Seamless multiscale modeling via dynamics on fiber bundles

E. Weinan, Jianfeng Lu

Research output: Contribution to journalArticle

12 Scopus citations

Abstract

We present a general mathematical framework for modeling the macroscale behavior of a multiscale system using only microscale models, by formulating the effective macroscale models as dynamic models on the underlying fiber bundles. This framework allows us to carry out seamless multiscale modeling using traditional numerical techniques. At the same time, they give rise to an interesting mathematical structure and new interesting mathematical problems. We discuss several examples from homogenization problems, continuum modeling of solids based on atomistic or electronic structure models, macroscale behavior of interacting diffusion, and continuum modeling of complex fluids based on kinetic and Brownian dynamics models.

Original languageEnglish (US)
Pages (from-to)649-663
Number of pages15
JournalCommunications in Mathematical Sciences
Volume5
Issue number3
DOIs
StatePublished - 2007

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Keywords

  • Fiber bundle
  • Multiscale modeling
  • Seamless

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