Nonlinear Hydrodynamics of a Hard Sphere Fluid Near the Glas(8)

We conduct a numerical study of the dynamic behavior of a dense hard sphere fluid by deriving and integrating a set of Langevin equations. The statics of the system is described by a free energy functional of the Ramakrishnan-Yussouff form. We find that th

function37oftheliquid.Thisappearstobeadequateforacorrectdescriptionofthestaticsofthefreezingoftheliquidintobothcrystalline35andglassy36states.Oneofthequestionsweaddressinthepresentstudyiswhetherthisisalsosu cientforacorrectdescriptionofthedynamicbehavior.TwonumericalstudiesofNFHequationsdescribingthedynamicsofdenseliquidshavebeenreportedrecently38,39.Themaindi erencebetweenthesestudiesandthepresentoneisthattheequilibriumstructureoftheliquidwastreatedonlyinanapproximatewayintheearliercalculations.ConsequentlytheresultsofthesecalculationscouldnotbecompareddirectlywithMDdata.Theresultsofthesecalculationsdidnotexhibitsomeofthefeatures(suchastwo-regimedecayofcorrelations)generallyassociatedwithglassydynamics,althoughnon-exponentialdecayofcorrelationsoftenassociatedwithitsonsetwasfound.InRef.(39),itwassuggestedthatthisfailurearisesfromtheapproximationsmadeinthetreatmentofliquidstructure.Thepresentstudyprovidestheopportunitytocheckwhetherthisexplanationiscorrectandtoinvestigateingeneraltheroleofstaticstructureinthedynamicsofadenseliquid.Further,perturbativetreatmentsoftheNFHequationssimilartotheonesweuseareknown9,10toleadtoresultswhichareveryclosetothoseobtainedfromtheMCapproach.Apartfromnumericalerrorsarisingfromspatialdiscretizationandtheintegrationprocedure,ourtreatmentoftheseequationsisexact.Inparticular,ournumericalsolutionoftheseequationsisobviouslynonperturbative,therefore,acomparisonoftheresultsofourcalculationwithMCpredictionsprovidesawaytotestthevalidityofsomeoftheapproximationsmadeintheanalyticstudies.Sinceourcalculationtakesfullaccountoftheshortrangestructureoftheliquid,ithasthemostdirectconnectionwiththeMCstudiesofKirkpatrick8andDas10.Finally,bymonitoringwhichminimaofthefreeenergyarevisitedduringthetimeevolutionofthesystemweareabletodeterminewhethertheobserveddynamicbehavior