This summative assessment has two parts. Part 1 is to be completed in Week 1, and Part 2 is to be completed in Week 2. You will submit both Part 1 and Part 2 of the assessment in Week 2. Read the following scenario and address the steps that follow in 525 to 700 words. Innovative Automotive is an automobile accessories company that has been in business for […]
Week11.docx Week 11 Instructions Your task this week is to complete an outline of your Signature Assignment. The outline should contain the following for two hypothetical studies, one that will use a qualitative method and one that will use a quantitative method. For the quantitative study, be sure to address the following in your outline: Include a brief explanation of the hypothetical study. Identify the […]
Acct 211 Quiz 2 1. When purchase costs of inventory regularly decline, which method of inventory costing will yield the lowest cost of goods sold? FIFO. LIFO. Weighted average. Specific identification. Gross margin. 2. Some companies choose to avoid assigning incidental costs of acquiring merchandise to inventory by recording them as expenses when incurred. The argument that supports this is called: The matching […]
ACCT-402-06 Section #11898 Professor Gregory Njoes Fall 2023 WRITING ASSIGNMENT GUIDELINES Assignment Passed Out: September 28, 2023 Assignment Due Date: November 28, 2023, 8:00 pm submitted on Canvas Topic – Background: As discussed in the early chapters of our text, and specifically in Chapters 1 through 6, auditors need to assess many risks when accepting a new audit engagement or determining that it is appropriate […]
HUMA 1301: Art Museum Assignment Purpose To evaluate art using the techniques and knowledge acquired in class. To historically situate art in the culture, era, and style of its production. To experience art and make connections! General Instructions For this assignment, you will visit The Contemporary Arts Museum Houston (free), The Menil Collection (free), The Museum of Fine Arts Houston (free on Thursdays), or […]
031422 Project 4 Questions – Report Template Instructions: Answer the five questions below, based on the information that you developed in the Excel workbook. Provide support for your reasoning from the readings in Project 4, Step 1, and the discussion in Project 4, Step 3. Be sure to cite any sources used in proper APA (7th ed.) format. Provide a detailed response below each question. […]
6 Natural Resource Economics. Jose Valdez Mr. Ward 11/8/23 Natural Resource Economics 1. Steiner, J. L., Devlin, D. L., Perkins, S., Aguilar, J. P., Golden, B., Santos, E. A., & Unruh, M. (2021). Policy, Technology, and Management Options for Water Conservation in the Ogallala Aquifer in Kansas, USA. Water, 13(23), 3406. The authors recommend Ogallala Aquifer to establish a policy that can promote more innovation […]
Students will research the historical and political development of victim rights and victim-centered policies related to a particular type of crime (rape, murder, kidnapping, child abuse, hate crimes, financial crimes, stalking, domestic violence). You are to focus on one crime and explain in-depth how the victims’ rights movement has developed in response to the crime. Questions to be addressed include the following: What types of […]
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Pick a topic in Real Estate, and you are encouraged to develop one on your own. The focusof the project is the real estate markets in the state of Tennessee. Some suggested topicsfor the project: Real Estate Laws/Taxes in Tennessee; the residential real estate marketin Tennessee; the commercial real estate market in Tennessee; the commercial vs.residential real estate market in Tennessee; working as a real […]
DeterministicModelingandSimulationExam1
1. (25 pts) Thecompound tanksystemshown in Figure1 consistsof asphericaltank ofradius R1and acylindrical tankofdiameterD2. A liquid ofconstantdensityis fed atavolumetricrateF1in intothetopof aspherical tankandvolumetric rateF2in intothetop ofthecylindricaltank. The sphericalandcylindrical tanks interactthrough thepipeconnectingthem.Theflowrates intotheconnecting pipedepend ontheheightsoftheliquid in thetanks. Thevolumetric flowrate outof thesphericaltank
intothepipeis given byF1out =k1
h1 , whilethevolumetric flow rateoutofthecylindricaltankinto
thepipeis given byF2out =k1
h2 whereh1 and h2 arethe heightsoftheliquid in thesphericaland
cylindrical tanks respectivelyandk1 is thecommonvalvecoefficient.Thecylindricaltank alsohas a
drain on theright-hand sidewhich hasvolumetricflowrateF3out =k2
coefficientfortheright-hand sidedrain.
h2 wherek2 is thevalve
a) Obtain a dynamicmodelthatdescribes theheightsoftheliquid in thetanks. Is this a linearornonlinearmodel?
b) For constantinputflow rates, F1in and F2in, analytically determine thesteady-statevaluesofh1 and
h2. Dotheshapesand dimensionsof thetanksaffectthesteady-statevalues?
Notethatyoudonotneedtosolvethedifferential equations for thesteady stateanalysis.
c) Simulatethesystem and plottheheightsoftheliquidin thetanks versustimeforconstantinputflowratesusing thevaluesgiven in thetablebelow.(Run thesimulation for2000sec)
|
F1in |
2.0 ft3/s |
F2in |
1.0 ft3/s |
|
R1 |
10.0 ft |
D2 |
20.0 ft |
|
k1 |
2.0ft5/2/s |
k2 |
3.0ft5/2/s |
|
h1(0) |
4.0 ft |
h2(0) |
4.0 ft |
2. (25pts) Chaoticsystemsareones forwhich small changes eventuallylead toresults thatcan bedramaticallydifferent. The Rösslersystemisoneofthesimplestsets ofdifferential equationsthatexhibits chaoticdynamics. In addition totheir theoretical valuein studyingchaotic systems,theRösslerequations areusefulin several areasofphysicalmodeling including analyzing chemicalkineticsforreaction networks. Consider thereaction network:
k1
A1+X2X
k-1
k2
X+Y2Y
k-2
k3
A5+YA2
k-3
k4
X+ZA3
k-4
k5
A4 +Z2Z
k-5
whereX,Y, and Z represent thechemical specieswhoseconcentrationsvaryandA1, A2, A3, A4, and A5 arechemicalspecies whoseconcentrationsareheldfixed bylargechemical reservoirs, serving tokeepthe system outofthermodynamicequilibrium.ki andk-i denote theforward and inversereaction rates.Thesystem of differentialequations thatdescribetheconcentrations x, y, and z(for chemicalspeciesX,Y, and Z) are:
dx =-y-zdt
dy =x+aydt
dz =b-cz+xzdt
a) Simulatethis systemfor a=0.380, b=0.300,and c=4.280with initial conditionsx(0)=0.1,
y(0)=0.2, z(0)=0.3. Run thesimulation for200seconds using a fixed-step size algorithm witha stepsizeof0.001seconds.Plottheconcentrationsx, y, andzversustimeononefigurewiththreesubplots. Additionally, in separategraphs, plotthephase-spaceplots:xversus y,xversusz, and yversus z. Finally,makea3-Dplotof xvs yvszusing theMatlab graphics command "plot3"
b) Illustratethesensitivityofthesolution to variations intheinitial conditions byrepeating thesimulation ofpart(a) withx(0)=0.0999and thenwith x(0)=0.1001. (A0.1%changein thevalueoftheinitial condition in either direction.)Keeptheinitial conditions for y(0) and z(0) thesameas inpart(a). Showthesensitivitybysuperimposing theplots forthenew valuesyouobtain forx(t),y(t),and z(t)with theoriginal plots forxvs t,yvs t,and zvs t. In addition,makeplotsof thedifferences:x(t)– xorginal(t) vst,y(t) –yorginal(t) vst, and z(t) –zorginal(t) vs t.
c) Illustratethesensitivityofthesolution to variations inparametervalues byrepeating thesimulationof part(a)withc=4.280001. [Use theoriginal initial conditions from part(a).]Show thesensitivitywith thesamesetof plotsas in part(b).
Whyisthis systemnon-linear?
Qualitatively describethesensitivity toinitial conditions and parametervalues.
3) (25 pts) Acontinuous stir tank reactor(CSTR)is used toproducea product P fromchemicals Aand B.Thereactionis A+BàP. Ais inexcess andtherateof decompositionofBisgiven by:
rb =
k1 x2
+ 2
(1 k2 x2 )
wherek1and k2areconstants and x2is theproductconcentration.Theequations describing thesystemaregiven by:
1 1 2 2
The parameters are: Cb1 =24.9,Cb2=0.1 ,k1=k2= 1,andu1 =u2 = 1.The initial conditions are: x1(0) =10and x2(0)=0.
a) First, simulatetheequation for x1onlysinceitdoesnot depend onx2.Notethesteady-statevaluethatyou find forx1.
b) Inthemodelforx2, initializetheintegrator for x1to thesteady-statevalue you found in part(a) andinitialize x2(0)=0. Run thesimulation for 1000seconds to determinex2(t)and thesteady-statevalueof x2.
c) Repeatthesimulation for x2 using an initial value x2(0)=10. Notethenewsteady-statevalueyoufindfor x2.
d) Bothof thepreviouscasesarestable.Thereis anothersteadystatecorresponding to everything elsebeingthesameand thesteadystates forx2and x1being x2= 2.793and
x1=100.This is an unstablesteadystate.Demonstratethis bysetting theinitialvalueoftheintegratorforx2tox2(0) =2.80andshowthatthesimulation goesto theuppersteady-statevalue.Repeatthesimulationwithx2(0)=2.79 and showthatitgoes tothelowersteady-statevalue.Thismeansthatanysmall fluctuation willcausethesystemtofalltosteadystateofpart(b)or risetothesteady stateof part(c).
e) Demonstratethatthesteadystatewith x2=2.793is unstablebylinearizing theequation forx2aboutthesteady-statevaluesandshowingthatthelinearsystem thatresultsis unstable. Youcan do this by either solving thedifferential equationor by simulating thesystem witha small initial Dx2.
4) (25 pts) Considerthefollowing linear system
G(s)=-8s+6 2s3 +9s2 +13s+6
For this problem, usea unit step input.
a) Createamodel for this systemusingonly integrators and run itfor10seconds.
b) Replacetheintegratorswith discreteintegratorsand investigatetheeffectof forward, backward,and trapezoidal integratorswith sampling timesof0.01, 0.1, and0.2seconds.
Notethatintheconfiguration parametersyouwillneedtospecify thestepsizeand changetheintegratortodiscretestates only.Also,setallof thesampling times inthevarious blocksequal tothediscretesampling time.
c) For each case, comparethetruesolution tothediscretesolution intwo ways:
(i) Plotthetruesolution (in blue) and discretesolution (in red)ona singleplot.
(ii) Plotthedifferencebetween thetruesolution and thediscretesolution.
If youwantto bereallyfancy, usethesubplotcommand toshowboth plotsin asinglefigure.
d) Computeanestimateof theintegral squareerror foreach caseand createa tableofthesedifferences.
e) Whatconclusionscanyoudrawregarding theaccuracyofthedifferentmethodsand step sizes?
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