Monday, June 17th, 11h30, Room 454 A, Condorcet Building.

Stanisław Żukowski

Laboratoire Matière et Systèmes Complexes MSC, UMR 7057, CNRS & Université Paris Cité

Breakthrough-Induced Loop Formation in Evolving Transport Networks

Abstract : Transport networks, such as jellyfish canal network or river networks, provide key functions in organisms and the environment. They usually contain loops whose significance for the stability and robustness of the network is well documented. However, the dynamics of their formation is usually not considered. Such structures often grow in response to the gradient of an external field. During evolution, extending branches compete for the available flux of the field, which leads to effective repulsion between them and screening of the shorter ones. Yet, in remarkably diverse processes, from the canal system of jellyfish to unstable fluid flows, loops suddenly form near the breakthrough when the longest branch reaches the boundary of the system. We provide a physical explanation for this universal behavior. Using a 1D model, we explain that the appearance of effective attractive forces results from the field drop inside the leading finger as it approaches the outlet. Furthermore, we numerically study the interactions between two fingers, including screening in the system and its disappearance near the breakthrough. Finally, we perform simulations of the temporal evolution of the fingers to show how revival and attraction to the longest finger leads to dynamic loop formation. We compare the simulations to the experiments and find that the dynamics of the shorter finger are well reproduced. Our results demonstrate that reconnection is a prevalent phenomenon in systems driven by diffusive fluxes, occurring both when the ratio of the mobility inside the growing structure to the mobility outside is low and near the breakthrough.

Legend: Jellyfish gastrovascular canal network. New canals appear at the rim and grow towards the stomachs in the center. Red circles mark breakthrough events – sprouts that reconnected to the stomachs (outlet). White dashed circles mark associated reconnections of the shorter sprouts.

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