简介:Theresultsofasimplecomputationalmodelfordifferentialsettlingarepresentedillustratingthesignificantrolethatparticlesizedistributionplaysincollisionfrequencyandsedimentationrateofparticlesinaquiescentenvironment.Themodeltracksalargenumberofparticles(order10~5)withlog-normallydistributeddiameters,astheysettleattheirStokessettlingvelocities.Particlecollisionsaredetectedandresultinlargerparticlesthatfallmorerapidly.Anumberofsimplifyingassumptionsaremadeinthemodelinordertoavoidempiricalcorrelationsforphenomenasuchascollisionefficiencyandparticleshape.Thesesimplifyingassumptionswereneededtoisolateandquantifytheroleoftheparticlesizedistribution.Simulatedconcentrationprofilesindicatethat,evenintheabsenceofcollisions,thestandarddeviation(σ_D)oftheparticlesizestronglyinfluencesthebulkmasssettlingrateas,forlargerσ_D,moremassisconcentratedinlarger,fasterfallingparticles.Thecollisionfrequencyisalsoastrongfunctionofσ_D.Foragivenmassconcentrationthecollisionfrequencyfirstincreaseslinearlywithincreasingσ_Dasgreatervariationinparticlesizeleadstogreatervariationinparticlevelocity,andshortertimesforparticlestocatcheachother.Forlargerσ_Dmoremassisconcentratedinlargerparticles,so,foragivenmassconcentration,therearefewerparticlesperunitvolume,increasingthemeandistancebetweentheparticlesandreducingthecollisionfrequency.Theimplicationsoftheseresultsforsedimentationmeasurementusingopticalattenuationtechniquesarediscussed.
简介:Wateristhemostactivecomponentinallgeologicalsystems.Ithasanimportanteffectonthephysicalpropertiesofmineralsandmelts.ItalsoplaysakeyroleintheevolutionoftheEarth.Accuratethermodynamicsdataonwaterarecurrentlyconfinedtopressuresbelow1.0GPaandtemperaturesbelow900℃.PresentedinthispaperarenewdataavailableontheP-Tpropertiesofwateratpressuresupto5.0GPa,develogedfromdifferentialthermalanalysisandultrasonicwaveamplitudeanalysis.Ithasbeenfoundthattheremayexistanotherternarypointat3.0GPaandthatultrasonicwaveamplitudechangeofice-watertransitionshowstwoinflectionpointsabove2.0GPa,consistentwiththetwopeaksofdifferentialthermalcurvesabove2.0GPa.Itmaybeanewphenomenonwhichneedsfurtherstudy.
简介:Inthispaper,theforecastingequationsofa2nd-orderspace-timedifferentialremainderarededucedfromtheNavier-StokesprimitiveequationsandEulerianoperatorbyTaylor-seriesexpansion.Hereweintroduceacubicsplinenumericalmodel(SplineModelforshort),whichiswithaquasi-Lagrangiantime-splitintegrationschemeoffittingcubicspline/bicubicsurfacetoallphysicalvariablefieldsintheatmosphericequationsonsphericaldiscretelatitude-longitudemesh.Anewalgorithmof'fittingcubicspline—timestepintegration—fittingcubicspline—……'isdevelopedtodeterminetheirfirst-and2nd-orderderivativesandtheirupstreampointsfortimediscreteintegraltothegoverningequationsinSplineModel.AndthecubicsplinefunctionanditsmathematicalpolaritiesarealsodiscussedtounderstandtheSplineModel’smathematicalfoundationofnumericalanalysis.ItispointedoutthattheSplineModelhasmathematicallawsof'convergence'ofthecubicsplinefunctionscontractingtotheoriginalfunctionsaswellasits1st-orderand2nd-orderderivatives.The'optimality'ofthe2nd-orderderivativeofthecubicsplinefunctionsisoptimalapproximationtothatoftheoriginalfunctions.Inaddition,aHermitebicubicpatchisequivalenttooperateonagridfora2nd-orderderivativevariablefield.Besides,theslopesandcurvaturesofacentraldifferenceareidentifiedrespectively,withasmoothingcoefficientof1/3,three-pointsmoothingofthatofacubicspline.Thentheslopesandcurvaturesofacentraldifferencearecalculatedfromthesmoothingcoefficient1/3andthree-pointsmoothingofthatofacubicspline,respectively.Furthermore,aglobalsimulationcaseofadiabatic,non-frictionaland'incompressible'modelatmosphereisshownwiththequasi-LagrangiantimeintegrationbyusingaglobalSplineModel,whoseinitialconditioncomesfromtheNCEPreanalysisdata,alongwithquasi-uniformlatitude-longitudegridsandtheso-called'shallowatmosphere'Navier-Stokesprimitiveequationsinthes