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Résumé |
Understanding the flow of discrete elements through networks is a challenge for non-linear physicists and is of importance for diverse phenomena, including microfluidics for controlled droplet traffic, blood flows for functioning cardiovascular systems, and even road traffic for optimized road networks. Addressing this issue requires a description of the mechanisms that govern flow partitioning at a node, the key element of these systems. In most cases, splitting rules are complex since they often involve either human decision-making or noise. Droplet traffic thus appears as a model system since a droplet reaching a node simply flows in the arm having the smallest hydrodynamic resistance. Despite this robust and simple rule, this paradigmatic system exhibits complex dynamics, also observed in traffic flows and in cellular automata, resulting from iterations of simple rules and time-delayed feedback. The presence of droplets in a channel modifies its hydrodynamic resistance, so that the path selection of a droplet at a node is affected by the trajectories of the previous droplets. This results in the appearance of periodic patterns which are common to any traffic flow. Thus the widely-studied situation of a droplet reaching a single node leads to the emergence of a wealth of bifurcations between different periodical partitioning regimes with discrete periods and aperiodical regimes. I propose here to present a simple theoretical background and confront its predictions to both recent numerical and experimental findings. |
