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1、Eur.Phys.J.SpecialTopics220,1–8(2013)THEEUROPEANcEDPSciences,Springer-Verlag2013DOI:10.1140/epjst/e2013-01792-4PHYSICALJOURNALSPECIALTOPICSEditorialElectromagnetic?owcontrolinmetallurgy,crystalgrowthandelectrochemistryGunterGerbeth1,a,KerstinEckert2,b,andStefanOdenbach2,c1
2、Helmholtz-ZentrumDresden-Rossendorf(HZDR),InstituteofFluidDynamics,01314Dresden,Germany2InstituteofFluidMechanics,ChairofMagneto?uiddynamics,MeasuringandAutomationTechnology,TechnischeUniversit¨atDresden,01069Dresden,GermanyElectromagnetic?elds,producedeitherbyalternating(A
3、C)orconstant(DC)elec-triccurrents,orbysimplepermanentmagnets,stronglyin?uencethe?owofliquidmetalsorelectrolytes.ThisiscausedbytheLorentzforce(density)fL=j×B,resultingfromtheinteractionbetweenthemagneticinductionBandtheelectriccurrentdensityj,eitherinducedbyFaraday’slawinliq
4、uidmetals,orinjectedinthecaseofweaklyconductingliquids,e.g.inelectrochemicalsystems.ThestudyofthefeedbackbetweenBandthevelocity?eldu,drivenbyfLiscalledmagnetohydro-dynamics(MHD),adisciplinedatingbacktothediscoveryoftheinductionlawin1831byFaraday.ForthebasicsofMHDwerefertoex
5、cellenttextbooks[1–3]orarecentreview[4].ImportantearlymilestonesinthedevelopmentofMHDwerethe?rstliquidmetalexperimentsinchannelsperformedbyHartmannin1937[5]andtheNobelprizedecorateddiscoveryofincompressiblewavesin1942[6],nowcalledAlfv′enwaves,thatplayanimportantroleinsolarp
6、hysics.Morerecentdevelopmentsconsistintherapidemergenceofanewdiscipline,theelectromagneticprocessingofmaterialswithownconferences[7],ortheexperimentalproofsofthedynamoaction,i.e.theself-excitationofBsolelycausedbythe?owingliquidmetalinspeci?callydesignedlaboratoryexperiment
7、s[8].ThisremarkablediversityofphenomenaissortedinMHDbythemagneticReynoldsnumberRm=μ0σul,whereμ0,σ,uandlrefertovacuumpermeability,electricconductivityandtothecharacteristicscalesofvelocityandlength,respec-tively.Thedynamoproblemaswellasotherimportantastrophysicalproblems,suc
8、hasphenomenainthesolaratmosphere,fallintotheclassofhigh-Rmproblemsduetothelargelen
