Physicists explore how fluctuations shape transport networks

Understanding how transport networks, such as river systems, form and develop is essential to optimizing their stability and resilience. It turns out that networks are not all the same. Tree-like structures are convenient for transport, while nets containing loops are more resistant to damage. What conditions favor the formation of loops?

Researchers from the Faculty of Physics at the University of Warsaw and the University of Arkansas sought to answer this question. The findings, published in Physical review papers, show that networks tend to form stable loop structures when flow fluctuations are properly tuned. This discovery will allow us to better understand the structure of dynamic transport networks.

Transport networks, such as blood vessels or river systems, are essential to many natural and man-made systems. Understanding how these networks form and grow is essential for optimizing their stability and resilience.

Even seemingly similar flow systems, such as river deltas, can include different morphologies. The outlet of Wax Lake in Louisiana, USA appears to branch into a tree pattern with smaller river outlets reaching the Atlantic Ocean. On the other hand, the Ganges-Brahmaputra river delta in Bangladesh shows a loop-like topology, with multiple channels connecting the main tributaries. What makes these two systems different is the magnitude of flow fluctuations, driven by an interaction of river flow and tidal currents.

The question of what environmental conditions can induce the formation of loops on tree-like structures has inspired a collaboration of scientists from the Faculty of Physics of the University of Warsaw, Poland, and the University of Arkansas, USA, to investigate the stability of loop-like topologies in networks. of the flow. Research results show that networks tend to remain similar when flow fluctuations remain tuned in a particular way.

“Simple growth rules can often lead to fascinating patterns. Tree-like structures are effective for transport, but networks containing loops are more resilient to damage,” says Prof. Piotr Szymczak from the Faculty of Physics of the University of Warsaw – contributing author of the study. “Understanding the conditions necessary for rings to appear in evolving networks is our long-term goal.”

“River networks can look extremely different depending on the river and the sea – geospatial data provides us with visual evidence on the changing morphologies of river deltas and with new data being collected on flow characteristics we are trying to learn more about the dynamics of their evolution, especially in times of rapid climate change,” notes Prof. John Shaw of the University of Arkansas, who spent his UW sabbatical in Poland thanks to a Fulbright Research Award.

“This publication arose from the fusion of geological observations, the equations of sedimentology, and the mathematical methods of physics.”

“Our collaboration began focused on rivers, but the observations generalize to an extremely large class of transportation networks,” says Radost Waszkiewicz, co-lead author of the paper and a Ph.D. student in the UW Faculty of Physics.

Scientists have found that the stability of loops in these networks depends on the interplay between geometric constraints and flow fluctuations. They found that loops require fluctuations in the relative magnitude of flow between nodes, not just temporal changes in flow at a single node, and that loops are most stable when the fluctuations are neither too small nor too large compared to the component of constant flow.

“If the fluctuation pattern changes due to external factors such as human intervention or climate change, new loops within transport networks may appear or disappear, transforming the shape of the network,” concludes Prof. Maciej Lisicki from the Faculty of Physics, UW.

“We hope this observation will attract more precise measurements in natural systems and take us a step further in understanding the dynamic remodeling of transport networks.”