Engineering Quarterly Winter 2022

EngineeringQuarterly

WELCOME!

Welcometothewinter issueofEngineering Quarterly,anewsletter publishedfourtimes ayearbytheUniversityofMarySchoolof Engineering.Initwe

trytoincludearticlesfromeachofthefive engineeringmajorsthatwecurrentlyoffer: ElectricalEngineering,MechanicalEngineering,CivilEngineering,ComputerScience, andConstructionManagement.

TheintendedaudienceoftheEngineeringQuarterlyareengineers,engineeringstudents,engineeringalumni,futureengineering students,andpeopleworkinginfieldsclosely relatedtoengineeringsuchasscience,computing,andmathematics.

Inthisissueweincludearticlesondesignprojectsourstudentsareworkingon, tripstheyhavegoneon,ourannualengineeringalumnievent,thenewconstructionwe haveunderwayforourCivilEngineeringconcretewetlab,companiesandorganizations whohavevisitedourcampus,andinteresting assignmentsandprojectsfromourcourses. Enjoy!

Dr.TerryPilling DeanofEngineering

KarsenfirstnoticedthiswiththeTrollMaster.Therewasapiecethatthecompanywas unabletogetinordertoinstallthedeviceon theirboats.KarsentookonehomeandstudieditandthencreatedaCADdesignandused his3Dprintertoprintone.

theinsighttorealizethat,asamechanicalengineeringstudent,hehastheskillstosolve theseproblemsinacost-effectiveway.

Evenwhentheoriginalsupplychainissueshavebeenresolvedheisconfidentthat hewillhaveaproductlineandasuccess ratethatwillallow himtocontinueto supplytheseproductsaswellasnew onesthroughoutthe manufacturingmarketplace.Itislikely thatcompanieswill continuetobesuppliedbyhiscompanyevenaftertheoriginal overseassupplierscomebackonline.

SUPPLY CHAIN SOLUTIONS

Karsenthenconductedstrengthanddurabilitystudiesonthepieceandtriedseveral different3Dprintingmaterials,contacting differentcompaniestoaskaboutmaterial strength,theeffectofthesunonmaterialsovertime,etc.,untilhefinallydecided thatthatcarbon-fiber polycarbonatewas thebestmaterialto usewithareasonablecostrange.He printedthepartnumeroustimesfrom thatmaterialandconductedstrengthtests basedontheneedsof thefinalinstalledproduct.Henoticedthatit wouldshearfromthesideandsoheinvented amethodofreinforcingthecenterofthepiece withpowdercoatedsteeltopreventshear.It workedperfectly.

“I’mstillworkingongettinganLLCset upandtositdownwithapatentattorney,butI havethepackagingclosetodone.Bytheend oftheweektheproducttestingwillbedone sothat’sexciting.AsoftodayMoritzSport andMarinehasinstalledatotalof5without anyadvertisingoranofficialsendoffofthe product!”

ALUMNI EVENT

OnNovember5,2021weheldourannual alumnieventoncampus.Thisyear,inadditiontotheusualbeer,nachos,andsocializing, wegaveourformerstudentsatourofthenew CivilEngineeringandConstructionManagementadditionthatisbeingconstructed.

MechanicalEngineeringstudentKarsen MeyerworksparttimeatMoritzSportand Marinewhileworkingonhisdegreeandhe noticedthatoverthepastsixmonthstherehas beenasupplychainbreakdowninthemarine industryamongmanyothersduetotheCovid19outbreak.Oftentimescompaniescannot completeaproductbecauseofonesimplepart thatismissingandtheproductcannotbeinstalledwithoutit.

Thesupplychainissueisnot,byany means,isolatedtothemarineindustry.Supplychainbreakdownshaveaffectedcompaniesandproductsfromdiversebranchesof industryintheUnitedStateswherecrucial componentstotheirproductsorotheressentialrawmaterialsthatcomefromothercountrieshavebecomeunavailableduetorestrictionsinshippingandotherlogisticalissuerelatedtothepandemic.

SincethenKarsenhasmadecontactwith othercompaniesandisworkingonsupply agreementswiththemaswell.Hehasalsoexpandedtosolvesimilarsupplychainissuesinotherareasof themarketplace.It isclearthatthesupplychainproblemis avastoneandisnot goingtoendforsome time.Karsenhashad

Thespacewillhousetheconcretewetlaboratory,anoverheadcraneandloadingdock,as wellasspacesforCivilengineeringcourses andconstructionprojects.

ThefacultyoftheUMaryEngineering Schoolarealwaysthrilledtohaveourgraduatesreturntocampusandtellusaboutallof

thecoolthingstheyhavebeenuptoandlet usshowthemournewdevelopmentsandthe designprojectsofourcurrentstudents.

MECHANICAL ENGINEERING DESIGN

Weplantocontinuehavinganalumnievent everyyearandhopetocontinueseeingthe amazingprogressourgraduatearemakingin theircareersasengineers.

CIVIL ENGINEERING DESIGN

ProfessionalEngineerMichaelDorafromUlteigEngineersisteachingourCivilEngineeringdesigncoursethisyearintheFall semester.MikehasanmastersdegreeinEnvironmentalEngineeringfromNewMexico StateUniversityaswellasabachelorsdegreeinCivilEngineeringandabachelorsdegreeinBiology.Heislicensedineightstates andweareveryhappytohavehimsharing hisvastexperiencewithourdesignstudents. Hehasdividedthestudentsintotwogroups, thefirstgroupconsistingofLoganMahoney, MitchellOehme,andDavidsAtelbauersare designinganewwatertowerandcitywater mainforthecityofNapoleon,ND.,andthe secondgroup,consistingofBlakeRubio,IsaiahBitz,andWilliamBlewettaredesigning fouroptionsfornewparkingoncampusrangingfromresurfacingallthewaytoinstalling aparkinggarage.

ThemechanicalengineeringstudentspresentedtheirseniordesignprojectsonDecember15,2021.Thefirstgroupconsistingof JamesJurek,KarsenMeyer,MarkSammons, presentedaprojectcommissionedbyBobcat/Doosaninwhichthestudentsweretodesigna innovativenewaugerattachmentfortheBobcatskid-steer.Duetoanon-disclosureagreementIcannotgivefurtherdetails.Theproject supervisor,DennisAgnew,fromBobcatwas veryimpressedwiththestudentsdesignand saidthatthecompanyplanstousetheirdesigninfutureproduction.

Thelastgroup,consistingofDaniel Turner,EthanMelder,andLucasMayer,designedathermodynamicsteststationforuse ineducatingstudentsaboutrefrigerationand HVACsystems.

Theysetitupwithanentirerefrigeration cycleaswellasaseriesofpressureandtemperaturesensorsanddigitalreadoutssothat thestudentscandirectlycomparetheirthermodynamicscalculationswiththeactualvaluesinaworkingmachine.Weplantoincorporatetheirteststationintoourthermodynamicscoursesinfuturesemesters.

ELECTRICAL ENGINEERING DESIGN

ElectricalengineeringseniorsRami Douri,MichaelStorrick,andChandlerOlsonconstructedaroboticchessboardthis semesterusingtheStockfishchessengineat itscorewiththeplayersettingthedifficulty ratingofthecomputerbysettingthenumberofmovesthecomputerisallowedtolook ahead.

ProfessorDorahasalsoarrangedfortheengineersfromMooreEngineeringA.J.Tuck, PE,andJerodKlabunde,PE,toadvisethestudentsontheNapoleonwaterlineupgradeand retiredengineer,RobertYouness,PE,whoactuallydesignedthedowntownBismarckparkinggarage,toadvisethesecondgroup.

ItwillbenicetoseetheirfinalprojectpresentationsinApril!

Thesecondgroup,consistingofPeter Smith,DanielMinor,andMatthewBitnerdesignedaprostheticarmforamputeeswhich canbecontrolledinaninterestingwayusing musclemovement.Theprojectrequiresnot onlymany3-dprintedlinkagesforthebones inthehand,butalsomanyservosandelectronicsdevicestocontrolit.Thegroupplans tocontinuewiththisdesignprojectthisspring andhopestohaveaworkingprototypebythe endnextsemester.

Theybuiltaboardand3Dprintedthepieces sothattheycouldhavemagneticattachments underneath.TheyinstalledHalleffectsensorsinorderfortheboardtodecidewhere allthepiecesareasmovesaremade.The computershowsanimageofthegameona computerscreenaswellasitisplayed.The studentswrotethecontrolcodeinPythonand designedaPrintedCircuitBoard(PCB)with surfacemountedelectronicsafterthedesign phasehadbeencompleted.Theyarecurrently waitingforthecompletedPCBtocomeback

fromthecompanythatismanufacturingit. Nextsemestertheyplantodesignandinstalla roboticarmforthecomputerplayersothat,as youmakemovesandthecomputerdecideson theirmove,aroboticarmwillreachoutover theboardandmovethepiecesforthecomputerplayer.Itwillbefuntoseethefinished productnextsemester!

DICKINSON BUS TRIP

uctsandarecommittedtofosteringaculture ofinnovation. Employeedevelopmentisa toppriority,and ourcompany culturepromotesmentorship,training, andeducation throughbothinternaldevelopmentprograms andprofessionaldevelopmentreimbursement toensureweareinvestinginthefutureofthe companybyinvestinginourteam.”

sionandleadershipallowed FisherSand& GravelCo.to quicklyemerge asaleaderin portablecrushingoperations.

Generecognizedaneed fordurable, customizable equipment.In

1967,heestablishedtheaffiliatecompany, GeneralSteel&SupplyCompany,torepair, remodel,design,andfabricatequalityaggregateprocessingequipment.Thispartnership fueledthefurthersuccessofFisherSand& GravelCo.,ultimatelyleadingtotheestablishmentofseveralmoreofficelocationsin theupperMidwest.

NDSPEMEETING

OnFriday,November12th,anumberofour MechanicalandElectricalEngineeringstudentsleftcampusat8:00amandtraveled toDickinson,ND.tovisitsomeengineeringcompaniesandtourtheirmanufacturing plants.

ThefirststopwasKilldeerMountainManufacturing.KilldeerMountainManufacturing, isacompanycommittedtoexcellinginrealms oftheiroperationsaswellascommitmentto community,country,andfamily.Acornerstoneprincipleforthecompanyisresponsivenesstocustomers.Thisresponsivenesshas openedmanydoorsforKMMonworld-class platformsinsupportofourmilitaryandcommercialaerospace.Ourstudentsweregiven atouroftheirmanufacturingplantwhichincludedtheirroboticstoolsandtheirmilitary contractprojects.Itwasafunandexciting timeforeveryone.

ThefinalstoponthetripwasFisherIndustries wherethestudentswereshownitsDickinson manufacturingplantandgivenanoverview ofthemanyexcitingprojectstheyhavedone aroundthecountryincludingsectionsofthe southernborderwallaswellasanamazing bridgeinLasVegas.

TheNorthDakotaSocietyofProfessionalEngineersheldtheirFallmeetinghereatthe EngineeringSchoolthisyear.Theybrought pizzaandsodasforthestudentsandthen stayedaftertheirmeetingforatourofthe engineeringbuilding.TheNDSPEsponsors ascholarshipeveryyearforourengineering studentsandwearealwayshappytohost themoncampus.HopefullyplentyofourfuturestudentswilljointheNDSPEwhenthey gettheirownPElicenses.

ThenextstoponourtripwasSteffeswhere thestudentsweregivenlunchandanintroductiontothecompanybyitsexecutivesincludingthefounderPaulSteffes.Steffesisa steelfabricationandelectricalservicesmanufacturerservingdiverseindustriesincluding oilandgas,electricthermalstorage,andcontractmanufacturing.

“Weuseleanoperatingprinciplestoreducewasteandincreasecustomervalue.EngineeringteamsatSteffeshaveextensiveexperienceintheindustriestheyserveandaccesstothelatesttechnologyincludingrobots, parametric3Dmodeling,mechanicalsystems,electricalsystems,toolanddie,hydraulicsandpneumatics.”

“Wetakeprideinthequalityofourprod-

FisherIndustriesisafamilyofbusinesses thatencompassallaspectsoftheaggregate productionandheavycivilconstructionindustries.Theirunique,vertically-integrated businessmodelallowsthemtohandlesmall projects,largescaleoperations,andevery toughjobinbetween.Theirgoalistoprovide reliableproductsandsustainablesolutionsfor innovativeglobalinfrastructure.

Theirparentcompany,FisherSand& GravelCo.,wasfoundedinruralNorth Dakotain1952byGeneFisher.Gene’svi-

OnthemorningofOctober18,2021,IreceivedacallinmyofficefromTroyBackstrom,aBismarckresident, whosaidthat heobserveda meteoriteimpactthepreviousnightonthe lawnnexttohis apartment.“It hadathreefoot flameasitshot downfromthe skyandhitthe lawn,”saidBackstrom.Iaskedwhetherit leftacraterandheconfirmedthattherewas asmallcircularshapedcraterintheyardbut therewasnometeoriteinit.ItoldTroythat

BISMARCK METEORITE IMPACT ByTERRYPILLING

Iwouldgetsomeoftheotherfacultyandwe wouldcomeoverandtakealook.

Afterwork,Rodrigo,HeatherWernke (Physicsprofessor),andIwentoverto thesite.We foundthecrater andthentook somesamples ofsometiny charredrocks thatwefound insideitusing somebiologicaltesttubes giventousby Prof.David Ronderosofthe Biologydepartment.Weknewthatevenif theoriginalmeteoritedisintegratedonimpact therewouldstillbetinyrockfragmentsthat couldbeanalyzed.WethankedMr.Backstromforcallingusand,aftertakingsome picturesandmeasurementsoftheimpact crater,weleft.

ThenextdayRodrigoandIgrabbedsomeradiationmeasuringequipmentaswellassome magnets.Meteoritesoften containIron, whichcanbe detectedmagnetically,and sometimesradioactivematerialsuchas Iridium.We foundthata numberofthe fragmentswere attractedtothemagnetimplyingthatthey probablycontainedIron.

relatedtotheso-called‘GoldenRatio’andthe ‘GoldenSpiral’andmanybiologicalsystems seemtopatternthemselvesinthisway.The waytogenerateFibonaccinumbers, Fn,isto startwith F0 =1 and F1 =1 andthengeneratethenextonebysummingthetwoprecedingones.So,forexample, F3 = F2 + F1 =2 Thegeneralformulaforany n isthus

Fn = Fn 1 + Fn 2

Aninterestingquestioniswhatsolutiondo yougetwhenyousumapowerserieswhose coefficientsareFibonaccinumbers?Inother words,whatisthesumofthisseries

Fn n! Hereisacleverwaytodoit.Firstsolvethe differentialequation y = y + y usingtwo methods.Firstusethemethodofpowerseriesyoulearnedinyourelementarydifferentialequationscourseandthenuseelementary methodsfromthatsamecourse,i.e.substitute ofexponentialandsettingtheboundaryconditions y(0)=0,and y (0)=1.Sincesolutionsareunique,theresultsfromeachmethod allowustowritedownthefollowingidentity: Fn n! xn = 2 √5 e x 2 sinh √5 2 x

Ofcourse,ifyoudon’tfeellikesolvingthe differentialequationyourselfyoucaneasily verifybysubstitutingeachsideoftheabove intothedifferentialequationandboundary conditionsandthenremindyourselfviathe existenceanduniquenesstheoremthatthetwo solutionsmustbethesame.Meaningtheyare alsothesameatthepoint x =1.Settingx=1 gives

∞ n=1 Fn n! =2 √e 5 sinh √5 2 = eφ+ eφ √5 where φ± = 1±√5 2 aretheGoldenRatioand it’sconjugate.

Fibonacci.c

#include <stdio.h> #include <stdlib.h> #include <gmp.h> int usage( char * name); int main( int argc, char ** argv){ if (argc!=2) return usage(argv[0]); int N=atoi(argv[1]); //Initializegmpvariablessettingthemequalto0 mpq_tFib,I,F,F1,F2,y,ifactorial; mpq_init(Fib); mpq_init(I); mpq_init(F); mpq_init(ifactorial); mpq_init(F1); mpq_init(F2); mpq_init(y); //set0!tobe1 mpq_set_ui(ifactorial,1,1); mpq_set_ui(F2,1,1); //variablefortheanswer????? mpf_t(answer); mpf_init2(answer,5000); //Okaynowdosomeloopystuff for ( int i=1;i<=N;i++){ mpq_set_ui(I,i,1); mpq_mul(ifactorial,ifactorial,I); mpq_div(Fib,F2,ifactorial); mpq_canonicalize(Fib); mpq_add(y,y,Fib); mpq_set(F,F1); mpq_set(F1,F2); mpq_add(F2,F1,F); } mpf_set_q(answer,y); gmp_printf("%.1234Ff",answer); //Cleargmpvariables mpq_clear(I); mpq_clear(Fib); mpq_clear(F); mpq_clear(F1); mpq_clear(F2); mpq_clear(y); mpq_clear(ifactorial); mpf_clear(answer); return 0; } int usage( char * name){ printf("Usage:%s<positivenumber>\n",name); return 1; }

PROBLEMSTOTRY

Herearesomeproblemsfromourcoursesthis semesterthatyoumightliketotry.Thesolutionscanbefoundattheendofthisissue.

HUMAN DNA ByTERRYPILLING

FIBONACCI CODE

Twoofoursophomorestudents,Megan AchbachandMayaWald,presentedtheirsolutiontoaproblemassignedintheirENR304 course.

Theproblemwastowriteacomputerprogram tocalculatethefirst1234digitsofaseries calledtheFibonacciSeries.Fibonaccinumbersoccurmanyplacesinnature.Theyare

2 0143227334583157365813462 Thestudents wereaskedtowriteaCprogramtogenerate thefirst1234digitsintheFibonacciseries F .Notethatthisisnotaseasyasyoumight assumeduetothelimitsofthecomputerand thevariabletypesinprogramminglanguages. Tosolvethisproblem,MeganandMayaused theGnuMultiprecisionLibrary,whichallows onetoworkwithastronomicallylargenumbers.Hereistheirsolutioncode:

TheProjectGutenbergwebsitehasfiles fromthe HumanGenomeProject which containtheDNAbasepairsequences forhumanchromosomes.Downloadthe datafromthehumanXchromosome( https://www.gutenberg.org/ebooks/3523) andfindthecharacterstatistics.Compareyourresultwiththefollowing(note thatthefirstlinecomesfromthe‘endof line’(EOL)character).Nowdothesame withthehumanmaleYchromosome( https://www.gutenberg.org/ebooks/3524).

Statistics

total=281540876charactersread characteroccurspercent

A6149161121.84% C4406485815.65% G4400192015.63% N6503048523.10% T6143159221.82%

TheN’sarenotDNAbases,butareregions whereinformationismissing.Modifythe programtoexcludetheN’sandtheEOLcharactersandtakeanotherlookatthestatistics. Doeachofthe4basesappearwiththesame percentagefrequency?Isthereanypatternin thefrequencywithwhicheachofthemappear?Couldyouusethisstatisticalmethodto distinguishbetweentwopeople?ortwoanimalsfromdifferentspecies?

CSC457PROBLEM ByTERRYPILLING

In CSC457 Studentslearnhowtodesign theirowncomputerprogramminglanguage andwritethecompiler.Thetoolsthatareused tocreatethecompileraretheLex/Flexlexical analyzerandtheYacc/Bisongrammarparser. InordertolearnFlexwebeginbyusingit asacontrollerwhichwillreadinaseriesof instructionsandconvertthemintoaseriesof tokensthatwillperformandaction–inthis caseturningLEDsonoroff.Theproblemis towriteaFlexscriptthatrecognizesthewords “ON”,“OFF”,“SWITCH”,and“END”.The firsttwowillreturnmessagesstatingthatan LEDisbeginturnedonoroff,theSWITCH instructionwillswitchbetweenthetwoLEDs, andtheENDinstructionwillendthecontrolprogram.Afterthestudenthavewritten andcompiledtheircodetheyshouldtestitby feedinginastringofinstructionsandensuring thatthecorrectoutputisgenerated.Thiscode canthenbemodifiedsothattheactionsaccess theGPIOofaraspberrybyortheUSBport oftheircomputerandconnectedtophysical LEDstomaketheLEDsbehaveaccordingly.

ENR200PROBLEMS ByDAMIANOWEIS

Problem1: Findthe final valuesof Rose, Lily,Tulip,iris and jasmine in thefollowingMATLAB/Octavecode.

Rose=0; Lily=0; Tulip=0; foriris=2:3:25

forjasmine=30:-4:1 Rose=Rose+1; ifmod(iris,2)==0 Lily=Lily+2; endif endfor Tulip=Tulip+3; endfor

Problem2: Findthevaluesof out iftheuser inputseachofthefollowingvaluesof num

ifnum<-8|num>10

out=(num)^2

elseifnum>0&&num<=5 out=(num)^3

elseifnum<0&&num>=-5

out=abs(num)

else out=100 endif where num=-20,out= num=4,out= num=10,out= num=-2,out= num=-7,out= num=6,out= num=0,out=

HerewasthefinalprojectfromourComputerAidedAnalysiscoursefortheFallsemester thisyear.

Alakeisaverycomplicatedecosystem andisdifficulttoeffectivelymodelmathematically.Tohaveatrulyeffectivemodel onewouldneedtoincludeitsdimensions, depth,temperature,chemicalconcentrations, biologicalconcentrations,interactionsamong aplethoraoforganismsbothplantandanimal thatliveinornearthelake,humanactivity fromcitiesandagriculturethatarenearthe lake,climatechangesovertime,etc.However,onemighthopethatifweareonlyinterestedinparticularproblemswiththelakewe mightbeabletodevelopmuchsimplermodelstohelpusstudythoseproblemswhileignoringalloftheotherdetailsthat,wehope, don’thaveahugeeffectontheproblemwe arestudying.Thismaynotbepossiblesince manyproblemsinnaturederivefromavast numberofsmalleffectsratherthanasmall numberoflargeeffects.Alakemaybelike thistoo,inwhichcasethetaskofdeveloping amodelwouldtakeahugeamountofmathematicalmodelinganddatacollection.Inthis projectwewillassumethatmodelingafewof theeffectsonthelakewillbeenoughtostudy theproblemathand.Howourresultscomparewiththedatawillindicatewhetherour assumptionisvalidornot.

Eutrophication

Alakemaybe Oligotrophic whichisastate withlownutrientinput,lowlevelsofplant material,andrelativelyclearwater.Alake mayalsobe Eutrophic whichisastatecharacterizedbyhighnutrientlevels,highamounts ofplantproduction,andtoxic,murky,water. Theproblemthatwewouldliketostudyin thisprojectislakeeutrophication,howitpersists,andwhatmethodswemightusetoreverseitsothatwecanrestoreaeutrophied laketoaclearandcleanstate.

Ultimately,eutrophicationiscausedby excessiveinputsofnutrientsasabyproduct ofagriculture,forestry,orurbandevelopment. Theprimarynutrientthatcauseseutrophicationisphosphorusfromagriculturalandurban runoff.Thephosphorusaccumulatesinsedimentatthebottomofthelakeandthenrecyclesbackfromthesedimenttowateragain. Thisrecyclingofthephosphorusmaybea largercontributiontothephosphoruslevelsin thewaterthantheflowintothelakefromthe outside.

Sincephosphorusseemstobethelargest contributortoeutrophicationinalakeourfirst attemptatmodelingtheproblemistomodel thephosphoruslevels.

MathematicalModel

Themodelwewilluseasourjump-offpoint istheonethatwasdevelopedin1999byCarpenter,Ludwig,andBrock 1.Theyuse p(t) astheamountofphosphorusinthewater, L astherateofinputofphosphorusfrom theoutsidewatershed,therateoflossof phosphorusfromsedimentationisassumedto

beproportionaltotheamountofphosphorus presentwithproportionalityconstant s,and theymodeltherecyclingofphosphorusfrom thesedimentby

r pq mq + pq where r isthemaximumrecyclingrateof phosphorus, m istheconcentrationofphosphorusatwhichitsrecyclingishalfofits maximumrate,andthepower q where q ≥ 2 mayrangefrom20forashallow,warm,lake downto2foradeep,cold,lake.Puttingthese contributionstogethertheyarriveatthefollowingequationforthechangeinphosphorus overtime

dp

dt = L sp + r pq mq + pq

EquilibriumCondition

Inthecasewherethelakeiseutrophicandhas constanthighlevelsofphosphorus.Theequilibriumwilloccurwhentheamountofphosphorusflowingintothelakeisequaltothe amountofphosphorusflowingout(bysedimentation).Fromtheequationforthemodel weseethat dp/dt =0 (equilibrium)willoccurwhen

sp = L + r pq mq + pq whichsaystheoutflowisequaltotheinflow.Ifwedefinethisequilibriumvalueof outflow/inflowas Q andploteachsideon agraphof Q versus p weseethattheoutflowsideoftheequationis Q = sp which isastraightlinethroughtheoriginwithslope equalto s.Theinflowsideoftheequationis Q = L + rpq /(mq + pq ) whichisacurve.

Equilibriumvaluesoccurwhenthelineintersectsthecurvesothattheybothhavethe samevalue(i.e.whenoutflowisequaltoinflow).

Theresultistheabovegraphwhichplotsthe outflowandinflowfunctionsforarbitrarily chosenvaluesoftheconstantstoseewhere theyintersect.Thegraphshowsthatthetwo functionsdocrosseachotheratthreedifferentphosphorusconcentrations.Ifwewereto changethevaluesofthevariousparameters ofthemodelitwouldchangethephosphorus levelswhereequilibriaoccur.

Thegraphshowsthreeequilibriumlevels, alowphosphorusonecorrespondingtoaoligotrophiclake,amediumphosphorusone,and ahighphosphorusonecorrespondingtoaeutrophiclake.Themediumlevelequilibrium isanunstableoneandthehighandlowlevel

1Managementofeutrophicationforlakessubjecttopotentiallyreversiblechange,S.R.Carpenter,D.Ludwig,andW.A.Brock, EcologicalApplications, 9,751-771 (1999).

onesarestableequilibria.Thechallengeof waterqualitymanagementistocontrolalake thatisataeutrophicequilibriumandmove ittoanoligotrophicequilibrium.Recallthat youcandecidewhetherequilibriaarestable orunstablebyexaminingthesecondderivativeorbyplottingthedirectionfield.

Ifweweretoincreasethevalueof L, meaningweincreasetherateofphosphorus inflowfromthewatershedawegetthefollowinggraphinstead

forLakeMendotaarecorrectbut thevaluesof m and r are m = 100, 000kgand r =800, 000 kg/year.Whatisthestateofthe lakeandcanitbesaved?

4. SupposethevaluesforLake Mendotaarecorrectandthen adevelopermakesaone-time dumpof40,000kgofphosphorus intothelake.Whatistheeffect onthelake?

5. SupposethevaluesforLake Mendotaarecorrectandthen anewdevelopmentraisesthe phosphorusinputlevelto8000 kgperyear.Whatistheeffect onthelake?

ProjectGuidelines

whichshowsthatthelowlevelandmedium levelequilibriahavedisappearedandallthere isleftisthehighleveleutrophicone.Inthis casetheinflowofphosphorusfromthewatershedissohighthatthereisnothingthatcan bedoneexcepttrytoreducethatinflow.

Inthecasewheretherearebotholigotrophicandeutrophicequilibriathegoal wouldbetoreducethephosphorusconcentrationtobelowtheunstableequilibrium.Then itwouldcontinuetoflownaturallyovertime totheoligotrophicstate.

LakeMendota

Oneofthemoststudiedlakesintheworldis LakeMendotawhichisnexttothecampusof theUniversityofWisconsininMadison.Detailedmeasurementshavebeentakenoverthe courseof20yearsofthephosphoruslevels andphosphorusinputtothelake.Thefollowingaretheestimatesoftheparametersofthe modelbasedonthedata:

s =0 817 /year

r =731000 kg/year

m =116000 kg

q =7 88

Unfortunatelythereisahugeamountof uncertaintyintheseestimatesandwhetherthe lakecanbesavedornotdependontheseparameters.

Exercises

1. Giventheparametersinequation forlakeMendotaabove,whatis thestateofthelake?

2. Supposethevaluesof s,r and m forLakeMendotaarecorrectbut ahugeerrorhasbeenmadein theestimateof q sothatactually q =2.Whatisthestateofthe lakeandcanitbebroughttooligotrophicequilibrium?

3. Supposethevaluesof s and q

YourgoalistostudythefourYaharalakesin Wisconsinusingthesimulationmethodswe exploredinclassaswellastheoutlinegiven above.Thefollowingpointsaresomeofthe onesthatyoushouldaddressinyourstudy.

• Exploretheissuebysearchingthe literatureandtheinternet.ForexampleseethearticlebyDanCorcoranwhichcanbefoundonwhywiidea.journalism.wisc.edu

• Collectalloftherelevantdataon theYaharalakes:Mendota,Menona, KegonsaandWaubesa.Thesecanbe foundonWikipediaandothersites.

• WriteacomputersimulationinCwhich takesthelakeparametersasinput(this canbefromthecommandlineorread fromafile.)andoutputsthephosphoruslevelsinthelakeovertime.

• Cantheselakesbesaved?Inother wordscantheinputlevel L ortheoutputlevelsinthelakebealteredinsome waysothatthelakewillswitchtoan oligotrophicequilibriumstate?

• Runthecodeforthemodelgivenabove andcomparewiththedata.

• Canyoucanfindamodifiedmodelthat doesabetterjoboffittingthedatathan themodelofCarpenter,et.al.

• Comeupwithsomepossiblesolutions totheEutrophicationproblemandthink ofawaytoincludeyoursolutionsin themodel.Forexampleyoucouldhave nutrientsextractedatacertainrateby filteringmachines,youcouldintroduce otherspeciesintothelakethatfeedon thealgae,ormanyotherpossibilities. Theimportantpartistofigureouthow toincludethoseeffectsinyoursimulationmodel.

• Explainyourreasoningandthemathematicsbehindyourchangestothe model.

• Simulatethelakeeutrophicationover timewithyoursolutionsincludedinthe modelandseehowitworks.

• WriteupyourprojectreportinLATEX usingtheprojecttemplateprovidedincludingthediscussion,thesourcecode,

graphs,pictures,explanations,results, andsuggestionsforpossiblesolutions.

• CreateaLATEXposterusingtheposter templateprovidedandhaveitprintedon ourlargeformatprinterintheEngineeringofficetobeusedinapostersession presentingyoursolution.

ENR351PROJECTS ByERICGARCIA

Juniorlevelcivilengineeringstudents completedseveralprojectsinECI351 StructuralMechanics,atrussbridgeandawind tunnelprojectwhichwasacollaborationwith theirENR306 FluidMechanics class.

Thetrussbridgeprojectisanannualproject wherestudentsaretaskedtoconstructatruss bridgethatwouldspana10footgaponlyusing1 × 2’sand1/2inplywood.Theyhad todesignthebridgetonotdeflectmorethan L/400(0.3in.)andL/800(0.15in.)when loadedwiththreeteammembersandjustthe professor,respectively.

Studentsperformedanalysisofmaterial strengths,influencelines,deflectionsusing energymethods,andmodelingusingRISAto dothedesignwork.

ThewindtunnelprojectwasincollaborationwiththeirENR306 FluidMechanics class.Studentsdesigned,builtandconducted experimentstocomparethetheoreticalforces theycalculateusingthemethodstheylearned intheclasstotheexperimentalvalues.

Studentsdesignedstructureswiththreevaryingdegreesofroofslope,aswellasthetest chamberandthesensormechanismssetupto detecttheforces.

SOLUTIONSTO PROBLEMS

ENR304:HumanDNA Thesolutiontothis wasgivenintheproblemstatement.Itisinterestingthatthestudentswhosolvedthisfound someveryinterestingthings.Forexample, BrianBiverdiscoveredthatthetheCGbase pairoccurswithafrequencythatis2/3thatof theATbasepairandthatthispatternseemsto occurwithotherchromosomesaswell.Also thefrequenciesofthesebasepairsseemtobe thesameregardlessofthechromosomewe arelookingat.Itseemsthatifyouusethe lengthsofthechromosomes(howmanybase pairsthereare)alongwiththepercentages,it

couldworktodistinguishbetweendifferent species.Ofcourse,findingoutallofthebase pairslikethisintheirproperorderwouldalreadyallowacompletegeneticprofileanda statisticalanalysislikewedoherewouldnot beneeded.Itisinterestingthoughatamore fundamentallevel.

CSC457:FlexCode Hereistheflexcode:

led.l

%{ intled=0; inton=0;

%}

led0isnow1 led0isnow0

switchingtoled1 led1isnow1 detectedENDstatement,exiting... andcanbehookeduptophysicalLEDsfor directcontrolviacommandsorascript.

ENR200:Problem1

Rose=64

Lily=64

Tulip=24

iris=23

jasmine=2

%%

"ON"{on=1; printf ("led%disnow%d\n",led, on);}

"OFF"{on=0; printf ("led%disnow%d\n",led, on);}

"SWITCH"{led=(led+1)%2; printf ("switchingto led%d\n",led);}

"END"{ printf ("detectedENDstatement,exiting ...\n"); exit (1);}

.{/ * skip * /}

%%

ENR200:Problem2

num=-20,out=400

num=4,out=64

num=10,out=100

num=-2,out=2

num=-7,out=100

intmain(intargc,char ** argv){

yylex(); printf ("led=%d,\ton=%d\n",led,on); } Itiscompiledtoanexecutableasfollows flexled.l

gcc-oledlex.yy.c-lfl andtestedwith

echo"ONOFFSWITCHONEND"|./led whichreturnsthefollowingcontroloutput

num=6,out=100

num=0,out=100

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Nextissue:March2022