简介：Inthispaper,weprovethatforholonomicnonconservativedynamicalsystemthePoincareandPoincaré-Cartanintegralinvariantsdonotexist.Insteadofthem,weintroducetheintegralvariantsofPoincaréCartan’stypeandofPoincaré’stypeforholonomienoneonservativedynamicalsystems,andusethesevariantstosolvetheproblemofnonlinearvibration.Wealsoprovethattheintegralinvariantsintro-ducedinreferences[1]and[2]aremerelythebasicintegralvariantsgivenbythispaper.

简介：Accordingtothebasicideaofdual-complementarity,inasimpleandunifiedwayproposedbytheauthor,somebasicprinciplesindynamictheoryofelasticmaterialswithvoidscanbeestablishedsys-tematically.Inthispaper,animportantintegralrelationintermsofconvolutionsisgiven,whichcanbecon-sideredasthegeneralizedprincipleofvirtualworkinmechanics.Basedonthisrelation,itispossiblenoton-lytoobtaintheprincipleofvirtualworkandthereciprocaltheoremindynamictheoryofelasticmaterialswithvoids,butalsotoderivesystematicallythecomplementaryfunctionalsfortheeight-field,six-field,four-fieldandtwo-fieldsimplifiedGurtin-typevariationalprinciples.Furthermore,withthisapproach,thein-trinsicrelationshipamongvariousprinciplescanbeexplainedclearly.

简介：Theexistingfundamentallawsofthermodynamicsformicropolarcontinuumfieldtheoriesarerestudiedandtheirincompletenessispointedout.Newfirstandsecondfundamentallawsforthermostaticsandthermodynamicsformicropolarcontinuaarepostulated.Fromthemallequilibriumequationsandtheentropyinequalityofthermostaticsaswellasallbalanceequationsandtheentropyrateinequalitiesarenaturallyandsimultaneouslydeduced.Thecomparisonsbetweenthenewresultspresentedhereandthecorrespondingresultsdemonstratedinexistingmonographsandtextbooksconcerningmicropolarcontinuummechanicsaremadeatanytime.Itshouldbeemphasizedtonotethat,theproblemofwhythelocalbalanceequationofenergyandthelocalentropyinequalitycouldnotbeobtainedfromtheexistingfundamentallawsofthermodynamicsformicropolarcontinua,isbelievedtobeclarified.

简介：这研究被奉献给磁性的过滤和方法的不同特征的解释这些特征影响重要过滤参数。在毛孔和磁性的粒子和包装的床的磁化性质上的这些地的力量效果的磁场铁磁性的范围创作了，金属薄片被评估。累积的侧面和粒子的俘获区域，在这些区域和粒子俘获半径的分析表情的液体速度的变化被介绍。磁性的过滤器性能上的过滤政体参数的效果被调查。一个分析表达式在过滤速度，过滤器元素的几何学，粒子尺寸和过滤的另外的参数上为对数的效率系数的依赖被获得了。磁性的过滤过程的静止、非静止的方程被给。磁性的过滤器性能的一个表达式被显示出，无尺寸的参数从过滤系统获得了。这些关系为在设计实践的计算是有用的，包括过滤器操作的磁性的过滤器，在建设的建议的预备，和优化和控制的设计。

简介：Thepurposeistoestablishtherathercompleteequationsofmotion,boundaryconditionsandequationofenergyrateofincrementalratetypeformicropolarcontinua.Tothisendtherathercompletedefinitionsforratesofdeformationgradientanditsinversearemade.Thenewrelationsbetweenvariousstressandcouplestressratetensorsarederived.Finally,thecoupledequationsofmotion,boundaryconditionsandequationofenergyrateofincrementalratetypeforcontinuummechanicsareobtainedasaspecialcase.

简介：Thepurposeistoreestablishthecoupledconservationlaws,thelocalconservationequationsandthejumpconditionsofmassandinertiaforpolarcontinuumtheories.Inthisconnectionthenewmaterialderivativesofthedeformationgradient,thelineelement,thesurfaceelementandthevolumeelementwerederivedandthegeneralizedReynoldstransporttheoremwaspresented.Combiningtheseconservationlawsofmassandinertiawiththebalancelawsofmomentum,angularmomentumandenergyderivedinourpreviouspapersofthisseries,arathercompletesystemofcoupledbasiclawsandprinciplesforpolarcontinuumtheoriesisconstitutedonthewhole.Fromthissystemthecouplednonlocalbalanceequationsofmass,inertia,momentum,angularmomentumandenergymaybeobtainedbytheusuallocalization.

简介：ThroughacomparisonbetweentheexpressionsofmasterbalancelawsandtheconservationlawsderivedbyNoether'stheorem,aunifiedmasterbalancelawandsixphysicallypossiblebalanceequationsformicropolarcontinuummechanicsarenaturallydeduced.Amongthem,byextendingthewell-knownconventionalconceptofenergymomentumtensor,therathergeneralconservationlawsandbalanceequationsnamedafterenergy-momentum,energy-angularmomentumandenergy-energyareobtained.Itisclearthattheformsofthephysicalfieldquantitiesinthemasterbalancelawforthelastthreecasescouldnotbeassumeddirectlybyperceivingthroughtheintuition.Finally,someexistingresultsarereducedimmediatelyasspecialcases.

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

简介：Basicmagnesiumcarbonatemicrosphereswitharedbloodcell（RBC）-likeappearanceanddiametersof3μmweresynthesizedbyamphiphilicmolecule-participatedself-assemblyunderhydrothermalconditions.Intheself-assembly,sodiumdodecylbenzenesulfonateservedasatemplatefortheformationofMg（OH）2sphericalmicellesandalsoasareactantprecursorthatreleasesCO2toreactwithMg（OH）2.Thegrowthofthemicrospheresisdrivenbythecontinuousgenerationofnewhydrophobiccentersbecauseoftheconsumptionofhydrophilicpoles（—SO3-）.Thesurfactant-directedself-assemblycanbeappliedtothesynthesisofothercarbonateormetallicoxideself-assemblies,indicatingthatitisauniversalself-assemblymethodforamphiphilicmolecules.