含迂曲度管道单分叉结构的优化

The optimization of the single fractal tree-like branch network based on tortuosity of tubes

对于生物系统,普遍存在着大量的树状分叉结构,Murray在对生物血液循环系统的研究中,在能耗最小作用原理下,得到了著名的Murray定律.本文研究了在考虑管道弯曲的迂曲度之后,对单分叉的树状分叉结构应用体积固定下最小化流阻的方法,同样也得到了Murray定律,并得到了分叉子管的长度之比等于其直径之比的结论.

Numerous tree-like branching network structures exist in biological systems. Murray has derived the well-known Murray-law for blood circulation systems under the least energy consumption principle. Taking the tortuosity in to consideration, we got minimizing the flow resistance of the single fractal tree-like branch network model at the total volume constraint. The result is the same as Murray law. We also found that the tube lengths and diameters change in the same proportion at the junction.