Nonlinear Hydrodynamics of a Hard Sphere Fluid Near the Glas(10)

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

thedecayofS(q,t)occursatrelativelylowerdensitiesforwavevectorsclosetothe rstandsecondpeaksinthestaticstructurefactor.Thisresultclearlyillustratestheimportantroleplayedbytheequilibriumstructureinthelong-timedynamicsoftheliquid.Theobservedq-dependenceofthedecayofS(q,t)alsosuggeststhattheglassybehaviorsetsinearlier(atlowerdensities)atshorterlengthscales.Finally,thesystemisfoundto uctuateabouttheliquid-stateminimumofthemean eldfreeenergyinalloursimulations.

Therestofthepaperisorganizedasfollows.SectionIIcontainsadescriptionofthemodelconsideredbyus.We rstde nethemodel,discussitsstaticsandderivetheappropriateNFHequations.Byde ningappropriateunitsoflength,timeandmass,theseequationsarethenwrittenindimensionlessform.ThemethodusedbyustointegratetheseequationsforwardintimeisdescribedinSectionIII.WealsodiscussinthisSectionthephysicalquantitiesmeasured,thedatacollectionprocedure,testsofequilibrationandotherrelatedmatters.TheresultsobtainedfromthenumericalworkaredescribedindetailinSectionIV.WealsocompareandcontrastourresultswiththoseobtainedfromMDsimulationsofthehard-sphereandsimilarsystemsandthepredictionsofMCtheories.

II.THEMODEL

WehaveexplainedintheIntroductionthatwewillanalyzethenumericalsolutionofasetofLangevinequationsappropriatetoadensehard-sphere uid.Webeginherebydiscussingthestaticsofthemodel.Thesearegivenintermsofafreeenergywhichisafunctionalofthetwo eldsintheproblem:thedensity eldρ(r,t)andthecurrent eldg(r,t).Thisfreeenergyhastwoterms:

g2

FTot[ρ,g]=(m0/2)dr