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Proceedings Paper

Co-ordinate transforms underpin multiscale modelling and reduction in deterministic and stochastic systems
Author(s): A. J. Roberts
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Paper Abstract

A persistent feature of complex systems in engineering and science is the emergence of macroscopic, coarse grained, coherent behaviour from microscale interactions. In current modeling, ranging from ecology to materials science, the underlying microscopic mechanisms are known, but the closures to translate microscale knowledge to a large scale macroscopic description are rarely available in closed form. Kevrekidis proposes new 'equation free' computational methodologies to circumvent this stumbling block in multiscale modelling. Nonlinear coordinate transforms underpin analytic techniques that support these computational methodologies. But to do so we must cross multiple space and time scales, in both deterministic and stochastic systems, and where the microstructure is either smooth or detailed. Using examples, I describe progress in using nonlinear coordinate transforms to illuminate such multiscale modelling issues.

Paper Details

Date Published: 5 January 2008
PDF: 11 pages
Proc. SPIE 6802, Complex Systems II, 68021F (5 January 2008); doi: 10.1117/12.767596
Show Author Affiliations
A. J. Roberts, Univ. of Southern Queensland (Australia)

Published in SPIE Proceedings Vol. 6802:
Complex Systems II
Derek Abbott; Tomaso Aste; Murray Batchelor; Robert Dewar; Tiziana Di Matteo; Tony Guttmann, Editor(s)

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