Minimal Model for Intermittent Dynamics and "Turbulence" in Many-Body Systems*

Complex systems are known to exhibit emergent properties that are missing on the constituent level. One particular property shared by many seemingly unrelated complex systems is intermittent switching between distinct dynamical states. Inspired by our previous experimental findings [1], here we present computational results for a particle-based system that exhibits intermittent switching between two distinct phases. The emergent dynamics are a direct consequence of coupling between structural disorder arising from particle polydispersity, inertial dynamics, and external forcing. Modelling the orthogonal mechanical energies of the system using ODEs with both noise and coupling terms based on kinetic arguments surprisingly results into predator-prey-like interactions. Such equations have recently been employed to describe intermittent turbulence in a pipe flow [2]. The only non-dimensional number derived from our equations resembles the Reynolds number in fluid flow and accurately predicts where intermittent dynamics are manifested.
1. G.Gogia, and J. C. Burton. PRL,119.17 (2017):178004
2. H-Y. Shih, T-L. Hsieh, and N.Goldenfeld. Nat.Phys. 12.3 (2016):245