EXCERPTS. Fire Dynamics Simulator (Version 5) Technical Reference Guide Volume 3: Validation

Size: px
Start display at page:

Download "EXCERPTS. Fire Dynamics Simulator (Version 5) Technical Reference Guide Volume 3: Validation"

Transcription

1 SCHULTE & ASSOCIATES Building Cde Cnsultants 880D Frest Avenue Evanstn, IL / EXCERPTS Fire Dynamics Simulatr (Versin 5) Technical Reference Guide Vlume 3: Validatin Vlume 3 f the Technical Reference Guide t Versin 5 f the Fire Dynamics Simulatr (FDS) was released n August 4, The fllwing are excerpts frm Vlume 3: The three vlumes f the FDS Technical Reference Guide are based in part n the Standard Guide fr Evaluating the Predictive Capability f Deterministic Fire Mdels, ASTM E 1355 [2]. ASTM E 1355 defines mdel evaluatin as the prcess f quantifying the accuracy f chsen results frm a mdel when applied fr a specific use. The mdel evaluatin prcess cnsists f tw main cmpnents: verificatin and validatin. Verificatin is a prcess t check the crrectness f the slutin f the gverning equatins. (Page i) Verificatin des nt imply that the gverning equatins are apprpriate; nly that the equatins are being slved crrectly. Validatin is a prcess t determine the apprpriateness f the gverning equatins as a mathematical mdel f the physical phenmena f interest. Typically, validatin invlves cmparing mdel results with experimental measurement. Differences that cannt be explained in terms f numerical errrs in the mdel r uncertainty in the measurements are attributed t the assumptins and simplificatins f the physical mdel. (Page i) Evaluatin is critical t establishing bth the acceptable uses and limitatins f a mdel. Thrughut its develpment, FDS has undergne varius frms f evaluatin, bth at NIST and beynd. This vlume prvides a survey f validatin wrk cnducted t date t evaluate FDS. (Page i) Thanks t Jerry Back, Craig Beyler and Phil DiNenn f Hughes Assciates and Pat Tatem f the Naval Research Labratry fr their cntributin f experimental data fr the HAI/ NRLWall Fire series. Thanks als t Craig Beyler fr assistance with the data fr the Beyler Hd Experiments. (Page v) FDS Technical Reference Guide-Vlume 3 1

2 Validatin typically invlves (1) cmparing mdel predictins with experimental measurements, (2) quantifying the differences in light f uncertainties in bth the measurements and the mdel inputs, and (3) deciding if the mdel is apprpriate fr the given applicatin. This Guide nly des (1) and (2). Number (3) is the respnsibility f the mdel user. (Page 1) Althugh the FDS develpers cntinuusly perfrm validatin studies, it is ultimately the end user f the mdel wh decides if the mdel is adequate fr the jb at hand. Thus, this Guide prvides the raw material fr a validatin study, but it des nt and cannt be cnsidered cmprehensive. (Page 1) The fllwing sectins discuss key issues that yu must cnsider when deciding whether r nt FDS has been validated. It depends n (a) the scenaris f interest, (b) the predicted quantities, and (c) the desired level f accuracy. Keep in mind that FDS can be used t mdel mst any fire scenari and predict almst any quantity f interest, but the predictin may nt be accurate because f limitatins in the descriptin f the fire physics, and als because f limited infrmatin abut the fuels, gemetry, and s n. (Page 1) When ding a validatin study, the first questin t ask is, What is the applicatin? (Page 1) Validatin studies f FDS t date have fcused mre n design applicatins than recnstructins. The reasn is that design applicatins usually invlve specified fires and demand a minimum f thermphysical prperties f real materials. Transprt f smke and heat is the primary fcus, and measurements can be limited t well-placed thermcuples, a few heat flux gauges, gas samplers, etc. Phenmena f imprtance in frensic recnstructins, like secnd item ignitin, flame spread, vitiatin effects and extinctin, are mre difficult t mdel and mre difficult t study with well-cntrlled experiments. Uncertainties in material prperties and measurements, as well as simplifying assumptins in the mdel, ften frce the cmparisn between mdel and measurement t be qualitative at best. Nevertheless, current validatin effrts are mving in the directin f these mre difficult issues. (Page 2) Keep in mind that fr any fire experiment, FDS might predict a particular quantity accurately (within the experimental uncertainty bunds, fr example), but anther quantity less accurately. Fr example, in the a series f 15 full-scale fire experiments cnducted at NIST in 2003, spnsred by the U.S. Nuclear Regulatry Cmmissin, the average ht gas layer (HGL) temperature predictins were within the accuracy f the experiments themselves, yet the smke cncentratin predictins differed frm the measurements by as much as a factr f 3. (Page 2) FDS Technical Reference Guide-Vlume 3 2

3 Mdel errr tends t be reduced by the averaging prcess, plus mst fire mdels, including FDS, are based n glbal mass and energy cnservatin laws that are expressed as spatial averages. (Page 2) The desired accuracy fr each predicted quantity depends n the technical issues assciated with the analysis. Yu must ask the questin: Hw accurate des the analysis have t be t answer the technical questin psed? Returning t the earlier definitins f design and recnstructin, design applicatins typically are mre accurate because the heat release rate is typically specified rather than predicted, and the initial and bundary cnditins are better characterized at least in the a- nalysis. Mathematically, a design calculatin is an example f a well-psed prblem in which the slutin f the gverning equatins is advanced in time starting frm a knwn set f initial cnditins and cnstrained by a knwn set f bundary cnditins. The accuracy f the results is a functin f the fidelity f the numerical slutin, which is mainly dependent n the size f the cmputatinal grid. (Page 3) If yu are embarking n a validatin study, yu might want t cnsider the fllwing steps: 1. Survey Chapter 2 t learn abut past effrts by thers t validate the mdel fr applicatins similar t yurs 2. Identify in Chapter 3 experimental data sets apprpriate fr yur applicatin 3. Read the specific chapters fr the quantities f interest (Page 3) Mre recently, validatin effrts have mved beynd just transprt issues t cnsider fire grwth, flame spread, suppressin, sprinkler/detectr activatin, and ther fire-specific phenmena. (Page 6) Frmal, rigrus validatin exercises are time-cnsuming and expensive. Mst validatin exercises are dne simply t assess if the mdel can be used fr a very specific purpse. While nt cmprehensive n their wn, these studies cllectively cnstitute a valuable assessment f the mdel. (Page 6) Experiments cnducted slely fr mdel validatin are smewhat rare. Mre cmmn are validatin studies that use data frm past experiments. (Page 7) FDS Technical Reference Guide-Vlume 3 3

4 In a fllw-up reprt, Vettri [47] extended his study t include slped ceilings, with and withut bstructins. He fund that the difference between predicted and measured sprinkler activatin times varied between 4 % and 26 % fr all cases studied. He als nted that FDS was able t predict the first activatin f a sprinkler twice as far frm the fire as anther; caused presumably by the re-directin f smke by the beams n the ceiling. (Page 9) Althugh FDS simulatins have been cmpared t actual and experimental largescale fires, it is difficult t quantify the accuracy because f the uncertainty assciated with material prperties. Mst quantified validatin wrk assciated with flame spread have been fr small, laminar flames with length scales ranging frm millimeters t a few centimeters. (Page 10) Fr real wd prducts, it is unlikely that all f the necessary prperties can be btained easily. Thus, grid sensitivity and uncertain material prperties make blind predictins f fire grwth n real materials beynd the reach f the current versin f the mdel. Hwever, the mdel can still be used fr a qualitative assessment f fire behavir as lng as the uncertainty in the flame spread rate is recgnized. (Page 10) A significant validatin effrt fr sprinkler activatin and suppressin was a prject entitled the Internatinal Fire Sprinkler, Smke and Heat Vent, Draft Curtain Fire Test Prject rganized by the Natinal Fire Prtectin Research Fundatin [60]. Thirty-nine large scale fire tests were cnducted at Underwriters Labratries in Nrthbrk, IL. The tests were aimed at evaluating the perfrmance f varius fire prtectin systems in large buildings with flat ceilings, like warehuses and big bx retail stres. (Page 10) Hwever, five experiments were perfrmed with 6 m high racks cntaining the Factry Mutual Standard Plastic Cmmdity, r Grup A Plastic. T mdel these fires, bench scale experiments were perfrmed t characterize the burning behavir f the cmmdity, and larger test fires prvided validatin data with which t test the mdel predictins f the burning rate and flame spread behavir [61, 62]. Tw t fur tier cnfiguratins were evaluated. Fr the perid f time prir t applicatin f water, the simulated heat release rate was within 20 % f the experimental heat release rates. It shuld be nted that the mdel was very sensitive t the thermal parameters and the numerical grid when used t mdel the fire grwth in the piled cmmdity tests. (Page 10) FDS Technical Reference Guide-Vlume 3 4

5 The scpe f the VTT wrk is cnsiderable. Assessing the accuracy f the mdel must be dne n a case by case basis. In sme cases, predictins f the burning rate f the material were based slely n its fundamental prperties, as in the heptane pl fire simulatins. In ther cases, sme prperties f the material are unknwn, as in the spruce timber simulatins. Thus, sme f the simulatins are true predictins, sme are calibratins. The intent f the authrs was t prvide guidance t engineers using the mdel as t apprpriate grid sizes and material prperties. In many cases, the numerical grid was made fairly carse t accunt fr the fact that in practice, FDS is used t mdel large spaces f which the fuel may nly cmprise a small fractin. (Page 13) The FDS results that best replicated the bserved fire behavir indicated that the pening f the basement sliding glass dr prvided xygen t a pre-heated, underventilated fire. Flashver was estimated t ccur in less than 60 s fllwing the entry f fire fighters int the basement. The resulting fire gases flwed up the basement stairs and mved acrss the living rm ceiling twards the back wall f the twnhuse. These ht gases came in direct cntact with the fire fighters wh were killed. The ht gases traversed the twnhuse in less than 2 s, giving the fire fighters little time t respnd. The mdel shwed that the xygen level was t lw t supprt flaming and, therefre, the fire fighters did nt have a visual cue f the thermal cnditins until it was t late. (Page 14) Hwever, in rder t assess the accuracy f FDS, there must be sme estimate f the cmbined effect f the uncertainty in the reprted input parameters, like the heat release rate f the fire, and the reprted measurement f the quantity f interest, like the ht gas layer (HGL) temperature. (Page 28) A summary scatter plt f the HGL predictins is given in Fig Mst f the predictins fall within the experimental uncertainty bunds. Nte, hwever, that bth f these quantities represent spatial averages. At any given pint in the cmpartment, a specific predictin f temperature may nt fall within the uncertainty bunds. Pint t pint cmparisns f temperature can be fund in the chapters fr plumes and ceiling jets. (Page 46) Nevertheless, temperature measurements near the ceiling can be used t evaluate the mdel s ability t predict the flw f ht gases acrss a relatively flat ceiling. (Page 57) FDS Technical Reference Guide-Vlume 3 5

6 The thermcuple nearest the ceiling in Tree 7, lcated twards the back f the cmpartment, has been chsen as a surrgate fr the ceiling jet temperature. Curiusly, the difference between measured and predicted temperatures is nticeably greater fr the pen dr tests. Certainly, the pen dr changes the flw pattern f the exhaust gases. Hwever, the predicted HGL heights fr the pen dr tests, shwn in the previus sectin, d nt shw a nticeable difference frm their clsed dr cunterparts. The predicted HGL temperatures are nly slightly less than thse measured in the pen dr tests, due in large part t the cntributin f Tree 7 in the layer reductin calculatin. (Page 57) Test Burner Vent First Act. (s) Ttal Acts. Draft Heat Release Rate N. Ps. Operatin Exp. FDS Exp. FDS Curtains s I-1 B Clsed Yes 50 I-2 B Manual (0:40) Yes 50 I-3 B Manual (1:30) Yes 50 I-4 C Clsed Yes 50 I-5 C Manual (0:40) Yes 50 I-6 C Manual (1:30) Yes 50 I-7 C 74 C link (DNO) Yes 50 I-8 B 74 C link (9:26) Yes 50 I-9 D 74 C link (DNO) Yes 50 I-10 D Manual (0:40) Yes 50 I-11 D 74 C link (4:48) N/A N/A N/A N/A Yes 50 I-12 A Clsed Yes 50 I-13 A 74 C link (1:04) Yes 60 I-14 A Manual (0:40) Yes 60 I-15 A Manual (1:30) Yes 60 I-16 A 74 C link (1:46) Yes 110 I-17 B 100 C link (DNO) N 50 I-18 C 100 C link (DNO) N 50 I-19 A 100 C link (10:00) N 50 I-20 A 74 C link (1:20) N 50 I-21 C 74 C link (7:00) N 50 I-22 D 100 C link (DNO) N 50 Table 6.1: Results f the UL/NFPRF Experiments. Nte that DNO means Did Nt Open. Als nte, the fires grew at a rate prprtinal t the square f the time until a certain flw rate f fuel was achieved at which time the flw rate was held steady. Thus, the Heat Release Rate was the size f the fire at the time when the fuel supply was leveled ff. (Page 63) FDS Technical Reference Guide-Vlume 3 6

7 Figure 6.2 displays graphically the difference between predicted and measured sprinkler activatin times as a functin f burner psitin. Nte that there are n experimental uncertainty bunds n the plt because it is difficult t estimate the cmbined uncertainty related t the varius parameters that are input int the mdel. Fr example, changing the median vlumetric drplet size frm 1000 m t 750 m led t a reductin f apprximately 50 % in the number f predicted sprinkler activatins due t the increased cling f the smaller drplets. Cnsequently, three replicate experiments are cmpared t shw hw much variatin ne can expect in sprinkler activatin times in repeat experiments. (Page 63) FDS treats smke like all ther cmbustin prducts, basically a tracer gas whse mass fractin is a functin f the mixture fractin. T mdel smke mvement, the user need nly prescribe the smke yield, that is, the fractin f the fuel mass that is cnverted t smke particulate. Fr the simulatins f the NIST/NRC tests, the smke yield is specified as ne f the test parameters. Figure and Figure cntain cmparisns f measured and predicted smke cncentratin at ne measuring statin in the upper layer. There are tw bvius trends in the figures: first, the predicted cncentratins are abut 50 % higher than the measured in the pen dr tests. Secnd, the predicted cncentratins are rughly three times the measured cncentratins in the clsed dr tests. (Page 73) * * * * * FDS Technical Reference Guide-Vlume 3 7

Differentiation Applications 1: Related Rates

Differentiation Applications 1: Related Rates Differentiatin Applicatins 1: Related Rates 151 Differentiatin Applicatins 1: Related Rates Mdel 1: Sliding Ladder 10 ladder y 10 ladder 10 ladder A 10 ft ladder is leaning against a wall when the bttm

More information

Fall 2013 Physics 172 Recitation 3 Momentum and Springs

Fall 2013 Physics 172 Recitation 3 Momentum and Springs Fall 03 Physics 7 Recitatin 3 Mmentum and Springs Purpse: The purpse f this recitatin is t give yu experience wrking with mmentum and the mmentum update frmula. Readings: Chapter.3-.5 Learning Objectives:.3.

More information

(1.1) V which contains charges. If a charge density ρ, is defined as the limit of the ratio of the charge contained. 0, and if a force density f

(1.1) V which contains charges. If a charge density ρ, is defined as the limit of the ratio of the charge contained. 0, and if a force density f 1.0 Review f Electrmagnetic Field Thery Selected aspects f electrmagnetic thery are reviewed in this sectin, with emphasis n cncepts which are useful in understanding magnet design. Detailed, rigrus treatments

More information

ENSC Discrete Time Systems. Project Outline. Semester

ENSC Discrete Time Systems. Project Outline. Semester ENSC 49 - iscrete Time Systems Prject Outline Semester 006-1. Objectives The gal f the prject is t design a channel fading simulatr. Upn successful cmpletin f the prject, yu will reinfrce yur understanding

More information

How do scientists measure trees? What is DBH?

How do scientists measure trees? What is DBH? Hw d scientists measure trees? What is DBH? Purpse Students develp an understanding f tree size and hw scientists measure trees. Students bserve and measure tree ckies and explre the relatinship between

More information

2004 AP CHEMISTRY FREE-RESPONSE QUESTIONS

2004 AP CHEMISTRY FREE-RESPONSE QUESTIONS 2004 AP CHEMISTRY FREE-RESPONSE QUESTIONS 6. An electrchemical cell is cnstructed with an pen switch, as shwn in the diagram abve. A strip f Sn and a strip f an unknwn metal, X, are used as electrdes.

More information

CS 477/677 Analysis of Algorithms Fall 2007 Dr. George Bebis Course Project Due Date: 11/29/2007

CS 477/677 Analysis of Algorithms Fall 2007 Dr. George Bebis Course Project Due Date: 11/29/2007 CS 477/677 Analysis f Algrithms Fall 2007 Dr. Gerge Bebis Curse Prject Due Date: 11/29/2007 Part1: Cmparisn f Srting Algrithms (70% f the prject grade) The bjective f the first part f the assignment is

More information

Module 4: General Formulation of Electric Circuit Theory

Module 4: General Formulation of Electric Circuit Theory Mdule 4: General Frmulatin f Electric Circuit Thery 4. General Frmulatin f Electric Circuit Thery All electrmagnetic phenmena are described at a fundamental level by Maxwell's equatins and the assciated

More information

Kinetic Model Completeness

Kinetic Model Completeness 5.68J/10.652J Spring 2003 Lecture Ntes Tuesday April 15, 2003 Kinetic Mdel Cmpleteness We say a chemical kinetic mdel is cmplete fr a particular reactin cnditin when it cntains all the species and reactins

More information

Lab 1 The Scientific Method

Lab 1 The Scientific Method INTRODUCTION The fllwing labratry exercise is designed t give yu, the student, an pprtunity t explre unknwn systems, r universes, and hypthesize pssible rules which may gvern the behavir within them. Scientific

More information

Five Whys How To Do It Better

Five Whys How To Do It Better Five Whys Definitin. As explained in the previus article, we define rt cause as simply the uncvering f hw the current prblem came int being. Fr a simple causal chain, it is the entire chain. Fr a cmplex

More information

Pipetting 101 Developed by BSU CityLab

Pipetting 101 Developed by BSU CityLab Discver the Micrbes Within: The Wlbachia Prject Pipetting 101 Develped by BSU CityLab Clr Cmparisns Pipetting Exercise #1 STUDENT OBJECTIVES Students will be able t: Chse the crrect size micrpipette fr

More information

Subject description processes

Subject description processes Subject representatin 6.1.2. Subject descriptin prcesses Overview Fur majr prcesses r areas f practice fr representing subjects are classificatin, subject catalging, indexing, and abstracting. The prcesses

More information

NUMBERS, MATHEMATICS AND EQUATIONS

NUMBERS, MATHEMATICS AND EQUATIONS AUSTRALIAN CURRICULUM PHYSICS GETTING STARTED WITH PHYSICS NUMBERS, MATHEMATICS AND EQUATIONS An integral part t the understanding f ur physical wrld is the use f mathematical mdels which can be used t

More information

CHAPTER 3 INEQUALITIES. Copyright -The Institute of Chartered Accountants of India

CHAPTER 3 INEQUALITIES. Copyright -The Institute of Chartered Accountants of India CHAPTER 3 INEQUALITIES Cpyright -The Institute f Chartered Accuntants f India INEQUALITIES LEARNING OBJECTIVES One f the widely used decisin making prblems, nwadays, is t decide n the ptimal mix f scarce

More information

A Few Basic Facts About Isothermal Mass Transfer in a Binary Mixture

A Few Basic Facts About Isothermal Mass Transfer in a Binary Mixture Few asic Facts but Isthermal Mass Transfer in a inary Miture David Keffer Department f Chemical Engineering University f Tennessee first begun: pril 22, 2004 last updated: January 13, 2006 dkeffer@utk.edu

More information

Computational modeling techniques

Computational modeling techniques Cmputatinal mdeling techniques Lecture 4: Mdel checing fr ODE mdels In Petre Department f IT, Åb Aademi http://www.users.ab.fi/ipetre/cmpmd/ Cntent Stichimetric matrix Calculating the mass cnservatin relatins

More information

UNIT 6 DETERMINATION OF FLASH AND FIRE POINT OF A LUBRICATING OIL BY OPEN CUP AND CLOSED CUP METHODS

UNIT 6 DETERMINATION OF FLASH AND FIRE POINT OF A LUBRICATING OIL BY OPEN CUP AND CLOSED CUP METHODS UNIT 6 DETERMINATION OF FLASH AND FIRE POINT OF A LUBRICATING OIL BY OPEN CUP AND CLOSED CUP METHODS Determinatin f Flash and Fire Pint f a Cup and Clsed Cup Structure 6. Intrductin Objectives 6. Experiment

More information

ChE 471: LECTURE 4 Fall 2003

ChE 471: LECTURE 4 Fall 2003 ChE 47: LECTURE 4 Fall 003 IDEL RECTORS One f the key gals f chemical reactin engineering is t quantify the relatinship between prductin rate, reactr size, reactin kinetics and selected perating cnditins.

More information

, which yields. where z1. and z2

, which yields. where z1. and z2 The Gaussian r Nrmal PDF, Page 1 The Gaussian r Nrmal Prbability Density Functin Authr: Jhn M Cimbala, Penn State University Latest revisin: 11 September 13 The Gaussian r Nrmal Prbability Density Functin

More information

Standard Title: Frequency Response and Frequency Bias Setting. Andrew Dressel Holly Hawkins Maureen Long Scott Miller

Standard Title: Frequency Response and Frequency Bias Setting. Andrew Dressel Holly Hawkins Maureen Long Scott Miller Template fr Quality Review f NERC Reliability Standard BAL-003-1 Frequency Respnse and Frequency Bias Setting Basic Infrmatin: Prject number: 2007-12 Standard number: BAL-003-1 Prject title: Frequency

More information

Study Group Report: Plate-fin Heat Exchangers: AEA Technology

Study Group Report: Plate-fin Heat Exchangers: AEA Technology Study Grup Reprt: Plate-fin Heat Exchangers: AEA Technlgy The prblem under study cncerned the apparent discrepancy between a series f experiments using a plate fin heat exchanger and the classical thery

More information

5 th grade Common Core Standards

5 th grade Common Core Standards 5 th grade Cmmn Cre Standards In Grade 5, instructinal time shuld fcus n three critical areas: (1) develping fluency with additin and subtractin f fractins, and develping understanding f the multiplicatin

More information

A Quick Overview of the. Framework for K 12 Science Education

A Quick Overview of the. Framework for K 12 Science Education A Quick Overview f the NGSS EQuIP MODULE 1 Framewrk fr K 12 Science Educatin Mdule 1: A Quick Overview f the Framewrk fr K 12 Science Educatin This mdule prvides a brief backgrund n the Framewrk fr K-12

More information

Aircraft Performance - Drag

Aircraft Performance - Drag Aircraft Perfrmance - Drag Classificatin f Drag Ntes: Drag Frce and Drag Cefficient Drag is the enemy f flight and its cst. One f the primary functins f aerdynamicists and aircraft designers is t reduce

More information

WRITING THE REPORT. Organizing the report. Title Page. Table of Contents

WRITING THE REPORT. Organizing the report. Title Page. Table of Contents WRITING THE REPORT Organizing the reprt Mst reprts shuld be rganized in the fllwing manner. Smetime there is a valid reasn t include extra chapters in within the bdy f the reprt. 1. Title page 2. Executive

More information

The standards are taught in the following sequence.

The standards are taught in the following sequence. B L U E V A L L E Y D I S T R I C T C U R R I C U L U M MATHEMATICS Third Grade In grade 3, instructinal time shuld fcus n fur critical areas: (1) develping understanding f multiplicatin and divisin and

More information

3. Mass Transfer with Chemical Reaction

3. Mass Transfer with Chemical Reaction 8 3. Mass Transfer with Chemical Reactin 3. Mass Transfer with Chemical Reactin In the fllwing, the fundamentals f desrptin with chemical reactin, which are applied t the prblem f CO 2 desrptin in ME distillers,

More information

CHAPTER 24: INFERENCE IN REGRESSION. Chapter 24: Make inferences about the population from which the sample data came.

CHAPTER 24: INFERENCE IN REGRESSION. Chapter 24: Make inferences about the population from which the sample data came. MATH 1342 Ch. 24 April 25 and 27, 2013 Page 1 f 5 CHAPTER 24: INFERENCE IN REGRESSION Chapters 4 and 5: Relatinships between tw quantitative variables. Be able t Make a graph (scatterplt) Summarize the

More information

MODULE 1. e x + c. [You can t separate a demominator, but you can divide a single denominator into each numerator term] a + b a(a + b)+1 = a + b

MODULE 1. e x + c. [You can t separate a demominator, but you can divide a single denominator into each numerator term] a + b a(a + b)+1 = a + b . REVIEW OF SOME BASIC ALGEBRA MODULE () Slving Equatins Yu shuld be able t slve fr x: a + b = c a d + e x + c and get x = e(ba +) b(c a) d(ba +) c Cmmn mistakes and strategies:. a b + c a b + a c, but

More information

February 28, 2013 COMMENTS ON DIFFUSION, DIFFUSIVITY AND DERIVATION OF HYPERBOLIC EQUATIONS DESCRIBING THE DIFFUSION PHENOMENA

February 28, 2013 COMMENTS ON DIFFUSION, DIFFUSIVITY AND DERIVATION OF HYPERBOLIC EQUATIONS DESCRIBING THE DIFFUSION PHENOMENA February 28, 2013 COMMENTS ON DIFFUSION, DIFFUSIVITY AND DERIVATION OF HYPERBOLIC EQUATIONS DESCRIBING THE DIFFUSION PHENOMENA Mental Experiment regarding 1D randm walk Cnsider a cntainer f gas in thermal

More information

Materials Engineering 272-C Fall 2001, Lecture 7 & 8 Fundamentals of Diffusion

Materials Engineering 272-C Fall 2001, Lecture 7 & 8 Fundamentals of Diffusion Materials Engineering 272-C Fall 2001, Lecture 7 & 8 Fundamentals f Diffusin Diffusin: Transprt in a slid, liquid, r gas driven by a cncentratin gradient (r, in the case f mass transprt, a chemical ptential

More information

BASD HIGH SCHOOL FORMAL LAB REPORT

BASD HIGH SCHOOL FORMAL LAB REPORT BASD HIGH SCHOOL FORMAL LAB REPORT *WARNING: After an explanatin f what t include in each sectin, there is an example f hw the sectin might lk using a sample experiment Keep in mind, the sample lab used

More information

Computational modeling techniques

Computational modeling techniques Cmputatinal mdeling techniques Lecture 2: Mdeling change. In Petre Department f IT, Åb Akademi http://users.ab.fi/ipetre/cmpmd/ Cntent f the lecture Basic paradigm f mdeling change Examples Linear dynamical

More information

Revision: August 19, E Main Suite D Pullman, WA (509) Voice and Fax

Revision: August 19, E Main Suite D Pullman, WA (509) Voice and Fax .7.4: Direct frequency dmain circuit analysis Revisin: August 9, 00 5 E Main Suite D Pullman, WA 9963 (509) 334 6306 ice and Fax Overview n chapter.7., we determined the steadystate respnse f electrical

More information

Physics 2B Chapter 23 Notes - Faraday s Law & Inductors Spring 2018

Physics 2B Chapter 23 Notes - Faraday s Law & Inductors Spring 2018 Michael Faraday lived in the Lndn area frm 1791 t 1867. He was 29 years ld when Hand Oersted, in 1820, accidentally discvered that electric current creates magnetic field. Thrugh empirical bservatin and

More information

making triangle (ie same reference angle) ). This is a standard form that will allow us all to have the X= y=

making triangle (ie same reference angle) ). This is a standard form that will allow us all to have the X= y= Intrductin t Vectrs I 21 Intrductin t Vectrs I 22 I. Determine the hrizntal and vertical cmpnents f the resultant vectr by cunting n the grid. X= y= J. Draw a mangle with hrizntal and vertical cmpnents

More information

Physics 2010 Motion with Constant Acceleration Experiment 1

Physics 2010 Motion with Constant Acceleration Experiment 1 . Physics 00 Mtin with Cnstant Acceleratin Experiment In this lab, we will study the mtin f a glider as it accelerates dwnhill n a tilted air track. The glider is supprted ver the air track by a cushin

More information

Department: MATHEMATICS

Department: MATHEMATICS Cde: MATH 022 Title: ALGEBRA SKILLS Institute: STEM Department: MATHEMATICS Curse Descriptin: This curse prvides students wh have cmpleted MATH 021 with the necessary skills and cncepts t cntinue the study

More information

Verification of Quality Parameters of a Solar Panel and Modification in Formulae of its Series Resistance

Verification of Quality Parameters of a Solar Panel and Modification in Formulae of its Series Resistance Verificatin f Quality Parameters f a Slar Panel and Mdificatin in Frmulae f its Series Resistance Sanika Gawhane Pune-411037-India Onkar Hule Pune-411037- India Chinmy Kulkarni Pune-411037-India Ojas Pandav

More information

ALE 21. Gibbs Free Energy. At what temperature does the spontaneity of a reaction change?

ALE 21. Gibbs Free Energy. At what temperature does the spontaneity of a reaction change? Name Chem 163 Sectin: Team Number: ALE 21. Gibbs Free Energy (Reference: 20.3 Silberberg 5 th editin) At what temperature des the spntaneity f a reactin change? The Mdel: The Definitin f Free Energy S

More information

22.54 Neutron Interactions and Applications (Spring 2004) Chapter 11 (3/11/04) Neutron Diffusion

22.54 Neutron Interactions and Applications (Spring 2004) Chapter 11 (3/11/04) Neutron Diffusion .54 Neutrn Interactins and Applicatins (Spring 004) Chapter (3//04) Neutrn Diffusin References -- J. R. Lamarsh, Intrductin t Nuclear Reactr Thery (Addisn-Wesley, Reading, 966) T study neutrn diffusin

More information

Thermodynamics Partial Outline of Topics

Thermodynamics Partial Outline of Topics Thermdynamics Partial Outline f Tpics I. The secnd law f thermdynamics addresses the issue f spntaneity and invlves a functin called entrpy (S): If a prcess is spntaneus, then Suniverse > 0 (2 nd Law!)

More information

Comprehensive Exam Guidelines Department of Chemical and Biomolecular Engineering, Ohio University

Comprehensive Exam Guidelines Department of Chemical and Biomolecular Engineering, Ohio University Cmprehensive Exam Guidelines Department f Chemical and Bimlecular Engineering, Ohi University Purpse In the Cmprehensive Exam, the student prepares an ral and a written research prpsal. The Cmprehensive

More information

APPLICATION OF THE BRATSETH SCHEME FOR HIGH LATITUDE INTERMITTENT DATA ASSIMILATION USING THE PSU/NCAR MM5 MESOSCALE MODEL

APPLICATION OF THE BRATSETH SCHEME FOR HIGH LATITUDE INTERMITTENT DATA ASSIMILATION USING THE PSU/NCAR MM5 MESOSCALE MODEL JP2.11 APPLICATION OF THE BRATSETH SCHEME FOR HIGH LATITUDE INTERMITTENT DATA ASSIMILATION USING THE PSU/NCAR MM5 MESOSCALE MODEL Xingang Fan * and Jeffrey S. Tilley University f Alaska Fairbanks, Fairbanks,

More information

AMERICAN PETROLEUM INSTITUTE API RP 581 RISK BASED INSPECTION BASE RESOURCE DOCUMENT BALLOT COVER PAGE

AMERICAN PETROLEUM INSTITUTE API RP 581 RISK BASED INSPECTION BASE RESOURCE DOCUMENT BALLOT COVER PAGE Ballt ID: Title: USING LIFE EXTENSION FACTOR (LEF) TO INCREASE BUNDLE INSPECTION INTERVAL Purpse: 1. Prvides a methd t increase a bundle s inspectin interval t accunt fr LEF. 2. Clarifies Table 8.6.5 Als

More information

NGSS High School Physics Domain Model

NGSS High School Physics Domain Model NGSS High Schl Physics Dmain Mdel Mtin and Stability: Frces and Interactins HS-PS2-1: Students will be able t analyze data t supprt the claim that Newtn s secnd law f mtin describes the mathematical relatinship

More information

Eric Klein and Ning Sa

Eric Klein and Ning Sa Week 12. Statistical Appraches t Netwrks: p1 and p* Wasserman and Faust Chapter 15: Statistical Analysis f Single Relatinal Netwrks There are fur tasks in psitinal analysis: 1) Define Equivalence 2) Measure

More information

8 th Grade Math: Pre-Algebra

8 th Grade Math: Pre-Algebra Hardin Cunty Middle Schl (2013-2014) 1 8 th Grade Math: Pre-Algebra Curse Descriptin The purpse f this curse is t enhance student understanding, participatin, and real-life applicatin f middle-schl mathematics

More information

Matter Content from State Frameworks and Other State Documents

Matter Content from State Frameworks and Other State Documents Atms and Mlecules Mlecules are made f smaller entities (atms) which are bnded tgether. Therefre mlecules are divisible. Miscnceptin: Element and atm are synnyms. Prper cnceptin: Elements are atms with

More information

OF SIMPLY SUPPORTED PLYWOOD PLATES UNDER COMBINED EDGEWISE BENDING AND COMPRESSION

OF SIMPLY SUPPORTED PLYWOOD PLATES UNDER COMBINED EDGEWISE BENDING AND COMPRESSION U. S. FOREST SERVICE RESEARCH PAPER FPL 50 DECEMBER U. S. DEPARTMENT OF AGRICULTURE FOREST SERVICE FOREST PRODUCTS LABORATORY OF SIMPLY SUPPORTED PLYWOOD PLATES UNDER COMBINED EDGEWISE BENDING AND COMPRESSION

More information

BOUNDED UNCERTAINTY AND CLIMATE CHANGE ECONOMICS. Christopher Costello, Andrew Solow, Michael Neubert, and Stephen Polasky

BOUNDED UNCERTAINTY AND CLIMATE CHANGE ECONOMICS. Christopher Costello, Andrew Solow, Michael Neubert, and Stephen Polasky BOUNDED UNCERTAINTY AND CLIMATE CHANGE ECONOMICS Christpher Cstell, Andrew Slw, Michael Neubert, and Stephen Plasky Intrductin The central questin in the ecnmic analysis f climate change plicy cncerns

More information

I.S. 239 Mark Twain. Grade 7 Mathematics Spring Performance Task: Proportional Relationships

I.S. 239 Mark Twain. Grade 7 Mathematics Spring Performance Task: Proportional Relationships I.S. 239 Mark Twain 7 ID Name: Date: Grade 7 Mathematics Spring Perfrmance Task: Prprtinal Relatinships Directins: Cmplete all parts f each sheet fr each given task. Be sure t read thrugh the rubrics s

More information

( ) kt. Solution. From kinetic theory (visualized in Figure 1Q9-1), 1 2 rms = 2. = 1368 m/s

( ) kt. Solution. From kinetic theory (visualized in Figure 1Q9-1), 1 2 rms = 2. = 1368 m/s .9 Kinetic Mlecular Thery Calculate the effective (rms) speeds f the He and Ne atms in the He-Ne gas laser tube at rm temperature (300 K). Slutin T find the rt mean square velcity (v rms ) f He atms at

More information

CONSTRUCTING STATECHART DIAGRAMS

CONSTRUCTING STATECHART DIAGRAMS CONSTRUCTING STATECHART DIAGRAMS The fllwing checklist shws the necessary steps fr cnstructing the statechart diagrams f a class. Subsequently, we will explain the individual steps further. Checklist 4.6

More information

General Chemistry II, Unit I: Study Guide (part I)

General Chemistry II, Unit I: Study Guide (part I) 1 General Chemistry II, Unit I: Study Guide (part I) CDS Chapter 14: Physical Prperties f Gases Observatin 1: Pressure- Vlume Measurements n Gases The spring f air is measured as pressure, defined as the

More information

Assessment Primer: Writing Instructional Objectives

Assessment Primer: Writing Instructional Objectives Assessment Primer: Writing Instructinal Objectives (Based n Preparing Instructinal Objectives by Mager 1962 and Preparing Instructinal Objectives: A critical tl in the develpment f effective instructin

More information

EXPERIMENTAL STUDY ON DISCHARGE COEFFICIENT OF OUTFLOW OPENING FOR PREDICTING CROSS-VENTILATION FLOW RATE

EXPERIMENTAL STUDY ON DISCHARGE COEFFICIENT OF OUTFLOW OPENING FOR PREDICTING CROSS-VENTILATION FLOW RATE EXPERIMENTAL STUD ON DISCHARGE COEFFICIENT OF OUTFLOW OPENING FOR PREDICTING CROSS-VENTILATION FLOW RATE Tmnbu Gt, Masaaki Ohba, Takashi Kurabuchi 2, Tmyuki End 3, shihik Akamine 4, and Tshihir Nnaka 2

More information

Math Foundations 20 Work Plan

Math Foundations 20 Work Plan Math Fundatins 20 Wrk Plan Units / Tpics 20.8 Demnstrate understanding f systems f linear inequalities in tw variables. Time Frame December 1-3 weeks 6-10 Majr Learning Indicatrs Identify situatins relevant

More information

OTHER USES OF THE ICRH COUPL ING CO IL. November 1975

OTHER USES OF THE ICRH COUPL ING CO IL. November 1975 OTHER USES OF THE ICRH COUPL ING CO IL J. C. Sprtt Nvember 1975 -I,," PLP 663 Plasma Studies University f Wiscnsin These PLP Reprts are infrmal and preliminary and as such may cntain errrs nt yet eliminated.

More information

Lecture 17: Free Energy of Multi-phase Solutions at Equilibrium

Lecture 17: Free Energy of Multi-phase Solutions at Equilibrium Lecture 17: 11.07.05 Free Energy f Multi-phase Slutins at Equilibrium Tday: LAST TIME...2 FREE ENERGY DIAGRAMS OF MULTI-PHASE SOLUTIONS 1...3 The cmmn tangent cnstructin and the lever rule...3 Practical

More information

Modelling of Clock Behaviour. Don Percival. Applied Physics Laboratory University of Washington Seattle, Washington, USA

Modelling of Clock Behaviour. Don Percival. Applied Physics Laboratory University of Washington Seattle, Washington, USA Mdelling f Clck Behaviur Dn Percival Applied Physics Labratry University f Washingtn Seattle, Washingtn, USA verheads and paper fr talk available at http://faculty.washingtn.edu/dbp/talks.html 1 Overview

More information

Distributions, spatial statistics and a Bayesian perspective

Distributions, spatial statistics and a Bayesian perspective Distributins, spatial statistics and a Bayesian perspective Dug Nychka Natinal Center fr Atmspheric Research Distributins and densities Cnditinal distributins and Bayes Thm Bivariate nrmal Spatial statistics

More information

I. Analytical Potential and Field of a Uniform Rod. V E d. The definition of electric potential difference is

I. Analytical Potential and Field of a Uniform Rod. V E d. The definition of electric potential difference is Length L>>a,b,c Phys 232 Lab 4 Ch 17 Electric Ptential Difference Materials: whitebards & pens, cmputers with VPythn, pwer supply & cables, multimeter, crkbard, thumbtacks, individual prbes and jined prbes,

More information

EDA Engineering Design & Analysis Ltd

EDA Engineering Design & Analysis Ltd EDA Engineering Design & Analysis Ltd THE FINITE ELEMENT METHOD A shrt tutrial giving an verview f the histry, thery and applicatin f the finite element methd. Intrductin Value f FEM Applicatins Elements

More information

Technical Bulletin. Generation Interconnection Procedures. Revisions to Cluster 4, Phase 1 Study Methodology

Technical Bulletin. Generation Interconnection Procedures. Revisions to Cluster 4, Phase 1 Study Methodology Technical Bulletin Generatin Intercnnectin Prcedures Revisins t Cluster 4, Phase 1 Study Methdlgy Release Date: Octber 20, 2011 (Finalizatin f the Draft Technical Bulletin released n September 19, 2011)

More information

Chem 115 POGIL Worksheet - Week 8 Thermochemistry (Continued), Electromagnetic Radiation, and Line Spectra

Chem 115 POGIL Worksheet - Week 8 Thermochemistry (Continued), Electromagnetic Radiation, and Line Spectra Chem 115 POGIL Wrksheet - Week 8 Thermchemistry (Cntinued), Electrmagnetic Radiatin, and Line Spectra Why? As we saw last week, enthalpy and internal energy are state functins, which means that the sum

More information

Thermodynamics and Equilibrium

Thermodynamics and Equilibrium Thermdynamics and Equilibrium Thermdynamics Thermdynamics is the study f the relatinship between heat and ther frms f energy in a chemical r physical prcess. We intrduced the thermdynamic prperty f enthalpy,

More information

Cambridge Assessment International Education Cambridge Ordinary Level. Published

Cambridge Assessment International Education Cambridge Ordinary Level. Published Cambridge Assessment Internatinal Educatin Cambridge Ordinary Level ADDITIONAL MATHEMATICS 4037/1 Paper 1 Octber/Nvember 017 MARK SCHEME Maximum Mark: 80 Published This mark scheme is published as an aid

More information

CHM112 Lab Graphing with Excel Grading Rubric

CHM112 Lab Graphing with Excel Grading Rubric Name CHM112 Lab Graphing with Excel Grading Rubric Criteria Pints pssible Pints earned Graphs crrectly pltted and adhere t all guidelines (including descriptive title, prperly frmatted axes, trendline

More information

Fabrication Thermal Test. Methodology for a Safe Cask Thermal Performance

Fabrication Thermal Test. Methodology for a Safe Cask Thermal Performance ENSA (Grup SEPI) Fabricatin Thermal Test. Methdlgy fr a Safe Cask Thermal Perfrmance IAEA Internatinal Cnference n the Management f Spent Fuel frm Nuclear Pwer Reactrs An Integrated Apprach t the Back-End

More information

Feasibility Testing Report Muscle Optimization Stage I

Feasibility Testing Report Muscle Optimization Stage I Feasibility Testing Reprt Muscle Optimizatin Stage I Team: P15001: Active Ankle Ft Orthtic Engineer: Nah Schadt Mechanical Engineer Engineer: Tyler Leichtenberger Mechanical Engineer Test Date: 10/14/2014

More information

THERMAL-VACUUM VERSUS THERMAL- ATMOSPHERIC TESTS OF ELECTRONIC ASSEMBLIES

THERMAL-VACUUM VERSUS THERMAL- ATMOSPHERIC TESTS OF ELECTRONIC ASSEMBLIES PREFERRED RELIABILITY PAGE 1 OF 5 PRACTICES PRACTICE NO. PT-TE-1409 THERMAL-VACUUM VERSUS THERMAL- ATMOSPHERIC Practice: Perfrm all thermal envirnmental tests n electrnic spaceflight hardware in a flight-like

More information

NAME TEMPERATURE AND HUMIDITY. I. Introduction

NAME TEMPERATURE AND HUMIDITY. I. Introduction NAME TEMPERATURE AND HUMIDITY I. Intrductin Temperature is the single mst imprtant factr in determining atmspheric cnditins because it greatly influences: 1. The amunt f water vapr in the air 2. The pssibility

More information

Chapter 1 Notes Using Geography Skills

Chapter 1 Notes Using Geography Skills Chapter 1 Ntes Using Gegraphy Skills Sectin 1: Thinking Like a Gegrapher Gegraphy is used t interpret the past, understand the present, and plan fr the future. Gegraphy is the study f the Earth. It is

More information

A New Evaluation Measure. J. Joiner and L. Werner. The problems of evaluation and the needed criteria of evaluation

A New Evaluation Measure. J. Joiner and L. Werner. The problems of evaluation and the needed criteria of evaluation III-l III. A New Evaluatin Measure J. Jiner and L. Werner Abstract The prblems f evaluatin and the needed criteria f evaluatin measures in the SMART system f infrmatin retrieval are reviewed and discussed.

More information

AP Statistics Notes Unit Two: The Normal Distributions

AP Statistics Notes Unit Two: The Normal Distributions AP Statistics Ntes Unit Tw: The Nrmal Distributins Syllabus Objectives: 1.5 The student will summarize distributins f data measuring the psitin using quartiles, percentiles, and standardized scres (z-scres).

More information

Interference is when two (or more) sets of waves meet and combine to produce a new pattern.

Interference is when two (or more) sets of waves meet and combine to produce a new pattern. Interference Interference is when tw (r mre) sets f waves meet and cmbine t prduce a new pattern. This pattern can vary depending n the riginal wave directin, wavelength, amplitude, etc. The tw mst extreme

More information

Chapter Outline 4/28/2014. P-V Work. P-V Work. Isolated, Closed and Open Systems. Exothermic and Endothermic Processes. E = q + w

Chapter Outline 4/28/2014. P-V Work. P-V Work. Isolated, Closed and Open Systems. Exothermic and Endothermic Processes. E = q + w Islated, Clsed and Open Systems 9.1 Energy as a Reactant r a Prduct 9.2 Transferring Heat and Ding Wrk 9.5 Heats f Reactin and Calrimetry 9.6 Hess s Law and Standard Heats f Reactin 9.7 Heats f Reactin

More information

Emphases in Common Core Standards for Mathematical Content Kindergarten High School

Emphases in Common Core Standards for Mathematical Content Kindergarten High School Emphases in Cmmn Cre Standards fr Mathematical Cntent Kindergarten High Schl Cntent Emphases by Cluster March 12, 2012 Describes cntent emphases in the standards at the cluster level fr each grade. These

More information

Guide to Using the Rubric to Score the Klf4 PREBUILD Model for Science Olympiad National Competitions

Guide to Using the Rubric to Score the Klf4 PREBUILD Model for Science Olympiad National Competitions Guide t Using the Rubric t Scre the Klf4 PREBUILD Mdel fr Science Olympiad 2010-2011 Natinal Cmpetitins These instructins are t help the event supervisr and scring judges use the rubric develped by the

More information

Space Shuttle Ascent Mass vs. Time

Space Shuttle Ascent Mass vs. Time Space Shuttle Ascent Mass vs. Time Backgrund This prblem is part f a series that applies algebraic principles in NASA s human spaceflight. The Space Shuttle Missin Cntrl Center (MCC) and the Internatinal

More information

Resampling Methods. Chapter 5. Chapter 5 1 / 52

Resampling Methods. Chapter 5. Chapter 5 1 / 52 Resampling Methds Chapter 5 Chapter 5 1 / 52 1 51 Validatin set apprach 2 52 Crss validatin 3 53 Btstrap Chapter 5 2 / 52 Abut Resampling An imprtant statistical tl Pretending the data as ppulatin and

More information

Edexcel IGCSE Chemistry. Topic 1: Principles of chemistry. Chemical formulae, equations and calculations. Notes.

Edexcel IGCSE Chemistry. Topic 1: Principles of chemistry. Chemical formulae, equations and calculations. Notes. Edexcel IGCSE Chemistry Tpic 1: Principles f chemistry Chemical frmulae, equatins and calculatins Ntes 1.25 write wrd equatins and balanced chemical equatins (including state symbls): fr reactins studied

More information

IB Sports, Exercise and Health Science Summer Assignment. Mrs. Christina Doyle Seneca Valley High School

IB Sports, Exercise and Health Science Summer Assignment. Mrs. Christina Doyle Seneca Valley High School IB Sprts, Exercise and Health Science Summer Assignment Mrs. Christina Dyle Seneca Valley High Schl Welcme t IB Sprts, Exercise and Health Science! This curse incrprates the traditinal disciplines f anatmy

More information

Assume that the water in the nozzle is accelerated at a rate such that the frictional effect can be neglected.

Assume that the water in the nozzle is accelerated at a rate such that the frictional effect can be neglected. 1 HW #3: Cnservatin f Linear Mmentum, Cnservatin f Energy, Cnservatin f Angular Mmentum and Turbmachines, Bernulli s Equatin, Dimensinal Analysis, and Pipe Flws Prblem 1. Cnservatins f Mass and Linear

More information

Chapter 16. Capacitance. Capacitance, cont. Parallel-Plate Capacitor, Example 1/20/2011. Electric Energy and Capacitance

Chapter 16. Capacitance. Capacitance, cont. Parallel-Plate Capacitor, Example 1/20/2011. Electric Energy and Capacitance summary C = ε A / d = πε L / ln( b / a ) ab C = 4πε 4πε a b a b >> a Chapter 16 Electric Energy and Capacitance Capacitance Q=CV Parallel plates, caxial cables, Earth Series and parallel 1 1 1 = + +..

More information

Bootstrap Method > # Purpose: understand how bootstrap method works > obs=c(11.96, 5.03, 67.40, 16.07, 31.50, 7.73, 11.10, 22.38) > n=length(obs) >

Bootstrap Method > # Purpose: understand how bootstrap method works > obs=c(11.96, 5.03, 67.40, 16.07, 31.50, 7.73, 11.10, 22.38) > n=length(obs) > Btstrap Methd > # Purpse: understand hw btstrap methd wrks > bs=c(11.96, 5.03, 67.40, 16.07, 31.50, 7.73, 11.10, 22.38) > n=length(bs) > mean(bs) [1] 21.64625 > # estimate f lambda > lambda = 1/mean(bs);

More information

Experiment #3. Graphing with Excel

Experiment #3. Graphing with Excel Experiment #3. Graphing with Excel Study the "Graphing with Excel" instructins that have been prvided. Additinal help with learning t use Excel can be fund n several web sites, including http://www.ncsu.edu/labwrite/res/gt/gt-

More information

Homology groups of disks with holes

Homology groups of disks with holes Hmlgy grups f disks with hles THEOREM. Let p 1,, p k } be a sequence f distinct pints in the interir unit disk D n where n 2, and suppse that fr all j the sets E j Int D n are clsed, pairwise disjint subdisks.

More information

7 TH GRADE MATH STANDARDS

7 TH GRADE MATH STANDARDS ALGEBRA STANDARDS Gal 1: Students will use the language f algebra t explre, describe, represent, and analyze number expressins and relatins 7 TH GRADE MATH STANDARDS 7.M.1.1: (Cmprehensin) Select, use,

More information

Determining the Accuracy of Modal Parameter Estimation Methods

Determining the Accuracy of Modal Parameter Estimation Methods Determining the Accuracy f Mdal Parameter Estimatin Methds by Michael Lee Ph.D., P.E. & Mar Richardsn Ph.D. Structural Measurement Systems Milpitas, CA Abstract The mst cmmn type f mdal testing system

More information

We can see from the graph above that the intersection is, i.e., [ ).

We can see from the graph above that the intersection is, i.e., [ ). MTH 111 Cllege Algebra Lecture Ntes July 2, 2014 Functin Arithmetic: With nt t much difficulty, we ntice that inputs f functins are numbers, and utputs f functins are numbers. S whatever we can d with

More information

Computational modeling techniques

Computational modeling techniques Cmputatinal mdeling techniques Lecture 11: Mdeling with systems f ODEs In Petre Department f IT, Ab Akademi http://www.users.ab.fi/ipetre/cmpmd/ Mdeling with differential equatins Mdeling strategy Fcus

More information

Methods for Determination of Mean Speckle Size in Simulated Speckle Pattern

Methods for Determination of Mean Speckle Size in Simulated Speckle Pattern 0.478/msr-04-004 MEASUREMENT SCENCE REVEW, Vlume 4, N. 3, 04 Methds fr Determinatin f Mean Speckle Size in Simulated Speckle Pattern. Hamarvá, P. Šmíd, P. Hrváth, M. Hrabvský nstitute f Physics f the Academy

More information

Lesson Plan. Recode: They will do a graphic organizer to sequence the steps of scientific method.

Lesson Plan. Recode: They will do a graphic organizer to sequence the steps of scientific method. Lessn Plan Reach: Ask the students if they ever ppped a bag f micrwave ppcrn and nticed hw many kernels were unppped at the bttm f the bag which made yu wnder if ther brands pp better than the ne yu are

More information

Least Squares Optimal Filtering with Multirate Observations

Least Squares Optimal Filtering with Multirate Observations Prc. 36th Asilmar Cnf. n Signals, Systems, and Cmputers, Pacific Grve, CA, Nvember 2002 Least Squares Optimal Filtering with Multirate Observatins Charles W. herrien and Anthny H. Hawes Department f Electrical

More information

AP Chemistry Assessment 2

AP Chemistry Assessment 2 AP Chemistry Assessment 2 DATE OF ADMINISTRATION: January 8 January 12 TOPICS COVERED: Fundatinal Tpics, Reactins, Gases, Thermchemistry, Atmic Structure, Peridicity, and Bnding. MULTIPLE CHOICE KEY AND

More information

Perfrmance f Sensitizing Rules n Shewhart Cntrl Charts with Autcrrelated Data Key Wrds: Autregressive, Mving Average, Runs Tests, Shewhart Cntrl Chart

Perfrmance f Sensitizing Rules n Shewhart Cntrl Charts with Autcrrelated Data Key Wrds: Autregressive, Mving Average, Runs Tests, Shewhart Cntrl Chart Perfrmance f Sensitizing Rules n Shewhart Cntrl Charts with Autcrrelated Data Sandy D. Balkin Dennis K. J. Lin y Pennsylvania State University, University Park, PA 16802 Sandy Balkin is a graduate student

More information