Boundary Conditions for Molecular Dynamics Simulations of Solids

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Molecular dynamics models materials at the level of atomic scale. In a computer simulation one follows the motion of the atoms, which obeys Newton's second law. For crystalline solids, molecular dynamics offers a microscopic description of the crystal and defect structure, which is ultimately responsible for the overall material properties. It offers more insight on why the material behaves the way it does, and it has become an extremely important tool in material modeling and simulations. However due to the computational complexity, such a simulation can only be conducted for a small system. Typically it is focused around material defects where the deformation is quite large, and the atoms in the far field are eliminated. Such a truncation procedure creates artificial boundaries, where boundary conditions have to be imposed in order to take into account the missing atoms. The boundary condition provides, for example, the position of the atoms at the boundary, which will be needed in the force calculation for the atoms inside the system, and therefore required to allow the simulation to proceed. Straightforward approaches often lead to wave reflection at the boundary and therefore severely deteriorate the simulation results. This project aims to develop systematic boundary conditions that serve the following purposes: (a) prevent wave reflection at the boundary; (b) maintain the external loading; (c) control the system temperature. These boundary conditions will greatly improve the accuracy and reliability of molecular dynamics simulations and will help to study the dynamics of material defects under various kinds of loading, and in different temperature regimes. The project also involves numerical analysis aspects and applications of these methods. The proposed research will expose the students to physical modeling, large-scale simulations, mathematical analysis, and interdisciplinary research.