Huajie Chen, Beijing Normal University
601 Pao Yue-Kong Library
We will present a rigorous framework for crystalline defects. We formulate the equilibration of crystal defects as variational problems in a discrete energy space and establish qualitatively sharp far-field decay estimates for the equilibrium states. This work extends the existing results to more general models, by overcoming the difficulties from infinite range interactions. We discuss several physical models, from both quantum mechanics and molecular mechanics, that are widely used in practical simulations and show that they fit our framework well.We will also discuss how to yield QM/MM (quantum/classical) multi-scale algorithms with guaranteed convergence rates in this framework.