Research Interest

 

My recent research has been focused on multiscale modeling of materials. The  main objectives are to,

  • extract material properties from atomistic models,

  • understand the energetics and dynamics of material defects,

  • design novel methods to model material behavior across different scales,

  • and develop effective continuum models.

I am currently involved in the following projects:

  1. General multiscale methods for solids

    • multiscale method for the dynamics of solids
      at finite temperature,

    • numerical analysis of multiscale methods,

  2. Boundary conditions for molecular dynamic simulations of crystalline solids

    • absorbing boundary conditions for molecular
      dynamic simulations of solids,

    • boundary conditions for molecular dynamics
      at finite temperature,

    • analysis of boundary conditions for molecular
      dynamics,

    • boundary conditions for molecular dynamics
      with applied stress,

  3. Martensitic phase transformations

    • interfacial energy of phase boundaries,

    • kinetics of twin boundary dynamics,

    • multiscale defect tracking method,

  4. Dynamic fracture mechanics

    5. Crack propagation

    • multiscale simulation of cracks under rapid loading,

    • kinetics of crack propagation.

     

    My PhD research involves, 

    • numerical methods for weakly hyperbolic systems,

    • multiphase phenomena in the small dispersion limits,

    • computing multi-valued solutions for some hyperbolic PDEs.

    Here are some specific projects that we have worked on,

    1. kinetic schemes for pressure-less gas dynamics,

    2. multiphase solution of the Schrodinger equation  in the semi-classical regime,

    3. multi-valued solution of the Euler-Poisson system with application to klystrons.

     

Curriculum Vita

Research Grant

NSF DMS-0609610: Boundary Conditions for Molecular Dynamics Simulations ofSolids,
06/15/2006 -- 05/31/2009, $126,371, PI.
Sloan Fellowship: 09/16/08 -- 09/15/09, $45,000.

Recent presentations:



Research Papers

  • Variational boundary condition for molecular dynamics: Treatment of the loading conditions. submitted.

  • On the stability of boundary conditions for molecular dynamics. submitted.

  • The Discontinuous Galerkin Method for the Multiscale Modeling of Dynamics of Crystalline Solids. (with Wei Wang and Chi-Wang Shu), SIAM: Multiscale Modeling and Simulation, Vol 7, 294-320. .

  • Boundary conditions for molecular dynamics simulations of solids I: Treatment of the heat bath. (with Weinan E), Phys. Rev. B, vol 76, 2007, 104107. .

  • Boundary conditions for molecular dynamics simulations of solids: a comparative study. (with Jerry Z. Yang), Phys. Rev. B, vol 73, 2006, 224111. .

  • Boundary conditions for molecular dynamics simulations of solids at low temperature. (with Weinan E), Comm. Com. Phys., 1 (2006), 136--176. PDF version .

  • Multiscale modeling of dynamics of solids at finite temperature .
    (with Weinan E), J. Mech. Phys. solids, (53) 2005, 1650-1685..
    Abstract , download the preprint version :
     
  • Error estimate for a multiscale method in Gas Dynamics
    (with Weinan E), method of analysis and application, vol 11, 2005, 557--572..
    Abstract , download the preprint version :
     
  • Multiscale modeling for crystalline solids.
    (with Weinan E), Handbook of multiscale material modeling (edited by Sidney Yip), 2004.
    Abstract , download the preprint version :
  • Some recent progress on multiscale modeling.
    (with Weinan E and Eric Vanden-Eijnden), lecture notes in Computational Science and Engineering, Vol. 3, 3--22.
    Abstract , download the preprint version :
  • 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.
    Abstract , download the preprint version :
     
  • On Two Moment Systems for computing multiphase semiclassical limits of the Schrödinger Equation
    (with Shi Jin and Laurent Gosse), Math. Model Methods Appl. Sci., vol 3, No. 12, 1689-1723, 2003 .
    Abstract.
     
  • Multi-phase Computations for semiclassical limits of Schrödinger Equation and related problems: Whitham vs Wigner.
    (with Shi Jin), Physica D, 182, 46-85, 2003.
    Abstract , download the preprint version :
     
  • Numerical solutions of Pressure-less Gas Equations
    (with Francois Bouchut and Shi Jin), SIAM J. Num. Anal.. 41, 135-158, 2003.
    Abstract, download the preprint version :
     

 

Recent Research Activities

  • May 2004, SIAM conference, L.A.

  • Oct. 2004, 2nd International Conference on Multiscale Materials Modeling (MMM-II), Los Angeles.

  • Nov. 2004, Future Challenges in Multiscale Modeling and Simulation, IMA.

  • May 2005, Multiscale Modeling in Solids, Universite de Montreal, Canada.

  • Jun. 2005, Multiscale Modeling and Simulation of Materials, Baton Rouge, Louisiana.

  • Nov. 2005, Bridging Time and Length Scales in Materials Science and Biophysics, UCLA.

Links

Citations and preprint

Technical Links