The geometry and dynamics of binary trees
The geometry and dynamics of binary trees
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DOI：
10.1016/j.matcom.2010.04.020
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发表时间：
2011-03
期刊：
影响因子：
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通讯作者：
T. David;T. Kempen;Huaxiong Huang;Phillip Lawrence Wilson
中科院分区：
文献类型：
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作者：
T. David;T. Kempen;Huaxiong Huang;Phillip Lawrence Wilson
能够动态调节的完全填充的3D树的建模仍然是一个相对未开发的领域。一个无量纲表示的“自动调节”加上一个不对称的二叉树算法已经开发出来。该树具有定义的拓扑结构以及3D空间表示。一个简单的线性化分析表明，系统动态时，扰动远离平衡。结果，根据以前发表的工作由Karch和Schreiner提出了各种参数，提供不同的形状的树，并表示一种可能的机制，“成长”的树在指定的方向。此外，通过使用局部标记，树具有经由耦合的一组守恒和回复微分方程局部地改变其大小的能力。
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.