Nonlinear Hydrodynamics of a Hard Sphere Fluid Near the Glas(20)

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

Thisisduetothefactthattheexpansionofthefreeenergyjustalludedtoisnotaswelljusti edatthosedensities.Whenaveragedovertimescalesoflessthanseveraltimest ,S(q,0)oscillatesbroadlyaboutitsstationaryvalue.OurresultsforS(q,0)atalldensitiesstudiedshowthatwearedealingwithaliquid-likestatehere.Ifweuseacommensuratevalueofσ,orifweincreasen to0.95,we ndindicationsthatcrystallizationbegins.Weplantostudythiscrystallizationquestioninfuturework.

Thestabilityofourdynamicallyobtainedresultsoverlongcomputationalruns,andtheiragreementwithstaticresultsconstituteaverystringentcheckofthestabilityofournumericalalgorithms.

Toanalyzeourresults,itisconvenienttointroducethenormalizedquantityC(q,t)de nedas:

C(q,t)=S(q,t)