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Topological Invariants in Microscopic Transport on Rough Landscapes: Morphology, Hierarchical Structure, and Horton Analysis of Riverlike Networks of Vortices

A. P. Mehta·C. Reichhardt·C. J. Olson·Franco Nori
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Abstract

River basins as diverse as the Nile, the Amazon, and the Mississippi satisfy certain topological invariants known as Horton's laws. Do these macroscopic (up to 10^3 km) laws extend to the micron scale? Through realistic simulations, we analyze the morphology and statistical properties of networks of vortex flow in flux-gradient-driven superconductors. We derive a phase diagram of the different network morphologies, including one in which Horton's laws of length and stream number are obeyed -- even though these networks are about 10^9 to 10^15 times smaller than geophysical river basins.

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A. P. Mehta, C. Reichhardt, C. J. Olson, Franco Nori. 1999-06-28. Topological Invariants in Microscopic Transport on Rough Landscapes: Morphology, Hierarchical Structure, and Horton Analysis of Riverlike Networks of Vortices. https://doi.org/10.1103/physrevlett.82.3641

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