instructions-random-walkdoc：随机walkdoc指令

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1、Theexercisebelowisnolongeranassessedpartofthecourse.Ithasbeenleftinthisfileshouldanystudentwanttotryamorechallengingexampleofasimulation.RandomwalkThesecondprocessyoucouldsimulateiswhat’scalledarandomwalk.Supposeaverysmallparticle,onlyslightlylargerinsizethanamoleculeof

2、air,isallowedtofallfreelyundergravity.Itstrajectoryisrecordedusingadigitalcamera.Thehorizontal(x)positionoftheparticleislocatedforeachof8000framesandstoredasasetofpictureelementvalues(pixels)relativetothex-positioninthefirstframe.Atheoreticalanalysisofthisproblemsuggest

3、sthattheaveragex-positionoftheparticleoverlongperiodsoftimeiszero.However,theprobabilityoffindingtheparticleataparticularx-positionshouldfollowanormal(Gaussian)distributioncentredonx=0,withavariancewhichincreaseslinearlywithtime(theframenumber).Thusthestandarddeviations

4、houldincreaseasthesquarerootofthetime.Thisexampleisaone-dimensionalversionofarandomwalkprocess,sometimescalledthe“Drunkard’sWalk”.Simulatethisprocessinathirdsheetoftheworkbook.·FillcolumnAwith8000rowsofrandomnumbersintheinterval-1to1.UsetheTools/DataAnalysis/RandomNumbe

5、rGenerationdialoguebox.·IncellB1enterthevalue0(theinitialpositionoftheparticle).·IncellB2entertheformula=B1+A1.CopythisformulaintocellsB3:B8000.ThuscolumnBcontainsthepositionsoftheparticleatsuccessiveintervalsoftime.·Plotthex-positionoftheparticle(columnB)againsttherown

6、umber(time).Thiswillshowtherandomwalk.Youhavegeneratedjustonesampleofarandomwalk.Thepositionofyoursattheendofthewalkmaywellnotbezero.Lookatthegraphsofyourneighbours.Iftheyhaveusedadifferentseedintherandomnumbergenerationtheywillhaveadifferentsetofplots.Perhapsthesamplef

7、ormedfromthedataofseveralofyourneighbours’resultswouldaveragetozerodisplacement.Youneed,therefore,togenerateseveralindependentrandomwalksofdifferenttimedurationstoseethestatisticalpredictionthatthevarianceofthedistributionincreaseslinearlywithtime.Useanotherworksheetint

8、heworkbook.·IncolumnsAtoGgenerate10000randomnumberspercolumn.(Usetools/DataAnalysis/RandomNumberGeneration,wit