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Journal of Statistical Physics

, Volume 167, Issue 3–4, pp 713–725 | Cite as

A Model for Branch Competition

  • Thomas C. Halsey
Article
  • 130 Downloads

Abstract

Branching (or tip-splitting) is a ubiquitous feature of growth processes in nature. We introduce a simple model, linear in growth probabilities, of branch competition that combines tip-splitting processes, local screening, and extinction of branches whose growth has come to an end. This model admits an exact solution; which is corroborated by numerical results. An extension of the model that depends quadratically upon growth probabilities exhibits a phase transition, with non-trivial scaling in the neighborhood of that transition.

Keywords

Pattern formation Multifractality Diffusion-limited aggregation Critical phenomena 

Notes

Acknowledgements

I am grateful to Prof. Ray Goldstein for his hospitality during a visit to the Department of Applied Mathematics and Theoretical Physics at Cambridge University, which afforded me time to organize my thoughts on this topic.

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.ExxonMobil Upstream Research CompanySpringUSA

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