D. A. D Ippolito, J. R. Myra, and D. A. Russell Lodestar Research Corporation
|
|
- Neil Houston
- 5 years ago
- Views:
Transcription
1 D. A. D Ippolito, J. R. Myra, ad D. A. Russell Research Corporatio Preseted at the 33rd EPS Coferece o Plasma Physics, Rome, Italy, Jue 9-3, 6
2 Coheret structures ( blobs ) created by edge turbulece covective trasport of particles ad heat across the SOL Experimets, simulatios ad theory show that the trasport rate icreases with collisioality. q q icreased collisioality Λ (ad resistivity η ) strog ballooig (discoectio from sheaths) faster ExB drift ew -regio D code ecapsulates the essetial physics reduced coectio to sheaths, larger turbulet flux at high Λ A correspodece rule (γ v x /a b ) has bee exploited to uderstad ew regimes of blob trasport q icludes collisioality ad geometry depedece q valid i ear SOL ad edge regio (blob birth zoe) q blob trasport ~ mixig legth trasport i edge plasma at high Λ
3 -regio thermal equilibrium model gives good agreemet with C-Mod experimets q covective desity limit (CDL) due to thermal istability q CDL correspods to q > q i edge plasma q occurs at high collisioality The geeral picture from all of this work is that: q q the distictio betwee edge ad SOL disappears at high collisioality because of shorter L ~ λ ei edge trasport icreases dramatically ad ca be estimated usig collisioal blob models with packig fractio ~
4 BOUT simulatio with δ/ ~ by X. Xu (3); Blob aalysis by D. Russell (4) 3D structure is importat! desity ad collisioality Λ icrease with time (gas puffig) blobs discoect from divertor regio ad move faster as η ad Λ icrease Φ eφ (ev) coected outboard midplae OM D divertor.5..5 t (ms) t (ms) discoected Russell et al, Phys. Rev. Lett 4
5 !" η ν e Λ Curvature drift curret source η J sheath Effective circuit resistace R eff potetial Φ R eff J κ L growth rate γ (liear) E B speed v x (blob) J η J pol divertor J κ + X-poit midplae large η Λ discoectio
6 # I the edge plasma, the blob ad mixig legth trasport estimates agree i order of magitude provided that the blob packig fractio ~ (skewess ~ ) ad we use the blob correspodece rule (see ext page). Mixig legth estimate: v~ x ~ ~ ~ i k ~ Φ, / ~ k Φ /( ωl Use saturatio coditio: Blob estimate: ω ), ~ ~ k Φ ~ ω/ k v~ ~ ~ Γ ~ Re[ v x ] ~ γ /(k L ) Γ ~ bvx where b ~ ad vx ~ γ a b (correspodece rule) Usig the correspodece rule, both estimates agree.
7 As oted by Edler et al. (NF 995) for sheathiterchage modes, there is a correspodece betwee the liear istability ad the resultig turbulece. For all istabilities that saturate by wave breakig ( ω ~ k v~ ) we postulate the followig correspodece rule betwee the istability ad the blob velocity: γ v a x b, k a b, L a b growth rate waveumber desity scale legth blob radius
8 $ %! Notes: similar eqs. for T j, but T = cost. here Bohm uits (dimesioless) charge d dt J Φ pol = : J J / L : β y curvature d Φ = (J3 J dt J pol : J sh : J ) / L desity d dt + Γ / L =, Γ = c s, d dt = ( Γ Γ3 ) / L, Γ3 = c s, d dt = + v t J σ ( Φ Φ), J3 = α Φ = L
9 $ " % &'$( Field lies from midplae regio (x, y) are mapped to stretched / squeezed coordiates i X-poit regio (x, y) by faig factor f <<. At preset the model eglects magetic shear. y Outboard Midplae = f, = x x y f y. x X-Poit y x charge is coserved betwee regios ad sheath boudary coditios are applied at the ed of regio J = ecs e ( e( Φ Φ ) ) / T e 3T e
10 ) " φ λφ, t λ σ λ ( ρ s 5 4µ / R, L σ, µ 3 / R) λ t, 5 3µ x ( ρ λ s µ / R, L x for arbitrary λ, µ / R) ivariat scalig method: Coor & Taylor, Phys. Fluids 984 the followig ivariat combiatios characterize the dimesioless parameter space (Λ = collisioality, Ω = scale size) Λ = ω ω η s ω a = ν Ω e e L ρ s, ω Ω = γ s mhd = L R L dispersio relatio ca be writte as ω = ω Λ, Ω(k), ε] ˆ mhd / same dispersio relatio applies to blobs usig the correspodece rule: ω v x /a b ad L, /k a b γ ω k ˆ[ ρ s,
11 Y (Poloidal) %$ & *( +, N Time = 4 a σ =. Λ = X (Radial) b σ =. Λ = c σ =. Λ = d σ =. Λ =.5... Vx.5.. Ω = Blob Dispersio Relatio with VxIm 5 Ω = 36 blobs speed up with icreasig collisioality Λ ( resistivity) for low Λ, small blobs move fastest (b: Ω = (a b /a * ) 5/ blob size)
12 collisioality Λ discoected RB ω Λ = ε / Ω IC ω ε / Λ = Ω ω Λ/Ω RX CR CR s ω /Ω coected electrostatic -regio model Ω = (a b /a * ) 5/ a* = ρ s 4/5 L /5 / R /5 ε ε x = f = X-pt faig factor /ε / scale size Ω
13 $ The two-regio fluid turbulece code predicts a icrease i turbulet particle flux with collisioality, as see i experimets. Figure: Time history of the turbulet (blob) particle flux Γ for two values of the collisioality parameter Λ with f = /4. Γ is averaged over poloidal directio y for a fixed radial poit i the SOL. Note the earlier oset of the oliear turbulet phase ad the much larger particle flux for large Λ. ~ ~ v x y collisioality parameter Λ = Λ at top of pedestal Λ = Λ = t D. Russell (6)
14 -. (x,y) φ (x,y), t.max PHI_, t.max.344 f = /4, β =, σ 3 =, t = Λ = y y, t.max PHI_, t.max.74 Note: more blobs ad faster v x as Λ icreases Λ = y y x D. Russell (6) blobs x
15 Λ Σ3 Σ a b c ix Red: midplae Blue: X-poit Λ = Λ φ (t), φ (t) x,y at x = b Φ x, Ly t max (l ) at x = b f = /4, β =, σ 3 = Λ = Λ Φ x, Ly t partially discoected: φ (t) > φ (t) D. Russell (6)
16 I this work, we iclude heat trasport i a aalytic -regio model for (Φ, T e ) with, = cost. SOL thermal equilibrium limit desity limit higher desity higher collisioality faster radial heat trasport lower T thermal istability thermal collapse of SOL C-Mod observes covective desity limit (CDL) with q > q our model CDL whe q icreases as X-poit cools (thermal istability aalogous to MARFE with radiative coolig radial covectio) (D Ippolito ad Myra, Phys. Plasmas, Jue, 6)
17 . T H H H T warm X-pt. cold X-pt. T T = midplae, T = X-pt T T H C C heat covectio warm X-pt root (solid) is thermally stable cold X-pt root (dashed) is ustable thermal istability of SOL.8.6 Q.4. Q Q Q Q C fixed root coalescece = CDL C
18 %$ ))" $/ # Model C-Mod data.8 Q Q.6.4 Q Q. Q heat covectio C α d Λ / C / LaBombard et al, NF 5
Perturbative Thermal Transport Studies on Alcator C-Mod
Perturbative Thermal Trasport Studies o Alcator C-Mod A.J. Creely 1 A.E. White, 1 E.M. Edlud, 1 N.T. Howard, 2 A.E. Hubbard, 1 S. Houshmadyar 3 1 MIT 2 ORISE 3 UT Austi This work is supported by the US
More informationAnalytic Models of Near-Field RF Sheaths
Aalytic Model of Near-Field RF Sheath D. A. D Ippolito ad J. R. Myra Lodetar Reearch Corporatio Preeted at the 18th Topical Coferece o Radio Frequecy Power i Plama, Ghet, Belgium, Jue 4 6, 9 Backgroud
More informationA STUDY ON MHD BOUNDARY LAYER FLOW OVER A NONLINEAR STRETCHING SHEET USING IMPLICIT FINITE DIFFERENCE METHOD
IRET: Iteratioal oural of Research i Egieerig ad Techology eissn: 39-63 pissn: 3-7308 A STUDY ON MHD BOUNDARY LAYER FLOW OVER A NONLINEAR STRETCHING SHEET USING IMPLICIT FINITE DIFFERENCE METHOD Satish
More informationCEE 522 Autumn Uncertainty Concepts for Geotechnical Engineering
CEE 5 Autum 005 Ucertaity Cocepts for Geotechical Egieerig Basic Termiology Set A set is a collectio of (mutually exclusive) objects or evets. The sample space is the (collectively exhaustive) collectio
More informationModeling of Plasmas and Neutrals Including Plasma-Wall Interaction for Long Term Tokamak Operation
odelig of Plasmas ad Neutrals Icludig Plasma-Wall Iteractio for Log Term Tokamak Operatio Akiyoshi Hatayama 1, Kousuke Okamoto 1, Ryoko Tatsumi 1, Kazuhiro. Abe 1, ad Kazuaki Haada 2 1. Backgroud/otivatio
More informationL-H transitions driven by ion heating in scrape-off layer turbulence (SOLT) model simulations
L-H transitions driven by ion heating in scrape-off layer turbulence (SOLT) model simulations D.A. Russell, D.A. D Ippolito and J.R. Myra Research Corporation, Boulder, CO, USA Presented at the 015 Joint
More informationGuiding-center transformation 1. δf = q ( c v f 0, (1) mc (v B 0) v f 0. (3)
Guidig-ceter trasformatio 1 This is my otes whe readig Liu Che s book[1]. 1 Vlasov equatio The liearized Vlasov equatio is [ t + v x + q m E + v B c ] δf = q v m δe + v δb c v f, 1 where f ad δf are the
More informationIntroduction to Astrophysics Tutorial 2: Polytropic Models
Itroductio to Astrophysics Tutorial : Polytropic Models Iair Arcavi 1 Summary of the Equatios of Stellar Structure We have arrived at a set of dieretial equatios which ca be used to describe the structure
More information17 Phonons and conduction electrons in solids (Hiroshi Matsuoka)
7 Phoos ad coductio electros i solids Hiroshi Matsuoa I this chapter we will discuss a miimal microscopic model for phoos i a solid ad a miimal microscopic model for coductio electros i a simple metal.
More informationMark Lundstrom Spring SOLUTIONS: ECE 305 Homework: Week 5. Mark Lundstrom Purdue University
Mark udstrom Sprig 2015 SOUTIONS: ECE 305 Homework: Week 5 Mark udstrom Purdue Uiversity The followig problems cocer the Miority Carrier Diffusio Equatio (MCDE) for electros: Δ t = D Δ + G For all the
More informationChapter 2 Motion and Recombination of Electrons and Holes
Chapter 2 Motio ad Recombiatio of Electros ad Holes 2.1 Thermal Eergy ad Thermal Velocity Average electro or hole kietic eergy 3 2 kt 1 2 2 mv th v th 3kT m eff 3 23 1.38 10 JK 0.26 9.1 10 1 31 300 kg
More informationa b c d e f g h Supplementary Information
Supplemetary Iformatio a b c d e f g h Supplemetary Figure S STM images show that Dark patters are frequetly preset ad ted to accumulate. (a) mv, pa, m ; (b) mv, pa, m ; (c) mv, pa, m ; (d) mv, pa, m ;
More informationUNIFORM FLOW. U x. U t
UNIFORM FLOW if : 1) there are o appreciable variatios i the chael geometry (width, slope, roughess/grai size), for a certai legth of a river reach ) flow discharge does ot vary the, UNIFORM FLOW coditios
More informationCollisionality and magnetic geometry effects on tokamak edge turbulent transport II. Many-blob turbulence in the two-region model
Collisionality and magnetic geometry effects on tokamak edge turbulent transport II. Many-blob turbulence in the two-region model D. A. Russell, J. R. Myra and D. A. D Ippolito Lodestar Research Corporation,
More informationRecent Experimental Results in ADITYA Tokamak
Recet Experimetal Results i ADITYA Tokamak R. Jha ad the ADITYA Team Istitute for Plasma Research, Bhat, Gadhiagar-382 428, INDIA e-mail:rjha@ipr.res.i Abstract. Recet studies o measuremets of edge turbulece
More informationMagnetic topology effects on Alcator C-Mod scrapeoff layer flow
PSFC/JA-08-15 Magetic topology effects o Alcator C-Mod scrapeoff layer flow Simakov, A.N.*, Catto, P.J, LaBombard, B. ad Glasser, A.H.* May 2008 *Los Alamos Natioal Laboratory, Los Alamos Plasma Sciece
More informationLecture 9: Diffusion, Electrostatics review, and Capacitors. Context
EECS 5 Sprig 4, Lecture 9 Lecture 9: Diffusio, Electrostatics review, ad Capacitors EECS 5 Sprig 4, Lecture 9 Cotext I the last lecture, we looked at the carriers i a eutral semicoductor, ad drift currets
More informationParasitic Resistance L R W. Polysilicon gate. Drain. contact L D. V GS,eff R S R D. Drain
Parasitic Resistace G Polysilico gate rai cotact V GS,eff S R S R S, R S, R + R C rai Short Chael Effects Chael-egth Modulatio Equatio k ( V V ) GS T suggests that the trasistor i the saturatio mode acts
More informationBoundary layer problem on conveyor belt. Gabriella Bognár University of Miskolc 3515 Miskolc-Egyetemváros, Hungary
Boudary layer problem o coveyor belt Gabriella Bogár Uiversity of Miskolc 355 Miskolc-Egyetemváros, Hugary e-mail: matvbg@ui-miskolc.hu Abstract: A techologically importat source of the boudary layer pheomeo
More informationMETHOD OF FUNDAMENTAL SOLUTIONS FOR HELMHOLTZ EIGENVALUE PROBLEMS IN ELLIPTICAL DOMAINS
Please cite this article as: Staisław Kula, Method of fudametal solutios for Helmholtz eigevalue problems i elliptical domais, Scietific Research of the Istitute of Mathematics ad Computer Sciece, 009,
More informationCO-LOCATED DIFFUSE APPROXIMATION METHOD FOR TWO DIMENSIONAL INCOMPRESSIBLE CHANNEL FLOWS
CO-LOCATED DIFFUSE APPROXIMATION METHOD FOR TWO DIMENSIONAL INCOMPRESSIBLE CHANNEL FLOWS C.PRAX ad H.SADAT Laboratoire d'etudes Thermiques,URA CNRS 403 40, Aveue du Recteur Pieau 86022 Poitiers Cedex,
More informationStreamfunction-Vorticity Formulation
Streamfuctio-Vorticity Formulatio A. Salih Departmet of Aerospace Egieerig Idia Istitute of Space Sciece ad Techology, Thiruvaathapuram March 2013 The streamfuctio-vorticity formulatio was amog the first
More informationpoint, requiring all 4 curves to be continuous Discontinuity in P
. Solutio Methods a Classical approach Basic equatios of stellar structure + boudary coditios i Classical (historical method of solutio: Outward itegratio from ceter, where l = m = ward itegratio from
More informationThe aim of the course is to give an introduction to semiconductor device physics. The syllabus for the course is:
Semicoductor evices Prof. Rb Robert tat A. Taylor The aim of the course is to give a itroductio to semicoductor device physics. The syllabus for the course is: Simple treatmet of p- juctio, p- ad p-i-
More informationTime-Domain Representations of LTI Systems
2.1 Itroductio Objectives: 1. Impulse resposes of LTI systems 2. Liear costat-coefficiets differetial or differece equatios of LTI systems 3. Bloc diagram represetatios of LTI systems 4. State-variable
More informationChapter 2 Motion and Recombination of Electrons and Holes
Chapter 2 Motio ad Recombiatio of Electros ad Holes 2.1 Thermal Motio 3 1 2 Average electro or hole kietic eergy kt mv th 2 2 v th 3kT m eff 23 3 1.38 10 JK 0.26 9.1 10 1 31 300 kg K 5 7 2.310 m/s 2.310
More informationOperational Phase Space of the Edge Plasma in Alcator C-Mod
Operational Phase Space of the Edge Plasma in B. LaBombard, T. Biewer, M. Greenwald, J.W. Hughes B. Lipschultz, N. Smick, J.L. Terry, Team Contributed talk RO.00008 Presented at the 47th Annual Meeting
More informationOn the Blasius correlation for friction factors
O the Blasius correlatio for frictio factors Trih, Khah Tuoc Istitute of Food Nutritio ad Huma Health Massey Uiversity, New Zealad K.T.Trih@massey.ac.z Abstract The Blasius empirical correlatio for turbulet
More informationOlli Simula T / Chapter 1 3. Olli Simula T / Chapter 1 5
Sigals ad Systems Sigals ad Systems Sigals are variables that carry iformatio Systemstake sigals as iputs ad produce sigals as outputs The course deals with the passage of sigals through systems T-6.4
More informationBlob sizes and velocities in the Alcator C-Mod scrapeoff
P1-59 Blob sizes and velocities in the Alcator C-Mod scrapeoff layer R. Kube a,b,*, O. E. Garcia a,b, B. LaBombard b, J. L. Terry b, S. J. Zweben c a Department of Physics and Technology, University of
More informationEcology of Flows and Drift Wave Turbulence: Reduced Models and Applications
1 Ecology of Flows ad Drift Wae Turbulece: Reduced Models ad Applicatios PhD Dissertatio Defese by Rima Hajjar PhD Adisor: P. H. Diamod Backgroud. Publicatios + Pla of Dissertatio Chapter : The Ecology
More informationDynamics of Zonal Shear Collapse in Hydrodynamic Electron Limit. Transport Physics of the Density Limit
Dynamics of Zonal Shear Collapse in Hydrodynamic Electron Limit Transport Physics of the Density Limit R. Hajjar, P. H. Diamond, M. Malkov This research was supported by the U.S. Department of Energy,
More information3. Z Transform. Recall that the Fourier transform (FT) of a DT signal xn [ ] is ( ) [ ] = In order for the FT to exist in the finite magnitude sense,
3. Z Trasform Referece: Etire Chapter 3 of text. Recall that the Fourier trasform (FT) of a DT sigal x [ ] is ω ( ) [ ] X e = j jω k = xe I order for the FT to exist i the fiite magitude sese, S = x [
More informationSize, shape and temperature effect on nanomaterials
Idia Joural of Pure & Applied Physics Vol. 53, November 2015, pp. 768-775 Size, shape ad temperature effect o aomaterials G Sharma, S Bhatt, R Kumar & M Kumar* Departmet of Physics, G.B. Pat Uiversity
More informationThe z-transform. 7.1 Introduction. 7.2 The z-transform Derivation of the z-transform: x[n] = z n LTI system, h[n] z = re j
The -Trasform 7. Itroductio Geeralie the complex siusoidal represetatio offered by DTFT to a represetatio of complex expoetial sigals. Obtai more geeral characteristics for discrete-time LTI systems. 7.
More informationThe axial dispersion model for tubular reactors at steady state can be described by the following equations: dc dz R n cn = 0 (1) (2) 1 d 2 c.
5.4 Applicatio of Perturbatio Methods to the Dispersio Model for Tubular Reactors The axial dispersio model for tubular reactors at steady state ca be described by the followig equatios: d c Pe dz z =
More informationSolid State Device Fundamentals
Solid State Device Fudametals ENS 345 Lecture Course by Alexader M. Zaitsev alexader.zaitsev@csi.cuy.edu Tel: 718 982 2812 4N101b 1 Thermal motio of electros Average kietic eergy of electro or hole (thermal
More informationThe Phi Power Series
The Phi Power Series I did this work i about 0 years while poderig the relatioship betwee the golde mea ad the Madelbrot set. I have fially decided to make it available from my blog at http://semresearch.wordpress.com/.
More informationShocks waves and discontinuities.
Shocks waes ad discotiuities Laurece Rezeau http://www.lpp.fr/?laurece-rezeau OUTLINE Obseratios of discotiuities Jump coditios at the boudary Differet kids of discotiuities What about the boudaries aroud
More informationNumerical simulation of two-phase Darcy-Forchheimer flow during CO 2 injection into deep saline aquifers. Andi Zhang Feb. 4, 2013
Numerical simulatio of two-phase Darcy-Forchheimer flow durig CO 2 ijectio ito deep salie aquifers Adi Zhag Feb. 4, 2013 Darcy flow VS o-darcy flow Darcy flow A liear relatioship betwee volumetric flow
More informationFluid Physics 8.292J/12.330J % (1)
Fluid Physics 89J/133J Problem Set 5 Solutios 1 Cosider the flow of a Euler fluid i the x directio give by for y > d U = U y 1 d for y d U + y 1 d for y < This flow does ot vary i x or i z Determie the
More informationFINALTERM EXAMINATION Fall 9 Calculus & Aalytical Geometry-I Questio No: ( Mars: ) - Please choose oe Let f ( x) is a fuctio such that as x approaches a real umber a, either from left or right-had-side,
More informationPHY4905: Nearly-Free Electron Model (NFE)
PHY4905: Nearly-Free Electro Model (NFE) D. L. Maslov Departmet of Physics, Uiversity of Florida (Dated: Jauary 12, 2011) 1 I. REMINDER: QUANTUM MECHANICAL PERTURBATION THEORY A. No-degeerate eigestates
More information1. Linearization of a nonlinear system given in the form of a system of ordinary differential equations
. Liearizatio of a oliear system give i the form of a system of ordiary differetial equatios We ow show how to determie a liear model which approximates the behavior of a time-ivariat oliear system i a
More informationModelling of plasma edge turbulence with neutrals
Modelling of plasma edge turbulence with neutrals Ben Dudson 1 1 York Plasma Institute, Department of Physics, University of York, Heslington, York YO1 5DD, UK 7 th IAEA TM on Plasma Instabilities 4-6
More information11 Correlation and Regression
11 Correlatio Regressio 11.1 Multivariate Data Ofte we look at data where several variables are recorded for the same idividuals or samplig uits. For example, at a coastal weather statio, we might record
More informationLecture 5-2: Polytropes. Literature: MWW chapter 19
Lecture 5-2: Polytropes Literature: MWW chapter 9!" Preamble The 4 equatios of stellar structure divide ito two groups: Mass ad mometum describig the mechaical structure ad thermal equilibrium ad eergy
More informationNonequilibrium Excess Carriers in Semiconductors
Lecture 8 Semicoductor Physics VI Noequilibrium Excess Carriers i Semicoductors Noequilibrium coditios. Excess electros i the coductio bad ad excess holes i the valece bad Ambiolar trasort : Excess electros
More informationEdge Zonal Flows and Blob Propagation in Alcator C-Mod P5.073 EPS 2011
Edge Zonal Flows and Blob Propagation in Alcator C-Mod S.J. Zweben 1, J.L. Terry 2, M. Agostini 3, B. Davis 1, O. Grulke 4,J. Hughes 2, B. LaBombard 2 D.A. D'Ippolito 6, R. Hager 5, J.R. Myra 6, D.A. Russell
More informationMiscellaneous Notes. Lecture 19, p 1
Miscellaeous Notes The ed is ear do t get behid. All Excuses must be take to 233 Loomis before oo, Thur, Apr. 25. The PHYS 213 fial exam times are * 8-10 AM, Moday, May 6 * 1:30-3:30 PM, Wed, May 8 The
More informationln(i G ) 26.1 Review 26.2 Statistics of multiple breakdowns M Rows HBD SBD N Atoms Time
EE650R: Reliability Physics of Naoelectroic Devices Lecture 26: TDDB: Statistics of Multiple Breadows Date: Nov 17, 2006 ClassNotes: Jaydeep P. Kulari Review: Pradeep R. Nair 26.1 Review I the last class
More information1. pn junction under bias 2. I-Vcharacteristics
Lecture 10 The p Juctio (II) 1 Cotets 1. p juctio uder bias 2. I-Vcharacteristics 2 Key questios Why does the p juctio diode exhibit curret rectificatio? Why does the juctio curret i forward bias icrease
More informationDiscrete-Time Systems, LTI Systems, and Discrete-Time Convolution
EEL5: Discrete-Time Sigals ad Systems. Itroductio I this set of otes, we begi our mathematical treatmet of discrete-time s. As show i Figure, a discrete-time operates or trasforms some iput sequece x [
More informationDYNAMIC ANALYSIS OF BEAM-LIKE STRUCTURES SUBJECT TO MOVING LOADS
DYNAMIC ANALYSIS OF BEAM-LIKE STRUCTURES SUBJECT TO MOVING LOADS Ivaa Štimac 1, Ivica Kožar 1 M.Sc,Assistat, Ph.D. Professor 1, Faculty of Civil Egieerig, Uiverity of Rieka, Croatia INTRODUCTION The vehicle-iduced
More informationCarriers in a semiconductor diffuse in a carrier gradient by random thermal motion and scattering from the lattice and impurities.
Diffusio of Carriers Wheever there is a cocetratio gradiet of mobile articles, they will diffuse from the regios of high cocetratio to the regios of low cocetratio, due to the radom motio. The diffusio
More informationBACKMIXING IN SCREW EXTRUDERS
BACKMIXING IN SCREW EXTRUDERS Chris Rauwedaal, Rauwedaal Extrusio Egieerig, Ic. Paul Grama, The Madiso Group Abstract Mixig is a critical fuctio i most extrusio operatios. Oe of the most difficult mixig
More informationNumerical Conformal Mapping via a Fredholm Integral Equation using Fourier Method ABSTRACT INTRODUCTION
alaysia Joural of athematical Scieces 3(1): 83-93 (9) umerical Coformal appig via a Fredholm Itegral Equatio usig Fourier ethod 1 Ali Hassa ohamed urid ad Teh Yua Yig 1, Departmet of athematics, Faculty
More informationToy models for Rayleigh- Taylor instability:
Toy models for Rayleigh- Taylor istability: Stuart Dalziel Departmet of Applied Mathematics ad Theoretical Physics iversity of Cambridge Iteratioal Workshop o the Physics of Compressible Turbulet Mixig
More informationEE / EEE SAMPLE STUDY MATERIAL. GATE, IES & PSUs Signal System. Electrical Engineering. Postal Correspondence Course
Sigal-EE Postal Correspodece Course 1 SAMPLE STUDY MATERIAL Electrical Egieerig EE / EEE Postal Correspodece Course GATE, IES & PSUs Sigal System Sigal-EE Postal Correspodece Course CONTENTS 1. SIGNAL
More informationEllipsoid Method for Linear Programming made simple
Ellipsoid Method for Liear Programmig made simple Sajeev Saxea Dept. of Computer Sciece ad Egieerig, Idia Istitute of Techology, Kapur, INDIA-08 06 December 3, 07 Abstract I this paper, ellipsoid method
More informationLecture 3. Electron and Hole Transport in Semiconductors
Lecture 3 lectro ad Hole Trasort i Semicoductors I this lecture you will lear: How electros ad holes move i semicoductors Thermal motio of electros ad holes lectric curret via lectric curret via usio Semicoductor
More informationHE ATOM & APPROXIMATION METHODS MORE GENERAL VARIATIONAL TREATMENT. Examples:
5.6 4 Lecture #3-4 page HE ATOM & APPROXIMATION METHODS MORE GENERAL VARIATIONAL TREATMENT Do t restrict the wavefuctio to a sigle term! Could be a liear combiatio of several wavefuctios e.g. two terms:
More informationSalmon: Lectures on partial differential equations. 3. First-order linear equations as the limiting case of second-order equations
3. First-order liear equatios as the limitig case of secod-order equatios We cosider the advectio-diffusio equatio (1) v = 2 o a bouded domai, with boudary coditios of prescribed. The coefficiets ( ) (2)
More informationBLUE PRINT FOR MODEL QUESTION PAPER 3
Uit Chapter Number Number of teachig Hours Weightage of marks Mark Marks Marks 5 Marks (Theory) 5 Marks (Numerical Problem) BLUE PNT FO MODEL QUESTON PAPE Class : PUC Subject : PHYSCS () CHAPTES Electric
More informationSLAC Summer School on Electron and Photon Beams. Tor Raubenheimer Lecture #3: High Gain FEL s
SLAC Summer School o Electro ad Photo Beams Tor Raubeheimer Lecture #3: High Gai FEL s Outlie Sychrotro radiatio Bedig magets Wigglers ad udulators Iverse Compto scatterig Free Electro Lasers FEL Oscillators
More informationTHEORETICAL RESEARCH REGARDING ANY STABILITY THEOREMS WITH APPLICATIONS. Marcel Migdalovici 1 and Daniela Baran 2
ICSV4 Cairs Australia 9- July, 007 THEORETICAL RESEARCH REGARDING ANY STABILITY THEOREMS WITH APPLICATIONS Marcel Migdalovici ad Daiela Bara Istitute of Solid Mechaics, INCAS Elie Carafoli, 5 C-ti Mille
More informationSOLUTIONS: ECE 606 Homework Week 7 Mark Lundstrom Purdue University (revised 3/27/13) e E i E T
SOUIONS: ECE 606 Homework Week 7 Mark udstrom Purdue Uiversity (revised 3/27/13) 1) Cosider a - type semicoductor for which the oly states i the badgap are door levels (i.e. ( E = E D ). Begi with the
More informationTaylor expansion: Show that the TE of f(x)= sin(x) around. sin(x) = x - + 3! 5! L 7 & 8: MHD/ZAH
Taylor epasio: Let ƒ() be a ifiitely differetiable real fuctio. A ay poit i the eighbourhood of 0, the fuctio ƒ() ca be represeted by a power series of the followig form: X 0 f(a) f() f() ( ) f( ) ( )
More informationB. Maddah ENMG 622 ENMG /27/07
B. Maddah ENMG 622 ENMG 5 3/27/7 Queueig Theory () What is a queueig system? A queueig system cosists of servers (resources) that provide service to customers (etities). A Customer requestig service will
More informationLecture 4 Conformal Mapping and Green s Theorem. 1. Let s try to solve the following problem by separation of variables
Lecture 4 Coformal Mappig ad Gree s Theorem Today s topics. Solvig electrostatic problems cotiued. Why separatio of variables does t always work 3. Coformal mappig 4. Gree s theorem The failure of separatio
More informationComputational Fluid Dynamics. Lecture 3
Computatioal Fluid Dyamics Lecture 3 Discretizatio Cotiued. A fourth order approximatio to f x ca be foud usig Taylor Series. ( + ) + ( + ) + + ( ) + ( ) = a f x x b f x x c f x d f x x e f x x f x 0 0
More informationShock-Turbulence Interaction
Shock-Turbulece Iteractio A.Sakurai ad M.Tsukamoto Tokyo Deki Uiversity, Nishikicho -, Kada, Chiyoda-ku, Tokyo, Japa Abstract. For the geeral purpose of ivestigatig pheomeo of shock-turbulece iteractio,
More informationMulticomponent-Liquid-Fuel Vaporization with Complex Configuration
Multicompoet-Liquid-Fuel Vaporizatio with Complex Cofiguratio William A. Sirigao Guag Wu Uiversity of Califoria, Irvie Major Goals: for multicompoet-liquid-fuel vaporizatio i a geeral geometrical situatio,
More informationNotes 12 Asymptotic Series
ECE 6382 Fall 207 David R. Jackso otes 2 Asymptotic Series Asymptotic Series A asymptotic series (as ) is of the form a ( ) f as = 0 or f a + a a + + ( ) 2 0 2 ote the asymptotically equal to sig. The
More informationAll Excuses must be taken to 233 Loomis before 4:15, Monday, April 30.
Miscellaeous Notes The ed is ear do t get behid. All Excuses must be take to 233 Loomis before 4:15, Moday, April 30. The PYS 213 fial exam times are * 8-10 AM, Moday, May 7 * 8-10 AM, Tuesday, May 8 ad
More information2.CMOS Transistor Theory
CMOS LSI esig.cmos rasistor heory Fu yuzhuo School of microelectroics,sju Itroductio omar fadhil,baghdad outlie PN juctio priciple CMOS trasistor itroductio Ideal I- characteristics uder static coditios
More informationBasic Physics of Semiconductors
Chater 2 Basic Physics of Semicoductors 2.1 Semicoductor materials ad their roerties 2.2 PN-juctio diodes 2.3 Reverse Breakdow 1 Semicoductor Physics Semicoductor devices serve as heart of microelectroics.
More informationElectrical Resistance
Electrical Resistace I + V _ W Material with resistivity ρ t L Resistace R V I = L ρ Wt (Uit: ohms) where ρ is the electrical resistivity Addig parts/billio to parts/thousad of dopats to pure Si ca chage
More information5.74 TIME-DEPENDENT QUANTUM MECHANICS
p. 1 5.74 TIME-DEPENDENT QUANTUM MECHANICS The time evolutio of the state of a system is described by the time-depedet Schrödiger equatio (TDSE): i t ψ( r, t)= H ˆ ψ( r, t) Most of what you have previously
More informationDynamic Instability of Taut Mooring Lines Subjected to Bi-frequency Parametric Excitation
Proceedigs of the 1 th Iteratioal Coferece o the Stability of Ships ad Ocea Vehicles, 14-19 Jue 15, Glasgow, UK. Dyamic Istability of Taut Moorig Lies Subjected to Bi-frequecy Parametric Excitatio Aiju
More informationModified Decomposition Method by Adomian and. Rach for Solving Nonlinear Volterra Integro- Differential Equations
Noliear Aalysis ad Differetial Equatios, Vol. 5, 27, o. 4, 57-7 HIKARI Ltd, www.m-hikari.com https://doi.org/.2988/ade.27.62 Modified Decompositio Method by Adomia ad Rach for Solvig Noliear Volterra Itegro-
More informationSECTION 2 Electrostatics
SECTION Electrostatics This sectio, based o Chapter of Griffiths, covers effects of electric fields ad forces i static (timeidepedet) situatios. The topics are: Electric field Gauss s Law Electric potetial
More informationTHE NUMERICAL SOLUTION OF THE NEWTONIAN FLUIDS FLOW DUE TO A STRETCHING CYLINDER BY SOR ITERATIVE PROCEDURE ABSTRACT
Europea Joural of Egieerig ad Techology Vol. 3 No., 5 ISSN 56-586 THE NUMERICAL SOLUTION OF THE NEWTONIAN FLUIDS FLOW DUE TO A STRETCHING CYLINDER BY SOR ITERATIVE PROCEDURE Atif Nazir, Tahir Mahmood ad
More informationToday. Homework 4 due (usual box) Center of Mass Momentum
Today Homework 4 due (usual box) Ceter of Mass Mometum Physics 40 - L 0 slide review Coservatio of Eergy Geeralizatio of Work-Eergy Theorem Says that for ay isolated system, the total eergy is coserved
More informationPhysics 7440, Solutions to Problem Set # 8
Physics 7440, Solutios to Problem Set # 8. Ashcroft & Mermi. For both parts of this problem, the costat offset of the eergy, ad also the locatio of the miimum at k 0, have o effect. Therefore we work with
More informationELEG 4603/5173L Digital Signal Processing Ch. 1 Discrete-Time Signals and Systems
Departmet of Electrical Egieerig Uiversity of Arasas ELEG 4603/5173L Digital Sigal Processig Ch. 1 Discrete-Time Sigals ad Systems Dr. Jigxia Wu wuj@uar.edu OUTLINE 2 Classificatios of discrete-time sigals
More informationOrthogonal transformations
Orthogoal trasformatios October 12, 2014 1 Defiig property The squared legth of a vector is give by takig the dot product of a vector with itself, v 2 v v g ij v i v j A orthogoal trasformatio is a liear
More informationMechatronics. Time Response & Frequency Response 2 nd -Order Dynamic System 2-Pole, Low-Pass, Active Filter
Time Respose & Frequecy Respose d -Order Dyamic System -Pole, Low-Pass, Active Filter R 4 R 7 C 5 e i R 1 C R 3 - + R 6 - + e out Assigmet: Perform a Complete Dyamic System Ivestigatio of the Two-Pole,
More information(c) Write, but do not evaluate, an integral expression for the volume of the solid generated when R is
Calculus BC Fial Review Name: Revised 7 EXAM Date: Tuesday, May 9 Remiders:. Put ew batteries i your calculator. Make sure your calculator is i RADIAN mode.. Get a good ight s sleep. Eat breakfast. Brig:
More informationSummary of pn-junction (Lec )
Lecture #12 OUTLNE Diode aalysis ad applicatios cotiued The MOFET The MOFET as a cotrolled resistor Pich-off ad curret saturatio Chael-legth modulatio Velocity saturatio i a short-chael MOFET Readig Howe
More informationPhysics 324, Fall Dirac Notation. These notes were produced by David Kaplan for Phys. 324 in Autumn 2001.
Physics 324, Fall 2002 Dirac Notatio These otes were produced by David Kapla for Phys. 324 i Autum 2001. 1 Vectors 1.1 Ier product Recall from liear algebra: we ca represet a vector V as a colum vector;
More informationELMs and Constraints on the H-Mode Pedestal:
ELMs and Constraints on the H-Mode Pedestal: A Model Based on Peeling-Ballooning Modes P.B. Snyder, 1 H.R. Wilson, 2 J.R. Ferron, 1 L.L. Lao, 1 A.W. Leonard, 1 D. Mossessian, 3 M. Murakami, 4 T.H. Osborne,
More informationUsing vegetation properties to predict flow resistance and erosion rates. Nick Kouwen University of Waterloo Waterloo, Canada
1/37 INTERNATIONAL WORKSHOP o RIParia FORest Vegetated Chaels: Hydraulic Morphological ad Ecological Aspects Treto, Italy, 20-22 February 2003 Usig vegetatio properties to predict flow resistace ad erosio
More informationNumerical Methods for PDEs
Numerical Methods for PDEs Hyperbolic PDEs: Coupled system/noliear coservatio laws/a oliear Lax-Wedroff scheme (Lecture 18, Week 6 Markus Schmuck Departmet of Mathematics ad Maxwell Istitute for Mathematical
More informationL 5 & 6: RelHydro/Basel. f(x)= ( ) f( ) ( ) ( ) ( ) n! 1! 2! 3! If the TE of f(x)= sin(x) around x 0 is: sin(x) = x - 3! 5!
aylor epasio: Let ƒ() be a ifiitely differetiable real fuctio. At ay poit i the eighbourhood of =0, the fuctio ca be represeted as a power series of the followig form: X 0 f(a) f() ƒ() f()= ( ) f( ) (
More informationMechanics Physics 151
Mechaics Physics 151 Lecture 4 Cotiuous Systems ad Fields (Chapter 13) What We Did Last Time Built Lagragia formalism for cotiuous system Lagragia L = L dxdydz d L L Lagrage s equatio = dx η, η Derived
More informationMATH 1080: Calculus of One Variable II Fall 2017 Textbook: Single Variable Calculus: Early Transcendentals, 7e, by James Stewart.
MATH 1080: Calculus of Oe Variable II Fall 2017 Textbook: Sigle Variable Calculus: Early Trascedetals, 7e, by James Stewart Uit 3 Skill Set Importat: Studets should expect test questios that require a
More informationMath 312 Lecture Notes One Dimensional Maps
Math 312 Lecture Notes Oe Dimesioal Maps Warre Weckesser Departmet of Mathematics Colgate Uiversity 21-23 February 25 A Example We begi with the simplest model of populatio growth. Suppose, for example,
More informationPropagation of Cathode-Directed Streamer Discharges in Air
Propagatio of Cathode-Directed Streamer Discharges i Air Yuriy Serdyuk Associate Professor High Voltage Egieerig Chalmers Uiversity of Techology SE-41296 Gotheburg, Swede E-mail: yuriy.serdyuk@chalmers.se
More informationSimple Polygons of Maximum Perimeter Contained in a Unit Disk
Discrete Comput Geom (009) 1: 08 15 DOI 10.1007/s005-008-9093-7 Simple Polygos of Maximum Perimeter Cotaied i a Uit Disk Charles Audet Pierre Hase Frédéric Messie Received: 18 September 007 / Revised:
More information