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

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.

arXiv comment4 pages, 4 figures

References in corpus (4)

• Superconducting vortex avalanches, voltage bursts, and vortex plastic flow: Effect of the microscopic pinning landscape on the macroscopic properties
• Vortex Plastic Flow, $B(x,y,H(t)),M(H(t)),J_c(B(t))$, Deep in the Bose Glass and Mott-Insulator Regimes
• Fractal Networks, Braiding Channels, and Voltage Noise in Intermittently Flowing Rivers of Quantized Magnetic Flux
• Intermittently Flowing Rivers of Quantized Magnetic Flux

Cited by in corpus (6)

• Depinning and nonequilibrium dynamic phases of particle assemblies driven over random and ordered substrates: a review
• Random Organization and Plastic Depinning
• Depinning and dynamics of vortices confined in mesoscopic flow channels
• Braided Rivers and Superconducting Vortex Avalanches
• A Simple Model for Plastic Dynamics of a Disordered Flux Line Lattice
• Pattern formation in vortex matter with pinning and frustrated inter-vortex interactions