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Title: Characterizing chaotic dynamics from simulations of large strain behavior of a granular material under biaxial compression
Authors: Small, M
Walker, DM
Tordesillas, A
Tse, CKM 
Keywords: Chaos
Time series
Issue Date: Mar-2013
Publisher: American Institute of Physics
Source: Chaos, Mar. 2013, v. 23, no. 1, 013113, p. 1-14 How to cite?
Journal: Chaos 
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 the original data. Using this approach, we not only build a model but also verify the performance of that model. The methodology is applied to simulations of a granular assembly under compression. In particular, we choose a single time series recording of bulk measurements of the stress ratio in a biaxial compression test of a densely packed granular assembly—observed during the large strain or so-called critical state regime in the presence of a fully developed shear band. We show that the observed behavior may best be modeled by structures capable of exhibiting (hyper-) chaotic dynamics.
ISSN: 1054-1500
EISSN: 1089-7682
DOI: 10.1063/1.4790833
Rights: © 2013 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Michael Small et al., Chaos: an interdisciplinary journal of nonlinear science 23, 013113 (2013) and may be found at
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