Journal article

Characterizing chaotic dynamics from simulations of large strain behavior of a granular material under biaxial compression

Michael Small, David M Walker, Antoinette Tordesillas, Chi K Tse

CHAOS | AMER INST PHYSICS | Published : 2013

Abstract

For a given observed time series, it is still a rather difficult problem to provide a useful and compelling description of the underlying dynamics. The approach we take here, and the general philosophy adopted elsewhere, is to reconstruct the (assumed) attractor from the observed time series. From this attractor, we then use a black-box modelling algorithm to estimate the underlying evolution operator. We assume that what cannot be modeled by this algorithm is best treated as a combination of dynamic and observational noise. As a final step, we apply an ensemble of techniques to quantify the dynamics described in each model and show that certain types of dynamics provide a better match to th..

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Grants

Awarded by Hong Kong University Grants Council


Awarded by US Army Research Office


Awarded by Australian Research Council


Awarded by Australian Research Council Future Fellowship


Funding Acknowledgements

This work was funded by a Hong Kong University Grants Council grant under the General Research Fund: grant number PolyU 5262/11E. This work was partially supported by US Army Research Office (W911NF-11-1-0175), the Australian Research Council (DP0986876 and DP120104759) and the Melbourne Energy Institute (AT, DMW). MS is supported by an Australian Research Council Future Fellowship (FT110100896) and would like to thank the Melbourne Energy Institute for travel support. We thank Dr John Peters for useful discussions and Mr Tuan Tran for the software implementation to calculate local Lyapunov exponents.