Lecture 3: Diffusion: Fick s first law
|
|
- Jonathan Goodwin
- 7 years ago
- Views:
Transcription
1 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 Fick s first law, and undrstand th maning of diffusion cofficint and diffusion lngth. In last two lcturs, w larnd th thrmodynamics, concrnd mainly with stabl or quilibrium systms. Th study of matrials Kintics, lik phas transformation, concrns thos mchanism by which a systm attmpts to rach th quilibrium stat and how long it taks. On of th most fundamntal procsss that control th rat at which many transformation occur is th diffusion, as w will larn in th following svral lcturs and us throughout th whol smstr. Gnral rviw of diffusion: Diffusion dscribs th sprad of particls (which can also b atoms, molculs) through random motion usually (but not always) from rgions of highr concntration to rgions of lowr concntration. Th tim dpndnc of th statistical distribution in spac is givn by th diffusion quation. Th concpt of diffusion is tid to that of mass transfr drivn by a concntration gradint, but diffusion can still occur whn thr is no concntration gradint (but thr will b no nt flux). History: Th concpt of diffusion mrgd from physical scincs. Th paradigmatic xampls wr hat diffusion, molcular diffusion and rownian motion. Thir mathmatical dscription was laboratd by Josph Fourir in 8, dolf Fick in 855 and by lbrt Einstin in 905. Spcifically, atomic diffusion is a diffusion procss whrby th random thrmally-activatd movmnt of atoms in a solid rsults in th nt transport of atoms. For xampl, hlium atoms insid a balloon can diffus through th wall of th balloon and scap, rsulting in th balloon slowly dflating. Othr air molculs (.g. oxygn, nitrogn) hav lowr mobilitis and thus diffus mor slowly through th balloon wall. Thr is a concntration gradint in th balloon wall, bcaus th balloon was initially filld with hlium, and thus thr is plnty of hlium on th insid, but thr is rlativly littl hlium on th outsid (hlium is not a major componnt of air). Th rat of transport is govrnd by th diffusivity and th concntration gradint. Diffusion in solid: In th crystal solid stat, diffusion within th crystal lattic occurs by ithr intrstitial or substitutional mchanisms and is rfrrd to as lattic diffusion. In intrstitial lattic diffusion, a diffusant (such as C in an iron alloy), will diffus in btwn th lattic structur of anothr crystallin lmnt. In substitutional lattic diffusion (slf-diffusion for xampl), th
2 atom can only mov by substituting plac with anothr atom. Substitutional lattic diffusion is oftn contingnt upon th availability of point vacancis throughout th crystal lattic. Diffusing particls migrat from point vacancy to point vacancy by th rapid, ssntially random jumping about (jump diffusion). S blow in this Lctur for dtails about intrstitial or substitutional. Diffusion is drivn by dcras in Gibbs fr nrgy or chmical potntial diffrnc. s a simpl illustration of this, considr th figur blow, whr two blocks of th sam - solid solution, but with diffrnt compositions (concntrations), ar wldd togthr and hld at a tmpratur high nough for long rang diffusion to occur. Cas : along concntration gradint - rich - rich μ G G a G μ G m For cas : μ > μ > => gos from to => gos from to Th molar fr nrgy diagram of th - alloy is shown at right: th molar fr nrgy of ach part is givn by G and G, and th initial total fr nrgy of th wldd block is G a, upon th diffusion as illustratd on th lft (so as to liminat th concntration diffrnc), th total fr nrgy dcrass towards G m, th fr nrgy charactristic of a homognous systm. In this cas, th dcras in fr nrgy is producd by and diffusion along th concntration gradint. Howvr, diffusion nds not always b along th concntration gradint. For xampl, in th alloy systms that contain a miscibility gap, th fr nrgy curv can hav a ngativ curvatur at low tmpratur, as shown blow in Cas. In such a cas, and atoms would diffus against th concntration gradint (i.., toward th rgions of high concntration as shown at lft blow), though this diffusion is still a natural (spontanous) procss as it rducs th total fr nrgy from G a to G m as shown. For cas : μ > μ > => gos from to => gos from to
3 Cas : against concntration gradint - rich - rich μ G G a G μ G m Diffusion is always along chmical potntial gradint! Diffusion stops whn chmical potntial of all spcis vrywhr ar sam. In most cass, chmical potntial incrass with incrasing concntration, so it is convnint to xprss diffusion in trm of concntration. Now lts considr Intrstitial diffusion vs. Substitutional diffusion: Intrstitial Substitutional (by vacancy) Considrd at low concntration Now Lt s dduc th Diffusion Equation for intrstitial diffusion basd on th following illustration, moving from position to. 3
4 x x+a c (x) ~ concntration at x, dc c (x+a) = c(x) + a ~ concntration at x+a μ(x) ~ chmical potntial at x, ΔG ~ activation barrir d µ( x) μ(x+a) =μ(x) + a ~ chmical potntial at x+a Th forward rat - G G ; RT --- s last Lctur for how to dduc this quation with an assumption that ΔG << RT, and this is usually tru for diffusion, whr th fr nrgy chang within short distanc is small. ΔG = G (x+a) - G (x) = μ(x+a) - μ(x) (hr ΔG is only contributd by th chang in chmical potntial ) Now G RT = µ ( x + a) µ ( x) a dµ = RT RT RT d µ( x) (as dfind abov, μ(x+a) =μ(x) + a ) Lt ν b vibrational frquncy, thn an atom will hav nough nrgy in unit tim (pr scond) to ovrcom th barrir ν can dfin as Γ. - G tims, i.., th numbr of jump of stp a pr scond, which w Γ = ν - G In a thr-dimnsional spac (lattic), an atom can jump in six quivalnt dirctions (±x, ±y, ±z), ν so th numbr of jumps toward right (along x ) in on scond is. So, th nt forward rat for an atom to jump from x to x+a is 4
5 Rat = ν a dµ dµ (- ) (whr <0) RT Lt n(x) b th numbr of atoms (solut) pr unit ara at x, thn th nt flux along x. (i.., numbr of atom passing through unit ara in unit tim along x ) is ν J = n(x) a dµ (- ) () RT Sinc n(x) = a c(x), Eq. () can b writtn as J = - c ( x) dµ RT () Now lt s considr th xprssion of chmical potntial as w larnd in th cours of Thrmodynamics: μ(x) = μ 0 + RTlna(x) = μ 0 + RT ln γ cx ( ) whr a(x) is th activity of solut (atom) at x, γ is th activity cofficint, a constant. Thn, w hav dµ RT dc ( x) = c(x) (3) Substituting Eq. (3) into Eq. (), w hav J = - dc ( x) (4) Lt s dfin D = Thn w hav dc ( x) J = -D as th intrinsic diffusion cofficint (Unit: D: cm /sc; J: numbr/cm /sc) This is th Fick s first law of diffusion. 5
6 Now, lt s considr diffusion in a thr-dimnsional spac, i.., random walk of an atom: s dfind on pag 4, Γ = ν - G Combining with D = W hav D = Γ a = Thn w hav - G Γ= ν = D / a (Γ: numbr of jump an atom mak pr scond) For a random walk in thr-dimnsions, an atom travls an avrag distanc of stps (i.., n tims of jump) with a stp lngth of a. n a aftr n Thus, aftr tim t, th atom jumps Γ t tims (stps). So it movs a distanc of r = a Dt Γ t = a a = D t.4 D t This is usually dfind as th diffusion lngth.
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 informationQuestion 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 informationFundamentals: NATURE OF HEAT, TEMPERATURE, AND ENERGY
Fundamntals: NATURE OF HEAT, TEMPERATURE, AND ENERGY DEFINITIONS: Quantum Mchanics study of individual intractions within atoms and molculs of particl associatd with occupid quantum stat of a singl particl
More informationNew 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 informationThe 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 informationCPS 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 informationEcon 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 informationTraffic 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 informationQUANTITATIVE 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 informationVibrational 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 informationAP 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 informationby 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 informationME 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 informationBasis 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 informationMathematics. Mathematics 3. hsn.uk.net. Higher HSN23000
hsn uknt Highr Mathmatics UNIT Mathmatics HSN000 This documnt was producd spcially for th HSNuknt wbsit, and w rquir that any copis or drivativ works attribut th work to Highr Still Nots For mor dtails
More informationForeign 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 informationIntroduction 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 informationAdverse 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 informationC 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 informationLecture 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 informationEFFECT 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 informationSPECIAL VOWEL SOUNDS
SPECIAL VOWEL SOUNDS Plas consult th appropriat supplmnt for th corrsponding computr softwar lsson. Rfr to th 42 Sounds Postr for ach of th Spcial Vowl Sounds. TEACHER INFORMATION: Spcial Vowl Sounds (SVS)
More informationInternational 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 informationSection 7.4: Exponential Growth and Decay
1 Sction 7.4: Exponntial Growth and Dcay Practic HW from Stwart Txtbook (not to hand in) p. 532 # 1-17 odd In th nxt two ction, w xamin how population growth can b modld uing diffrntial quation. W tart
More informationCurrent 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 informationFactorials! Stirling s formula
Author s not: This articl may us idas you havn t larnd yt, and might sm ovrly complicatd. It is not. Undrstanding Stirling s formula is not for th faint of hart, and rquirs concntrating on a sustaind mathmatical
More information81-1-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 information5.4 Exponential Functions: Differentiation and Integration TOOTLIFTST:
.4 Eponntial Functions: Diffrntiation an Intgration TOOTLIFTST: Eponntial functions ar of th form f ( ) Ab. W will, in this sction, look at a spcific typ of ponntial function whr th bas, b, is.78.... This
More informationCapacitance and Dielectrics
Chaptr 5 Capacitanc and Dilctrics 5.1 Introduction...5-3 5. Calculation of Capacitanc...5-4 Exampl 5.1: Paralll-Plat Capacitor...5-4 Intractiv Simulation 5.1: Paralll-Plat Capacitor...5-6 Exampl 5.: Cylindrical
More information(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 informationSPREAD 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 informationESCI 241 Meteorology Lesson 6 Humidity
ESCI 41 Mtorology Lsson 6 Humiity Raing: MT Chatr 5 PARTIAL PRESSURE In a mixtur of gass, ach gas scis contributs to th total rssur. ο Th rssur xrt by a singl gas scis is known as th artial rssur for that
More informationA Theoretical Model of Public Response to the Homeland Security Advisory System
A Thortical Modl of Public Rspons to th Homland Scurity Advisory Systm Amy (Wnxuan) Ding Dpartmnt of Information and Dcision Scincs Univrsity of Illinois Chicago, IL 60607 wxding@uicdu Using a diffrntial
More informationConstraint-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 informationTIME MANAGEMENT. 1 The Process for Effective Time Management 2 Barriers to Time Management 3 SMART Goals 4 The POWER Model e. Section 1.
Prsonal Dvlopmnt Track Sction 1 TIME MANAGEMENT Ky Points 1 Th Procss for Effctiv Tim Managmnt 2 Barrirs to Tim Managmnt 3 SMART Goals 4 Th POWER Modl In th Army, w spak of rsourcs in trms of th thr M
More information5 2 index. e e. Prime numbers. Prime factors and factor trees. Powers. worked example 10. base. power
Prim numbrs W giv spcial nams to numbrs dpnding on how many factors thy hav. A prim numbr has xactly two factors: itslf and 1. A composit numbr has mor than two factors. 1 is a spcial numbr nithr prim
More informationLong run: Law of one price Purchasing Power Parity. Short run: Market for foreign exchange Factors affecting the market for foreign exchange
Lctur 6: Th Forign xchang Markt xchang Rats in th long run CON 34 Mony and Banking Profssor Yamin Ahmad xchang Rats in th Short Run Intrst Parity Big Concpts Long run: Law of on pric Purchasing Powr Parity
More informationCIRCUITS AND ELECTRONICS. Basic Circuit Analysis Method (KVL and KCL method)
6. CIRCUITS AND ELECTRONICS Basic Circuit Analysis Mthod (KVL and KCL mthod) Cit as: Anant Agarwal and Jffry Lang, cours matrials for 6. Circuits and Elctronics, Spring 7. MIT 6. Fall Lctur Rviw Lumpd
More informationChapter 5: Diffusion. 5.1 Steady-State Diffusion
: Diffusion Diffusion: the movement of particles in a solid from an area of high concentration to an area of low concentration, resulting in the uniform distribution of the substance Diffusion is process
More informationAn 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 informationChapter 19: Permanent Magnet DC Motor Characteristics
Chaptr 19: Prmannt Magnt DC Motor Charactristics 19.1: ntroduction Dirct currnt (DC) motors compris on of th most common typs of actuator dsignd into lctromchanical systms. hy ar a vry straightforward
More informationArchitecture of the proposed standard
Architctur of th proposd standard Introduction Th goal of th nw standardisation projct is th dvlopmnt of a standard dscribing building srvics (.g.hvac) product catalogus basd on th xprincs mad with th
More informationVersion 1.0. General Certificate of Education (A-level) January 2012. Mathematics MPC3. (Specification 6360) Pure Core 3. Final.
Vrsion.0 Gnral Crtificat of Education (A-lvl) January 0 Mathmatics MPC (Spcification 660) Pur Cor Final Mark Schm Mark schms ar prpard by th Principal Eaminr and considrd, togthr with th rlvant qustions,
More informationDevelopment of Financial Management Reporting in MPLS
1 Dvlopmnt of Financial Managmnt Rporting in MPLS 1. Aim Our currnt financial rports ar structurd to dlivr an ovrall financial pictur of th dpartmnt in it s ntirty, and thr is no attmpt to provid ithr
More informationChapter 4: Biochemical redox reactions
Chaptr 4: Biochmical ractions 4.1 Introduction 4.2 Biochmical half-ractions, th Faraday conststant and th uction potntial 4.2.1 Dfining th uction potntial: 4.2.2 Th standard uction potntial is also th
More informationCategory 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 informationHOMEWORK FOR UNIT 5-1: FORCE AND MOTION
Nam Dat Partnrs HOMEWORK FOR UNIT 51: FORCE AND MOTION 1. You ar givn tn idntial springs. Dsrib how you would dvlop a sal of for (i., a mans of produing rpatabl fors of a varity of sizs) using ths springs.
More informationNoise Power Ratio (NPR) A 65-Year Old Telephone System Specification Finds New Life in Modern Wireless Applications.
TUTORIL ois Powr Ratio (PR) 65-Yar Old Tlphon Systm Spcification Finds w Lif in Modrn Wirlss pplications ITRODUTIO by Walt Kstr Th concpt of ois Powr Ratio (PR) has bn around sinc th arly days of frquncy
More informationAP Calculus Multiple-Choice Question Collection 1969 1998. connect to college success www.collegeboard.com
AP Calculus Multipl-Choic Qustion Collction 969 998 connct to collg succss www.collgboard.com Th Collg Board: Conncting Studnts to Collg Succss Th Collg Board is a not-for-profit mmbrship association whos
More informationCloud and Big Data Summer School, Stockholm, Aug., 2015 Jeffrey D. Ullman
Cloud and Big Data Summr Scool, Stockolm, Aug., 2015 Jffry D. Ullman Givn a st of points, wit a notion of distanc btwn points, group t points into som numbr of clustrs, so tat mmbrs of a clustr ar clos
More informationRemember you can apply online. It s quick and easy. Go to www.gov.uk/advancedlearningloans. Title. Forename(s) Surname. Sex. Male Date of birth D
24+ Advancd Larning Loan Application form Rmmbr you can apply onlin. It s quick and asy. Go to www.gov.uk/advancdlarningloans About this form Complt this form if: you r studying an ligibl cours at an approvd
More informationFinancial Mathematics
Financial Mathatics A ractical Guid for Actuaris and othr Businss rofssionals B Chris Ruckan, FSA & Jo Francis, FSA, CFA ublishd b B rofssional Education Solutions to practic qustions Chaptr 7 Solution
More informationInfrared Vibration-Rotation Spectroscopy of HCl and DCl
Chmistry 363 JMS 1/05 Spring 010 DLC 1/10 Infrard Vibration-Rotation Spctroscopy of HCl and DCl Exprimnt Objctiv: to obtain th quilibrium bond lngth (r ) and vibration-rotation spctroscopic constants from
More informationPlanning and Managing Copper Cable Maintenance through Cost- Benefit Modeling
Planning and Managing Coppr Cabl Maintnanc through Cost- Bnfit Modling Jason W. Rup U S WEST Advancd Tchnologis Bouldr Ky Words: Maintnanc, Managmnt Stratgy, Rhabilitation, Cost-bnfit Analysis, Rliability
More informationEntity-Relationship Model
Entity-Rlationship Modl Kuang-hua Chn Dpartmnt of Library and Information Scinc National Taiwan Univrsity A Company Databas Kps track of a company s mploys, dpartmnts and projcts Aftr th rquirmnts collction
More informationLecture notes: 160B revised 9/28/06 Lecture 1: Exchange Rates and the Foreign Exchange Market FT chapter 13
Lctur nots: 160B rvisd 9/28/06 Lctur 1: xchang Rats and th Forign xchang Markt FT chaptr 13 Topics: xchang Rats Forign xchang markt Asst approach to xchang rats Intrst Rat Parity Conditions 1) Dfinitions
More informationVan der Waals Forces Between Atoms
Van dr Waals Forcs twn tos Michal Fowlr /8/7 Introduction Th prfct gas quation of stat PV = NkT is anifstly incapabl of dscribing actual gass at low tpraturs, sinc thy undrgo a discontinuous chang of volu
More informationProduction Costing (Chapter 8 of W&W)
Production Costing (Chaptr 8 of W&W).0 Introduction Production costs rfr to th oprational costs associatd with producing lctric nrgy. Th most significant componnt of production costs ar th ful costs ncssary
More informationParallel 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 informationAnalyzing the Economic Efficiency of ebaylike Online Reputation Reporting Mechanisms
A rsarch and ducation initiativ at th MIT Sloan School of Managmnt Analyzing th Economic Efficincy of Baylik Onlin Rputation Rporting Mchanisms Papr Chrysanthos Dllarocas July For mor information, plas
More informationA Project Management framework for Software Implementation Planning and Management
PPM02 A Projct Managmnt framwork for Softwar Implmntation Planning and Managmnt Kith Lancastr Lancastr Stratgis Kith.Lancastr@LancastrStratgis.com Th goal of introducing nw tchnologis into your company
More informationElectronic Commerce. and. Competitive First-Degree Price Discrimination
Elctronic Commrc and Comptitiv First-Dgr Pric Discrimination David Ulph* and Nir Vulkan ** Fbruary 000 * ESRC Cntr for Economic arning and Social Evolution (ESE), Dpartmnt of Economics, Univrsity Collg
More informationA 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 informationPerformance Evaluation
Prformanc Evaluation ( ) Contnts lists availabl at ScincDirct Prformanc Evaluation journal hompag: www.lsvir.com/locat/pva Modling Bay-lik rputation systms: Analysis, charactrization and insuranc mchanism
More informationHost Country: Czech Republic Other parties: Denmark Expected ERUs in 2008 2012: ~ 1,250,000 tco 2
Projct CZ1000033: Nitrous Oxid Emission Rductions at Lovochmi Host Country: Czch Rpublic Othr partis: Dnmark Expctd ERUs in 2008 2012: ~ 1,250,000 tco 2 Th projct at Lovochmi in th Czch Rpublic aims to
More informationJune 2012. Enprise Rent. Enprise 1.1.6. Author: Document Version: Product: Product Version: SAP Version: 8.81.100 8.8
Jun 22 Enpris Rnt Author: Documnt Vrsion: Product: Product Vrsion: SAP Vrsion: Enpris Enpris Rnt 88 88 Enpris Rnt 22 Enpris Solutions All rights rsrvd No parts of this work may b rproducd in any form or
More informationAdsorption of Malachite Green Dye onto Activated Carbon Derived from Durian Peel
Adsorption of Malachit Grn Dy onto Activatd Carbon Drivd from Durian Pl SARAWUT SRIKHUN, SAMORN HIRUNPRADITKUN, KAMCHAI NUITHITIKUL* Dpartmnt of Chmical Enginring King Mongkut s Univrsity of Tchnology
More informationDefining Retirement Success for Defined Contribution Plan Sponsors: Begin with the End in Mind
Dfining Rtirmnt Succss for Dfind Contribution Plan Sponsors: Bgin with th End in Mind David Blanchtt, CFA, CFP, AIFA Had of Rtirmnt Rsarch Morningstar Invstmnt Managmnt david.blanchtt@morningstar.com Nathan
More informationGold 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 informationFleet vehicles opportunities for carbon management
Flt vhicls opportunitis for carbon managmnt Authors: Kith Robrtson 1 Dr. Kristian Stl 2 Dr. Christoph Hamlmann 3 Alksandra Krukar 4 Tdla Mzmir 5 1 Snior Sustainability Consultant & Lad Analyst, Arup 2
More informationEffect of Design Parameter on the Performance of Lithium Ion Battery
Aadil Ahmad, Mohd. Parvz / Intrnational Journal of Enginring Rarch and Application Vol. 3, Iu 4, Jul-Aug 2013, pp.1196-1201 Effct of Dign Paramtr on th Prformanc of Lithium Ion Battry Aadil Ahmad 1, Mohd.
More informationUpper Bounding the Price of Anarchy in Atomic Splittable Selfish Routing
Uppr Bounding th Pric of Anarchy in Atomic Splittabl Slfish Routing Kamyar Khodamoradi 1, Mhrdad Mahdavi, and Mohammad Ghodsi 3 1 Sharif Univrsity of Tchnology, Thran, Iran, khodamoradi@c.sharif.du Sharif
More informationExpert-Mediated Search
Exprt-Mdiatd Sarch Mnal Chhabra Rnsslar Polytchnic Inst. Dpt. of Computr Scinc Troy, NY, USA chhabm@cs.rpi.du Sanmay Das Rnsslar Polytchnic Inst. Dpt. of Computr Scinc Troy, NY, USA sanmay@cs.rpi.du David
More informationLecture 4: Thermodynamics of Diffusion: Spinodals
Materials Science & Metallurgy Master of Philosophy, Materials Modelling, Course MP6, Kinetics and Microstructure Modelling, H. K. D. H. Bhadeshia Lecture 4: Thermodynamics of Diffusion: Spinodals Fick
More informationFinite Elements from the early beginning to the very end
Finit Elmnts from th arly bginning to th vry nd A(x), E(x) g b(x) h x =. x = L An Introduction to Elasticity and Hat Transfr Applications x Prliminary dition LiU-IEI-S--8/535--SE Bo Torstnflt Contnts
More informationCHAPTER 4c. ROOTS OF EQUATIONS
CHAPTER c. ROOTS OF EQUATIONS A. J. Clark School o Enginring Dpartmnt o Civil and Environmntal Enginring by Dr. Ibrahim A. Aakka Spring 00 ENCE 03 - Computation Mthod in Civil Enginring II Dpartmnt o Civil
More informationLift Selection Guide
Lift Slction Guid Hlping you choos th right lifts to kp your staff and rsidnts saf Th Dirct Supply diffrnc Kp your community saf DIRECT SUPPLY MAKES EQUIPMENT SELECTION EASY BENEFITS OF SAFE LIFTING PRACTICES
More informationOn the moments of the aggregate discounted claims with dependence introduced by a FGM copula
On th momnts of th aggrgat discountd claims with dpndnc introducd by a FGM copula - Mathiu BARGES Univrsité Lyon, Laboratoir SAF, Univrsité Laval - Hélèn COSSETTE Ecol Actuariat, Univrsité Laval, Québc,
More informationPrecise Memory Leak Detection for Java Software Using Container Profiling
Distinguishd Papr Prcis Mmory Lak Dtction for Java Softwar Using Containr Profiling Guoqing Xu Atanas Rountv Dpartmnt of Computr Scinc and Enginring Ohio Stat Univrsity {xug,rountv}@cs.ohio-stat.du ABSTRACT
More informationPhysics 106 Lecture 12. Oscillations II. Recap: SHM using phasors (uniform circular motion) music structural and mechanical engineering waves
Physics 6 Lctur Oscillations II SJ 7 th Ed.: Chap 5.4, Rad only 5.6 & 5.7 Rcap: SHM using phasors (unifor circular otion) Physical pndulu xapl apd haronic oscillations Forcd oscillations and rsonanc. Rsonanc
More informationHigher. Exponentials and Logarithms 160
hsn uknt Highr Mthmtics UNIT UTCME Eponntils nd Logrithms Contnts Eponntils nd Logrithms 6 Eponntils 6 Logrithms 6 Lws of Logrithms 6 Eponntils nd Logrithms to th Bs 65 5 Eponntil nd Logrithmic Equtions
More informationProjections - 3D Viewing. Overview Lecture 4. Projection - 3D viewing. Projections. Projections Parallel Perspective
Ovrviw Lctur 4 Projctions - 3D Viwing Projctions Paralll Prspctiv 3D Viw Volum 3D Viwing Transformation Camra Modl - Assignmnt 2 OFF fils 3D mor compl than 2D On mor dimnsion Displa dvic still 2D Analog
More informationAQA. Physical Education. Questions and Answers
AQA AS Physical Education Qustions and Answrs Qustions and answrs This CD compriss a worksht with som xam-styl qustions, a summary of som frquntly askd qustions and, finally, a sampl unit tst. Mark schms,
More informationUse a high-level conceptual data model (ER Model). Identify objects of interest (entities) and relationships between these objects
Chaptr 3: Entity Rlationship Modl Databas Dsign Procss Us a high-lvl concptual data modl (ER Modl). Idntify objcts of intrst (ntitis) and rlationships btwn ths objcts Idntify constraints (conditions) End
More informationKey Management System Framework for Cloud Storage Singa Suparman, Eng Pin Kwang Temasek Polytechnic {singas,engpk}@tp.edu.sg
Ky Managmnt Systm Framwork for Cloud Storag Singa Suparman, Eng Pin Kwang Tmask Polytchnic {singas,ngpk}@tp.du.sg Abstract In cloud storag, data ar oftn movd from on cloud storag srvic to anothr. Mor frquntly
More informationThe Neolithic transition, a major episode in human history, is
Synthsis btwn dmic and cultural diffusion in th Nolithic transition in Europ Joaquim Fort 1 Complx Systms Laboratory, Dpartmnt of hysics, Univrsity of Girona, ES-1771 Girona, Catalonia, Spain Editd by
More informationFree 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 informationCALCULATING MARGINAL PROBABILITIES IN PROC PROBIT Guy Pascale, Memorial Health Alliance
CALCULATING MARGINAL PROBABILITIES IN PROC PROBIT Guy Pascal, Mmorial Halth Allianc Introduction Th PROBIT procdur within th SAS systm provids a simpl mthod for stimating discrt choic variabls (i.. dichotomous
More informationLAB 3: VELOCITY AND ACCELERATION GRAPHS
Goas: LAB 3: ELOCITY AND ACCELERATION GRAPHS Invstigat accration vs. tim graphs Prdict accration graphs from vocity graphs Invstigat accration as sop of vocity vs. tim graph Part 1 - Making ocity- Graphs
More informationVector Network Analyzer
Cours on Microwav Masurmnts Vctor Ntwork Analyzr Prof. Luca Prrgrini Dpt. of Elctrical, Computr and Biomdical Enginring Univrsity of Pavia -mail: luca.prrgrini@unipv.it wb: microwav.unipv.it Microwav Masurmnts
More informationSharp bounds for Sándor mean in terms of arithmetic, geometric and harmonic means
Qian t al. Journal of Inqualitis and Applications (015) 015:1 DOI 10.1186/s1660-015-0741-1 R E S E A R C H Opn Accss Sharp bounds for Sándor man in trms of arithmtic, gomtric and harmonic mans Wi-Mao Qian
More informationFredy 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 informationHardware 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 informationChapter 10 Function of a Matrix
EE448/58 Vrsion. John Stnsby Chatr Function of a atrix t f(z) b a comlx-valud function of a comlx variabl z. t A b an n n comlxvalud matrix. In this chatr, w giv a dfinition for th n n matrix f(a). Also,
More informationThe 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 informationAbstract. 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 informationCUTTING METHODS AND CARTESIAN ROBOTS KESME YÖNTEMLERİ VE KARTEZYEN ROBOTLAR
ournal of Naval Scinc and Enginring 2009, Vol. 5, No.2, pp. 35-42 CUTTING METHODS AND CARTESIAN ROBOTS Asst. Prof. Ugur SIMSIR, Lt.Cdr. Turkish Naval Acady Mchanical Enginring Dpartnt Tuzla, Istanbul,Turkiy
More informationCPU. 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 informationEstimating Aboveground Tree Biomass on Forest Land in the Pacific Northwest: A Comparison of Approaches
Unitd Stats Dpartmnt of Agricultur Forst Srvic Pacific Southwst Rsarch Station Rsarch Papr PNW-RP-584 Novmbr 2009 Estimating Abovground Tr Biomass on Forst Land in th Pacific Northwst: A Comparison of
More informationIncomplete 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