Xiaojie's personal webpage

Research

Quantum Chemistry, Quantum Physics

Solving quantum many-body problem using neural networks
Quantum embedding (density matrix embedding theory)
Strongly Correlated Materials

Molecular Dynamics

Absorbing boundary conditions
Neural-network-based empirical potentials
Materials science.

Previous projects

Absorbing boundary conditions (ABCs) for molecular dynamics

The main purpose of ABCs is mathematically truncating a large or infinite region into a relative small region by removing the exterior fields.

The proposed ABCs are based the Drichlet-to-Neumann map. They are able to deal with a general geometry, and are easy-to-implement. They have been proved to be stable.

Reference:

Wu, Xiaojie, and Xiantao Li. "Stable absorbing boundary conditions for molecular dynamics in general domains." arXiv preprint arXiv:1710.09520 (2017)

Movie 1. Plane waves across the boundaries with minor reflections. The color indicates the velocity in the x-direction.

Dynamic atomistic/continuum coupling.

The dynamic coupling method not only absorbs the phonons generated in atomistic regions, but also allows the elastic waves pass across the interface.

This method is based on the Dirichlet-to-Neumann (DtN) map. More variables are needed to make a better approximation of the DtN map. The additional variables help the dynamics 'memorize' the propagation of the low-frequency waves.

Movie 2: One dimensional coupling. High-frequency waves (phonons) are generated in MD region. They are eliminated on the interface by the coupling method. However, the low-frequency waves still are able to cross the interface.

Discrete absorbing boundary conditions for the Schrodinger's equation

Instead of using the coordinate transform technique or discretizing the continuous DtN map, we formulate ABCs from the discrete model (after the discretization by finite difference methods). We aim to provide a type of accurate ABCs when higher order finite difference formulas are adopted.

Figure 3: Numerical solutions of one-dimensional Schrodinger's equaiton with ABCs. The solutions are compared with the exact solution in an infinite region

Simulations of fracture by coupling atomistic-based boundary element method and atomistic model.

The atomistic-based boundary element method (ABEM) is a novel technique to seek approximate solutions to the static problems of crystalline solids. The formulation of ABEM is an analogue to continuous boundary element method (BEM).

ABEM is coupled with the atomistic model to simulate the fracture problems. As a test problem, we simulated 2 billion atoms in a square region. Most atoms in the domain are eliminated by ABEM. Only 2248 atoms are selected as the degrees of freedom. One crack and partial atomistic region are shown in Figure 5.

Reference:

Li, Xiantao. "An atomistic-based boundary element method for the reduction of molecular statics models." Computer Methods in Applied Mechanics and Engineering 225 (2012): 1-13.

Wu, Xiaojie, and Xiantao Li. "Simulations of micron-scale fracture using atomistic-based boundary element method." Modelling and Simulation in Materials Science and Engineering 25.8 (2017): 085008.