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.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)
- Applied Mathematics