Coarse-Grained Molecular Dynamics: Dissipation Due to Internal Modes
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Coarse-Grained Molecular Dynamics: Dissipation due to Internal Modes Robert E. Rudd Lawrence Livermore National Laboratory Condensed Matter Physics Division, L-045 Livermore, CA 94551 USA ABSTRACT We describe progress on the issue of pathological elastic wave reflection in atomistic and multiscale simulation. First we briefly review Coarse-Grained Molecular Dynamics (CGMD). Originally CGMD was formulated as a Hamiltonian system in which energy is conserved. This formulation is useful for many applications, but recently CGMD has been extended to include generalized Langevin forces. Here we describe how Langevin dynamics arise naturally in CGMD, and we examine the implication for elastic wave scattering. INTRODUCTION Multiple scales arise in many physical systems. Much of the richness of materials science is due to the endless combinations of interplay between processes at diverse scales, including cooperative dynamics and competition. The multiscale modeling tools developed in recent years have proven to be an effective way to treat the length scale problem. In most cases studied to date, multiple length scales are treated sequentially: ab initio calculations are used to develop classical interatomic potentials that are in turn used in large-scale molecular dynamics (MD) simulations that form the basis for mesoscale and continuum models such as finite element (FE) models. This approach works well when the scales are weakly coupled. When the scales are strongly coupled, multiple scales must be treated simultaneously. This has become known as concurrent multiscale modeling. [1] Coarse-grained molecular dynamics (CGMD) is an example of concurrent multiscale modeling that is optimized to simulate dynamical and finite temperature processes at, and above, the nanoscale. It unifies atomistic simulation with a generalization of finite element modeling in a concurrent simulation. [2] The methodology is designed for inhomogeneous systems with regions that require the precision of a full, atomistic description and regions that are well modeled by a simplified description. An example of such a system is the microresonator shown in Fig. 1. [3] The resonator is a bar of semiconductor that has been etched from a single crystal. The etching has released the bar from the substrate so that it is free to oscillate much like a violin string. Bridge-type resonators of this general design have been used in a variety of Micro-Electro-Mechanical Systems (MEMS). [4] Currently several experimental groups are developing sub-micron resonators for use in Nano-Electro-Mechanical Systems (NEMS). [5,6] The NEMS resonator is an archetypical system with two relevant length scales. The width of the bar can be less than 100 atoms, so nanoscale atomistic effects can be important; at the same time, elastic fields extend from the resonating bar for microns out into the substrate. These elastic fields are well described by continuum mechanics. [3] CGMD allows both the atomistic and the continuum physics to be modeled concurrently in a single simulation.
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