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A Model for Branch Competition

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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.

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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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  1. ExxonMobil Upstream Research Company, 22777 Springwoods Village Parkway, Spring, TX, 77389, USA

    Thomas C. Halsey

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  1. Thomas C. Halsey
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Correspondence to Thomas C. Halsey.

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This article is dedicated to the memory of Leo P. Kadanoff, 1937–2015.

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Halsey, T.C. A Model for Branch Competition. J Stat Phys 167, 713–725 (2017). https://doi.org/10.1007/s10955-016-1670-1

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