A Nonlinear Dynamical Analysis of History Dependence in Granular Media

Researchers have observed that key properties of granular materials, including the density at which systems jam, depend on the details of their history, such as the compression rate or the initial compression density. In this work, we employ the tools of nonlinear dynamics, particularly Lyapunov exponents and vectors, to provide new insights on history dependence in two-dimensional systems of soft disks. We characterize how the Lyapunov spectra differ when systems are prepared using various protocols, focusing especially on the transition from chaotic to non-chaotic behavior. Further, using Lyapunov vectors, we quantify how the shapes and sizes of the most important dynamical modes are affected by the preparation protocol.