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Random organization in periodically driven systems

Abstract

Understanding self-organization is one of the key tasks for controlling and manipulating the structure of materials at the micro- and nanoscale. In general, self-organization is driven by interparticle potentials and is opposed by the chaotic dynamics characteristic of many driven non-equilibrium systems. Here we introduce a new model that shows how the irreversible collisions that generally produce diffusive chaotic dynamics can also cause a system to self-organize to avoid future collisions. This can lead to a self-organized non-fluctuating quiescent state, with a dynamical phase transition separating it from fluctuating diffusing states. We apply the model to recent experiments on periodically sheared particle suspensions where a transition from reversible to irreversible behaviour was observed. New experiments presented here exhibit remarkable agreement with this simple model. More generally, the model and experiments provide new insights into how driven systems can self-organize.

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Figure 1: Schematic representation of one cycle of the collision model, in which particles that collide when sheared are given small random displacements.
Figure 2: Simulation results for the 2D model, showing particle activity above and below the strain threshold.
Figure 3: Simulation results for the characteristic time τ to reach steady state as a function of the strain amplitude γ0 for an area fraction of φ=0.20 and 1,000 particles.
Figure 4: Experimental results showing particle activity above and below the strain threshold.
Figure 5: Experimental results for the characteristic time τ to reach steady state as a function of the strain amplitude γ0 for a volume fraction φ=0.30.

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Acknowledgements

We thank J.-P. Bouchaud for suggesting the relevance of directed percolation and related models. We also benefited from discussions with E. Ben-Naim, S. Ramaswamy and G. I. Menon. This work was partially supported by National Science Foundation grants DMR 0604295 and DMR 0243001, and by a Lavoisier grant from the French government.

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Correspondence to D. J. Pine.

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Corté, L., Chaikin, P., Gollub, J. et al. Random organization in periodically driven systems. Nature Phys 4, 420–424 (2008). https://doi.org/10.1038/nphys891

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