雨课堂学堂在线学堂云《计算物理（东南）》单元测试考核答案

第1题Whichoneisthecurrentfastestsuper-computerintheworld?

AFugakuBTianheIICTaihuLightDSierra第2题

WhichtypeofCPUisusedinthecurrentfastestsuper-computerintheworld?

AIntelXeonBIBMPowerCAMDOpetronDFujitsuA64FX第3题Thevalueofπcanbeestimatedfromthecalculationsofthesidelengthsofregularpolygonsinscribingacircle.Ingeneral,πk=π∞+c1/k+c2/k2+c3/k3+···,whereπkistheratiooftheperimetertothediameterofaregulark-sidedpolygon.Determinetheapproximatevalueofπ~=π∞fromπ8=3.061467,π16=3.121445,π32=3.136548,andπ64=3.140331oftheinscribingpolygons.Whichciismostsignificant?Aπ8Bπ16Cπ32Dπ64第4题Thevalueofπcanbeestimatedfromthecalculationsofthesidelengthsofregularpolygonsinscribingacircle.Ingeneral,πk=π∞+c1/k+c2/k2+c3/k3+···,whereπkistheratiooftheperimetertothediameterofaregulark-sidedpolygon.

weusethevaluesfromthepolygonscircumscribingthecircle,forexample,π8=3.313708,π16=3.182598,π32=3.151725,andπ64=3.144118,Whichciismostsignificant?Ac1Bc2Cc3Dc4第5题Today,Fortranisstillbyfarthedominantprogramminglanguageinscientificcomputingfortwoveryimportantreasons:ManyapplicationpackagesareavailableinFortran,andthestructureofFortranisextremelypowerfulindealingwithequations.第6题Ahigh-levellanguageistypicallyinbinaryformandisdesignedtoworkwiththeuniquehardwareofacomputer.第7题Theveryfirstcomputerprogramwaswrittenby?AAdaByronBStanisławMarcin

UlamCJohnvonNeumannDAlanMathisonTuring第8题TheveryfirstcomputerprogramwasintendedfortheanalyticalengineproposedbyBabbageinthemid-1840s,whichisfarbeforetheinventionofelectronicgeneralpurposecomputer.第9题Translation：自由软件

____正确答案：:Freesoftware第10题Translation：私有软件____正确答案：:proprietarysoftware第11题Translation:polynomial____正确答案：:多项式第12题Translation:numerator____正确答案：:分子第13题Translation:denominator____正确答案：:分母第1题Tochangealineinthecode,makeitworkforlinearinterpolationofdampedoscillationf(x)=-k*x-b*vAline2Bline9Cline17Dline21第2题Discretedatasetgivenfromadiscretefunctionfi=f(xi)withi=0,1,...,n.Thesimplestwaytoobtaintheapproximationoff(x)forx∈[xi,xi+1]istoconstructastraightlinebetweenxiandxi+1.第3题Acontinuouscurveisconstructedfromthegivendiscretesetofdataandthentheinterpolatedvalueisreadofffromthecurve.Themorepointsthereare,thehighertheorderofthecurvecanbe.第4题Itisknownthatf(-1)=-3,f(0)=-1/2,f(1/2)=0,f(1)=1,thenthecoefficientofxintheLagrangemethodinterpolationpolynomialis

A15/4B4C3

D17/4第5题ThelocaltruncationerrororderofEuler'smethodisAO(h)BO(h^2)CO(h^3)DO(h^4)第6题Iff(1)=2,f(2)=3,andf(4)=5.9,thenintheLagrangedifferencepolynomial,thecoefficientofx^2isA0.25B0.15C0.55D1.3第二章第二节作业第1题ThemainadvantageofNewtoninterpolationmethodcomparedtoLagrangeinterpolationisthatlesscalculationstepsormodifictionareneededwhennewdatapointsaddedtothedataset.第2题OnewaytoachievetheLagrangeinterpolationefficientlyisbyperformingasequenceoflinearinterpolations.Thisschemewasfirstdevelopedby

____正确答案：:Aitken第3题Abetterwayistoconstructanindirectschemethatimprovestheinterpolatedvalueateveryotherstepbyupdatingthedifferencesoftheinterpolatedvaluesfromtheadjacentcolumns第4题Whentheinterpolatedpolynomialisincreasedfromn-1tontimes,Lagrangeinterpolationmustrecalculateallthebasicinterpolationpolynomials;forNewtoninterpolation,onlyonemoren-ordermeandifferenceneedstobecalculatedandthenadded.第二章第三节作业第1题A1.855B1.805C1.705D1.905第2题Least-squareapproximationismainlyusedtofindthelocalapproximationofagivendiscretesetofdata第3题Whenwedealwithcontinuousfunctionswithoutdiscretization,wecangeneratetheorthogonalpolynomialswithacontinuousvariableandapplyanintegrationquadraturefortheevaluationoftheintegralsinvolved.第4题Notethatthismethodisonlyfordiscretefunctions,withboththepolynomialsandleast-squaresfittingcoefficientsreturnedina

____.正确答案：:combinedmatrix第5题Fromtheaveragechargesoftheoildrops,Millikanconcludedthatthefundamentalchargeise=____正确答案：:1.65×10^−19C第三章第一节作业第1题Toperformthenumericaldifferentiation,theaccuracyofthree-pointmethodforthefirst-orderderivativereaches:AO(h)BO(h2)

CO(h3)DO(h4)第2题Tocalculatethenumericaldifferentiation,whichmethodgivesthebestaccuracy?

Atwo-pointmethod

Bthree-pointmethodCfive-pointmethod

Dseven-pointmethod第3题thederivativesatpointsclosetotheboundariesareimportantandneedtobecalculatedaccurately.Theerrorsinthederivativesoftheboundarypointswillaccumulateinotherpointswhentheschemeisusedtointegrateanequation第4题Thealgorithmsforfirst-orderorsecond-orderderivativesareusuallyfullyvectorized,soavectorprocessorcancalculatemanypointsinjustonecomputerclockcycle.第5题Innumericaldifferentiation,theaccuracyinfive-pointformulaforthesecond-orderderivativecanreachtoAO(h^3)BO(h^4)CO(h^5)DO(h^6)第三章第二节作业第1题whatistheaccuracyofnumericalintegrationbythetrapezoidalruleAO(h^2)BO(h^3)CO(h^4)DO(h)第2题Wecanobtainaquadraturewithahigheraccuracybyworkingontwoslicestogether.IfweapplytheLagrangeinterpolationtothefunctionf(x),

whichisknownasthe?AUlamruleBSimpsonruleCNewtonruleDLandaurule第3题Weshouldconsiderhowcriticalandpracticaltheaccuracysoughtintheevaluationisagainstthespeedofcomputationandpossibleerrorsduetootherfactorsinvolvedbecausethe

accuracyandthespeedofthecalculationare

mutual

exclusive第4题Translation:Trapezoidalrule____

正确答案：:梯形法则第三章第三节作业第1题Whichmethodmentionedbelowhasthefastestwaytoderivearootofafunction?ABisectionmethodBNewtonmethodCSecantmethodDdiscreteNewtonmethod第2题Forbisectionmethod,Theerrorcomesfromthefinalimprovementinthesearch.Thiserrorcanbereducedtoalowervaluebymakingthetoleranceδdevelopedtowards?AlargerBsmallerCstaystill

Dnoneofaboveisright第3题InNewtonmethod,forthesamefunctionvalue,alargestepiscreatedforthesmall-slopecase,whereasasmallstepismadeforthe

Alarge-slopecase.Bsmall-slopecase.Czero-slopecase.Dvertical-slopecase.第4题Asexpected,thesecantmethodis____efficientthanthebisectionmethodbut____efficientthantheNewtonmethod,becauseofthetwo-pointapproximationofthefirst-orderderivative正确答案：:more正确答案：:less第5题Usethebisectionmethodtofindtherootoftheequationf(x)=x^3+x-1=0intheinterval[0,1],andtheregionwheretherootislocatedafterperformingthetwostepsisA[0,0.25]B[0.25,0.5]C

[0.5,0.75]D[0.75,1]第6题Translation:bisectionmethod____正确答案：:二分法第三章第四节作业第1题Searchfortheminimumofthefunctiong(x,y)=sin(x+y)+cos(x+2*y)inthewholespace,howmanyminimumdoesthefunctionhave?A1B2C3D4第2题severaladvancedmethodshavebeenintroducedfordealingwithfunctionoptimization,mostnoticeably,thesimulatedannealingscheme,theMonteCarlomethod,andthegeneticalgorithm.第3题Themotionofatwo-particlesystemwithanisotropicinteractionisequivalenttotheconstant-velocitymotionofthecenterofmassplustherelativemotionoftwoparticlesthatisdescribedbyaneffectiveparticleofmassminacentralpotentialV(r).第4题Whataretheconservativevalueofthescatteringprocess?AtotalmomentumBtotalangularmomentum

Ctotalenergy

Dtotalvelocity正确答案：ABC第5题Translation:steepest-descentmethod____正确答案：:最速下降法第四章第一节作业第1题TheNewton'sequationf=mawhereaandmaretheaccelerationandmassoftheparticle,respectively,andfistheforceexertedontheparticle,xandvvariesbytinaperiodicway.第2题Wehave100pointsinoneperiodofthemotionbyEulerandPicardmethods,whichisatypicalnumberofpointschoseninmostnumericalcalculations.Ifwegoontothesecondperiod,theerrorwillincreasefurther.Forproblemswithoutperiodicmotion,theresultsatalatertimewouldbebetter.第3题wecanincludemorepointsintheintegralofpredictor-correctormethodswithapparentlyhigheraccuracy,butwewillneedthevaluesofmorepointsinordertostartthealgorithm.Thisbecomesimpracticalifweneedmorethantwopointsinordertostartthealgorithm,becausetheerrorsaccumulatedfromtheapproximationsofthefirstfewpointswilleliminatethehighaccuracyofthealgorithm.第4题Forasimplemodelofamotorcyclejumpoveragap,Theairresistanceonamovingobjectisroughlygivenbyfr=-kv,Themaximumrangeisreachedaboutatataking-offangleofabout?A45◦B46◦C42.5◦D50◦第四章第二节作业第1题Whatistheprecisionofclassical(4thorder)Runge-KuttamethodwhenappliedtoaODE.AO(h)BO(h^2)CO(h^3)DO(h^4)第2题Theselectionofparametersforthefourth-orderRunge–Kuttaalgorithmisnotuniqueandcanbemodifiedaccordingtotheproblemunderstudy.第3题AmorepracticalmethodthatrequiresonlythefirstpointinordertostartortoimprovethealgorithmistheRunge–Kuttamethod第四章第三节作业第1题Whichoneofthegivenphysicalproblemisnotaboundary-conditionproblem?AThePoissonequationwithagivenchargedistributionBThewaveequationsinafinitemediaCThestationarySchrodingerequationDthedynamicsofarocketwithinitialspeedandcoordinate.第2题Theboundary-valueproblemismoredifficulttosolvethanthesimilarinitialvalueproblemwiththedifferentialequation,andeigenvalueproblemsareevenmorecomplicated,becauseatleastonemoreparameter,thatis,theeigenvalue,isinvolvedintheequation第3题Theshootingmethodworksforthe?Aboundaryvalueproblem

BeigenvalueproblemCinitialvalueproblemDrootofthefunction正确答案：AB第五章第一节作业第1题Ax=

λMxisasecularequation,can

λbeanegativenumber?第2题

Toinvestigatethevibrationalspectrumofamoleculewithnvibrationaldegreesoffreedomisbyexpandingthepotentialenergyuptothesecondorderofthegeneralizedcoordinatesaroundtheequilibriumstructure.第3题WecanapplytheKirchhoffrulestoobtainasetofequationsforthevoltagesandcurrents,andthenwecansolvetheequationsettofindtheunknownsoftheunbalancedWheatstonebridge,wecangetamatrixof?A2-orderB3-orderC4-orderD5-order第4题ThenwecancasttheSchr¨odingerequationasamatrixequationHΨ=EΨ,thequantumproblemherehasamathematicalstructuresimilartothatoftheclassicalproblemofmolecularvibrations第5题Thesummationoverkrequiresthenumberofcolumnsofthefirstmatrixtobethesameasthenumberofrowsofthesecondmatrix.Otherwise,theproductdoesnotexist第6题Themultiplationoftheallmatrixobeyscommutativeproperty第7题Translationofterminologies:

酉矩阵____正确答案：:Unitarymatrix第8题Translationofterminologies:

厄密矩阵____正确答案：:Hermitianmatrix第9题Translation：正交____正确答案：:orthogonal第10题Translation:完备____正确答案：:complete第11题Translation:

转置共轭____正确答案：:Transposedconjugate第12题Translation:相似变换____正确答案：:similaritytransformation第13题Translation:久期方程____正确答案：:secularequation第14题Translation：本征值____正确答案：:Eigenvalue第15题Translation:本征矢____正确答案：:eigenvector第16题Translation:Product____正确答案：:乘积第17题Translation:factorial

____正确答案：:阶乘第五章第二节作业第1题UseGaussianEliminationmethodtocalculatethedeterminantofthematrixgivenbelow1

2

3

45

6

7

810

10

11

12A-1B-2C-3D-4第2题Amatrixiscalledanupper-triangular(lower-triangular)matrixiftheelementsabove(below)thediagonalareallzero,thesimplestschemeforsolvingmatrixproblemsisGaussianelimination.第3题Gaussianelimiationdestroystheoriginalmatrix.Ifwewanttopreserveit,wecanjustduplicateitinthemethodandworkonthenewmatrixandreturnitaftercompletingtheprocedureasdoneintheLagrangeinterpolationprogramsforthedataarray.第4题Theprocedureusedinthepartial-pivotingGaussianeliminationdoesnotchangethevalueofthedeterminant,andthesignofthedeterminant,whichcanbefixedwiththeknowledgeoftheorderofpivotingelements.第5题ThelocalenergyforaFermisysteminthevariationalanddiffusionquantumMonteCarlosimulationsneedrepeatedevaluationofthedeterminantofalargematrix第五章第三节作业第1题SeveralcharactersofHermitianmatrixaregivenbelow,whichamongthefourarecorrect?AtheeigenvaluesareallrealBtheeigenvectorscanbeorthonormalCcanbetransformedintoadiagonalmatrixwiththesamesetofeigenvaluesunderasimilaritytransformationofaunitarymatrixDtheeigenvaluescanbeimaginary正确答案：CAB第2题Theeigenvalueproblemofann*ncomplexHermitianmatrixisequivalenttothatofa2n*2nrealsymmetricmatrix.第3题Newtonmethodisintroducedinobtainingthezerosofasingle-variablefunctionandcanalsoextendourstudytothesolutionofasetofmultivariableequations.第4题Arealsymmetriceigenvalueproblemwiththesamesetofeigenvaluesthathaveanoveralldoubledegeneracy.ThereforeweneedtosolveonlytherealsymmetriceigenvalueproblemifthematrixisHermitian.第5题Inthestudyofmatrixoperations,welearnedtherecursivecalculationofthematrixdeterminant,andthefollowinggivesfouroptionstoselectthemostsuitableoneasthevalueofthelasttermatrecursivetermination(a_ijisamatrixelement)A(-1)^(i+j)a_ijB|a_ij|Ca_ijD(-1)^(i+j-1)a_ij第五章第四节作业第1题int*p1[6];

inC++languagemeansapointerarraywithsix

int*elements.第2题Thedsyevd_()isafunctionusedtocalculatealltheeigenvectorandeigenvalueofa

symmetry

matrix

thesolutionoftheeigenvectorisstoredintheformofcolumnvector.第3题Fortheinverseiterationmethod,therecursionateachstepasalinearequationsetcanbesolvedwithGaussianelimination,forexample,fromoneiterationtoanother,thisiterativeschemealsosolvestheeigenvectorsofthematrixatthesametime.第4题TheHartree–Fockapproximationisusedforthecalculationoftheelectronicstructuresofmany-electronatomicsystems第5题Thesingle-particlewavefunctionsintheatomicsystemscanbeassumedtohavetheformY_lm(θ,φ),whichisa

Legendre

function第6题Oneofthemostpowerfulmethodsinlarge-scalematrixcomputingistheLanczosmethod,whichisaniterativeschemesuitableforlarge,especiallysparse(mostelementsarezero)matrices.第六章第一节作业第1题Ifacomputerneed0.1msformultiplyoperation,0.02msforaddoperation,forN=1024pointsDFT[x(n)],directcalculationneeds

____seconds,FFTneeds

____seconds.(keepthedecimalpointof0.1)正确答案：:125.8正确答案：:0.7第2题ItwasFourierwhofirstpointedoutthatanarbitraryperiodicfunctionf(t),withaperiodT,canbedecomposedintoasummationofsimpleharmonicterms第3题Translation:

Orthogonalfunctions____

正确答案：:正交函数第六章第二节作业第1题TheFouriercoefficientg(q)isthree-dimensional.Thespacedefinedbyqisusuallycalledthecoordinatespace.第2题DFT(discreteFouriertransform)isastraightforwardalgorithmfortheFouriertransformandcanonlyworkfortheone-dimensionalcase.第3题ThemultiplycalculationstepsneededforNpoints'DFTdirectcalculationisproportionaltowhatvalue?ANBN^2CN^3D(N/2)*logN第4题SeparatingtherealandimaginarypartsisconvenientbecausethenweonlyneedtodealwithrealnumberstomaketheDFTmoreefficient.第5题TheresultoftheinversediscreteFouriertransformfromtheaboveprogramandtheoriginaldata,inaccuracycanstillappearatthesedatapoints,becauseofthe

roundingerrorincurredduringthecomputing.第六章第三节作业第1题WhichstatementgivenbelowiswrongabouttheFFT?

AFFTisanewtransformationBFFTisafasterversionofDFTCFFTcanbedividedintodecimationintimemethodanddecimationinfrequencymethodDthedevidedpointNhavetobeevennumber.第2题DiscreteFouriertransformalgorithmintroducedintheprecedingsectionisveryinefficient,becausethecomputingtimeneededisproportionaltoN^2.第3题bit-reversedorderwillputeachpairofdatapointsnexttoeachotherforthesummationsatthefirstlevel,themethodisdevelopedby?AGaussBCooleyandTukeyCGoldstineDMetropolisandUlam第4题TotalcomputingtimeinthefastFouriertransformalgorithmisproportionaltoNlog2N第5题AveryimportantissuehereishowmuchtimecanuseofthefastFouriertransformsave.Onavectormachine,itisquitesignificant.However,onascalarmachine,thesavingissomewhatrestricted.第6题TheprincipleoffastFourierchangesistodivideadiscreteFourierchangeintotwoidenticaldiscreteFouriertransforms第7题ThetimecomplexityofthefastFouriertransformalgorithmisAO(n⋅logn)BO(logn)CO(n)DO(n^2)第七章作业第1题LAMMPS:Large-scaleAtomic/MolecularMassivelyParallelSimulatorisafreesoftwaredistributedunderthetermsoftheGNUGeneralPublicLicense第2题Moleculardynamicscansolvethedynamicsofaclassicalmany-bodysystemdescribedbytheHamiltonian第3题Browniandynamics,whichissimilartomoleculardynamicsexceptforthepresenceofarandomdissipativeforce.第4题Langevinisperformedundertheconditionthattheaccelerationisbalancedoutbythedriftingandrandomdissipativeforces.第5题Foranisolatedsystemweusethecanonicalensemble,whichassumesaconstanttotalenergy,numberofparticles,andvolume.第6题Ifthesystemisergodic,thetimeaverageisequivalenttotheensembleaverage第7题Thebehaviorofthepair-distributionfunctionin

many-bodysystemsmoleculedynamicssimulationcanprovidealotofinformationregardingthe_____natureoftheparticlesinthesystemAtranslationalBrotationalCtime-reversalDspace-reversal第8题Forasolidsystem,delta_tisrelativelysmallanddoesnotgrowwithtime,andtheparticlesareinnondiffusive,oroscillatorystates.Foraliquidsystemdelta_tgrowslinearlywithtime.第9题Theveryfirstissueinnumericalsimulationsforabulksystemishowtoextendafinitesimulationboxtomodelthenearlyinfinitesystem.Acommonpracticeistousea____.ADirichlet

boundaryconditionBperiodicboundaryconditionCadiabatboundaryconditionDAntiperiodicboundarycondition第10题Aperiodicboundaryconditionremovestheconservationofthetranslationalmomentumofthesimulatedsystem(particlesinonesimulationbox),butstillpreservestheangularsymmetryofthecenterofmass.第11题TheVerletalgorithmhasadvantagesanddisadvantages.ItpreservesthetimereversibilitythatisoneoftheimportantpropertiesofNewton’sequation.第12题ForVerletalgorithm,theerrorinthevelocityistwoordersofmagnitudehigherthantheerrorintheposition第13题ThebiggestdisadvantageoftheVerletalgorithmisthatthevelocityisevaluatedonetimestepbehindtheposition.However,thislagcanberemovedifthevelocityisevaluateddirectlyfromtheforce.第14题Theinitialvelocitiesoftheparticlesshouldalsobeassignedreasonably.AcommonpracticeistoassignvelocitiesfromtheMaxwelldistribution.第八章第一节作业第1题WhichalgorithmisusedinMonteCarlosimulations?

ARunge-KuttaalgorithmBMetropolisalgorithmCFastFouriertransformalgorithmDPicardalgorithm第2题TheMonteCarlomethodisrelatedtowhichfundamentalprinciplesofphysicsarefundamental

AquantummechanicsBClassicalmechanicsCStatisticalMechanicsDElectrodynamics第3题TherandomnumbersappliedinMonteCarlo'smethodareusuallyrealrandomnumbersproducedbystochasticprocesses.第4题UsetheMonteCarlomethodtocalculatePi,duetotechnicalconstraints,onlyasequenceofrandomnumbersfrom0to0.5canbegenerated,pleaseselecttheconditionsneededforthecalculationAr^2<0.25Br^2<0.5Cr^2<1D0.5<r^2<1第5题Byproducingarandomθ∈[0,2π],φ∈[0,π],itispossibletoproduceuniformrandomvectorsx=cosθsinφ,y=sinθsinφ,z=cosφinasphericalcoordinatesystem第6题MorereliableresultscanbeobtainedfromtheaverageofseveralindependentrunswhencalculatetheintegralbyMonte-Carlomethod.第7题Thetrapezoidruleyieldsmuchhigheraccuracywiththesamenumberofpoints.points.ThereasonisthattheerrorfromtheMonteCarloquadratureisdelta_S∝1/M^1/2,第8题Forad-dimensionalspace,theerrorof

MonteCarloquadratureisproportionaltodelta_S∝1/M^2/d,whereMisthenumberofpointssampled.第9题However,forarealmany-bodysystem,thedimensionalityinanintegralis(),whereNisthenumberofparticlesinthesystem.WhenNisontheorderof10orlarger,anyotherworkablequadraturewouldperformworsethantheMonteCarloquadrature.A4B3NC6NDN第10题Translation:RRNgenerator

____正确答案：:实随机数生成器第八章第二节作业第1题WhenuseMCmethodwithdirectrandomsamplingtocalculatetheintegraloff(x)fromatob,thenormalizationconstantZisgivenbywhatformalism?ABCD第2题Howtogenerate0~5pseudo-randomrealnumbers?A5＊rand（）/32767B5.0＊rand（）/32767C5.0＊rand（）/RAND_MAXDrand（）%5第3题Thissamplingbyimportanceismuchmoreefficientthanthedirect,randomsampling

第4题Thestepsizeisadjustable,andweshouldtrytokeepitsuchthattheacceptingrateofthenewconfigurationsislessthanoraround().A0B50%C100%D33.33%第5题Suchachoiceofacceptingrateof50%iscompatiblewithconsiderationsofspeedandaccuracy.第6题TheMetropolisalgorithmwasfirstappliedinthesimulationofthestructureofABoseliquidsBclassicalliquidsCFermigasDTBAmodel第7题Asystemisingoodcontactwithathermalbathandhasafixednumberofparticlesandvolumesize,thatis,thesystemisdescribedbytheAmicrocanonicalensembleBcanonicalensembleC

grandcanonicalensembleDensemble第8题ThetypicaldistanceforthetruncationintheLennard–Jonespotentialisaboutr=3σ,whereσistheseparationofthezeropotential第9题TheMonteCarlostepsizehisdeterminedfromthedesiredrejectionrate,alargerhproducesahigherrejectionrate.第10题higherrejectionrateproducesdatapointswithmorefluctuation第11题Thedecisionismadeaccordingtotheoptimizationofthecomputingtimeandtheaccuracyofthedatasought.Typically,()usedastherejectionrateinthemostMonteCarlosimulations.A50%-75%B<50%C25%D