Co-ordinate transforms underpin multiscale modelling and reduction in deterministic and stochastic systems

Roberts, A. J. (2008) Co-ordinate transforms underpin multiscale modelling and reduction in deterministic and stochastic systems. In: Complex Systems II: SPIE Symposium on Microelectronics, MEMS, and Nanotechnology 2007, 5-7 Dec 2007, Canberra, Australia.

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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.

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Item Type: Conference or Workshop Item (Commonwealth Reporting Category E) (Poster)
Refereed: Yes
Item Status: Live Archive
Additional Information: This is a poster paper.
Faculty / Department / School: Historic - Faculty of Sciences - Department of Maths and Computing
Date Deposited: 18 Mar 2018 23:53
Last Modified: 10 Aug 2018 02:53
Uncontrolled Keywords: fast-slow systems; multiscale modelling; normal form; singular perturbations; stochastic systems
Fields of Research : 01 Mathematical Sciences > 0104 Statistics > 010406 Stochastic Analysis and Modelling
02 Physical Sciences > 0299 Other Physical Sciences > 029902 Complex Physical Systems
09 Engineering > 0912 Materials Engineering > 091202 Composite and Hybrid Materials
Socio-Economic Objective: E Expanding Knowledge > 97 Expanding Knowledge > 970109 Expanding Knowledge in Engineering
Identification Number or DOI: 10.1117/12.767596

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