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Last update Sep 16, 2009.  

A. Submitted and Published journal papers:
  1. X. Li, Coarse-graining molecular dynamics models using an extended Galerkin projection, submitted.

  2. X. Li and P. Ming, On the effect of ghost force in the quasicontinuum method: dynamic problems in one dimension, submitted.

  3. X. Li, Boundary condition for molecular dynamics models of solids: A variational formulation based on lattice Green's functions, submitted.



  1. X. Li, A Bifurcation Study of Crack Initiation and Kinking, The European Physical Journal B, Accepted for publication.

  2. J. Z. Yang, X. Wu and X. Li, A generalized Irving-Kirkwood formula for the calculation of stress in molecular dynamics models, Journal of Chemical Physics, 137, 134104 (2012).

  3. X. Li, An atomistic-based boundary element method for the reduction of the molecular Statics Models. Computer Methods in Applied Mechanics and Engineering .
    Vol 225, 1-13, 2012
  4. X. Li, A coarse-grained molecular dynamics model for crystalline solids, Int. J. Num. Meth. Eng. Vol 83, 986--997, 2010. [download preprint]

  5. X. Li, J.Z. Yang, and W. E, A multiscale coupling method for the modeling of dynamics of solids with application to brittle cracks, J. Comp. Phys. Vol 229, 3970-3987, 2010. [download preprint]

  6. X. Li, Efficient boundary condition for molecular statics models of solids Phys. Rev. B , Vol 80, 104112, 2009.

  7. X. Li, On the stability of boundary conditions for molecular dynamics. Journal of Computational and Applied Mathematics, Vol 231, 493-505, 2009.

  8. X. Li, Variational boundary condition for molecular dynamics: Treatment of the loading conditions. Journal of Computational Physics, Vol 227, 10078--10093, 2008.

  9. W. Wang, X. Li and C.W. Shu, The Discontinuous Galerkin Method for the Multiscale Modeling of Dynamics of Crystalline Solids. SIAM: Multiscale Modeling and Simulation, Vol 7, 294-320, 2008. .

  10. X. Li and W. E, Boundary conditions for molecular dynamics simulations of solids I: Treatment of the heat bath. Phys. Rev. B, vol 76, 104107, 2007.

  11. W. E, B. Engquist, X. Li, Weiqing Ren and E. Vanden-Eijnden, Heterogeneous multiscale methods: A review Commun. Comput. Phys. Vol 2, 367, 2007.

  12. J. Z. Yang and X. Li, Boundary conditions for molecular dynamics simulations of solids: a comparative study. Phys. Rev. B, vol 73, 224111, 2006. .

  13. X. Li and W. E, Boundary conditions for molecular dynamics simulations of solids at low temperature. Comm. Com. Phys., Vol 1, 136--176, 2006. PDF version .

  14. X. Li and W. E, Multiscale modeling of dynamics of solids at finite temperature .
    J. Mech. Phys. solids, Vol 53, 1650-1685, 2005..

  1. Error estimate for a multiscale method in Gas Dynamics
    (with Weinan E), method of analysis and application, Vol 11, 557--572, 2005..

  2. Multiscale modeling for crystalline solids.
    (with Weinan E), Handbook of multiscale material modeling (edited by Sidney Yip), 1491--1596, 2004.

  3. Some recent progress on multiscale modeling.
    (with Weinan E and Eric Vanden-Eijnden), lecture notes in Computational Science and Engineering, Vol. 3, 3--22, 2004..

  1. An Eulerian method for computing multi-valued solutions of the Euler-Poisson equations
    (with John G. Wohlbier, Shi Jin and John Booske), Phys. Rev. E 70, 016502, 2004.

  2. On Two Moment Systems for computing multiphase semiclassical limits of the Schroedinger Equation
    (with Shi Jin and Laurent Gosse), Math. Model Methods Appl. Sci., vol 3, No. 12, 1689-1723, 2003 .
  3. Multi-phase Computations for semiclassical limits of Schroedinger Equation and related problems: Whitham vs Wigner.
    (with Shi Jin), Physica D, 182, 46-85, 2003.

  4. Numerical solutions of Pressure-less Gas Equations
    (with Francois Bouchut and Shi Jin), SIAM J. Num. Anal. 41, 135-158, 2003

B. Reports and Conference Proceedings:
  1. Coarse-graining molecular dynamics.
    Mathematisches Forschungsinstitut Oberwolfach, Report 21, 2008, page 1148.

  2. Interface conditions for coupled atomistic and continuum models of solids for dynamics problems at finite temperature
    Material Research Society Proceedings, Paper no. 0978-GG06-02, 2006.