Consistent Embedding: A Theoretical Framework for Multiscale Modeling

  • Keith Runge
Conference paper
Part of the Conference Proceedings of the Society for Experimental Mechanics Series book series (CPSEMS)


A fundamental framework for the undertaking of computational science provides clear distinctions between theory, model, and simulation. Consistent embedding provides a set of principles which when appropriately applied can create multi-scale models that capture the physical behavior of more computationally challenging methods within methods that are more easily computed. The consistent embedding methodology is illustrated within the context of brittle fracture for two serial and one concurrent multi-scale modeling examples. The examples demonstrate how predictive modeling hierarchies can be established.


Quantum Chemical Brittle Fracture Multiscale Modeling Newtonian Dynamic Fundamental Framework 
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  1. 1.
    Trickey, S. B., Yip, S., Cheng, H.-P., Runge, K., and Deymier, P. A. A perspective on multiscale simulation: Toward understanding water-silica, J. Computer-Aided Mat. Design 13, 75 (2006).CrossRefGoogle Scholar
  2. 2.
    Taylor, C. E., Cory, M. G., Bartlett, R. J. and Thiel, W., The transfer Hamiltonian: a tool for large scale simulations with quantum mechanical forces, Comp. Mater. Sci. 27, 204 (2003).CrossRefGoogle Scholar
  3. 3.
    van Beest, B. W. H, Kramer, G. J. and van Santen, R. A., Force fields for silicas and aluminophosphates based on ab initio calculations, Phys. Rev. Lett. 64, 1955 (1990).CrossRefGoogle Scholar
  4. 4.
    Tsuneyuki, S., Tsukada, M., Aoki, H. and Matsui, Y., First-Principles Interatomic Potential of Silica Applied to Molecular Dynamics, Phys. Rev. Lett. 61, 869 (1988).CrossRefGoogle Scholar
  5. 5.
    Tsuneyuki, S., Tsukada, M., Aoki, H. and Matsui, Y., Molecular-dynamics study of the α to β structural phase transition of quartz, Phys. Rev. Lett. 64, 776 (1990).CrossRefGoogle Scholar
  6. 6.
    Mallik, A., Runge, K., Cheng, H.-P. and Dufty, J. W., Constructing a Small Strain Potential for Multi-Scale Modeling, Molecular Simulation 31, 695 (2005).CrossRefGoogle Scholar
  7. 7.
    Mallik, A., Taylor, D. E., Runge, K., Dufty, J. W. and Cheng, H.-P., Procedure for building a consistent embedding at the QMCM interface, J. Computer-Aided Mat. Design 13, 45 (2006).CrossRefGoogle Scholar

Copyright information

© Springer Science+Businees Media, LLC 2011

Authors and Affiliations

  • Keith Runge
    • 1
  1. 1.Quantum Theory ProjectUniversity of FloridaGainesvilleUnited States

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