简介：Inthispaper,wederivetheanalyticalsolutionsinathree-dimensionalanisotropicmagnetoelectroelasticbimaterialspacesubjecttouniformextendeddislocationsandtractionswithinahorizontalcirculararea.ByvirtueoftheStrohformalismandFouriertransformation,thefinalexpressionofsolutionsinthephysicaldomaincontainsonlylineintegralsover[0,2π]ratherthaninfiniteintegrals.Asthereducedcases,thehalf-spaceandhomogeneousfull-spacesolutionscanbedirectlyderivedfromthepresentsolutions.Also,intermsofmaterialdomains,thepresentsolutionscanbereducedtothepiezoelectric,piezomagnetic,purelyelasticmaterialswithdifferentsymmetriesofmaterialproperty.Tocarryoutnumericalcalculations,Gaussquadratureisadopted.Inthenumericalexamples,theeffectofdifferentloadinglocationsontheresponseattheinterfaceisanalyzed.Itisshownthat,whenthemagnetictractionorelectricdislocationisapplied,thephysicalquantitiesontheinterfacemaynotdecreasemonotonicallyastheloadingareamovesawayfromtheinterface.Thedistributionsofdifferentin-planephysicalquantitiesontheupperandlowerinterfacesundervariousextendedhorizontalloadingsarecomparedandthedifferencesarediscussed.Theworkpresentedinthispapercanserveasbenchmarksforfuturenumericalstudiesinrelatedresearchfields.

简介：Inthispaper,aresearchontheproblemofmultiplesolutionsofthethree-coefficientlow-spectrummodelforthequasi-geostrophicoceancurrentequationwithforcinganddissipationtermsiscarriedout.Thestateoftheoceancurrentunderwindconditionssuchasthoseoftyphoonisdiscussedcarefullyandtherela-tionsbetweenthemultiplesolutionsandthecoefficientsRandεareanalyzed.Itisseenthatinanapproxi-matetriangularregionwiththeRossby-coefficientRlessthan0.5,andthefriction-coefficientεlessthan0.22,thereexistthreeequifibriumsolutions,amongwhichtwoarestableandoneisunstable.Fortheformer,thecoefficientAorBintheexpansionisratherlarge,whileforthelatter,AorBisrelativelysmall.TheyrespectivelyimplyhowmuchtheoceanenergyisfedbackfromthewindstressandthesolutionwithalargeAismuchmorestablethanthatwithalargerB.

简介：ThePainlev'eintegrabilityandexactsolutionstoacouplednonlinearSchr¨odinger(CNLS)equationappliedinatmosphericdynamicsarediscussed.SomeparametricrestrictionsoftheCNLSequationaregiventopassthePainlev'etest.TwentyperiodiccnoidalwavesolutionsareobtainedbyapplyingtherationalexpansionsoffundamentalJacobiellipticfunctions.TheexactsolutionstotheCNLSequationareusedtoexplainthegenerationandpropagationofatmosphericgravitywaves.

简介：Twodimensionalequationsofsteadymotionforthirdorderfluidsareexpressedinaspecialcoordinatesystemgeneratedbythepotentialflowcorrespondingtoaninviscidfluid.Fortheinviscidflowaroundanarbitraryobject,thestreamlinesarethephicoordinatesandvelocitypotentiallinesarepsi-coordinateswhichformanorthogonalcurvilinearsetofcoordinates.Theoutcome,boundarylayerequations,isthenshowntobeindependentofthebodyshapeimmersedintotheflow.Asafirstapproximation,assumptionthatsecondgradetermsarenegligiblecomparedtoviscousandthirdgradeterms.Secondgradetermsspoilscalingtransformationwhichisonlytransformationleadingtosimilaritysolutionsforthirdgradefluid.ByusingLiegroupmethods,infinitesimalgeneratorsofboundarylayerequationsarecalculated.Theequationsaretransformedintoanordinarydifferentialsystem.NumericalsolutionsofoutcomingnonlineardifferentialequationsarefoundbyusingcombinationofaRunge-Kuttaalgorithmandshootingtechnique.

简介：Optimalcontrolsystemofstatespaceisaconservativesystem,whoseapproximatemethodshouldbesymplecticconservation.Basedonthepreciseintegrationmethod,analgorithmofsymplecticconservativeperturbationispresented.Itgivesauniformwaytosolvethelinearquadraticcontrol(LQcontrol)problemsforlineartime-varyingsystemsaccuratelyandefficiently,whosekeypointsaresolutionsofdifferentialRiccatiequation(DRE)withvariablecoefficientsandthestatefeedbackequation.Themethodissymplecticconservativeandhasagoodnumericalstabilityandhighprecision.Numericalexamplesdemonstratetheeffectivenessoftheproposedmethod.

简介：Aclassofperiodicinitialvalueproblemsfortwo-dimensionalNewton-Boussinesqequationsareinvestigatedinthispaper.TheNewton-Boussinesqequationsareturnedintotheequivalentintegralequations.Withiterationmethods,thelocalexistenceofthesolutionsisobtained.Usingthemethodofaprioriestimates,theglobalexistenceofthesolutionisproved.

简介：TheSchmidtmethodisadoptedtoinvestigatethefractureproblemofmultipleparallelsymmetricandpermeablefinitelengthmode-IIIcracksinafunctionallygradedpiezoelectric/piezomagneticmaterialplane.Thisproblemisformulatedintodualintegralequations,inwhichtheunknownvariablesarethedisplacementjumpsacrossthecracksurfaces.Inordertoobtainthedualintegralequations,thedisplacementjumpsacrossthecracksurfacesaredirectlyexpandedasaseriesofJacobipolynomials.Theresultsshowthatthestress,theelectricdisplacement,andthemagneticfluxintensityfactorsofcracksdependonthecracklength,thefunctionallygradedparameter,andthedistanceamongthemultipleparallelcracks.Thecrackshieldingefectisalsoobviouslypresentedinafunctionallygradedpiezoelectric/piezomagneticmaterialplanewithmultipleparallelsymmetricmode-IIIcracks.

简介：Thispaperinvestigatesthestaticbehaviorofafunctionallygradedcircularplatemadeofmagneto-electro-elastic(MEE)materialsundertensionandbending.Theanalysisisdirectlybasedonthethree-dimensionalgoverningequationsformagnetoelectro-elasticity,withtheboundaryconditionsontheupperandlowersurfacessatisfiedexactlyandthoseonthecylindricalsurfacesatisfiedapproximately(intheSaintVenantsense).Theanalyticalsolutions,derivedwithadirectdisplacementmethod,arevalidforanyfunctionallygradedmaterial(FGM)withitspropertiesvaryingindependentlyinacontinuousmanneralongthethicknessdirection.Forhomogeneousmaterials,thesesolutionsaredegeneratedtotheonesavailableintheliterature.Interestingrelationsarealsofoundbetweenthesolutionsforafunctionallygradedmagneto-electro-elastic(FGMEE)circularplateandthoseforanFGMEErectangularbeam,andeventhoseforafunctionallygradedelasticbeamwhenonlytheelasticdisplacementsareconsidered.Thebeamsolutionsarealsoderivedusingadirectdisplacementmethod.Numericalexamplesarepresentedtoverifythepresentanalyticalsolutions,showtheeffectsofmaterialheterogeneityandmulti-fieldcoupling,andindicatethecorrespondencebetweentheplatesolutionsandbeamsolutions.

简介：Ironcatalystnanoparticleswerepreparedonsiliconwafersbyspin-coatingcolloidalsolutionscontainingironnitrate,polyethyleneglycol(PEG)andabsoluteethanol.Theeffectsofvariousspin-coatingconditionswereinvestigated.Thefindingsshowedthatthesizeoftheironparticleswasgovernedbythecompositionofthecolloidalsolutionusedandthatahighangularspeedwasresponsiblefortheformationofathincolloidalfilm.Theeffectofangularaccelerationonthesizeanddistributionoftheironparticleswerefoundtobeinsignificant.Itwasobservedthatalongerspin-coatingdurationprovokedtheagglomerationofironparticles,leadingtotheformationoflargeparticles.Wealsoshowedthatsingle-walledcarbonnanotubescouldbegrownfromthesmallestironcatalystnanoparticlesafterthechemicalvapordepositionofmethane.