简介：AccordingtoLorenz,chaoticdynamicsystemshavesensitivedependenceoninitialconditions(SDIC),i.e.,thebutterfly-effect:atinydifferenceoninitialconditionsmightleadtohugedifferenceofcomputer-generatedsimulationsafteralongtime.Thus,computer-generatedchaoticresultsgivenbytraditionalalgorithmsindoubleprecisionareakindofmixtureof'true'(convergent)solutionandnumericalnoisesatthesamelevel.Today,thisdefectcanbeovercomebymeansofthe'cleannumericalsimulation'(CNS)withnegligiblenumericalnoisesinalongenoughintervaloftime.TheCNSisbasedontheTaylorseriesmethodathighenoughorderanddatainthemultipleprecisionwithlargeenoughnumberofdigits,plusaconvergencecheckusinganadditionalsimulationwithevensmallernumericalnoises.Intheory,convergent(reliable)chaoticsolutionscanbeobtainedinanarbitrarylong(butfinite)intervaloftimebymeansoftheCNS.TheCNScanreducenumericalnoisestosuchalevelevenmuchsmallerthanmicro-leveluncertaintyofphysicalquantitiesthatpropagationofthesephysicalmicro-leveluncertaintiescanbepreciselyinvestigated.Inthispaper,webrieflyintroducethebasicideasoftheCNS,anditsapplicationsinlong-termreliablesimulationsofLorenzequation,three-bodyproblemandRayleigh-Bénardturbulentflows.UsingtheCNS,itisfoundthatachaoticthree-bodysystemwithsymmetrymightdisruptwithoutanyexternaldisturbance,say,itssymmetry-breakingandsystem-disruptionare'self-excited',i.e.,out-of-nothing.Inaddition,bymeansoftheCNS,wecanprovidearigoroustheoreticalevidencethatthemicro-levelthermalfluctuationistheoriginofmacroscopicrandomnessofturbulentflows.Naturally,muchmoreprecisethantraditionalalgorithmsindoubleprecision,theCNScanprovideusanewwaytomoreaccuratelyinvestigatechaoticdynamicsystems.

简介：ThenumericalsolutionofBoussinesqequationsisworkedoutasaninitial-valueproblemtostudytheeffectoftheinstabilitiesofflowontheinitialerrorgrowthandmesoscalepredictability.Thedevelopmentofweathersystemsdependsondifferentdynamicinstabilitymechanismsaccordingtothespatialscalesofthesystemandthedevelopmentofmesoscalesystemsisdeterminedbysymmetricinstability.Sincesymmetricinstabilitydominatesamongthethreetypesofdynamicinstability,itmakesthepredictionoftheassociatedmesoscalesystemsmoresensitivetoinitialuncertainties.Thisindicatesthatthestrongerinstabilityleadstofasterinitialerrorgrowthandthuslimitsthemesoscalepredictability.Besidesdynamicinstability,theimpactofthermodynamicinstabilityisalsoexplored.Theevolvementofconvectiveinstabilitymanifestsasdramaticvariationinsmallspatialscaleandshorttemporalscale,andfurthermore,itexhibitstheupscalegrowth.Sincethesefeaturesdeterminetheinitialerrorgrowth,themesoscalesystemsarisingfromconvectiveinstabilityarelesspredictableandtheupscaleerrorgrowthlimitsthepredictabilityoflargerscales.Thelatentheatingisresponsibleforchangingthestabilityofflowandsubsequentlyinfluencingtheerrorgrowthandthepredictability.

简介：Pertainingtodynamicsystemsingeneral,areviewisgivenofrelationsbetweenmathematicaldescriptionsinthefrequencydomainortimedomainandstate-spacedescriptions.Fortheanalysisofhydrodynamicproblemsinoceanengineeringwaveforcesmayberepresentedbyconvolutionintegrals.Thepaperpresentsamethodtoconstructafinite-orderstate-spacemodelwhichrepresentsagoodapproximationtosuchaconvolutionintegral.Themethodutilizesaparticularalgorithmtocomputethepartialderivativeoftheexponentialfunctionofa(state-space)matrixwithrespecttothematrixelements.Themethodisappliedtoanexampleoffittingastatespacemodeloforderfivetothefreeoscillationscorrespondingtowaveradiationinatransientexperimentwithanoscillatingwatercolumn.

简介：Thispaperdealswiththeproblemofdeterminingtwounknownparametersofsomenonlinearreaction-diffusionmodels.Thesereaction-diffusionmodelsarederivedfromapplicationsinthegroundwaterflowtransport,environmentalsciences,gasdynamics,heatandmasstransfer,industrialautomatizationandsomeotherengineeringtechnologicalfields.Theadjointmethodbasedonthevariationalprincipleisarelativelynewoptimalcontrolmethod.Itisusedintheidentificationoftheunknowndiffusioncoefficient,andsomecoefficientsofthenonlinearsinkorsourcetermsinthesesystems.Atfirst,theproblemistransferredintoanoptimizationproblemofminimizingafunctional,andtheadjointequationsofthegoverningequationsarederivedfromtheadjointmethod.Then,theformulasaregiventocalculatethegradientoftheobjectivefunctionwithrespecttothecoupleofunknownparameters.Atlast,aniterativegradient-basedoptimizationalgorithmispresentedforsolvingtheoptimizationproblem.Anumericalexampleisofferedintheend.Itshowstheeffectivenessoftheproposedapproach.

简介：Thepartiallyfilledpipeflowsencounteredindrainagesystemsbelongtoafamilyofunsteadyflowproblemscapableofnumericalsolutionviathemethodofcharacteristics.Thedefiningequationsintermsofflowdepth,velocityandsurfacewavespeedaredevelopedandnumericallysolvedbycharacteristic-differencemethodwithtime-lineinterpolationscheme.Boundaryconditionsforinflow,outflow,movinghydraulicjumpandjunctionsaredevelopedbothexperimentallyandnumerically.Fullscalemodelexperimentswerecarriedoutanditwasconsequentlyclarifiedthatnumericalmodeliscapableofpredictingflowcharacteristicsinrealisticdrainagenetworks.