The Burnett Problem: Molecular Dynamics' Grand Challenge

The nonlinear Burnett coeecients are the Tay-lor series coeecients for the functional dependence describing how the Thermodynamic Flux responds to a Thermodynamic Force acting on a uid. Ernst et. al. computed the functional dependence exactly for a hard disk/sphere uid (a uid made up of idealised billiard balls) undergoing shear ow, and found that the relationship was non-analytic, i.e. that the nonlinear Burnett coeecients were innnite. It is of considerable interest to know if these coeecients are nite for other uids, particularly uids of industrial importance. Theoretical work by this author and collaborators allow the possibility of a Molecular Dynamics calculation of the Bur-nett coeecients. For some years, the Burnett project has been working to perform this calculation for a Lennard-Jones Fluid with 108 particles. The current incarnation of this project couples the 128 processor CM5 located at Adelaide University, the 1024 processor AP1000 located at Fujitsu Parallel Laboratory, the 20 processor Power Challenge located at the Parallel Computing and Visualisation Laboratory, Redfern, Sydney and an 12 processor Convex SPP2000 located at UNSW to form a sustained aggregate computing facility of 11.5GFlops. 1 The Burnett Problem Molecular Dynamics Simulations refer to simulating a uid by solving the equations of motion for its substituent particles (the molecules). Typical simulations have only a few hundred molecules, but some simulations have been done involving hundreds of thousands. Even though only a microscopic chunk of the uid is simulated , many bulk properties of the system can be obtained from it. More detailed theoretical and practical information can be found in Refss5, 1]. The bulk properties are related to Transient Time Correlation Functions, which typically have the form hA(?(0))B(?(t))i, where ?(t) refers to the positions and momenta of all the molecules at time t, and hi implies that this quantity has been averaged over an ensemble of systems and/or over time. Nonlinear transport coeecients (or nonlinear Burnett coeecientss2]), B i , give a Taylor series representation of a nonlinear transport coee-cient L, in terms of the thermodynamic force F, i.e. if a thermodynamic ux J is written in terms of the coeecient's deening constitutive relation as J = L(F)F, then the Burnett coeecients are related example, in the case of electrical conductivity, we may write the relation between the current density j and the electric eld E as j = (E)E. In this case, (0) is the usual Ohmic conductivity. The Burnett coeecients have …