Last update Dec 16, 2014.  

Manuscripts in preparation:

  1. On the microscopic origin of non-Fourier heat conduction models.

  2. On the fundamental mechanism of the Collapse and Recovery of a Single-wall Carbon Nanotube

A. Submitted and Published journal papers:

  1. With Weiqi Chu, On the asymptotic behavior of the kernel function of the Generalized Langevin equation -- a one-dimensional lattice model. submitted.

  2. With Weiqi Chu, The Mori-Zwanzig formalism for the derivation of a fluctuating heat conduction model from molecular dynamics, submitted.

  3. With Adam Telatovich, The strong convergence of operator-splitting methods for the Langevin dynamics model, submitted.

  4. With J. Harlim and H. Zhang, A Parameter Estimation Method Using Linear Response Statistics, Journal of Statistical Physics, Vol 168, 146-170, 2017.

  5. With L Ma and C Liu, Fluctuation-Dissipation Theorem Consistent Approximation of the Langevin Dynamics Model, Comm. Math. Sci., in press.

  6. With L Lin and J Lu, PEXSI-$\Sigma$: A Green's function embedding method for Kohn-Sham density functional theory, Annals of Mathematical Sciences and Applications, in press.

  7. With H Lei and N Baker, Data-driven parameterization of the generalized Langevin equation, Proc. Natl. Acad. Sci., 1609587113.

  8. With L. Ma and C. Liu, From Generalized Langevin Equations to Brownian Dynamics and Embedded Brownian Dynamics, Journal of Chemical Physics, Vol 145, 114102, 2016.

  9. With L. Ma and C. Liu, Derivation and approximation of coarse-grained dynamics from Langevin dynamics, Journal of Chemical Physics, 145, 204117 (2016).

  10. With Xiaojie Wu, Simulations of Micron-scale Fracture using Atomistic-based Boundary Element Method, submitted.

  11. With Zhen Li, Xin Bian, and George Em Karniadakis, Incorporation of memory effects in coarse-grained modeling via the Mori-Zwanzig formalism , Journal of Chemical Physics, 143, 243128 (2015).

  12. With Jerry Z Yang, and Cheng Yuan, An effective and easy-to-implement boundary condition for molecular dynamics simulations, submitted.

  13. With L Wu and G Lin, The Mori-Zwanzig formalism for coarse-graining molecular dynamics models: A quasi-harmonic approximation, submitted.

  14. With Jianfeng Lu, Traction Boundary Conditions for Molecular Static Simulations, Computer Methods in Applied Mechanics and Engineering, Vol 308, 310--329, 2016.

  15. With J. Harlim, Parametric reduced models for the nonlinear Schrodinger equation, Physical Review E, 91, 053306.

  16. With C. Liang and X. Yuan, Some New Symplectic Multiple Timestepping Methods for Multiscale Molecular Dynamics Models, submitted.

  17. With Jingrun Chen and Carlos García-Cervera, An atomistic/continuum coupling method using enriched bases, Multiscale Modeling and Simulations, 13, 766-789, 2015.

  1. Heat conduction in nanoscale materials: A statistical-mechanics derivation of the local heat flux, Physical Review E, 90 032112 (2014) .

  2. With Xiaojie Wu, On Consistent Definitions of Momentum and Energy Fluxes for Molecular Dynamics Models with Multi-body Interatomic Potentials, Modelling and Simulation in Materials Science and Engineering, 23, 015003, 2015.

  3. With M. Chen and C. Liu, Computation of the Memory Functions in the Generalized Langevin Models for Collective Dynamics of Macromolecules, J. Chemical Physics, Vol 141 064112, 2014.

  4. A numerical study of crack initiation in a bcc iron system based on dynamic bifurcation theory, J. Appl. Phys.. (116), 164314 (2014).

  1. With P. Ming, A study on the quasiconinuum approximations of a one-dimensional fracture model, SIAM Multiscale Modeling and Simulation, 12, 1379-1400, 2014.

  2. With J.Z. Yang, C. Mao and C. Liu, On the Cauchy-Born Approximation at Finite Temperature, Computational Materials Science, 99, 21-28, 2015.

  3. With J.Z. Yang and X. Wu, Accurate Evaluations of Strain and Stress in Atomistic Simulations of Crystalline Solids, Modelling and Simulation in Materials Science and Engineering, 22, Page 045008, 2014.

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

  1. X. Li, Coarse-graining molecular dynamics models using an extended Galerkin projection, International Journal for Numerical Methods in Engineering, Vol 99, pages 157--182, 2014.

  2. X. Li and P. Ming, On the effect of ghost force in the quasicontinuum method: dynamic problems in one dimension, Commun. Comput. Phys., 15 (2014), pp. 647-676.

  3. X. Li, A Bifurcation Study of Crack Initiation and Kinking, The European Physical Journal B, 86, 258, 2013.

  4. 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).

  5. 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
  6. X. Li, A coarse-grained molecular dynamics model for crystalline solids, Int. J. Num. Meth. Eng. Vol 83, 986--997, 2010. [download preprint]

  7. 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]

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

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

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

  11. 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. .

  12. 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.

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

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

  15. 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 .

  16. 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, Book Chapters and Conference Proceedings:

  1. Introduction to molecular dynamics simulations.
    Lecture Notes Series, Multiscale Modeling and Analysis for Materials Simulation, Institute for Mathematical Sciences, National University of Singapore: Volume 22, 95-146, 2011.

  2. Coarse-graining molecular dynamics.
    Mathematisches Forschungsinstitut Oberwolfach, Report 21, 2008, page 1148.

  3. 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.