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1、REVIEWSOFMODERNPHYSICS,VOLUME82,APRIL–JUNE2010VorticesoncurvedsurfacesAriM.TurnerDepartmentofPhysics,HarvardUniversity,CambridgeMassachusetts02138,USAandDepartmentofPhysics,UniversityofCalifornia,Berkeley,California94720,USAVincenzoVitelliInstituut-LorentzforThe
2、oreticalPhysics,LeidenUniversity,LeidenNL2333CA,TheNetherlandsDavidR.NelsonDepartmentofPhysics,HarvardUniversity,CambridgeMassachusetts02138,USAPublished30April2010TopologicaldefectsinthinÞlmscoatingadeformedsubstrateinteractwiththeunderlyingcurvature.Thiscoup
3、lingmechanisminßuencestheshapeofbiologicalstructuresandprovidesanewstrategyforthedesignofinterfaceswithprescribedfunctionality.Inthisarticle,amathematicalformalismbasedonthemethodofconformalmappingthatispresentedpermitsthecalculationoftheenergeticsofdisclination
4、s,dislocations,andvorticesonrigidsubstratesofspatiallyvaryingGaussiancurvature.SpecialemphasisisplacedondeterminingthegeometricforceexertedonvorticesincurvedsuperßuidÞlms.Thisforce,whichattractsrepelsvorticestowardsregionsofnegativepositiveGaussiancurvature,
5、isanillustrationofhowmaterialshapecaninßuencequantummechanicaldegreesoffreedom.DOI:10.1103/RevModPhys.82.1301PACSnumbers:67.25.dk,61.30.Jf,02.40.Hw,05.30.JpCONTENTSRevolution1341AppendixF:DerivationsofBoundsValidEvenforStrongDistortions1345I.Introduction1301Re
6、ferences1347II.OverviewofBasicConcepts1303III.FluidDynamicsandVortex-CurvatureInteractions1306A.Anomalousforceonrotationallysymmetricsurfaces1308I.INTRODUCTIONB.Vortex-trappingsurfaces1310Thedelicateinterplaybetweengeometryandcon-C.Negativecurvaturewhichdoesnott
7、rap1311densedmatterorderhasprovidedafascinatingvenuetoD.Hysteresisofvorticesandtrappingstrength1313developsophisticatedtheoreticalideasthat,alongwithIV.RotatingSuperßuidFilmsonaCorrugatedSubstrate1313experimentalinvestigations,contributetotheappealofA.Theeffecto
8、frotation1313thesubjectBowickandTravesset,2001;Kamien,2002;B.Singledefectgroundstate1314Nelson,2002b;Witten,2007.ThisisparticularlyevidentC.MultipledefectconÞgurati
