed, b may be promsng. Horzonal Momenm Eqn. ( ) y p y g Fne Dfference Eqalen n 1 n 1 /, 1 /,, 1, ( 1 /, 1 / )( 1 /, 1 / ) ( 1 /, 1 / )( 1 /, 1 / ) y p, p 1, 1-3 /, 1-1 /, 3 /, 1 /, 1 1 /, 1 Harlow, F.H. and Welch, J. E. (1965) Nmercal Calclaon of Tme-Dependen Vscos Incompressble Flow of Fld wh Free Srface, Physcs of Flds, V. 8 Nmber 1. y 1 /, g 1

22 11/11/017 Inerpolae he elocy and pressre felds p l l, n l l, n p p l l, n l l l Sbse nerpolaons no he goernng eqaons. Conny X/Y momenm Sole he sysem of eqaons eraely Flecher, C.A.J (006) Compaonal Technqes for Fld Dynamcs, Volme II, nd Ed. Sprnger-Verlag.,k,k+1-1,k p,k,k -1,k+1 p,k+1,k+1,k Conny Eqn.,,k-1 +1, k+1 V-1,k -1,k,k p,k,k +1,k -1,k p,k,k p+1,k +1,k V,k-1 y Momenm Eqn. +1,k,k-1 Momenm Eqn. +1,k-1 Paankar, S. V. (1980) Nmercal Hea Transfer and Fld Flow, Hemsphere Pblshng.

23 11/11/017 Vore Mehods Deeloped by Chorn Random walk of ore blobs SPH Lagrangan mehod deeloped from asrophyscs PEREIRA, L. A. A.; HIRATA, M. H. and SILVEIRA NETO, A.. Vore mehod wh rblence sb-grd scale modellng. J. Braz. Soc. Mech. Sc. & Eng. [onlne]. 003, ol.5, n. [ced ], pp Transform he goernng eqaons: Vorcy / sream fncon mehod se eraon and conergence SIMPLE Boh of hese mehods hae been sed n CFD for wasewaer. 3

24 11/11/017 4 y Defnon of Vorcy y Vorcy Transpor Eqn. Defnon of Sream Fncon y Posson Eqn. for Sream Fncon Roach, P.J. (198) Compaonal Fld Dynamcs, Hermosa Pblshers. 0 Re 1 ) ( ) ( y y Gess he pressre feld Sole he momenm eqaons Sole pressre correcon Calclae eloces Sole for oher properes (emperare, solds) pdae he pressre feld and erae o conergence Paankar, S. V., (1980) Nmercal Hea Transfer and Fld Flow.

25 11/11/ D ranspor models can be copled o he elocy calclaons o smlae sedmenaon and mng. Solds Transpor Veslnd selng Densy cople kc o s e V V s w w c 1 k s s C V C C C Samsag, e al. (199) Conny Eqaon: Fld Marker Eqaon: Momenm Eqaons: 1 1 y y p y y p y 0 y F F F F=1 f fld s presen F=0 f fld s no presen Hr and Nchols (1981), Volme of Fld Mehod, Los Alamos Scenfc Laboraory, Los Alamos, NM. 0 y

26 11/11/017 An elemenary oral n OpenFOAM s based on VOF mehod sng he nerfoam soler. The famos dam break problem was smlaed frs sng he MAC mehod by Harlow and Welsh. Ths smlaon sng a RANS rblence approach. 3D ranspor models can be mplemened for wasewaer qaly parameers as well. Boknec Models ASM Models Adanced odaon Models Dsnfecon models Sobremsana, Dcose and de los Reyes III (011) 6

27 11/11/ ) ( d d 0 ) ( c c d V d d d T p, ) ( ) ( ) ( c V c c c T p, ) ( ) ( ) ( Crowe, Sommerfeld, and Ts (1998) Mlphase Flows wh Droples and Parcles. Mre Conny Eqaon Drf Eqaon Mre Momenm Eqaon Brennan, D. (001) The Nmercal Smlaon of Two-Phase Flows n Selng Tanks, PhD Dsseraon, nersy of London.

28 11/11/017 Ferzger, J.H. and Perc, M. (00) Compaonal Technqes for Fld Dynamcs, 3 rd Edon, Sprnger. Roach, P.J. (198) Compaonal Fld Dynamcs, Hermosa Pblshers. r and Nchols (1981), Volme of Fld Mehod, Los Alamos Scenfc Laboraory, Los Alamos, NM. Henze, J.O. (1975) Trblence, nd Ed, McGraw-Hll Rod (1980) Trblence Models and Ther Applcaon n Hydralcs: A sae-of-he ar reew, IAHR / AIRH. Harlow, F.H. and Welch, J.E. (1965) Nmercal Calclaon of Tme-Dependen Vscos Incompressble Flow of Fld wh Free Srface, Physcs of Flds, V. 8 Nmber 1. Fnlayson, B. (1980) Nonlnear Analyss n Chemcal Engneerng, McGraw-Hll. Paankar, S. V. (1980) Nmercal Hea Transfer and Fld Flow, Hemsphere Pblshng. Chorn, A.J. (1989) Compaonal Fld Mechancs, Academc Press. Samsag, R.W., McCorqodale, J.A. and Zho, S.P. (199) Prospecs for ranspor modelng of process anks, Waer Scence and Technology. 6 (5/6), Hr and Nchols (1981), Volme of Fld Mehod, Los Alamos Scenfc Laboraory, Los Alamos, NM. Sobremsana, Dcose, and de los Reyes III 011 Combnng CFD, floc dynamcs, and bologcal reacon knecs o model carbon and nrogen remoal n an acaed sldge sysem. Waer Enronmen Conference, WEFTEC Conference. Crowe, Sommerfeld, and Ts (1998) Mlphase Flows wh Droples and Parcles. Wcklen, E., Basone, D.J., Dcose, J., Laren, J., Grboro, A., Wcks, J., Sanders, S., Samsag, R., Poer, O. and Nopens, I. 016 Good modellng pracce n applyng compaonal fld dynamcs for WWTP modellng. Waer Scence and Technology. 73 (5) R. W. Samsag, J. J. Dcose, A. Grboro, I. Nopens, D. J. Basone, J. D. Wcks, S. Sanders, E. A. Wcklen, G. Kenny and J. Laren (016) CFD for Wasewaer: An Oerew, Waer Scence and Technology, 74 (3),

11/11/2017. Randal W. Samstag, MS, PE, BCEE Civil and Sanitary Engineer Bainbridge Island, WA US

11/11/2017. Randal W. Samstag, MS, PE, BCEE Civil and Sanitary Engineer Bainbridge Island, WA US //07 Randal W. Samsag MS PE BCEE Cl and Sanar Engneer Banbrdge Island WA S To gan some ndersandng of how compaonal fld dnamcs (CFD can help s o beer ndersand waer resorce recoer facles sng an open sorce

More information

OPTIMIZATION OF A NONCONVENTIONAL ENGINE EVAPORATOR

OPTIMIZATION OF A NONCONVENTIONAL ENGINE EVAPORATOR Jornal of KONES Powerran and Transpor, Vol. 17, No. 010 OPTIMIZATION OF A NONCONVENTIONAL ENGINE EVAPORATOR Andre Kovalí, Eml Toporcer Unversy of Žlna, Facly of Mechancal Engneerng Deparmen of Aomove Technology

More information

Calculation of the Resistance of a Ship Mathematical Formulation. Calculation of the Resistance of a Ship Mathematical Formulation

Calculation of the Resistance of a Ship Mathematical Formulation. Calculation of the Resistance of a Ship Mathematical Formulation Ressance s obaned from he sm of he frcon and pressre ressance arables o deermne: - eloc ecor, (3) = (,, ) = (,, ) - Pressre, p () ( - Dens, ρ, s defned b he eqaon of sae Ressance and Proplson Lecre 0 4

More information

Cartesian tensors. Order (rank) Scalar. Vector. 3x3 matrix

Cartesian tensors. Order (rank) Scalar. Vector. 3x3 matrix Caresan ensors Order (rank) 0 1 3 a b c d k Scalar ecor 33 mar Caresan ensors Kronecker dela δ = 1 f = 0 f Le- Ca epslon ε k = 1 f,, k are cclc 1 f,, k are ancclc 0 oherse Smmaon conenon (o eqal ncces

More information

Outline. Review Solution Approaches. Review Basic Equations. Nature of Turbulence. Review Fluent Exercise. Turbulence Models

Outline. Review Solution Approaches. Review Basic Equations. Nature of Turbulence. Review Fluent Exercise. Turbulence Models Trblence Models Larry areo Mechancal Engneerng 69 ompaonal Fld Dynamcs Febrary, Olne Revew las lecre Nare of rblence Reynolds-average Naver-Soes (RNS) Mng lengh heory Models sng one dfferenal eqaon Two-eqaon

More information

Numerical simulation of flow reattachment length in a stilling basin with a step-down floor

Numerical simulation of flow reattachment length in a stilling basin with a step-down floor 5 h Inernaonal Symposm on Hydralc Srcres Brsbane, Asrala, 5-7 Jne 04 Hydralc Srcres and Socey: Engneerng hallenges and Eremes ISBN 97874756 - DOI: 0.464/ql.04.3 Nmercal smlaon of flow reaachmen lengh n

More information

VI. Computational Fluid Dynamics 1. Examples of numerical simulation

VI. Computational Fluid Dynamics 1. Examples of numerical simulation VI. Comaonal Fld Dnamcs 1. Eamles of nmercal smlaon Eermenal Fas Breeder Reacor, JOYO, wh rmar of coolan sodm. Uer nner srcre Uer lenm Flow aern and emerare feld n reacor essel n flow coas down Core Hh

More information

Prediction of Wing Downwash Using CFD

Prediction of Wing Downwash Using CFD Predcon of Wng Downwash Usng CFD Mohammed MAHDI* *Correspondng ahor Aeronacal Research Cener-Sdan P.O. Bo 334 momahad7@homal.com DOI:.3/66-8.5.7.. 3 rd Inernaonal Worshop on Nmercal Modellng n Aerospace

More information

Block 5 Transport of solutes in rivers

Block 5 Transport of solutes in rivers Nmeral Hydrals Blok 5 Transpor of soles n rvers Marks Holzner Conens of he orse Blok 1 The eqaons Blok Compaon of pressre srges Blok 3 Open hannel flow flow n rvers Blok 4 Nmeral solon of open hannel flow

More information

Observer Design for Nonlinear Systems using Linear Approximations

Observer Design for Nonlinear Systems using Linear Approximations Observer Desgn for Nonlnear Ssems sng Lnear Appromaons C. Navarro Hernandez, S.P. Banks and M. Aldeen Deparmen of Aomac Conrol and Ssems Engneerng, Unvers of Sheffeld, Mappn Sree, Sheffeld S 3JD. e-mal:

More information

CONSISTENT EARTHQUAKE ACCELERATION AND DISPLACEMENT RECORDS

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

More information

CFD for Wastewater: What Can it Do?

CFD for Wastewater: What Can it Do? CFD for Wastewater: What Can t Do? Presentaton to the Department of Cvl and Envronmental Engneerng Unversty of Washngton 7 Aprl 2016 Randal W. Samstag, MS, PE, BCEE Cvl and Santary Engneer Banbrdge Island,

More information

Improvement of Two-Equation Turbulence Model with Anisotropic Eddy-Viscosity for Hybrid Rocket Research

Improvement of Two-Equation Turbulence Model with Anisotropic Eddy-Viscosity for Hybrid Rocket Research evenh Inernaonal onference on ompaonal Fld Dynamcs (IFD7), Bg Island, awa, Jly 9-, IFD7-9 Improvemen of Two-Eqaon Trblence Model wh Ansoropc Eddy-Vscosy for ybrd oce esearch M. Mro * and T. hmada ** orrespondng

More information

by Lauren DeDieu Advisor: George Chen

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

More information

Turbulence Modelling (CFD course)

Turbulence Modelling (CFD course) Trblence Modellng (CFD corse) Sławomr Kbac slawomr.bac@mel.pw.ed.pl 14.11.016 Copyrgh 016, Sławomr Kbac Trblence Modellng Sławomr Kbac Conens 1. Reynolds-averaged Naver-Soes eqaons... 3. Closre of he modelled

More information

Chapter 1 Introduction of boundary layer phenomena

Chapter 1 Introduction of boundary layer phenomena Chaper 1 Inrodcon of bondary layer phenomena T-S Le Jan. 13, 018 Man Topcs Hsory of Fld Mechancs Developmen Idea of Bondary Layer Bondary Layer Eqaons 1 Fld Mechancs Developmen Hsory Ideal fld: Invscd

More information

CFD MODELING FOR HELIUM RELEASES IN A PRIVATE GARAGE WITHOUT FORCED VENTILATION

CFD MODELING FOR HELIUM RELEASES IN A PRIVATE GARAGE WITHOUT FORCED VENTILATION CFD MODELING FOR HELIUM RELEASES IN A PRIVATE GARAGE WITHOUT FORCED VENTILATION Papankolao, E.A. 1 and Venesanos, A.G. 1 1 Envronmenal Research Laboraory, NCSR Demokros, Agha Paraskev, Aks, 15310, Greece,

More information

Solution of a diffusion problem in a non-homogeneous flow and diffusion field by the integral representation method (IRM)

Solution of a diffusion problem in a non-homogeneous flow and diffusion field by the integral representation method (IRM) Appled and ompaonal Mahemacs 4; 3: 5-6 Pblshed onlne Febrary 4 hp://www.scencepblshnggrop.com//acm do:.648/.acm.43.3 olon of a dffson problem n a non-homogeneos flow and dffson feld by he negral represenaon

More information

SMS-618, Particle Dynamics, Fall 2003 (E. Boss, last updated: 10/8/2003) Conservation equations in fluids

SMS-618, Particle Dynamics, Fall 2003 (E. Boss, last updated: 10/8/2003) Conservation equations in fluids SMS-68 Parcle Dnamcs Fall 3 (E. Boss las daed: /8/3) onseraon eqaons n flds onces e need: ensor (Sress) ecors (e.g. oson eloc) and scalars (e.g. S O). Prode means o descrbe conseraon las h comac noaon

More information

Stochastic Programming handling CVAR in objective and constraint

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

More information

Dynamic Model of the Axially Moving Viscoelastic Belt System with Tensioner Pulley Yanqi Liu1, a, Hongyu Wang2, b, Dongxing Cao3, c, Xiaoling Gai1, d

Dynamic Model of the Axially Moving Viscoelastic Belt System with Tensioner Pulley Yanqi Liu1, a, Hongyu Wang2, b, Dongxing Cao3, c, Xiaoling Gai1, d Inernaonal Indsral Informacs and Comper Engneerng Conference (IIICEC 5) Dynamc Model of he Aally Movng Vscoelasc Bel Sysem wh Tensoner Plley Yanq L, a, Hongy Wang, b, Dongng Cao, c, Xaolng Ga, d Bejng

More information

[ ] 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 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

More information

, t 1. Transitions - this one was easy, but in general the hardest part is choosing the which variables are state and control variables

, 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

More information

Ordinary Differential Equations in Neuroscience with Matlab examples. Aim 1- Gain understanding of how to set up and solve ODE s

Ordinary Differential Equations in Neuroscience with Matlab examples. Aim 1- Gain understanding of how to set up and solve ODE s Ordnary Dfferenal Equaons n Neuroscence wh Malab eamples. Am - Gan undersandng of how o se up and solve ODE s Am Undersand how o se up an solve a smple eample of he Hebb rule n D Our goal a end of class

More information

Modelling of Diffusion Process in Porous Bricks

Modelling of Diffusion Process in Porous Bricks hp://www.aras.org/aras/ornals/mcm Modellng of Dffson Process n Poros Brcs KRNIATI ORNAM, MASYKR KIMSAN, LA ODE NGKOIMANI 3, EDI CAHYONO 4 Deparmen of Archecre, Hal Oleo nversy, Jl.H.E.A Moodomp Kamps Ha

More information

Separated Turbulent Flow Simulations Using a Reynolds Stress Model and Unstructured Meshes

Separated Turbulent Flow Simulations Using a Reynolds Stress Model and Unstructured Meshes AIAA-5-194 AIAA 43rd Aerospace Scences Meeng & Exhb Reno, NV, Janary, 5 Separaed rblen Flo Smlaons Usng a Reynolds Sress Model and Unsrcred Meshes Emre Alpman and Lyle N. Long Deparmen of Aerospace Engneerng

More information

HEAT CONDUCTION PROBLEM IN A TWO-LAYERED HOLLOW CYLINDER BY USING THE GREEN S FUNCTION METHOD

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,

More information

A NEW TECHNIQUE FOR SOLVING THE 1-D BURGERS EQUATION

A NEW TECHNIQUE FOR SOLVING THE 1-D BURGERS EQUATION S19 A NEW TECHNIQUE FOR SOLVING THE 1-D BURGERS EQUATION by Xaojun YANG a,b, Yugu YANG a*, Carlo CATTANI c, and Mngzheng ZHU b a Sae Key Laboraory for Geomechancs and Deep Underground Engneerng, Chna Unversy

More information

Cubic Bezier Homotopy Function for Solving Exponential Equations

Cubic Bezier Homotopy Function for Solving Exponential Equations Penerb Journal of Advanced Research n Compung and Applcaons ISSN (onlne: 46-97 Vol. 4, No.. Pages -8, 6 omoopy Funcon for Solvng Eponenal Equaons S. S. Raml *,,. Mohamad Nor,a, N. S. Saharzan,b and M.

More information

Robustness Experiments with Two Variance Components

Robustness Experiments with Two Variance Components Naonal Insue of Sandards and Technology (NIST) Informaon Technology Laboraory (ITL) Sascal Engneerng Dvson (SED) Robusness Expermens wh Two Varance Componens by Ana Ivelsse Avlés avles@ns.gov Conference

More information

Approximate Analytic Solution of (2+1) - Dimensional Zakharov-Kuznetsov(Zk) Equations Using Homotopy

Approximate Analytic Solution of (2+1) - Dimensional Zakharov-Kuznetsov(Zk) Equations Using Homotopy Arcle Inernaonal Journal of Modern Mahemacal Scences, 4, (): - Inernaonal Journal of Modern Mahemacal Scences Journal homepage: www.modernscenfcpress.com/journals/jmms.aspx ISSN: 66-86X Florda, USA Approxmae

More information

FAIPA_SAND: An Interior Point Algorithm for Simultaneous ANalysis and Design Optimization

FAIPA_SAND: An Interior Point Algorithm for Simultaneous ANalysis and Design Optimization FAIPA_AN: An Ineror Pon Algorhm for mlaneos ANalyss an esgn Opmzaon osé Hersos*, Palo Mappa* an onel llen** *COPPE / Feeral Unersy of Ro e anero, Mechancal Engneerng Program, Caa Posal 6853, 945 97 Ro

More information

Numerical Simulation on Wind Flow over Step-shaped Cliff Topography with Rough Surface

Numerical Simulation on Wind Flow over Step-shaped Cliff Topography with Rough Surface In. J. Envron. Res., 7(1):173-186, Wner 013 ISSN: 1735-6865 Nmercal Smlaon on Wnd Flow over Sep-shaped Clff Topography wh Rogh Srface Yassn, M.F. 1,* and Al-Harb, M. 1 1 Deparmen of Envronmenal Technology

More information

The Elastic Wave Equation. The elastic wave equation

The Elastic Wave Equation. The elastic wave equation The Elasc Wave Eqaon Elasc waves n nfne homogeneos soropc meda Nmercal smlaons for smple sorces Plane wave propagaon n nfne meda Freqency, wavenmber, wavelengh Condons a maeral dsconnes nell s Law Reflecon

More information

Research Article Cubic B-spline for the Numerical Solution of Parabolic Integro-differential Equation with a Weakly Singular Kernel

Research Article Cubic B-spline for the Numerical Solution of Parabolic Integro-differential Equation with a Weakly Singular Kernel Researc Jornal of Appled Scences, Engneerng and Tecnology 7(): 65-7, 4 DOI:.96/afs.7.5 ISS: 4-7459; e-iss: 4-7467 4 Mawell Scenfc Pblcaon Corp. Sbmed: Jne 8, Acceped: Jly 9, Pblsed: Marc 5, 4 Researc Arcle

More information

National Exams December 2015 NOTES: 04-BS-13, Biology. 3 hours duration

National Exams December 2015 NOTES: 04-BS-13, Biology. 3 hours duration Naonal Exams December 205 04-BS-3 Bology 3 hours duraon NOTES: f doub exss as o he nerpreaon of any queson he canddae s urged o subm wh he answer paper a clear saemen of any assumpons made 2 Ths s a CLOSED

More information

Real-Time Trajectory Generation and Tracking for Cooperative Control Systems

Real-Time Trajectory Generation and Tracking for Cooperative Control Systems Real-Tme Trajecor Generaon and Trackng for Cooperave Conrol Ssems Rchard Mrra Jason Hcke Calforna Inse of Technolog MURI Kckoff Meeng 14 Ma 2001 Olne I. Revew of prevos work n rajecor generaon and rackng

More information

Background and Motivation: Importance of Pressure Measurements

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

More information

TSS = SST + SSE An orthogonal partition of the total SS

TSS = SST + SSE An orthogonal partition of the total SS ANOVA: Topc 4. Orhogonal conrass [ST&D p. 183] H 0 : µ 1 = µ =... = µ H 1 : The mean of a leas one reamen group s dfferen To es hs hypohess, a basc ANOVA allocaes he varaon among reamen means (SST) equally

More information

ON THE ACCURACY OF NUMERICAL PREDICTION IN TRANSONIC-SUPERSONIC FLOW ARROUND MISSILES

ON THE ACCURACY OF NUMERICAL PREDICTION IN TRANSONIC-SUPERSONIC FLOW ARROUND MISSILES U.P.B. Sc. Bll., Seres D, Vol. 7, Iss. 3, ISSN 454-358 ON THE ACCURACY OF NUMERICAL PREDICTION IN TRANSONIC-SUPERSONIC FLOW ARROUND MISSILES Crsna MIHAILESCU, Teodor Vorel CHELARU, Seran DANAILA 3, Cornel

More information

Introduction to. Computer Animation

Introduction to. Computer Animation Inroducon o 1 Movaon Anmaon from anma (la.) = soul, spr, breah of lfe Brng mages o lfe! Examples Characer anmaon (humans, anmals) Secondary moon (har, cloh) Physcal world (rgd bodes, waer, fre) 2 2 Anmaon

More information

XIII International PhD Workshop OWD 2011, October Three Phase DC/DC Boost Converter With High Energy Efficiency

XIII International PhD Workshop OWD 2011, October Three Phase DC/DC Boost Converter With High Energy Efficiency X nernaonal Ph Workshop OW, Ocober Three Phase C/C Boos Converer Wh Hgh Energy Effcency Ján Perdľak, Techncal nversy of Košce Absrac Ths paper presens a novel opology of mlphase boos converer wh hgh energy

More information

2.1 Constitutive Theory

2.1 Constitutive Theory Secon.. Consuve Theory.. Consuve Equaons Governng Equaons The equaons governng he behavour of maerals are (n he spaal form) dρ v & ρ + ρdv v = + ρ = Conservaon of Mass (..a) d x σ j dv dvσ + b = ρ v& +

More information

2/20/2013. EE 101 Midterm 2 Review

2/20/2013. EE 101 Midterm 2 Review //3 EE Mderm eew //3 Volage-mplfer Model The npu ressance s he equalen ressance see when lookng no he npu ermnals of he amplfer. o s he oupu ressance. I causes he oupu olage o decrease as he load ressance

More information

CFD-aided modelling for hydrodynamic analysis of biological reactor

CFD-aided modelling for hydrodynamic analysis of biological reactor European Waer 58: 47-51, 017. 017 E.W. Publcaons FD-aded modellng for hydrodynamc analyss of bologcal reacor S. Manen *, S. odeschn, M.. ollgnarell and A. Abbà Dparmeno d Ingegnera le e Archeura, Unersà

More information

Mechanics Physics 151

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

More information

Solving Parabolic Partial Delay Differential. Equations Using The Explicit Method And Higher. Order Differences

Solving Parabolic Partial Delay Differential. Equations Using The Explicit Method And Higher. Order Differences Jornal of Kfa for Maemacs and Compe Vol. No.7 Dec pp 77-5 Solvng Parabolc Paral Delay Dfferenal Eqaons Usng e Eplc Meod And Hger Order Dfferences Asss. Prof. Amal Kalaf Haydar Kfa Unversy College of Edcaon

More information

Multi-Fuel and Mixed-Mode IC Engine Combustion Simulation with a Detailed Chemistry Based Progress Variable Library Approach

Multi-Fuel and Mixed-Mode IC Engine Combustion Simulation with a Detailed Chemistry Based Progress Variable Library Approach Mul-Fuel and Med-Mode IC Engne Combuson Smulaon wh a Dealed Chemsry Based Progress Varable Lbrary Approach Conens Inroducon Approach Resuls Conclusons 2 Inroducon New Combuson Model- PVM-MF New Legslaons

More information

CFD Analysis of Aerodynamic Drag Effects on Vacuum Tube Trains

CFD Analysis of Aerodynamic Drag Effects on Vacuum Tube Trains Jornal of Appled Fld Mechancs, ol. 1, No. 1, pp. 303-309, 019. Aalable onlne a.afmonlne.ne, ISSN 1735-357, EISSN 1735-3645. DOI: 10.95/afm.75.53.9091 CFD Analss of Aerodnamc Drag Effecs on acm Tbe Trans

More information

Modelling of test case particle-laden jet with NEPTUNE_CFD

Modelling of test case particle-laden jet with NEPTUNE_CFD Modelln of es case arcle-laden e wh NEPTNE_CFD H. D. Le 1 J-M. Lacome 1 A. Vnes 1 B. Debray 1 B. Trcho 1 P. Fede 3 E. Clmen 3 1 INERIS Parc echnoloe ALATA B.P. FR-60550 Vernel-en-Halae nversé de Tolose

More information

Comparison between two solar tower receivers of different geometry

Comparison between two solar tower receivers of different geometry Reve des Energes Renovelables Vol. 20 N 4 (2017) 713-720 Comparson beween wo solar ower recevers of dfferen geomery M. Hazmone 1.2 *, B. Aor 2, M.M. Hada 1 and A. Male 1 1 Cenre de Développemen des Energes

More information

3.2 Models for technical systems

3.2 Models for technical systems onrol Laboraory 3. Mahemacal Moelng 3. Moels for echncal sysems 3.. Elecrcal sysems Fg. 3. shows hree basc componens of elecrcal crcs. Varables = me, = volage [V], = crren [A] omponen parameers R = ressance

More information

ABSTRACT. Keywords: Finite Element, Active Optics, Adaptive Optics, WaveFront Error, System Analysis, Optomechanical 1.

ABSTRACT. Keywords: Finite Element, Active Optics, Adaptive Optics, WaveFront Error, System Analysis, Optomechanical 1. Analyss echne or conrollng Sysem Waveron Error wh Acve/Adapve Opcs Vcor L. Genberg*, Gregory J. Mchels Sgmadyne, 83 Wes Ave, ocheser, NY 14611 *genberg@sgmadyne.com (585)35-746 ABSTACT The lmae goal o

More information

Reconstruction of Variational Iterative Method for Solving Fifth Order Caudrey-Dodd-Gibbon (CDG) Equation

Reconstruction of Variational Iterative Method for Solving Fifth Order Caudrey-Dodd-Gibbon (CDG) Equation Shraz Unvery of Technology From he SelecedWor of Habbolla Lafzadeh Reconrcon of Varaonal Ierave Mehod for Solvng Ffh Order Cadrey-Dodd-Gbbon (CDG Eqaon Habbolla Lafzadeh, Shraz Unvery of Technology Avalable

More information

P R = P 0. The system is shown on the next figure:

P R = P 0. The system is shown on the next figure: TPG460 Reservor Smulaon 08 page of INTRODUCTION TO RESERVOIR SIMULATION Analycal and numercal soluons of smple one-dmensonal, one-phase flow equaons As an nroducon o reservor smulaon, we wll revew he smples

More information

Real Time Hybrid Simulation using Shaking Tabels

Real Time Hybrid Simulation using Shaking Tabels Real Tme Hybrd Smlaon sng Shakng Tabels Deparmen o Cvl and Envronmenal Engneerng Unversy o Kassel, Germany Olne Inrodcon A ndamenal sbsrcre algorhm wh sb seppng Applcaons o he algorhm Conclsons Inrodcon

More information

Wronskian Determinant Solutions for the (3 + 1)-Dimensional Boiti-Leon-Manna-Pempinelli Equation

Wronskian Determinant Solutions for the (3 + 1)-Dimensional Boiti-Leon-Manna-Pempinelli Equation Jornal of Appled Mahemacs and Physcs 0 8-4 Pblshed Onlne ovember 0 (hp://www.scrp.org/jornal/jamp) hp://d.do.org/0.46/jamp.0.5004 Wronskan Deermnan Solons for he ( + )-Dmensonal Bo-Leon-Manna-Pempnell

More information

GENERATING CERTAIN QUINTIC IRREDUCIBLE POLYNOMIALS OVER FINITE FIELDS. Youngwoo Ahn and Kitae Kim

GENERATING CERTAIN QUINTIC IRREDUCIBLE POLYNOMIALS OVER FINITE FIELDS. Youngwoo Ahn and Kitae Kim Korean J. Mah. 19 (2011), No. 3, pp. 263 272 GENERATING CERTAIN QUINTIC IRREDUCIBLE POLYNOMIALS OVER FINITE FIELDS Youngwoo Ahn and Kae Km Absrac. In he paper [1], an explc correspondence beween ceran

More information

THE PREDICTION OF COMPETITIVE ENVIRONMENT IN BUSINESS

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

More information

A comparison of Lagrangian dispersion models coupled to a meteorological model for high stack air pollution forecast

A comparison of Lagrangian dispersion models coupled to a meteorological model for high stack air pollution forecast Ar Pollon X C.A. Brebba J.F. Marín-Dqe eds. WIT Press A comparson of Lagrangan dsperson models copled o a meeorologcal model for hgh sack ar pollon forecas E. Penabad V. Pere-Mñr J.A. Soo J.J. Casares

More information

Dual Approximate Dynamic Programming for Large Scale Hydro Valleys

Dual Approximate Dynamic Programming for Large Scale Hydro Valleys Dual Approxmae Dynamc Programmng for Large Scale Hydro Valleys Perre Carpener and Jean-Phlppe Chanceler 1 ENSTA ParsTech and ENPC ParsTech CMM Workshop, January 2016 1 Jon work wh J.-C. Alas, suppored

More information

Chapter Lagrangian Interpolation

Chapter Lagrangian Interpolation Chaper 5.4 agrangan Inerpolaon Afer readng hs chaper you should be able o:. dere agrangan mehod of nerpolaon. sole problems usng agrangan mehod of nerpolaon and. use agrangan nerpolans o fnd deraes and

More information

Mechanics Physics 151

Mechanics 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 information

Mechanics Physics 151

Mechanics 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 information

In the complete model, these slopes are ANALYSIS OF VARIANCE FOR THE COMPLETE TWO-WAY MODEL. (! i+1 -! i ) + [(!") i+1,q - [(!

In the complete model, these slopes are ANALYSIS OF VARIANCE FOR THE COMPLETE TWO-WAY MODEL. (! i+1 -! i ) + [(!) i+1,q - [(! ANALYSIS OF VARIANCE FOR THE COMPLETE TWO-WAY MODEL The frs hng o es n wo-way ANOVA: Is here neracon? "No neracon" means: The man effecs model would f. Ths n urn means: In he neracon plo (wh A on he horzonal

More information

Chapters 2 Kinematics. Position, Distance, Displacement

Chapters 2 Kinematics. Position, Distance, Displacement Chapers Knemacs Poson, Dsance, Dsplacemen Mechancs: Knemacs and Dynamcs. Knemacs deals wh moon, bu s no concerned wh he cause o moon. Dynamcs deals wh he relaonshp beween orce and moon. The word dsplacemen

More information

Displacement, Velocity, and Acceleration. (WHERE and WHEN?)

Displacement, Velocity, and Acceleration. (WHERE and WHEN?) Dsplacemen, Velocy, and Acceleraon (WHERE and WHEN?) Mah resources Append A n your book! Symbols and meanng Algebra Geomery (olumes, ec.) Trgonomery Append A Logarhms Remnder You wll do well n hs class

More information

Content. What is CFD Why CFD Application of CFD CFD for oil & gas CFD analysis process Related software Issue related with software selection

Content. What is CFD Why CFD Application of CFD CFD for oil & gas CFD analysis process Related software Issue related with software selection Content What s CFD Why CFD Applcaton of CFD CFD for ol & gas CFD analyss process Related software Isse related wth software selecton Pre-processng Solver Post-processng Typcal CFD problem Grd Independence

More information

CS286.2 Lecture 14: Quantum de Finetti Theorems II

CS286.2 Lecture 14: Quantum de Finetti Theorems II CS286.2 Lecure 14: Quanum de Fne Theorems II Scrbe: Mara Okounkova 1 Saemen of he heorem Recall he las saemen of he quanum de Fne heorem from he prevous lecure. Theorem 1 Quanum de Fne). Le ρ Dens C 2

More information

Computational results on new staff scheduling benchmark instances

Computational results on new staff scheduling benchmark instances TECHNICAL REPORT Compuaonal resuls on new saff shedulng enhmark nsanes Tm Curos Rong Qu ASAP Researh Group Shool of Compuer Sene Unersy of Nongham NG8 1BB Nongham UK Frs pulshed onlne: 19-Sep-2014 las

More information

Significance of buoyancy in turbulence closure for computational fluid dynamics modelling of ultraviolet disinfection in maturation ponds

Significance of buoyancy in turbulence closure for computational fluid dynamics modelling of ultraviolet disinfection in maturation ponds IWA Plshng 2018. The defnve peer-revewed and eded verson of hs arcle s plshed n Waer, Scence & Technology, Volme 77, Isse 3, DOI: 10.2166/ws.2018.012 and s avalale a www.waplshng.com Sgnfcance of oyancy

More information

SOME NOISELESS CODING THEOREMS OF INACCURACY MEASURE OF ORDER α AND TYPE β

SOME NOISELESS CODING THEOREMS OF INACCURACY MEASURE OF ORDER α AND TYPE β SARAJEVO JOURNAL OF MATHEMATICS Vol.3 (15) (2007), 137 143 SOME NOISELESS CODING THEOREMS OF INACCURACY MEASURE OF ORDER α AND TYPE β M. A. K. BAIG AND RAYEES AHMAD DAR Absrac. In hs paper, we propose

More information

( ) () we define the interaction representation by the unitary transformation () = ()

( ) () we define the interaction representation by the unitary transformation () = () Hgher Order Perurbaon Theory Mchael Fowler 3/7/6 The neracon Represenaon Recall ha n he frs par of hs course sequence, we dscussed he chrödnger and Hesenberg represenaons of quanum mechancs here n he chrödnger

More information

Variants of Pegasos. December 11, 2009

Variants of Pegasos. December 11, 2009 Inroducon Varans of Pegasos SooWoong Ryu bshboy@sanford.edu December, 009 Youngsoo Cho yc344@sanford.edu Developng a new SVM algorhm s ongong research opc. Among many exng SVM algorhms, we wll focus on

More information

Method of Characteristics for Pure Advection By Gilberto E. Urroz, September 2004

Method of Characteristics for Pure Advection By Gilberto E. Urroz, September 2004 Mehod of Charaerss for Pre Adveon By Glbero E Urroz Sepember 004 Noe: The followng noes are based on lass noes for he lass COMPUTATIONAL HYDAULICS as agh by Dr Forres Holly n he Sprng Semeser 985 a he

More information

NATIONAL UNIVERSITY OF SINGAPORE PC5202 ADVANCED STATISTICAL MECHANICS. (Semester II: AY ) Time Allowed: 2 Hours

NATIONAL UNIVERSITY OF SINGAPORE PC5202 ADVANCED STATISTICAL MECHANICS. (Semester II: AY ) Time Allowed: 2 Hours NATONAL UNVERSTY OF SNGAPORE PC5 ADVANCED STATSTCAL MECHANCS (Semeser : AY 1-13) Tme Allowed: Hours NSTRUCTONS TO CANDDATES 1. Ths examnaon paper conans 5 quesons and comprses 4 prned pages.. Answer all

More information

Variational method to the second-order impulsive partial differential equations with inconstant coefficients (I)

Variational method to the second-order impulsive partial differential equations with inconstant coefficients (I) Avalable onlne a www.scencedrec.com Proceda Engneerng 6 ( 5 4 Inernaonal Worksho on Aomoble, Power and Energy Engneerng Varaonal mehod o he second-order mlsve aral dfferenal eqaons wh nconsan coeffcens

More information

CORRELATION. two variables may be related. SAT scores, GPA hours in therapy, self-esteem grade on homeworks, grade on exams

CORRELATION. two variables may be related. SAT scores, GPA hours in therapy, self-esteem grade on homeworks, grade on exams Inrodcion o Saisics in sychology SY 1 rofessor Greg Francis Lecre 1 correlaion Did I damage my dagher s eyes? CORRELATION wo ariables may be relaed SAT scores, GA hors in herapy, self-eseem grade on homeworks,

More information

ME 425: Aerodynamics

ME 425: Aerodynamics ME 45: Aerodnamics Dr. A.B.M. Toiqe Hasan Proessor Deparmen o Mechanical Engineering Bangladesh Uniersi o Engineering & Technolog BUET, Dhaka Lecre-7 Fndamenals so Aerodnamics oiqehasan.be.ac.bd oiqehasan@me.be.ac.bd

More information

Motion of Wavepackets in Non-Hermitian. Quantum Mechanics

Motion 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 information

ME 321: FLUID MECHANICS-I

ME 321: FLUID MECHANICS-I 8/7/18 ME 31: FLUID MECHANICS-I Dr. A.B.M. Toiqe Hasan Proessor Dearmen o Mechanical Engineering Bangladesh Uniersi o Engineering & Technolog BUET, Dhaka Lecre-13 8/7/18 Dierenial Analsis o Flid Moion

More information

CORRELATION. two variables may be related. SAT scores, GPA hours in therapy, self-esteem grade on homeworks, grade on exams

CORRELATION. two variables may be related. SAT scores, GPA hours in therapy, self-esteem grade on homeworks, grade on exams Inrodcion o Saisics in sychology SY 1 rofessor Greg Francis Lecre 1 correlaion How changes in one ariable correspond o change in anoher ariable. wo ariables may be relaed SAT scores, GA hors in herapy,

More information

Li An-Ping. Beijing , P.R.China

Li An-Ping. Beijing , P.R.China A New Type of Cpher: DICING_csb L An-Png Bejng 100085, P.R.Chna apl0001@sna.com Absrac: In hs paper, we wll propose a new ype of cpher named DICING_csb, whch s derved from our prevous sream cpher DICING.

More information

Handout # 6 (MEEN 617) Numerical Integration to Find Time Response of SDOF mechanical system Y X (2) and write EOM (1) as two first-order Eqs.

Handout # 6 (MEEN 617) Numerical Integration to Find Time Response of SDOF mechanical system Y X (2) and write EOM (1) as two first-order Eqs. Handou # 6 (MEEN 67) Numercal Inegraon o Fnd Tme Response of SDOF mechancal sysem Sae Space Mehod The EOM for a lnear sysem s M X DX K X F() () X X X X V wh nal condons, a 0 0 ; 0 Defne he followng varables,

More information

Existence and Uniqueness Results for Random Impulsive Integro-Differential Equation

Existence and Uniqueness Results for Random Impulsive Integro-Differential Equation Global Journal of Pure and Appled Mahemacs. ISSN 973-768 Volume 4, Number 6 (8), pp. 89-87 Research Inda Publcaons hp://www.rpublcaon.com Exsence and Unqueness Resuls for Random Impulsve Inegro-Dfferenal

More information

Computing Relevance, Similarity: The Vector Space Model

Computing Relevance, Similarity: The Vector Space Model Compung Relevance, Smlary: The Vecor Space Model Based on Larson and Hears s sldes a UC-Bereley hp://.sms.bereley.edu/courses/s0/f00/ aabase Managemen Sysems, R. Ramarshnan ocumen Vecors v ocumens are

More information

Dynamic Team Decision Theory. EECS 558 Project Shrutivandana Sharma and David Shuman December 10, 2005

Dynamic Team Decision Theory. EECS 558 Project Shrutivandana Sharma and David Shuman December 10, 2005 Dynamc Team Decson Theory EECS 558 Proec Shruvandana Sharma and Davd Shuman December 0, 005 Oulne Inroducon o Team Decson Theory Decomposon of he Dynamc Team Decson Problem Equvalence of Sac and Dynamc

More information

Existence of Periodic Solution for a Non-Autonomous Stage-Structured Predator-Prey System with Impulsive Effects

Existence of Periodic Solution for a Non-Autonomous Stage-Structured Predator-Prey System with Impulsive Effects Appled ahemacs 55-6 do:.6/am.. Pblshed Onlne arch (hp://www.scrp.org/jornal/am) Exsence o Perodc Solon or a Non-Aonomos Sage-Srcred Predaor-Prey Sysem wh Implsve Eecs Absrac eng W Zolang Xong Ypng Deng

More information

Motion in Two Dimensions

Motion in Two Dimensions Phys 1 Chaper 4 Moon n Two Dmensons adzyubenko@csub.edu hp://www.csub.edu/~adzyubenko 005, 014 A. Dzyubenko 004 Brooks/Cole 1 Dsplacemen as a Vecor The poson of an objec s descrbed by s poson ecor, r The

More information

On computing differential transform of nonlinear non-autonomous functions and its applications

On computing differential transform of nonlinear non-autonomous functions and its applications On compung dfferenal ransform of nonlnear non-auonomous funcons and s applcaons Essam. R. El-Zahar, and Abdelhalm Ebad Deparmen of Mahemacs, Faculy of Scences and Humanes, Prnce Saam Bn Abdulazz Unversy,

More information

Chapter 6 DETECTION AND ESTIMATION: Model of digital communication system. Fundamental issues in digital communications are

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

More information

FTCS Solution to the Heat Equation

FTCS Solution to the Heat Equation FTCS Soluon o he Hea Equaon ME 448/548 Noes Gerald Reckenwald Porland Sae Unversy Deparmen of Mechancal Engneerng gerry@pdxedu ME 448/548: FTCS Soluon o he Hea Equaon Overvew Use he forward fne d erence

More information

Introduction to Turbulence Modelling

Introduction to Turbulence Modelling Introdcton to Trblence Modellng 1 Nmercal methods 0 1 t Mathematcal descrpton p F Reslts For eample speed, pressre, temperatre Geometry Models for trblence, combston etc. Mathematcal descrpton of physcal

More information

An introduction to Support Vector Machine

An introduction to Support Vector Machine An nroducon o Suppor Vecor Machne 報告者 : 黃立德 References: Smon Haykn, "Neural Neworks: a comprehensve foundaon, second edon, 999, Chaper 2,6 Nello Chrsann, John Shawe-Tayer, An Inroducon o Suppor Vecor Machnes,

More information

PHYS 1443 Section 001 Lecture #4

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

More information

Tools for Analysis of Accelerated Life and Degradation Test Data

Tools for Analysis of Accelerated Life and Degradation Test Data Acceleraed Sress Tesng and Relably Tools for Analyss of Acceleraed Lfe and Degradaon Tes Daa Presened by: Reuel Smh Unversy of Maryland College Park smhrc@umd.edu Sepember-5-6 Sepember 28-30 206, Pensacola

More information

Gear System Time-varying Reliability Analysis Based on Elastomer Dynamics

Gear System Time-varying Reliability Analysis Based on Elastomer Dynamics A publcaon of CHEMICAL ENGINEERING TRANSACTIONS VOL. 33, 013 Gues Edors: Enrco Zo, Pero Barald Copyrgh 013, AIDIC Servz S.r.l., ISBN 978-88-95608-4-; ISSN 1974-9791 The Ialan Assocaon of Chemcal Engneerng

More information

INTERNATIONAL JOURNAL OF LOGIC AND COMPUTATION (IJLP)

INTERNATIONAL JOURNAL OF LOGIC AND COMPUTATION (IJLP) ITERATIOAL JOURAL OF LOI A OMPUTATIO (IJLP) VOLUME ISSUE 2 2 EITE BY R. ABEEL TAHIR ISS (Onlne): 28-29 Inernaonal Jornal of Logc and ompaon (IJLP) s pblshed boh n radonal paper form and n Inerne. Ths jornal

More information

Hierarchical Sliding Mode Control for Series Double Inverted Pendulums System

Hierarchical Sliding Mode Control for Series Double Inverted Pendulums System Herarchcal Sldng Mode Conrol for Seres Doble Invered Pendlms Sysem Danwe Qan, Janqang Y, Dongbn Zhao, and Ynxng Hao Laboraory of Complex Sysems and Inellgence Scence Inse of Aomaon, Chnese Academy of Scences

More information

Today s topic: IMPULSE AND MOMENTUM CONSERVATION

Today s topic: IMPULSE AND MOMENTUM CONSERVATION Today s opc: MPULSE ND MOMENTUM CONSERVTON Reew of Las Week s Lecure Elasc Poenal Energy: x: dsplaceen fro equlbru x = : equlbru poson Work-Energy Theore: W o W W W g noncons W non el W noncons K K K (

More information