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September 2007 Seamless multiscale modeling via dynamics on fiber bundles
Weinan E, Jianfeng Lu
Commun. Math. Sci. 5(3): 649-663 (September 2007).

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.

Citation

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Weinan E. Jianfeng Lu. "Seamless multiscale modeling via dynamics on fiber bundles." Commun. Math. Sci. 5 (3) 649 - 663, September 2007.

Information

Published: September 2007
First available in Project Euclid: 29 August 2007

zbMATH: 1133.65029
MathSciNet: MR2352335

Subjects:
Primary: 65J05
Secondary: 35B27 , 74B20 , 74Q05 , 76M25

Keywords: fiber bundle , multiscale modeling , seamless

Rights: Copyright © 2007 International Press of Boston

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Vol.5 • No. 3 • September 2007
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