Spanning the Length Scales in Dynamic Simulation

couple different length and time scales in serial fashion. By this we mean that one set of calculations at a fundamental level, and of high computational complexity, is used to evaluate constants for use in a more approximate or phenomenological computational methodology at longer length or time scales. In pioneering work of this sort in the 1980s, Clementi and coworkers1 used high-quality quantum-mechanical methods to evaluate the interaction of several water molecules. From this database they parameterized an empirical potential for use in molecular-dynamics atomistic simulations. Such a simulation was then used to evaluate the viscosity of water from the atomic autocorrelation function. Finally, the computed viscosity was used in a computational-fluid-dynamics calculation to predict tidal circulation in Buzzards Bay, MA. This tour de force of computational physics is a powerful example of the sequential coupling of length and time scales: one series of calculations is used as input to the next up the length and time hierarchy. There are many other examples in the literature. But what underlies all these schemes is that an appropriate computational methodology is used for a given scale or task, whether it be the accuracy of quantum mechanics at the shortest scales or fluid dynamics at the longest scales. In contrast, there has been comparatively little effort devoted to the parallel coupling of different computational schemes for a simultaneous attack on a given problem; in our case, our interest dictates specific attention toward issues in materials or solid-state physics. We will focus specifically on the coupling of length scales for the three mechanics describing materials phenomena: quantum mechanics, atomistic mechanics, and continuum mechanics.