The geometry and dynamics of binary trees

T. David, T. Kempen, van, Huaxiong Huang, P. Wilson

Research output: Contribution to journalArticleAcademicpeer-review

11 Citations (Scopus)
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Abstract

The modeling of a fully populated 3D tree able to regulate dynamically remains a relatively unexplored field. A non-dimensional representation of "autoregulation" coupled with an asymmetric binary tree algorithm has been developed. The tree has a defined topology as well as a spatial representation in 3D. An analysis using a simple linearization shows the systems dynamics when perturbed away from equilibrium. Results, based on previously published work by Karch and Schreiner are presented for a variety of parameters which provide different shapes of the tree and indicate a possible mechanism for "growing" the tree in specified directions. In addition the tree, through the use of local tagging has the ability to vary its size locally via a coupled set of conservation and reverting differential equations.
Original languageEnglish
Pages (from-to)1464-1481
Number of pages18
JournalMathematics and Computers in Simulation
Volume81
Issue number7
DOIs
Publication statusPublished - 2011

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