Abstract
In natural settings, intermittent dynamics are ubiquitous and often arise from a coupling between external driving and spatial heterogeneities. A well-known example is the generation of transient, turbulent puffs of fluid through a pipe with rough walls. Here we show how similar dynamics can emerge in a discrete, crystalline system of particles driven by noise. Polydispersity in particle masses leads to localized vibrational modes that effectuate a transition to a gas-like phase. A minimal model for the evolution of the system's mechanical energies exhibits quasi-cyclic oscillations, and a single, dimensionless number captures the essential features of the intermittent dynamics, analogous to the Reynolds number for pipe flow.
Highlights
The dynamics of complex systems that are driven away from equilibrium are usually characterized by minor fluctuations around some steady state, which are abruptly punctuated by a “big jump” [1], leading to a dramatically different state
Since laminar flow in a pipe is linearly stable for all Reynolds numbers (Re) [7], the emergence of turbulence requires a finite disturbance, such as rough walls [8] or other localized perturbations [9,10]
We introduce a minimal model for the evolution of the total mechanical energy in the vertical and horizontal directions, reminiscent of stochastic predator-prey systems used to describe turbulence [14]
Summary
The dynamics of complex systems that are driven away from equilibrium are usually characterized by minor fluctuations around some steady state, which are abruptly punctuated by a “big jump” [1], leading to a dramatically different state. The main challenge, as in many other complex systems, lies in relating the local spatiotemporal interactions to the global emergent behavior We illustrate this connection in a simple, many-body system that manifests intermittent “turbulence.” A spatially extended, horizontal layer of charged particles, forced vertically by white noise, continuously switches between crys-. We introduce a minimal model for the evolution of the total mechanical energy in the vertical and horizontal directions, reminiscent of stochastic predator-prey systems used to describe turbulence [14]. In both the simulation and the model, a single dimensionless number that incorporates external driving, dissipation, and disorder, successfully predicts the intermittent dynamical regime
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