Multiscale Modeling Of Crystalline Solids

  • Weinan E
  • Xiantao Li

Abstract

Multiscale modeling and computation has recently become one of the most active research areas in applied science. With rapidly growing computing power, we are increasingly more capable of modeling the details of physical processes. Nevertheless, we still face the challenge that the phenomena of interest are oftentimes the result of strong interaction between multiple spatial and temporal scales, and the physical processes are described by radically different models at different scales.

Keywords

Strain Energy Density Crystalline Solid Atomistic Region Born Rule Microscale Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    E.B. Tadmor, M. Ortiz, and R. Phillips, “Quasicontinuum analysis of defects in crystals,” Phil. Mag. A, 73, 1529, 1996.CrossRefADSGoogle Scholar
  2. [2]
    R.E. Miller and E.B. Tadmor, “The quasicontinuum method: overview, applications and current directions,” J. Comput.-Aided Mater. Des., in press, 2003.Google Scholar
  3. [3]
    J. Knap and M. Ortiz, “An analysis of the quasicontinuum method,” J. Mech. Phys. Solid, 49, 1899, 2001.MATHCrossRefADSGoogle Scholar
  4. [4]
    V. Shenoy and R. Phillips, “Finite temperature quasicontinuum methods,” Mat. Res. Soc. Symp. Proc., 538, 465, 1999.Google Scholar
  5. [5]
    F.F. Abraham, J.Q. Broughton, N. Bernstein, and E. Kaxiras, “Spanning the continuum to quantum length scales in a dynamic simulation of brittle fracture,” Europhys. Lett., 44(6), 783, 1998.CrossRefADSGoogle Scholar
  6. [6]
    J.Q. Broughton, F.F. Abraham, N. Bernstein, and E. Kaxiras, “Concurrent coupling of length scales: methodology and application,” Phys. Rev. B, 60(4), 2391, 1999.CrossRefADSGoogle Scholar
  7. [7]
    R.E. Rudd and J.Q. Broughton, “Coarse-grained molecular dynamics and the atomic limit of finite element,” Phys. Rev. B, 58(10), R5893, 1998.CrossRefADSGoogle Scholar
  8. [8]
    R.E. Rudd and J.Q. Broughton, Unpublished, 2000.Google Scholar
  9. [9]
    X.T. Li and W.E, “Multiscal modeling of solids,” Preprint, 2003.Google Scholar
  10. [10]
    W.E and B. Engquist, “The heterogeneous multi-scale methods,” Comm. Math. Sci., 1(1), 87, 2002.MathSciNetGoogle Scholar
  11. [11]
    E. Godlewski, and P.A. Raviart, Numerical Approximation of Hyperbolic systems of Conservation Laws, Springer-Verlag, New York, 1996.MATHGoogle Scholar
  12. [12]
    H. Nessyahu and E. Tadmor, “Nonoscillatory central differencing for hyperbolic conservation laws,” J. Comp. Phys., 87(2), 408, 1990.MATHCrossRefMathSciNetADSGoogle Scholar
  13. [13]
    G.J. Wagner, G.K. Eduard, and W.K. Liu, Molecular Dynamics Boundary Conditions for Regular Crystal Lattice, Preprint, 2003.Google Scholar
  14. [14]
    W.E and Z. Huang, “Matching conditions in atomistic-continuum modeling of material,” Phys. Rev. Lett., 87(13), 135501, 2001.CrossRefADSGoogle Scholar
  15. [15]
    W.E and Z. Huang, “A dynamic atomistic-continuum method for the simulation of crystalline material,” J. Comp. Phys., 182, 234, 2002.MATHCrossRefADSGoogle Scholar

Copyright information

© Springer 2005

Authors and Affiliations

  • Weinan E
    • 1
  • Xiantao Li
    • 1
  1. 1.Program in Applied and Computational MathematicsPrinceton UniversityUSA

Personalised recommendations