Through history to growth dynamics: deciphering the evolution of spatial networks

Żukowski, Stanisław; Morawiecki, Piotr; Seybold, Hansjörg; Szymczak, Piotr

doi:10.1038/s41598-022-24656-x

Sci Rep

2022

DOI: 10.1038/s41598-022-24656-x

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Through history to growth dynamics: deciphering the evolution of spatial networks

Stanisław Żukowski

Piotr Morawiecki

Hansjörg Seybold

et al.

Abstract: Many ramified, network-like patterns in nature, such as river networks or blood vessels, form as a result of unstable growth of moving boundaries in an external diffusive field. Here, we pose the inverse problem for the network growth—can the growth dynamics be inferred from the analysis of the final pattern? We show that by evolving the network backward in time one can not only reconstruct the growth rules but also get an insight into the conditions under which branch splitting occurs. Determining the growth … Show more

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2024

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Cited by 4 publications

References 58 publications

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Effects of liquid viscosity and air injection rate on air invasion in a highly compacted granular material

Qin,

Huang,

Wang

et al. 2024

Physics of Fluids

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Using laboratory experiments on a network scale together with numerical simulations on a granular scale, we investigate the displacement process as air invades a highly compacted granular material. Experiments in a vertically placed Hell-Shaw cell reveal a non-monotonic behavior of branching formation as air injection rate Q increases from 0.1 to 50 ml min–1 when the liquid viscosity is less than 22.5 mPa s. In the low-injection-rate region where Q < 1 ml min–1, fractures grow in random directions, and the number of branches increases as the air injection rate decreases. However, after the transition to the high-injection-rate region where Q≥ 1 ml min–1, the number of branches increases with increasing air injection rate. At a given air injection rate, increasing the liquid viscosity from 1.01 to 219 mPa s leads to an increasingly concentrated air flow. The numerical simulations exhibit good agreement with the experimental results. More importantly, they shed light on the physics underlying the growth of the fractures by capturing the distribution of the magnitude of velocity, as well as computing the inter-grain force chains in the granular material. The simulations suggest that a high liquid viscosity concentrates the velocity field and force chains and reduces the speeds and inter-grain forces of the grains adjacent to fractures, while a higher air injection rate increases the grain speeds and inter-grain forces. In addition, the distribution of the forces chains behaviors non-monotonically as the air injection rate decreases, which explains the non-monotonic behavior of branching formation observed in the experiments.

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Effects of liquid viscosity and air injection rate on air invasion in a highly compacted granular material

Qin,

Huang,

Wang

et al. 2024

Physics of Fluids

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Breakthrough-induced loop formation in evolving transport networks

Żukowski,

Cornelissen,

Osselin

et al. 2024

Proc. Natl. Acad. Sci. U.S.A.

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Transport networks, such as vasculature 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 unstable fluid flows to the canal system of jellyfish, 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.

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TheDrosophilatracheal terminal cell as a model for branching morphogenesis

Gavrilchenko,

Simpkins,

Simpson

et al. 2024

Proc. Natl. Acad. Sci. U.S.A.

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The terminal cells of the Drosophila larval tracheal system are perhaps the simplest delivery networks, providing an analogue for mammalian vascular growth and function in a system with many fewer components. These cells are a prime example of single-cell morphogenesis, branching significantly over time to adapt to the needs of the growing tissue they supply. While the genetic mechanisms governing local branching decisions have been studied extensively, an understanding of the emergence of a global network architecture is still lacking. Mapping out the full network architecture of populations of terminal cells at different developmental times of Drosophila larvae, we find that cell growth follows scaling laws relating the total edge length, supply area, and branch density. Using time-lapse imaging of individual terminal cells, we identify that the cells grow in three ways: by extending branches, by the side budding of new branches, and by internally growing existing branches. A generative model based on these modes of growth recapitulates statistical properties of the terminal cell network data. These results suggest that the scaling laws arise from the coupled contributions of branching and internal growth. This study establishes the terminal cell as a uniquely tractable model system for further studies of transportation and distribution networks.

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Through history to growth dynamics: deciphering the evolution of spatial networks

Cited by 4 publications

References 58 publications

Effects of liquid viscosity and air injection rate on air invasion in a highly compacted granular material

Effects of liquid viscosity and air injection rate on air invasion in a highly compacted granular material

Breakthrough-induced loop formation in evolving transport networks

TheDrosophilatracheal terminal cell as a model for branching morphogenesis

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