Optimization of Smart Spoiler for Race Car

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Optimization of Smart Spoiler for Race Car"

Transcription

1 Intrnational Confrnc on Fluid Dynamics and Thrmodynamics, Dubai, January 25-27,2 Optimization of Smart Spoilr for Rac Car M.H. Djavarshkian, A. Esmali Abstract A prssur-basd implicit procdur to solv Navir- Stoks quations on a nonorthogonal msh with collocatd finit volum formulation is usd to simulat flow around th smart and convntional flaps of spoilr undr th ground ffct. Cantilvr bam with uniformly varying load with rollr support at th fr nd is considrd for smart flaps. Th bounddnss critria for this procdur ar dtrmind from a Normalizd Variabl diagram (NVD) schm. Th procdur incorporats th k ε ddyviscosity turbulnc modl. Th mthod is first validatd against xprimntal data. Thn, th algorithm is applid for turbulnt arodynamic flows around a spoilr sction with smart and convntional flaps for diffrnt attack angl, flap angl and ground claranc whr th rsults of two flaps ar compard. Finally, th bst position of spoilr basd on PSO optimization algorithm is calculatd. Kywords Smart spoilr, Ground Effct, Flap, Arodynamic cofficints, Rac car. I. INTRODUCTION h total arodynamic packag of th rac car is Tmphasizd now mor than vr bfor. Th us of arodynamics to incras th cars' grip was pionrd in Formula on in th lat 96s by Lotus, Frrari and Brabham. Arodynamics plays a vital rol in dtrmining spd and acclration and thus prformanc. hil drag rduction is an important part of th rsarch, down forc gnration plays a gratr rol in lap tim rduction. Ground ffct arodynamics of rac cars is concrnd with gnrating down forc, principally via low prssur on th surfacs narst to th ground. Ths phnomna happn whn a wing is going nar th surfac. Airfoils or wings ar usd in th front and rar of th car in an ffort to gnrat mor down forc. Th front wing of a rac car is an important pic to mak safty at high spd and producs about /3 of th car s down forc, it has xprincd mor modifications than rar wing. Th front wing assmbly is th first part of th car to mt th air mass. Th flow fild hr is bttr than at othr parts of th car bcaus th air hr has bn disturbd th last. Th wing is dsignd to produc down forc and guid th air as it movs toward th body and rar of th car. Flaps and winglts may also b usd. In stting up th front wing assmbly, nginrs M.H. Djavarshkian is with th Frdowsi Univrsity of Mashhad (corrsponding author to provid phon: ; fax: ; -mail: A. Esmali, is with th Frdowsi Univrsity of Mashhad. H is now M.S Studnt in th Dpartmnt of Michanics, Frdowsi Univrsity of Mashhad, must considr what happns to th airflow as it travls toward th back of th car. Jonathan and Xin [], studid about flap wing in ground ffct for racing car application. A gnral ovrviw of th racing vhicl R&D procss is studid by Daisuk t al. [2]. A CFD simulation and analysis for a 5% scald car modl is prsntd in sufficint dtail, with an mphasis on addrssing its arodynamic aspcts. Kngo and Hiroshi [3] found th optimal flap chord lngth with using CFD simulations in two-dimnsion FX63-37 airfoil. Jagadp and Mayank [4] invstigatd about front wing in th rac car by using CFD softwar and foundd th optimum angl of attack for a F car(formula on rac). Josph [5] invstigatd arodynamic of rac car and typical dsign tools such as wind tunnl tsting, computational fluid dynamics, track tsting and thir rlvanc to rac car dvlopmnt ar discussd as wll. Mokhtar [6] and [7] studid for low Rynold's numbr flow around wings with and without ground ffct. Th mntion study was xtndd to thr-dimnsional flow around a wing with ground ffct [7]. Mokhtar and Jonathan [8], invstigatd about a numrical study of a rac car front wing. Th focus of thir study is to invstigat th arodynamics charactristics of a wing oprating in a small ground claranc. A computational study in ordr to modl th flow around an invrtd airfoil in ground ffct wr prformd by Zrihan and Zhang [9]. Th knowldg of th ffcts that th ground can hav on airfoils dats back to th arly 92 s. In rcnt yars, thr hav bn succssful invstigations on th arodynamics of airfoil and wing. On of th mor rcnt wind tunnl xprimnts was don by Ahmd and Sharma [] and []. Jung t al. [2], simulatd thr-dimnsional NACA649 in ground proximity. Smith [3] prformd th computational analysis of airfoils in ground ffct. Influnc of ndplat on arodynamic charactristics for low-aspct-ratio wing in ground ffct is prformd by Park and L [4]. Effct of ground proximity on th arodynamic prformanc and stability of a light unmannd arial vhicl has bn prformd by Boschtti t al. [5]. Th shap optimization using th multi-objctiv gntic algorithm and th analysis of th thr-dimnsional wings in ground ffct hav bn prformd by L t al. [6]. Du to th potntial bnfits of mploying adaptiv airfoil, thr has bn an intnsiv attmpt by rsarchrs in dvloping a working modl. ith th advancmnt of matrials, many ar now considring using smart matrials to produc airfoil with variabl cambr capability. An analytical study conductd by NASA on th bnfits of variabl-cambr capability [7]. Anothr advantag of adaptiv airfoil is that it

2 Intrnational Confrnc on Fluid Dynamics and Thrmodynamics, Dubai, January 25-27,2 causs smallr vortx with lss powr. This was th rsult of Prn and Jacob [8] rsarch. Thy usd pizolctric stimulus with a stl layr in airfoil. Kudva t al. [9] discussd about smart structur tchnologis and thir bnfits. In 23, Forstr t al. [2] dsignd a two dimnsional airfoil with a control surfac in trailing dg that has a chord wis gomtrical changs. Convntional spoilrs hav bn usd in most of th rsarchs for rac cars. To improv arodynamic cofficint prformanc, a smart spoilr can b usd in ths cars. In this rsarch, th smart flap is mployd and simulatd for a spoilr sction in ground claranc. In this simulation, th prformanc of airfoil with smart and convntional flaps for diffrnt lngth, flap angl and ground claranc ar studid. Bsid, in ordr to achiv maximum of lift to drag ratio, th PSO algorithm is usd to find th bst of distanc approximation of surfac, angl of flap dflction and flap lngth. Fig. Smart and Convctional Flap II. NUMERICAL SOLUTION SETUP AND CONDITIONS A. Simulation smart flap dflction In this study, a smart flap dflction is dsignd with a cantilvr bam so that th bam bnding quation is sam a smart flap chord dflction. Bsid a flap shap is a triangl (s.g. Fig. ), so th cantilvr bams with uniformly varying load ar considrd (s.g. Fig. 2). Th mntion profil is givn blow: w ( 2 ) X + BX BX Y = () 2EIB Sinc th paramtric quation only nds, quation () is substitutd by quation (2). 5 3 Y Uppr =Y u +k u (-X -ax +X) 5 3 Y Lowr =Y L +k L (-X -ax +X) 4 -B a= B 2 Th bnding quation can b usd for midlin. For uppr and lowr flap surfac, th configuration was manipulatd by making minor modifications. Th cofficints of quation(2) ar dtrmind by an itrativ procss. Each profil is visualizd using FORTRAN, and th valu of th cofficint is ithr incrasd or dcrasd until th dsird profil is obtaind. A paramtric smart airfoil is dsignd, and computational fluid dynamics simulation is don ovr thm. (2) Fig. 2 Cantilvr bam modl. B. Govrning Equation for Fluid Th basic quations, which dscrib consrvation of mass, momntum and scalar quantitis, can b xprssd in th following vctor form, which is indpndnt of th coordinat systm. div ( ρ V r ) = S m (3) div( ρ V V T ) = S r v (4) div( ρ V r φ q) = S r Φ (5) Th lattr two ar usually xprssd in trms of basic dpndnt variabls. Th strss tnsor for a Nwtonian fluid is: r 2 r r T= ( P+ µ div V) I+ (6) 3 and th Fourir-typ law usually givs th scalar flux vctor:

3 Intrnational Confrnc on Fluid Dynamics and Thrmodynamics, Dubai, January 25-27,2 q r = Γ φ gradφ (7) Sinc th k ε modl is simpl and has good stability with asy convrgnc. Bsids th angl of attack is zro, th maximum angl of flap is 7.5 and thr is not strong sparation thrfor, flow fild is not swirl and complicat. Th k ε modl has bn chosn in this simulation. C. Finit-Volum Discrtization Th discrtization of th abov diffrntial quations is carrid out using a finit-volum approach. First, th solution domain is dividd into a finit numbr of discrt volums or clls, whr all variabls ar stord at thir gomtric cntrs (s.g. Fig.3). Th quations ar thn intgratd ovr all th control volums by using th Gaussian thorm. Th discrt xprssions ar prsntd affctd concrning only on fac of th control volum, namly, for th sak of brvity. For any variabl φ (which may also stand for th vlocity componnts), th rsult of th intgration yilds: I Iw + In Is = S φ δ υ (8) c whr I s ar th combind cll-fac convction I and D diffusion I fluxs. Th diffusion flux is approximatd by cntral diffrncs and can b writtn for cll-fac of th control volum in Fig. 3 as: D I = D ( φ φ ) (9) P E xprssion for th φ is dtrmind by th SBIC schm [2], that is basd on th NVD tchniqu, usd for intrpolation from th nods E, P and. Th xprssion can b writtn as: φ So that: whr ~ φ + ( φ φ ). φ = () P E ~ ~ φ = φ,if ~ φ [,] (2) ~ φ p φ φ p =, φ φ ~ x p E x = x p E x x, C ~ φ φ φ = φe φ ~ x x x = x x E (3) Th limits on th slction of K could b dtrmind in th following way. Obviously, th lowr limit is K =, which would rprsnt switching btwn upwind and cntral diffrncing. This is not favorabl bcaus, it is ssntial to avoid th abrupt switching btwn th schms in ordr to achiv th convrgd solution. Th valu of K should b kpt as low as possibl in ordr to achiv th maximum rsolution of th schm. Th final form of th discrtizd quation from ach approximation is givn as: A. ϕ = A. ϕ + S (4) ϕ P P m m m = E,, N, S Fig. 3 Finit volum and storag arrangmnt. Th rsults ar prsntd and discussd in th nxt sction. At th first, grid stup and computational domain has bn dscribd. D. Grid Stratgy Th grid structur that usd in CFD simulation was cratd by a structurd msh mployd bcaus of its simplicity and applicability to th currnt flow configuration (i.., with a nar-by ground). Schmatic shap of ths two-dimnsional structurd grids is shown in Fig. 4. Th discrtization of th convctiv flux, howvr, rquirs spcial attntion and is th subjct of th various schms dvlopd. A rprsntation of th convctiv flux for cllfac is: I c = ρ. V. Α) φ = F φ ( () Th valu of φ is not known and should b stimatd by intrpolation, from th valus at nighboring grid points. Th Fig. 4 grid topology and H grid. According to Fig. 5 th dimnsion of domain has bn

4 Intrnational Confrnc on Fluid Dynamics and Thrmodynamics, Dubai, January 25-27,2 obtaind aftr doing svral various lngths for b, f, u and indpndnt lngths hav bn chosn. Th grid sizing was dtrmind aftr grid indpndnc that was found by doing svral diffrnt trials, which show for surfac prssur cofficint distribution. For xampl, th ffct of grid siz is shown in Fig. 6. For othr cass, th abov procss is usd for grid and domain indpndncs. own flying xprinc as wll as th flying xprinc of othr particls. Each particl kps track of its coordinats in th solution spac which ar associatd with th bst solution (fitnss) that has achivd so far by that particl. This valu is calld prsonal bst, pbst. Anothr bst valu that is trackd by th PSO is th bst valu obtaind so far by any particl in th nighborhood of that particl. This valu is calld gbst. Th basic concpt of PSO lis in acclrating ach particl toward its pbst and th gbst locations, with a random wightd acclration at ach tim stp as shown in Fig. 7. v k v k+ s k+ v gbst Fig. 5 Dimnsion of domain. s k v pbst 2 Fig.7 Concpt of modification of a sarching point by PSO Cp Each particl tris to modify its position using th following information: th currnt positions, th currnt vlocitis, th distanc btwn th currnt position and pbst, th distanc btwn th currnt position and th gbst. Th modification of th particl s position can b mathmatically modld according th following quation: - 9*5 Grid 3*2 Grid 45*2 Grid -2.5 X/C Fig. 6 Effct of grid sizing on prssur distribution on th surfac of th airfoil for an angl of attack and h/c=.2. E. Boundary Conditions Fig. 5 shows th boundary condition. At th inlt, vlocity has bn prscribd. At th outlt, th prssur is fixd. Slip boundary conditions ar usd on uppr walls of th domain and wall boundary conditions ar usd for airfoil surfac and ground surfac. III. PARTICLE SARM OPTIMIZATION (PSO) Th PSO mthod is a robust stochastic optimization tchniqu basd on th movmnt and intllignc of swarms. This mthod applis th concpt of social intraction to problm solving. It was dvlopd in 995 by Jams Knndy (social-psychologist) and Russll Ebrhart (lctrical nginr). It uss a numbr of agnts (particls) that constitut a swarm moving around in th sarch spac looking for th bst solution. Each particl is tratd as a point in a N- dimnsional spac which adjusts its flying according to its V + = wv + c rand (...) x ( pbst - s ) + c rand x gbst s k k k i i i i k 2 2(...) ( - i )... (5) Rand is uniformly distributd random numbr btwn and. Th pbst i is th prsonal bst of agnt i, and th gbst is global bst of th particl group. Th following wighting function (w) is usually utilizd in (5): ( ) /max w = w Max - éw Max w Min xitr ù ë - û itr (6) hr w Max is initial wight, w Min is final wight, maxitr is maximum itration numbr, and itr is currnt itration numbr. s = s + V (7) k + k k + i i i IV. RESULTS AND DISCUSSION Th rsults ar prsntd and discussd in this sction. Tabl I shows th stting for numrical simulation. At th first, simulation of flow around th airfoil NACA5 has bn prformd. Thn, th ffcts of flow around airfoil NACA9 with flap in smart and convntional conditions, angl of flap and ground claranc hav bn invstigatd.

5 Intrnational Confrnc on Fluid Dynamics and Thrmodynamics, Dubai, January 25-27,2 Th simulation is two-dimnsional. Prssur cofficint distribution, Lift and drag cofficints of th airfoil hav bn analyzd. Th Rynolds numbr for this study is This numbr indicats that th airflow has both laminar and turbulnt rgions. TABLEI SETTINGS FOR NUMERICAL SIMULATION Flow turbulnt Prcision Two-dimnsion Doubl Prcision Schm Normaliz variabl diagram Solvr SIMPLE turbulnt modl k ε Th numrical and xprimntal prssur cofficint distributions on th surfac of th airfoil for angls of attack 7.5 and ground claranc h/c=.8 ar compard in Fig. 8. It can b sn that thr is good agrmnt btwn prsnt numrical and xprimntal data []. Tabl II also shows lift cofficints and rror prcnt. Th numrical rsults ar in good agrmnt with xprimnt data. 2 Numric Exprimnt for AOF= +5 and diffrnt ground claranc. hn th flap dflctd to upward, prssur sid is rlatd to th uppr surfac of airfoil and suction sid is rlatd to th lowr surfac of airfoil. As figurs show prssur is rducd with dcrasing ground claranc in th prssur sid. This bhavior happns in both smart and convntional flaps. CP -.5 X/C Fig. 9 Prssur cofficint distribution on th surfac of th smart airfoil for AOF= +5º. h/c=.2 h/c=.5 h/c=.8 h/c=.2 h/c=.5 h/c=.8 CP - -2 CP -3.5 x/c Fig. 8 Prssur cofficint distribution on th surfac of th airfoil NACA 5 for an AOA 7.5º and h/c=.8. Th airfoil which was slctd to b usd in this study is th NACA9. Th simulation mthod for this tst cas is th sam of prvious tst. Airflow tratmnt and ffct of th flap in smart and convntional conditions in ground proximity ar invstigatd. TABLEII COMPARISON OF LIFT COEFFICIENTS FOR AIRFOIL NACA 5 AND AOA= 7.5. h/c Exprimnt Numric Error% Fig. 9 and, rspctivly, show th prssur cofficint distribution on th surfac of smart and convntional airfoils -.5 X/C Fig. Prssur cofficint distribution on th surfac of th convntional airfoil for AOF= +5º. Tabl III shows down forc(lift) and drag cofficints and L/D for smart and convntional flaps. Comparisons show that down forc cofficints of smart flaps incras and thir drag cofficints dcras as rsults L/D ratio for smart flaps ar highr than convntional flaps. TABLE III DON FORCE(LIFT) (A) AND DRAG (B) COEFFICIENTS AND LIFT - DRAG RATIO(C) FOR SMART AND CONVENTIONAL AIRFOILS FOR AOF= +5. h/c Smart Flap Convction Flap

6 Intrnational Confrnc on Fluid Dynamics and Thrmodynamics, Dubai, January 25-27, (a) h/c Smart Flap Convction Flap (b) h/c Smart Flap Convction Flap (c) CD CF, AOF= +2.5 dg CF, AOF= +5 dg CF, AOF= +7.5 dg SF, AOF= +2.5 dg SF, AOF= +5 dg SF, AOF= +7.5 dg Tabl VI shows down forc(lift), and Drag cofficints and L/D for smart and convntional airfoils for h/c=.8. Comparisons show that down forc cofficint of a smart flap is mor than a convntional flap. Down forc and drag cofficints incras slightly with angl of flap for two airfoils. TABLE VI DON FORCE (LIFT) (A) AND DRAG (B) COEFFICIENT AND LIFT - DRAG RATIO(C) FOR SMART AND CONVENTIONAL AIRFOILS FOR H/C=.8. AOF (dg) Smart Flap Convction Flap (a) AOF (dg) Smart Flap Convction Flap (b) AOF (dg) Smart Flap Convction Flap (c) Fig. and 2 show lift and drag cofficints for th diffrnt h/c. Fig. shows that drag cofficint incrass with rduction ground claranc and this cofficint for convntional flaps is mor than th smart mod for all th h/c and AOF h/c Fig. Variations in CD as a function of h/c for smart and convntional flap and diffrnt angl of flap. Fig. 2 indicats lift cofficint incrass with ground claranc initially, thn this cofficint dcrass with incrasing ground claranc. Th positiv dflction of flap passs flow btwn th lowr surfac of airfoil and ground surfac lik flow passing a nozzl. Nozzl Charactristics rvald that vlocity incrass and prssur rducs in th convrgnt part so vlocity rachs maximum in th gorg and prssur incras and vlocity dcras in th divrgnt part. hn th ground claranc is rducd, th cross sction ratio is gratr and flow xpansion is mor on th lowr surfac of airfoil. As a rsult, vlocity on th lowr surfac of airfoil incrass. This incras of vlocity in th lowr surfac with ground claranc from h / c =.8 to h / c =.5 incrass lift cofficint. hn th ground claranc dcrass from h/c=.5 to h/c=.2, boundary layr has an important rol, th vlocity in lowr surfac and lift cofficint dcras. Fig. 3 shows th L/D absolut valu ratio for th diffrnt h/c. CL -.2 CF, AOF= +2.5 dg CF, AOF= +5 dg CF, AOF= +7.5 dg SF, AOF= +2.5 dg SF, AOF= +5 dg SF, AOF= +7.5 dg h/c Fig. 2 Variations in CL as a function of h/c for smart and convntional flap and diffrnt angl of flap.

7 Intrnational Confrnc on Fluid Dynamics and Thrmodynamics, Dubai, January 25-27,2 5 CF, AOF= +2.5 dg CF, AOF= +5 dg CF, AOF= +7.5 dg SF, AOF= +2.5 dg SF, AOF= +5 dg SF, AOF= +7.5 dg CL/CD h/c Fig. 3 Variations in L/D as a function of h/c for smart and convntional flap and diffrnt angl of flap. Fig. 5 Variations in absolut valu of L/D as a function of h/c and angl of smart flap. TABLE V VOLUME FLO RATE PASSING BETEEN LOER SURFACE OF AIRFOIL AND GROUND FOR H/C=.2. AOF(dg) Smart Flap Convntional Flap So far, th ffcts of angl of flap dflction, distanc approximation from th car surfac and flap lngth hav bn invstigatd. Th rsults show that if th smart flap is usd, th arodynamic prformanc of spoilr will b incrasd. In ordr to gt th bst optimal mod, th optimization has bn don basd on PSO algorithm. Fig. 4 shows variations in absolut of lift to drag ratio as a function of flap lngth and angl of flap. This figur shows that th absolut valu of th lift to drag ratio is incrasd with incrasing th angl of flap and flap lngth. Fig. 6 Variations in absolut valu of L/D as a function of h/c and flap lngth for smart flap. Finally, th optimization is don with th prsnt rsults. Initially th absolut valu of th lift to drag ratio is obtaind as a function of flap lngth(fl/c), flap angl(aof) and distanc approximation from th surfac by using nural ntwork-fuzzy and ultimatly optimization is prformd basd on L/D=f(FL/c,h/c,AOF). According to th availabl data optimization mod is obtaind in tabl VI. L/D AOF(dg) TABLE VI OPTIMIZATION CASE FOR SMART FLAP h/c FL/c Abs(L/D) Fig. 4 Variations in absolut of L/D as a function of flap lngth and angl of smart flap. Fig. 5 shows variations in absolut valu of th lift to drag ratio as a function of h/c and angl of flap. This figur shows that th absolut valu of th lift to drag ratio is incrasd with incrasing th distanc. Fig. 6 shows variations in absolut valu of th lift to drag ratio as a function of flap angl and flap lngth. This figur shows that th absolut valu of th lift to drag ratio is incrasd with incrasing flap lngth and h/c. hil flap lngth to chord ratio, angl of flap dflction and spoilr distanc from surfac ar.28, 7.47 and.78 rspctivly, th maximum of arodynamic prformanc is obtaind. In th mntion conditions, th lift to drag ratio is V. CONCLUTION A prssur-basd implicit procdur to solv Navir-Stoks quations on a non orthogonal msh with collocatd finit volum formulation is usd to simulat flow around th smart and convntional flaps of a spoilr sction undr th ground ffct. Th algorithm is applid for diffrnt flap lngth, flap

8 Intrnational Confrnc on Fluid Dynamics and Thrmodynamics, Dubai, January 25-27,2 angl and ground claranc. Th main findings can b summarizd as follows: -Th agrmnt btwn prsntd prdation and xprimntal data is considrabl 2-Th prssur cofficint distribution in a smart flap is smoothr than convntional flap 3- Lift-drag ratio in a smart flap is highr than a convntional flap 4- Th highst lift-drag ratio is at flap angl 7.5º 5- Th ground claranc with h/c=.5 has th highst lift cofficint 6- Th lift and drag cofficints slightly incras for longr flap lngth and L/D ratio incrass too 7- Th optimal mod is obtaind basd on PSO algorithm. NOMENCLATURE h = Ground Clarancs AOA = Angl of Attack A = Cll Fac Ara µ = Dynamic Viscosity = Normalizd Scalar Quantity φ % K = a factor in SBIC schm to dtrmin a spcial schm ω = ight/unit Lngth(N/m) I = Ara momnt of inrtia(m 4 ) B = Lngth of th Bam X = Horizontal Cartsian Coordinat Y = Vrtical Cartsian Coordinat E = Young s Modulus ρ = Dnsity P = Prssur Γ = Diffusivity Cofficint q r = Scalar Flux Vctor F = Mass Flux T r = Strss Tnsor δυ = Cll Volum S r = Sourc Trm V r = Vlocity Vctor φ = Scalar Quantity I = Flux S k = Currnt Sarching Point S k+ = Modifid Sarching Point V k = Currnt Vlocity V k+ = Modifid Vlocity V pbst = Vlocity basd on pbst V gbst = Vlocity basd on gbst k v i = Vlocity of agnt i at Itration k c j = ighting Factor k s i = Currnt Position of agnt i at Itration k REFERENCES [] J. Zrihan and X. Zhang, "Arodynamics of Gurny Flaps on a ing in Ground Effct," AIAA journal, vol. 39, pp , 2. [2] D. Uno, G. Hu, I. Komada, K. Otaki, and Q. Fan, "CFD Analysis in Rsarch and Dvlopmnt of Racing Car," prsntd at th Motorsports Enginring Confrnc & Exposition, Darborn, MI, USA, 26. [3] K. Goto and H. Sakurai, "Numrical Study for th Optimal Flap Chord Lngth of a Two-Elmnt Airfoil," SAE Intrnational Journal of Passngr Cars-Mchanical Systms, pp , 26. [4] J. Rddy and M. Gupta, "Finding th Optimum Angl of Attack for th Front ing of an F Car Using CFD," in 4th SEAS Intrnational Confrnc on Fluid Mchanics and Arodynamics, Elounda, Grc, 26, pp [5] J. Katz, "Arodynamics of Rac Cars," Annual Rviw of Fluid Mchanics, vol. 38, p. 27, 25. [6]. Mokhtar, "A Numrical Study of High-Lift Singl Elmnt Airfoils with Ground Effct for Racing Cars," SAE transactions, vol. 4, pp , 25. [7]. Mokhtar, "Arodynamics of High-Lift ings with Ground Effct for Raccars," prsntd at th SAE orld Congrss, 28. [8]. Mokhtar and J. Lan, "Raccar Front ing Arodynamics," SAE Intrnational Journal of Passngr Cars-Mchanical Systms, vol., p. 392, 29. [9] J. Zrihan and Z. Xin, "Arodynamics of a Singl Elmnt ing in Ground Effct," Journal of aircraft, vol. 37, pp , 2. [] M. Ahmd, S. H. Ali, G. M. Imran, and S. D. Sharma, "Exprimntal Invstigation of th Flow Fild of a Symmtrical Airfoil in Ground Effct," in 2st Applid Arodynamics Confrnc, Orlando, Florida, 23. [] M. Ahmd and S. Sharma, "An Invstigation on th Arodynamics of a Symmtrical Airfoil in Ground Effct," Exprimntal Thrmal and Fluid Scinc, vol. 29, pp , 25. [2] K. Jung, H. Chun, and H. Kim, "Exprimntal Invstigation of ing-in-ground Effct with a NACA649 Sction," Journal of marin scinc and tchnology, vol. 3, pp , 28. [3] J. Smith, "Computational Analysis of Airfoils in Ground Effct for Us as a Dsign Tool," M.Sc Mchanical and Arospac Enginring Dpartmnt, st Virginia Univrsity, st Virginia, 27. [4] K. Park and J. L, "Influnc of Endplat on Arodynamic Charactristics of Low-Aspct-Ratio ing in Ground Effct," Journal of mchanical scinc and tchnology, vol. 22, pp , 28. [5] J. P. Boschtti, M. E. Cárdnas, and A. AmrioCLq, "Stability and Prformanc of a Light Unmannd Airplan in Ground Effct," in 48th AIAA Arospac Scincs Mting Including th Nw Horizons Forum and Arospac Exposition, Florida, 2. [6] J. L, C. Hong, B. Kim, K. Park, and J. Ahn, "Optimization of ings in Ground Effct Using Multi-Objctiv Gntic Algorithm," in 48th AIAA Arospac Scincs Mting Including th Nw Horizons Forum and Arospac Exposition, Florida, 2. [7] A. Bolonkin, G. Gilyard, H. L. D. F. R. Cntr, U. S. N. Aronautics, and S. Administration, Estimatd bnfits of variablgomtry wing cambr control for transport aircraft: Citsr, 999. [8] N. J. Prn and J. D. Jacob, "ak Vortx Mitigation using Adaptiv Airfoils," prsntd at th 37th AIAA. Arospac Scincs Mting and Exhibit, 999. [9] J. Kudva, C. Martin, A. Jardin, G. Sndckyj, T. Harris, A. McGowan, and R. Lak, "Dsign, Fabrication, and Tsting of th DARPA/right Lab" Smart ing" ind Tunnl Modl," Journal of Amrican Institut of Aronautics and Astronautics (AIAA), 997. [2] E. Forstr, B. Sandrs, and F. Eastp, "Synthsis of a Variabl Gomtry Trailing Edg Control Surfac," AIAA papr, vol. 77, 23. [2] M. Djavarshkian, "A nw NVD Schm in Prssur-Basd Finit- Volum Mthods," in 4th Australasian Fluid Mchanics confrnc,, Adlaid Univrsity, Adlaid, Australia, 2, pp. -4.

EFFECT OF GEOMETRICAL PARAMETERS ON HEAT TRANSFER PERFORMACE OF RECTANGULAR CIRCUMFERENTIAL FINS

EFFECT OF GEOMETRICAL PARAMETERS ON HEAT TRANSFER PERFORMACE OF RECTANGULAR CIRCUMFERENTIAL FINS 25 Vol. 3 () January-March, pp.37-5/tripathi EFFECT OF GEOMETRICAL PARAMETERS ON HEAT TRANSFER PERFORMACE OF RECTANGULAR CIRCUMFERENTIAL FINS *Shilpa Tripathi Dpartmnt of Chmical Enginring, Indor Institut

More information

Lecture 3: Diffusion: Fick s first law

Lecture 3: Diffusion: Fick s first law Lctur 3: Diffusion: Fick s first law Today s topics What is diffusion? What drivs diffusion to occur? Undrstand why diffusion can surprisingly occur against th concntration gradint? Larn how to dduc th

More information

Introduction to Finite Element Modeling

Introduction to Finite Element Modeling Introduction to Finit Elmnt Modling Enginring analysis of mchanical systms hav bn addrssd by driving diffrntial quations rlating th variabls of through basic physical principls such as quilibrium, consrvation

More information

Analysis Of Injection Moulding Process Parameters

Analysis Of Injection Moulding Process Parameters Analysis Of Injction Moulding Procss Paramtrs Mr. M.G. Rathi Assistant Profssor, partmnt of Mchanical Enginring, Govrnmnt Collg of Enginring Aurangabad, (MS), India. Mr. Manoj amodar Salunk Studnt, partmnt

More information

Installation Saving Space-efficient Panel Enhanced Physical Durability Enhanced Performance Warranty The IRR Comparison

Installation Saving Space-efficient Panel Enhanced Physical Durability Enhanced Performance Warranty The IRR Comparison Contnts Tchnology Nwly Dvlopd Cllo Tchnology Cllo Tchnology : Improvd Absorption of Light Doubl-sidd Cll Structur Cllo Tchnology : Lss Powr Gnration Loss Extrmly Low LID Clls 3 3 4 4 4 Advantag Installation

More information

Statistical Machine Translation

Statistical Machine Translation Statistical Machin Translation Sophi Arnoult, Gidon Mailltt d Buy Wnnigr and Andra Schuch Dcmbr 7, 2010 1 Introduction All th IBM modls, and Statistical Machin Translation (SMT) in gnral, modl th problm

More information

by John Donald, Lecturer, School of Accounting, Economics and Finance, Deakin University, Australia

by John Donald, Lecturer, School of Accounting, Economics and Finance, Deakin University, Australia Studnt Nots Cost Volum Profit Analysis by John Donald, Lcturr, School of Accounting, Economics and Financ, Dakin Univrsity, Australia As mntiond in th last st of Studnt Nots, th ability to catgoris costs

More information

e = C / electron Q = Ne

e = C / electron Q = Ne Physics 0 Modul 01 Homwork 1. A glass rod that has bn chargd to +15.0 nc touchs a mtal sphr. Aftrword, th rod's charg is +8.00 nc. What kind of chargd particl was transfrrd btwn th rod and th sphr, and

More information

Traffic Flow Analysis (2)

Traffic Flow Analysis (2) Traffic Flow Analysis () Statistical Proprtis. Flow rat distributions. Hadway distributions. Spd distributions by Dr. Gang-Ln Chang, Profssor Dirctor of Traffic safty and Oprations Lab. Univrsity of Maryland,

More information

Non-Homogeneous Systems, Euler s Method, and Exponential Matrix

Non-Homogeneous Systems, Euler s Method, and Exponential Matrix Non-Homognous Systms, Eulr s Mthod, and Exponntial Matrix W carry on nonhomognous first-ordr linar systm of diffrntial quations. W will show how Eulr s mthod gnralizs to systms, giving us a numrical approach

More information

Exponential Growth and Decay; Modeling Data

Exponential Growth and Decay; Modeling Data Exponntial Growth and Dcay; Modling Data In this sction, w will study som of th applications of xponntial and logarithmic functions. Logarithms wr invntd by John Napir. Originally, thy wr usd to liminat

More information

81-1-ISD Economic Considerations of Heat Transfer on Sheet Metal Duct

81-1-ISD Economic Considerations of Heat Transfer on Sheet Metal Duct Air Handling Systms Enginring & chnical Bulltin 81-1-ISD Economic Considrations of Hat ransfr on Sht Mtal Duct Othr bulltins hav dmonstratd th nd to add insulation to cooling/hating ducts in ordr to achiv

More information

Question 3: How do you find the relative extrema of a function?

Question 3: How do you find the relative extrema of a function? ustion 3: How do you find th rlativ trma of a function? Th stratgy for tracking th sign of th drivativ is usful for mor than dtrmining whr a function is incrasing or dcrasing. It is also usful for locating

More information

QUANTITATIVE METHODS CLASSES WEEK SEVEN

QUANTITATIVE METHODS CLASSES WEEK SEVEN QUANTITATIVE METHODS CLASSES WEEK SEVEN Th rgrssion modls studid in prvious classs assum that th rspons variabl is quantitativ. Oftn, howvr, w wish to study social procsss that lad to two diffrnt outcoms.

More information

Settlement of a Soil Layer. One-dimensional Consolidation and Oedometer Test. What is Consolidation?

Settlement of a Soil Layer. One-dimensional Consolidation and Oedometer Test. What is Consolidation? On-dimnsional Consolidation and Odomtr Tst Lctur No. 12 Octobr 24, 22 Sttlmnt of a Soil Layr Th sttlmnt is dfind as th comprssion of a soil layr du to th loading applid at or nar its top surfac. Th total

More information

A Note on Approximating. the Normal Distribution Function

A Note on Approximating. the Normal Distribution Function Applid Mathmatical Scincs, Vol, 00, no 9, 45-49 A Not on Approimating th Normal Distribution Function K M Aludaat and M T Alodat Dpartmnt of Statistics Yarmouk Univrsity, Jordan Aludaatkm@hotmailcom and

More information

Simulated Radioactive Decay Using Dice Nuclei

Simulated Radioactive Decay Using Dice Nuclei Purpos: In a radioactiv sourc containing a vry larg numbr of radioactiv nucli, it is not possibl to prdict whn any on of th nucli will dcay. Although th dcay tim for any on particular nuclus cannot b prdictd,

More information

Abstract. Introduction. Statistical Approach for Analyzing Cell Phone Handoff Behavior. Volume 3, Issue 1, 2009

Abstract. Introduction. Statistical Approach for Analyzing Cell Phone Handoff Behavior. Volume 3, Issue 1, 2009 Volum 3, Issu 1, 29 Statistical Approach for Analyzing Cll Phon Handoff Bhavior Shalini Saxna, Florida Atlantic Univrsity, Boca Raton, FL, shalinisaxna1@gmail.com Sad A. Rajput, Farquhar Collg of Arts

More information

Genetic Drift and Gene Flow Illustration

Genetic Drift and Gene Flow Illustration Gntic Drift and Gn Flow Illustration This is a mor dtaild dscription of Activity Ida 4, Chaptr 3, If Not Rac, How do W Explain Biological Diffrncs? in: How Ral is Rac? A Sourcbook on Rac, Cultur, and Biology.

More information

The Normal Distribution: A derivation from basic principles

The Normal Distribution: A derivation from basic principles Th Normal Distribution: A drivation from basic principls Introduction Dan Tagu Th North Carolina School of Scinc and Mathmatics Studnts in lmntary calculus, statistics, and finit mathmatics classs oftn

More information

International Association of Scientific Innovation and Research (IASIR) (An Association Unifying the Sciences, Engineering, and Applied Research)

International Association of Scientific Innovation and Research (IASIR) (An Association Unifying the Sciences, Engineering, and Applied Research) Intrnational Association of Scintific Innovation and Rsarch (IASIR) (An Association Unifing th Scincs, Enginring, and Applid Rsarch) ISSN (Print): 79-000 ISSN (Onlin): 79-009 Intrnational Journal of Enginring,

More information

Principles of Humidity Dalton s law

Principles of Humidity Dalton s law Principls of Humidity Dalton s law Air is a mixtur of diffrnt gass. Th main gas componnts ar: Gas componnt volum [%] wight [%] Nitrogn N 2 78,03 75,47 Oxygn O 2 20,99 23,20 Argon Ar 0,93 1,28 Carbon dioxid

More information

Econ 371: Answer Key for Problem Set 1 (Chapter 12-13)

Econ 371: Answer Key for Problem Set 1 (Chapter 12-13) con 37: Answr Ky for Problm St (Chaptr 2-3) Instructor: Kanda Naknoi Sptmbr 4, 2005. (2 points) Is it possibl for a country to hav a currnt account dficit at th sam tim and has a surplus in its balanc

More information

Finite Element Vibration Analysis

Finite Element Vibration Analysis Finit Elmnt Vibration Analysis Introduction In prvious topics w larnd how to modl th dynamic bhavior of multi-dof systms, as wll as systms possssing infinit numbrs of DOF. As th radr may raliz, our discussion

More information

Lecture 20: Emitter Follower and Differential Amplifiers

Lecture 20: Emitter Follower and Differential Amplifiers Whits, EE 3 Lctur 0 Pag of 8 Lctur 0: Emittr Followr and Diffrntial Amplifirs Th nxt two amplifir circuits w will discuss ar ry important to lctrical nginring in gnral, and to th NorCal 40A spcifically.

More information

Improving Managerial Accounting and Calculation of Labor Costs in the Context of Using Standard Cost

Improving Managerial Accounting and Calculation of Labor Costs in the Context of Using Standard Cost Economy Transdisciplinarity Cognition www.ugb.ro/tc Vol. 16, Issu 1/2013 50-54 Improving Managrial Accounting and Calculation of Labor Costs in th Contxt of Using Standard Cost Lucian OCNEANU, Constantin

More information

LG has introduced the NeON 2, with newly developed Cello Technology which improves performance and reliability. Up to 320W 300W

LG has introduced the NeON 2, with newly developed Cello Technology which improves performance and reliability. Up to 320W 300W Cllo Tchnology LG has introducd th NON 2, with nwly dvlopd Cllo Tchnology which improvs prformanc and rliability. Up to 320W 300W Cllo Tchnology Cll Connction Elctrically Low Loss Low Strss Optical Absorption

More information

Proceedings of the 6th WSEAS International Conference on Simulation, Modelling and Optimization, Lisbon, Portugal, September 22-24, 2006 246

Proceedings of the 6th WSEAS International Conference on Simulation, Modelling and Optimization, Lisbon, Portugal, September 22-24, 2006 246 Procdings of th 6th WSEAS Intrnational Confrnc on Simulation, Modlling and Optimization, Lisbon, Portugal, Sptmbr 22-24, 2006 246 Larg dformation modling in soil-tillag tool intraction using advancd 3D

More information

Gold versus stock investment: An econometric analysis

Gold versus stock investment: An econometric analysis Intrnational Journal of Dvlopmnt and Sustainability Onlin ISSN: 268-8662 www.isdsnt.com/ijds Volum Numbr, Jun 202, Pag -7 ISDS Articl ID: IJDS20300 Gold vrsus stock invstmnt: An conomtric analysis Martin

More information

Ground Fault Current Distribution on Overhead Transmission Lines

Ground Fault Current Distribution on Overhead Transmission Lines FACTA UNIVERSITATIS (NIŠ) SER.: ELEC. ENERG. vol. 19, April 2006, 71-84 Ground Fault Currnt Distribution on Ovrhad Transmission Lins Maria Vintan and Adrian Buta Abstract: Whn a ground fault occurs on

More information

AP Calculus AB 2008 Scoring Guidelines

AP Calculus AB 2008 Scoring Guidelines AP Calculus AB 8 Scoring Guidlins Th Collg Board: Conncting Studnts to Collg Succss Th Collg Board is a not-for-profit mmbrship association whos mission is to connct studnts to collg succss and opportunity.

More information

Solutions to Homework 8 chem 344 Sp 2014

Solutions to Homework 8 chem 344 Sp 2014 1. Solutions to Homwork 8 chm 44 Sp 14 .. 4. All diffrnt orbitals mans thy could all b paralll spins 5. Sinc lctrons ar in diffrnt orbitals any combination is possibl paird or unpaird spins 6. Equivalnt

More information

The Matrix Exponential

The Matrix Exponential Th Matrix Exponntial (with xrciss) 92.222 - Linar Algbra II - Spring 2006 by D. Klain prliminary vrsion Corrctions and commnts ar wlcom! Th Matrix Exponntial For ach n n complx matrix A, dfin th xponntial

More information

Gas Radiation. MEL 725 Power-Plant Steam Generators (3-0-0) Dr. Prabal Talukdar Assistant Professor Department of Mechanical Engineering IIT Delhi

Gas Radiation. MEL 725 Power-Plant Steam Generators (3-0-0) Dr. Prabal Talukdar Assistant Professor Department of Mechanical Engineering IIT Delhi Gas Radiation ME 725 Powr-Plant Stam Gnrators (3-0-0) Dr. Prabal Talukdar Assistant Profssor Dpartmnt of Mchanical Enginring T Dlhi Radiation in absorbing-mitting mdia Whn a mdium is transparnt to radiation,

More information

A Derivation of Bill James Pythagorean Won-Loss Formula

A Derivation of Bill James Pythagorean Won-Loss Formula A Drivation of Bill Jams Pythagoran Won-Loss Formula Ths nots wr compild by John Paul Cook from a papr by Dr. Stphn J. Millr, an Assistant Profssor of Mathmatics at Williams Collg, for a talk givn to th

More information

14.3 Area Between Curves

14.3 Area Between Curves 14. Ara Btwn Curvs Qustion 1: How is th ara btwn two functions calculatd? Qustion : What ar consumrs and producrs surplus? Earlir in this chaptr, w usd dfinit intgrals to find th ara undr a function and

More information

CPU. Rasterization. Per Vertex Operations & Primitive Assembly. Polynomial Evaluator. Frame Buffer. Per Fragment. Display List.

CPU. Rasterization. Per Vertex Operations & Primitive Assembly. Polynomial Evaluator. Frame Buffer. Per Fragment. Display List. Elmntary Rndring Elmntary rastr algorithms for fast rndring Gomtric Primitivs Lin procssing Polygon procssing Managing OpnGL Stat OpnGL uffrs OpnGL Gomtric Primitivs ll gomtric primitivs ar spcifid by

More information

7 Timetable test 1 The Combing Chart

7 Timetable test 1 The Combing Chart 7 Timtabl tst 1 Th Combing Chart 7.1 Introduction 7.2 Tachr tams two workd xampls 7.3 Th Principl of Compatibility 7.4 Choosing tachr tams workd xampl 7.5 Ruls for drawing a Combing Chart 7.6 Th Combing

More information

Chi-Square. Hypothesis: There is an equal chance of flipping heads or tails on a coin. Coin A. Expected (e) (o e) (o e) 2 (o e) 2 e

Chi-Square. Hypothesis: There is an equal chance of flipping heads or tails on a coin. Coin A. Expected (e) (o e) (o e) 2 (o e) 2 e Why? Chi-Squar How do you know if your data is th rsult of random chanc or nvironmntal factors? Biologists and othr scintists us rlationships thy hav discovrd in th lab to prdict vnts that might happn

More information

Fredy Vélez. Centro Tecnológico CARTIF, Valladolid, España. frevel@cartif.es

Fredy Vélez. Centro Tecnológico CARTIF, Valladolid, España. frevel@cartif.es Slcting working fluids in an organic Rankin cycl for powr gnration from low tmpratur hat sourcs Frdy Vélz Cntro Tcnológico CARTIF, Valladolid, España. frvl@cartif.s Rcivd: January 21th, d 2014. Rcivd in

More information

10/06/08 1. Aside: The following is an on-line analytical system that portrays the thermodynamic properties of water vapor and many other gases.

10/06/08 1. Aside: The following is an on-line analytical system that portrays the thermodynamic properties of water vapor and many other gases. 10/06/08 1 5. Th watr-air htrognous systm Asid: Th following is an on-lin analytical systm that portrays th thrmodynamic proprtis of watr vapor and many othr gass. http://wbbook.nist.gov/chmistry/fluid/

More information

Module 7: Discrete State Space Models Lecture Note 3

Module 7: Discrete State Space Models Lecture Note 3 Modul 7: Discrt Stat Spac Modls Lctur Not 3 1 Charactristic Equation, ignvalus and ign vctors For a discrt stat spac modl, th charactristic quation is dfind as zi A 0 Th roots of th charactristic quation

More information

5. Design of FIR Filters. We want to address in this Chapter the issue of approximating a digital filter with a desired frequency response

5. Design of FIR Filters. We want to address in this Chapter the issue of approximating a digital filter with a desired frequency response 5. Dsign of FIR Filtrs Rfrnc: Sctions 7.2-7.4 of Txt W want to addrss in this Chaptr th issu of approximating a digital filtr with a dsird frquncy rspons Hd ( ω ) using filtrs with finit duration. 5.1

More information

A Multi-Heuristic GA for Schedule Repair in Precast Plant Production

A Multi-Heuristic GA for Schedule Repair in Precast Plant Production From: ICAPS-03 Procdings. Copyright 2003, AAAI (www.aaai.org). All rights rsrvd. A Multi-Huristic GA for Schdul Rpair in Prcast Plant Production Wng-Tat Chan* and Tan Hng W** *Associat Profssor, Dpartmnt

More information

The international Internet site of the geoviticulture MCC system Le site Internet international du système CCM géoviticole

The international Internet site of the geoviticulture MCC system Le site Internet international du système CCM géoviticole Th intrnational Intrnt sit of th goviticultur MCC systm L sit Intrnt intrnational du systèm CCM géoviticol Flávio BELLO FIALHO 1 and Jorg TONIETTO 1 1 Rsarchr, Embrapa Uva Vinho, Caixa Postal 130, 95700-000

More information

The example is taken from Sect. 1.2 of Vol. 1 of the CPN book.

The example is taken from Sect. 1.2 of Vol. 1 of the CPN book. Rsourc Allocation Abstract This is a small toy xampl which is wll-suitd as a first introduction to Cnts. Th CN modl is dscribd in grat dtail, xplaining th basic concpts of C-nts. Hnc, it can b rad by popl

More information

SRPioneers Science and Research Pioneers Institute 3rd International Conference on Nanotechnology (ICN2015), August 2015, Istanbul, Turkey

SRPioneers Science and Research Pioneers Institute 3rd International Conference on Nanotechnology (ICN2015), August 2015, Istanbul, Turkey rd Intrnational Confrnc on Nanotchnology (ICN5), 7-8 August 5, Istanbul, Turky Fr torsional vibration and static analysis of th conical nano-shll basd on modifid coupl strss thory Y. Tadi Bni, I. Solimani

More information

An Adaptive Clustering MAP Algorithm to Filter Speckle in Multilook SAR Images

An Adaptive Clustering MAP Algorithm to Filter Speckle in Multilook SAR Images An Adaptiv Clustring MAP Algorithm to Filtr Spckl in Multilook SAR Imags FÁTIMA N. S. MEDEIROS 1,3 NELSON D. A. MASCARENHAS LUCIANO DA F. COSTA 1 1 Cybrntic Vision Group IFSC -Univrsity of São Paulo Caia

More information

Incomplete 2-Port Vector Network Analyzer Calibration Methods

Incomplete 2-Port Vector Network Analyzer Calibration Methods Incomplt -Port Vctor Ntwork nalyzr Calibration Mthods. Hnz, N. Tmpon, G. Monastrios, H. ilva 4 RF Mtrology Laboratory Instituto Nacional d Tcnología Industrial (INTI) Bunos irs, rgntina ahnz@inti.gov.ar

More information

MEASUREMENT AND ASSESSMENT OF IMPACT SOUND IN THE SAME ROOM. Hans G. Jonasson

MEASUREMENT AND ASSESSMENT OF IMPACT SOUND IN THE SAME ROOM. Hans G. Jonasson MEASUREMENT AND ASSESSMENT OF IMPACT SOUND IN THE SAME ROOM Hans G. Jonasson SP Tchnical Rsarch Institut of Swdn Box 857, SE-501 15 Borås, Swdn hans.jonasson@sp.s ABSTRACT Drum sound, that is th walking

More information

I. INTRODUCTION. Figure 1, The Input Display II. DESIGN PROCEDURE

I. INTRODUCTION. Figure 1, The Input Display II. DESIGN PROCEDURE Ballast Dsign Softwar Ptr Grn, Snior ighting Systms Enginr, Intrnational Rctifir, ighting Group, 101S Spulvda Boulvard, El Sgundo, CA, 9045-438 as prsntd at PCIM Europ 0 Abstract: W hav dvlopd a Windows

More information

Foreign Exchange Markets and Exchange Rates

Foreign Exchange Markets and Exchange Rates Microconomics Topic 1: Explain why xchang rats indicat th pric of intrnational currncis and how xchang rats ar dtrmind by supply and dmand for currncis in intrnational markts. Rfrnc: Grgory Mankiw s Principls

More information

Constraint-Based Analysis of Gene Deletion in a Metabolic Network

Constraint-Based Analysis of Gene Deletion in a Metabolic Network Constraint-Basd Analysis of Gn Dltion in a Mtabolic Ntwork Abdlhalim Larhlimi and Alxandr Bockmayr DFG-Rsarch Cntr Mathon, FB Mathmatik und Informatik, Fri Univrsität Brlin, Arnimall, 3, 14195 Brlin, Grmany

More information

Deer: Predation or Starvation

Deer: Predation or Starvation : Prdation or Starvation National Scinc Contnt Standards: Lif Scinc: s and cosystms Rgulation and Bhavior Scinc in Prsonal and Social Prspctiv s, rsourcs and nvironmnts Unifying Concpts and Procsss Systms,

More information

FACULTY SALARIES FALL 2004. NKU CUPA Data Compared To Published National Data

FACULTY SALARIES FALL 2004. NKU CUPA Data Compared To Published National Data FACULTY SALARIES FALL 2004 NKU CUPA Data Compard To Publishd National Data May 2005 Fall 2004 NKU Faculty Salaris Compard To Fall 2004 Publishd CUPA Data In th fall 2004 Northrn Kntucky Univrsity was among

More information

New Basis Functions. Section 8. Complex Fourier Series

New Basis Functions. Section 8. Complex Fourier Series Nw Basis Functions Sction 8 Complx Fourir Sris Th complx Fourir sris is prsntd first with priod 2, thn with gnral priod. Th connction with th ral-valud Fourir sris is xplaind and formula ar givn for convrting

More information

Renewable Energy Sources. Solar Cells SJSU-E10 S John Athanasiou

Renewable Energy Sources. Solar Cells SJSU-E10 S John Athanasiou Rnwabl Enrgy Sourcs. Solar Clls SJSU-E10 S-2008 John Athanasiou 1 Rnwabl Enrgy Sourcs Rnwabl: Thy can last indfinitly 1. Wind Turbin: Convrting th wind nrgy into lctricity Wind, Propllr, Elctric Gnrator,

More information

Adverse Selection and Moral Hazard in a Model With 2 States of the World

Adverse Selection and Moral Hazard in a Model With 2 States of the World Advrs Slction and Moral Hazard in a Modl With 2 Stats of th World A modl of a risky situation with two discrt stats of th world has th advantag that it can b natly rprsntd using indiffrnc curv diagrams,

More information

Simulation of a Solar Cell considering Single-Diode Equivalent Circuit Model

Simulation of a Solar Cell considering Single-Diode Equivalent Circuit Model Simulation of a Solar Cll considring Singl-Diod Equivalnt Circuit Modl E.M.G. Rodrigus, R. Mlício,, V.M.F. Mnds and J.P.S. Catalão, Univrsity of Bira Intrior R. Font do Lamiro, - Covilhã (Portugal) Phon:

More information

Basis risk. When speaking about forward or futures contracts, basis risk is the market

Basis risk. When speaking about forward or futures contracts, basis risk is the market Basis risk Whn spaking about forward or futurs contracts, basis risk is th markt risk mismatch btwn a position in th spot asst and th corrsponding futurs contract. Mor broadly spaking, basis risk (also

More information

Current and Resistance

Current and Resistance Chaptr 6 Currnt and Rsistanc 6.1 Elctric Currnt...6-6.1.1 Currnt Dnsity...6-6. Ohm s Law...6-4 6.3 Elctrical Enrgy and Powr...6-7 6.4 Summary...6-8 6.5 Solvd Problms...6-9 6.5.1 Rsistivity of a Cabl...6-9

More information

(Analytic Formula for the European Normal Black Scholes Formula)

(Analytic Formula for the European Normal Black Scholes Formula) (Analytic Formula for th Europan Normal Black Schols Formula) by Kazuhiro Iwasawa Dcmbr 2, 2001 In this short summary papr, a brif summary of Black Schols typ formula for Normal modl will b givn. Usually

More information

Analyzing Product Attributes using Logical Framework of Quality Function Deployment (Phase I): Concept and Application

Analyzing Product Attributes using Logical Framework of Quality Function Deployment (Phase I): Concept and Application Intrnational Journal Enginring Rsarch & Tchnology (IJERT) Vol. 2 Issu 10, Octobr - 2013 Analyzing Product Attributs using Logical Framwork Quality Function Dploymnt (Phas I): Concpt and Application Dvndra

More information

SPREAD OPTION VALUATION AND THE FAST FOURIER TRANSFORM

SPREAD OPTION VALUATION AND THE FAST FOURIER TRANSFORM RESEARCH PAPERS IN MANAGEMENT STUDIES SPREAD OPTION VALUATION AND THE FAST FOURIER TRANSFORM M.A.H. Dmpstr & S.S.G. Hong WP 26/2000 Th Judg Institut of Managmnt Trumpington Strt Cambridg CB2 1AG Ths paprs

More information

ME 612 Metal Forming and Theory of Plasticity. 6. Strain

ME 612 Metal Forming and Theory of Plasticity. 6. Strain Mtal Forming and Thory of Plasticity -mail: azsnalp@gyt.du.tr Makin Mühndisliği Bölümü Gbz Yüksk Tknoloji Enstitüsü 6.1. Uniaxial Strain Figur 6.1 Dfinition of th uniaxial strain (a) Tnsil and (b) Comprssiv.

More information

http://www.wwnorton.com/chemistry/tutorials/ch14.htm Repulsive Force

http://www.wwnorton.com/chemistry/tutorials/ch14.htm Repulsive Force ctivation nrgis http://www.wwnorton.com/chmistry/tutorials/ch14.htm (back to collision thory...) Potntial and Kintic nrgy during a collision + + ngativly chargd lctron cloud Rpulsiv Forc ngativly chargd

More information

Maximum and minimum void ratios and median grain size of granular soils: their importance and correlations with material properties

Maximum and minimum void ratios and median grain size of granular soils: their importance and correlations with material properties 3 r d Intrnational Confrnc on Nw Dvlopmnts in Soil Mchanics and Gotchnical Enginring, 8-30 Jun 01, Nar East Univrsity, Nicosia, North Cyprus Maximum and minimum void ratios and mdian grain siz of granular

More information

Simple Analytical Expressions for the Force and Torque of Axial Magnetic Couplings

Simple Analytical Expressions for the Force and Torque of Axial Magnetic Couplings Simpl Analytical Exprssions for th Forc and Torqu of Axial Magntic Couplings Thirry Lubin, Mzani Smail, Abdrrza zzoug To cit this vrsion: Thirry Lubin, Mzani Smail, Abdrrza zzoug. Simpl Analytical Exprssions

More information

Comparison between Empirical Correlation and Computational Fluid Dynamics Simulation for the Pressure Gradient of Multiphase Flow

Comparison between Empirical Correlation and Computational Fluid Dynamics Simulation for the Pressure Gradient of Multiphase Flow rocdings o World Congrss on nginring 2008 Vol III Comparison btwn mpirical Corrlation and Computational Fluid Dynamics Simulation or rssur Gradint o Multiphas Flow Yvonn S. H. Chang, T. Gansan and K. K.

More information

Chapter 9 Nuclear Radiation Radioactive Isotopes 9.1 radioactive isotope Natural Radioactivity

Chapter 9 Nuclear Radiation Radioactive Isotopes 9.1 radioactive isotope Natural Radioactivity Chaptr 9 Nuclar Radiation 9. Natural Radioactivity Radioactiv Isotops A radioactiv isotop has an unstabl nuclus. mits radiation to bcom mor stabl. can b on or mor of th isotops of an lmnt 2 Nuclar Radiation

More information

Modelling and Solving Two-Step Equations: ax + b = c

Modelling and Solving Two-Step Equations: ax + b = c Modlling and Solving To-Stp Equations: a + b c Focus on Aftr this lsson, you ill b abl to φ modl problms φ ith to-stp linar quations solv to-stp linar quations and sho ho you ord out th ansr Cali borrod

More information

Ethanolic Extraction of Soybean Oil: Oil Solubility Equilibria and Kinetic Studies

Ethanolic Extraction of Soybean Oil: Oil Solubility Equilibria and Kinetic Studies Ethanolic Extraction of Soyban Oil: Oil Solubility Equilibria and Kintic Studis Christiann E. C. Rodrigus*, Natália M. Longo, Cibl C. Silva, Kila K.. Aracava, Bruna R. Garavazo Sparation Enginring Laboratory

More information

CHARACTERISTICS OF FREE SURFACE OF HOT STRANGE QUARK MATTER

CHARACTERISTICS OF FREE SURFACE OF HOT STRANGE QUARK MATTER PROCEEDINGS OF THE YEREVAN STATE UNIVERSITY Physical and Mathmatical Scincs 2016, 3, p. 6 10 CHARACTERISTICS OF FREE SURFACE OF HOT STRANGE QUARK MATTER P h y s i c s A. G. ALAVERDYAN Chair of Wav Procsss

More information

WORKLOAD STANDARD DEPARTMENT OF CIVIL ENGINEERING. for the. Workload Committee : P.N. Gaskin (Chair) J.W. Kamphuis K. Van Dalen. September 24, 1997

WORKLOAD STANDARD DEPARTMENT OF CIVIL ENGINEERING. for the. Workload Committee : P.N. Gaskin (Chair) J.W. Kamphuis K. Van Dalen. September 24, 1997 WORKLOAD STANDARD for th DEPARTMENT OF CIVIL ENGINEERING Sptmbr 24, 1997 Workload Committ : P.N. Gaskin (Chair) J.W. Kamphuis K. Van Daln 9 2 TABLE OF CONTENTS l. INTRODUCTION... 3 2. DEFINITION OF WORKLOAD

More information

CPS 220 Theory of Computation REGULAR LANGUAGES. Regular expressions

CPS 220 Theory of Computation REGULAR LANGUAGES. Regular expressions CPS 22 Thory of Computation REGULAR LANGUAGES Rgular xprssions Lik mathmatical xprssion (5+3) * 4. Rgular xprssion ar built using rgular oprations. (By th way, rgular xprssions show up in various languags:

More information

Flow Switch Diaphragm Style Flow Switch IFW5 10 N Diaphragm style flow switch. Thread type. Model Body size Set flow rate

Flow Switch Diaphragm Style Flow Switch IFW5 10 N Diaphragm style flow switch. Thread type. Model Body size Set flow rate Flo Sitch Diaphragm Styl Flo Sitch Sris IFW5 [Option] Th flo sitch, sris IFW is usd for dtction and confirmation of th flo as a rlaying dvic for th gnral atr applications in som various uipmnt such as

More information

Effect of Graphite Nodularity on Mechanical Properties of Ductile Iron for Waterworks Fittings and Accessories

Effect of Graphite Nodularity on Mechanical Properties of Ductile Iron for Waterworks Fittings and Accessories Intrnational Journal of Civil & Environmntal Enginring IJCEE-IJENS Vol: 1 No: 3 1 Effct of Graphit Nodularity on Mchanical Proprtis of Ductil Iron for Watrworks Fittings and Accssoris A. I. Al-Ghonamy

More information

Theoretical approach to algorithm for metrological comparison of two photothermal methods for measuring of the properties of materials

Theoretical approach to algorithm for metrological comparison of two photothermal methods for measuring of the properties of materials Rvista Invstigación Cintífica, ol. 4, No. 3, Nuva época, sptimbr dicimbr 8, IN 187 8196 Thortical approach to algorithm for mtrological comparison of two photothrmal mthods for masuring of th proprtis

More information

SPECIFIC HEAT AND HEAT OF FUSION

SPECIFIC HEAT AND HEAT OF FUSION PURPOSE This laboratory consists of to sparat xprimnts. Th purpos of th first xprimnt is to masur th spcific hat of to solids, coppr and rock, ith a tchniqu knon as th mthod of mixturs. Th purpos of th

More information

TEMPERATURE COMPENSATION OF A THERMAL FLOW SENSOR BY USING TEMPERATURE COMPENSATION NETWORK. *Corresponding author: sima@tatiuc.edu.

TEMPERATURE COMPENSATION OF A THERMAL FLOW SENSOR BY USING TEMPERATURE COMPENSATION NETWORK. *Corresponding author: sima@tatiuc.edu. National Confrnc on Postgraduat sarch (NCON-PG) 2009 st Octobr 2009, UMP Confrnc Hall, Malaysia Cntr for Graduat Studis, Univrsiti Malaysia Pahang Editors: M.M. Noor; M.M. ahman and K. Kadirgama EMPEAUE

More information

II. Equipment. Magnetic compass, magnetic dip compass, Helmholtz coils, HP 6212 A power supply, Keithley model 169 multimeter

II. Equipment. Magnetic compass, magnetic dip compass, Helmholtz coils, HP 6212 A power supply, Keithley model 169 multimeter Magntic fild of th arth I. Objctiv: Masur th magntic fild of th arth II. Equipmnt. Magntic compass, magntic dip compass, Hlmholtz s, HP 6212 A powr supply, Kithly modl 169 multimtr III Introduction. IIIa.

More information

An Analysis of Synergy Degree of Primary-Tertiary Industry System in Dujiangyan City

An Analysis of Synergy Degree of Primary-Tertiary Industry System in Dujiangyan City www.ccsnt.org/ijbm Intrnational Journal of Businss and Managmnt Vol. 6, No. 8; August An Analysis of Synrgy Dgr of Primary-Trtiary Industry Systm in Dujiangyan City Qizhi Yang School of Tourism, Sichuan

More information

Vibrational Spectroscopy

Vibrational Spectroscopy Vibrational Spctroscopy armonic scillator Potntial Enrgy Slction Ruls V( ) = k = R R whr R quilibrium bond lngth Th dipol momnt of a molcul can b pandd as a function of = R R. µ ( ) =µ ( ) + + + + 6 3

More information

Free ACA SOLUTION (IRS 1094&1095 Reporting)

Free ACA SOLUTION (IRS 1094&1095 Reporting) Fr ACA SOLUTION (IRS 1094&1095 Rporting) Th Insuranc Exchang (301) 279-1062 ACA Srvics Transmit IRS Form 1094 -C for mployrs Print & mail IRS Form 1095-C to mploys HR Assist 360 will gnrat th 1095 s for

More information

Poisson Distribution. Poisson Distribution Example

Poisson Distribution. Poisson Distribution Example Poisson Distribution Can b usd to valuat th probability of an isolatd vnt occurring a spcific numbr of tims in a givn tim intrval,.g. # of faults, # of lightning stroks tim intrval Rquirmnts: -Evnts must

More information

Variance Components (VARCOMP)

Variance Components (VARCOMP) Varianc Componnts (VARCOP) Notation Th Varianc Componnts procdur provids stimats for variancs of random ffcts undr a gnral linar modl framwor. Four typs of stimation mthods ar availabl in this procdur.

More information

An Broad outline of Redundant Array of Inexpensive Disks Shaifali Shrivastava 1 Department of Computer Science and Engineering AITR, Indore

An Broad outline of Redundant Array of Inexpensive Disks Shaifali Shrivastava 1 Department of Computer Science and Engineering AITR, Indore Intrnational Journal of mrging Tchnology and dvancd nginring Wbsit: www.ijta.com (ISSN 2250-2459, Volum 2, Issu 4, pril 2012) n road outlin of Rdundant rray of Inxpnsiv isks Shaifali Shrivastava 1 partmnt

More information

EVALUATING EFFICIENCY OF SERVICE SUPPLY CHAIN USING DEA (CASE STUDY: AIR AGENCY)

EVALUATING EFFICIENCY OF SERVICE SUPPLY CHAIN USING DEA (CASE STUDY: AIR AGENCY) Indian Journal Fundamntal and Applid Lif Scincs ISSN: 22 64 (Onlin) An Opn Accss, Onlin Intrnational Journal Availabl at www.cibtch.org/sp.d/jls/20/0/jls.htm 20 Vol. (S), pp. 466-47/Shams and Ghafouripour

More information

3. Yes. You can put 20 of the 6-V lights in series, or you can put several of the 6-V lights in series with a large resistance.

3. Yes. You can put 20 of the 6-V lights in series, or you can put several of the 6-V lights in series with a large resistance. CHAPTE 6: DC Circuits sponss to Qustions. Evn though th bird s ft ar at high potntial with rspct to th ground, thr is vry littl potntial diffrnc btwn thm, bcaus thy ar clos togthr on th wir. Th rsistanc

More information

Category 7: Employee Commuting

Category 7: Employee Commuting 7 Catgory 7: Employ Commuting Catgory dscription This catgory includs missions from th transportation of mploys 4 btwn thir homs and thir worksits. Emissions from mploy commuting may aris from: Automobil

More information

Universities as role models for sustainable development

Universities as role models for sustainable development EUA Annual confrnc "Th Sustainability of Europan Univrsitis", Warwick, 120322-23. Sssion - "Sustainabl Campuss" Univrsitis as rol modls for sustainabl dvlopmnt Pam Frdman Vic-Chancllor /miljo Structur

More information

Parallel and Distributed Programming. Performance Metrics

Parallel and Distributed Programming. Performance Metrics Paralll and Distributd Programming Prformanc! wo main goals to b achivd with th dsign of aralll alications ar:! Prformanc: th caacity to rduc th tim to solv th roblm whn th comuting rsourcs incras;! Scalability:

More information

NUMERICAL COMPUTATION OF THE EFFECTIVENESS-NUMBER OF TRANSFER UNITS FOR SEVERAL CROSS-FLOW HEAT EXCHANGERS WITH DIFFERENT FLOW ARRANGEMENTS

NUMERICAL COMPUTATION OF THE EFFECTIVENESS-NUMBER OF TRANSFER UNITS FOR SEVERAL CROSS-FLOW HEAT EXCHANGERS WITH DIFFERENT FLOW ARRANGEMENTS Prodings of COBEM 2009 20th Intrnational Congrss of Mhanial Enginring Novmbr 15-20, 2009, Gramado, RS, Brazil NUMERICAL COMPUTATION OF THE EFFECTIVENESS-NUMBER OF TRANSFER UNITS FOR SEVERAL CROSS-FLOW

More information

C H A P T E R 1 Writing Reports with SAS

C H A P T E R 1 Writing Reports with SAS C H A P T E R 1 Writing Rports with SAS Prsnting information in a way that s undrstood by th audinc is fundamntally important to anyon s job. Onc you collct your data and undrstand its structur, you nd

More information

14.02 Principles of Macroeconomics Problem Set 4 Solutions Fall 2004

14.02 Principles of Macroeconomics Problem Set 4 Solutions Fall 2004 art I. Tru/Fals/Uncrtain Justify your answr with a short argumnt. 4.02 rincipls of Macroconomics roblm St 4 Solutions Fall 2004. High unmploymnt implis that th labor markt is sclrotic. Uncrtain. Th unmploymnt

More information

Hardware Modules of the RSA Algorithm

Hardware Modules of the RSA Algorithm SERBIAN JOURNAL OF ELECTRICAL ENGINEERING Vol. 11, No. 1, Fbruary 2014, 121-131 UDC: 004.3`142:621.394.14 DOI: 10.2298/SJEE140114011S Hardwar Moduls of th RSA Algorithm Vlibor Škobić 1, Branko Dokić 1,

More information

EAS44600 Groundwater Hydrology Lecture 8: Storage Properties of Aquifers Dr. Pengfei Zhang

EAS44600 Groundwater Hydrology Lecture 8: Storage Properties of Aquifers Dr. Pengfei Zhang EAS44600 Groundatr Hydrology Lctur 8: Storag Proprtis of Aquifrs Dr. Pngfi Zhang Moistur Contnt Rcall that th porosity (n) of arth matrials is th ratio of th volum of th voids (V v ) to th total volum

More information

L13: Spectrum estimation nonparametric and parametric

L13: Spectrum estimation nonparametric and parametric L13: Spctrum stimation nonparamtric and paramtric Lnnart Svnsson Dpartmnt of Signals and Systms Chalmrs Univrsity of Tchnology Problm formulation Larning objctivs Aftr today s lctur you should b abl to

More information

SUBATOMIC PARTICLES AND ANTIPARTICLES AS DIFFERENT STATES OF THE SAME MICROCOSM OBJECT. Eduard N. Klenov* Rostov-on-Don. Russia

SUBATOMIC PARTICLES AND ANTIPARTICLES AS DIFFERENT STATES OF THE SAME MICROCOSM OBJECT. Eduard N. Klenov* Rostov-on-Don. Russia SUBATOMIC PARTICLES AND ANTIPARTICLES AS DIFFERENT STATES OF THE SAME MICROCOSM OBJECT Eduard N. Klnov* Rostov-on-Don. Russia Th distribution law for th valus of pairs of th consrvd additiv quantum numbrs

More information

Simulation of the electric field generated by a brown ghost knife fish

Simulation of the electric field generated by a brown ghost knife fish C H A P T R 2 7 Simulation of th lctric fild gnratd by a brown ghost knif fish lctric fild CONCPTS 27.1 Th fild modl 27.2 lctric fild diagrams 27.3 Suprposition of lctric filds 27.4 lctric filds and forcs

More information