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Abstract
From its inception in the mid-Fifties, the method of molecular-dynamics (MD) computer simulations has been used to probe the foundations of statistical me- chanics, first for equilibrium equation-of-state averages, and then for transport proper- ties from equilibrium fluctuations. Traditional statistical mechanical theoreticians were shocked to see that this new-fangled computational physics approach was feasible, even with incredibly tiny samples (on the order of a hundred atoms). When direct measurement of transport coefficients by non-equilibrium molecular dynamics (NEMD) was proposed in the early Seventies, even greater resistance was encountered from the traditionalists - though evidence for convergence with the equilibrium fluctuation method gradually accu- mulated. In the late Seventies and early Eighties, shock-wave simulations by NEMD made it possible to test directly the principal continuum constitutive theory for fluids, namely, Navier-Stokes viscous flow and Fourier's Law of heat conduction. To everyone's surprise - and the consternation of many - NEMD, once again, demonstrated that continuum the- ory applies at embarrassingly small (atomistic) time and length scales. We pursue this early line of work into the modern era, showing how NEMD shock-wave simulations can still provide surprising insights and improvements upon our understanding of constitutive modeling.
Highlights
From its inception in the mid-Fifties, the method of molecular-dynamics (MD) computer simulations has been used to probe the foundations of statistical mechanics, first for equilibrium equation-of-state averages, and for transport properties from equilibrium fluctuations
There’s a dark side to this otherwise beneficial development, : It was the need to use hydrodynamic simulation at the macroscopic, rather than microscopic scale, in order to understand the details of nuclear explosions, which led to the creation of computing machines that filled entire rooms at the national nuclear weapons laboratories – Los Alamos, in New Mexico, and Livermore, in California. (In the intervening half century, the computing power of these enormous machines has been dwarfed by the memory and speed of my iPhone.)
A year later, believing that non-equilibrium molecular dynamics (NEMD) had already shown that hydrodynamics applies at the shockingly small atomistic scale, Bill Hoover at Livermore boldly ignored conventional wisdom and solved Navier-Stokes and Fourier continuum theory for both of the shock waves studied by the Russians [21]
Summary
From its inception in the mid-Fifties, the method of molecular-dynamics (MD) computer simulations has been used to probe the foundations of statistical mechanics, first for equilibrium equation-of-state averages, and for transport properties from equilibrium fluctuations. Green-Kubo (GK) theory suggested that equilibrium fluctuations relax on time-scales accessible to MD simulations, and A&W proved the point by computing transport coefficients (viscosity and thermal conductivity) from GK, where the long-time integral of flux autocorrelation functions give the transport coefficients [9].
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