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

Poster

*Complex Systems II: SPIE Symposium on Microelectronics, MEMS, and Nanotechnology 2007.*Canberra, Australia 05 - 07 Dec 2007 United States. SPIE. https://doi.org/10.1117/12.767596

Paper/Presentation Title | Co-ordinate transforms underpin multiscale modelling and reduction in deterministic and stochastic systems |
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Presentation Type | Poster |

Authors | |

Author | Roberts, A. J. |

Editors | Abbott, Derek, Aste, Tomaso, Batchelor, Murray and Dewar, Robert |

Journal or Proceedings Title | Proceedings of SPIE (International Society for Optical Engineering) |

Journal Citation | 6802, pp. C292-C307 |

Number of Pages | 16 |

Year | 2008 |

Publisher | SPIE |

Place of Publication | United States |

ISSN | 0277-786X |

ISBN | 9780819469731 |

Digital Object Identifier (DOI) | https://doi.org/10.1117/12.767596 |

Web Address (URL) of Paper | https://www.spiedigitallibrary.org/conference-proceedings-of-spie/6802/1/Co-ordinate-transforms-underpin-multiscale-modelling-and-reduction-in-deterministic/10.1117/12.767596.short?SSO=1 |

Conference/Event | Complex Systems II: SPIE Symposium on Microelectronics, MEMS, and Nanotechnology 2007 |

Event Details | Complex Systems II: SPIE Symposium on Microelectronics, MEMS, and Nanotechnology 2007 Event Date 05 to end of 07 Dec 2007Event Location Canberra, Australia |

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. |

Keywords | fast-slow systems; multiscale modelling; normal form; singular perturbations; stochastic systems |

ANZSRC Field of Research 2020 | 490510. Stochastic analysis and modelling |

519901. Complex physical systems | |

401602. Composite and hybrid materials | |

Public Notes | This is a poster paper. |

Byline Affiliations | Department of Mathematics and Computing |

Institution of Origin | University of Southern Queensland |

https://research.usq.edu.au/item/q135z/co-ordinate-transforms-underpin-multiscale-modelling-and-reduction-in-deterministic-and-stochastic-systems

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