Durand Marc
Matière et Systèmes Complexes, UMR 7057 CNRS & Université Paris 7-Denis Diderot, 2 Place Jussieu-75251 Paris Cedex 05, France.
Phys Rev Lett. 2007 Feb 23;98(8):088701. doi: 10.1103/PhysRevLett.98.088701. Epub 2007 Feb 21.
The structure of pipe networks minimizing the total energy dissipation rate is studied analytically. Among all the possible pipe networks that can be built with a given total pipe volume (or pipe lateral surface area), the network which minimizes the dissipation rate is shown to be loopless. Furthermore, such an optimal network is shown to contain at most N-2 nodes in addition to the N sources plus sinks that it connects. These results are valid whether the possible locations for the additional nodes are chosen freely or from a set of nodes (such as points of a grid). Applications of these results to various physical situations and to the efficient computation of optimal pipe networks are also discussed.
对使总能量耗散率最小化的管网结构进行了分析研究。在所有可以用给定的总管体积（或管道侧表面积）构建的可能管网中，使耗散率最小化的管网被证明是无环的。此外，这样一个最优管网除了它所连接的N个源和汇之外，最多还包含N - 2个节点。无论额外节点的可能位置是自由选择还是从一组节点（如网格点）中选择，这些结果都是有效的。还讨论了这些结果在各种物理情况中的应用以及最优管网的高效计算。
