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Journal of Statistical Physics

, Volume 167, Issue 3–4, pp 703–712 | Cite as

Path Selection in a Poisson field

  • Yossi Cohen
  • Daniel H. Rothman
Article

Abstract

A criterion for path selection for channels growing in a Poisson field is presented. We invoke a generalization of the principle of local symmetry. We then use this criterion to grow channels in a confined geometry. The channel trajectories reveal a self-similar shape as they reach steady state. Analyzing their paths, we identify a cause for branching that may result in a ramified structure in which the golden ratio appears.

Keywords

Laplacian paths Poisson paths Local symmetry Ramified networks Golden ratio 

Notes

Acknowledgements

We thank M. Z. Bazant, O. Devauchelle, M. Mineev-Weinstein and P. Szymczak for interesting discussions and helpful interactions. This work was supported by U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Chemical Sciences, Geosciences, and Biosciences Division under Award Number FG02-99ER15004.

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Lorenz Center, Department of Earth Atmospheric, and Planetary SciencesMassachusetts Institute of TechnologyCambridgeUSA

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