标题： 生物运输网络的介观模型 显示英文标题

标题： A mesoscopic model of biological transportation networks

摘要： 我们引入了一个介观模型，用于自然网络形成过程，作为Hu和Cai提出的离散和连续网络方法之间的桥梁。 这些模型基于一种共同的方法，其中导电网络的动力学受到压力力效应的影响。 我们首先研究了离散模型的拓扑特性，并证明如果代谢能量消耗项相对于导电性是凹的，那么最优网络结构是一个树（即没有环）。 然后，我们分析了介观建模方法的各个方面，特别是它与离散模型的关系及其稳态解，包括离散网络解。 此外，我们提出了一个介观模型的替代公式，避免了能量泛函中显式的压力存在。 显示英文摘要

摘要： We introduce a mesoscopic model for natural network formation processes, acting as a bridge between the discrete and continuous network approach proposed by Hu and Cai. The models are based on a common approach where the dynamics of the conductance network is subject to pressure force effects. We first study topological properties of the discrete model and we prove that if the metabolic energy consumption term is concave with respect to the conductivities, the optimal network structure is a tree (i.e., no loops are present). We then analyze various aspects of the mesoscopic modeling approach, in particular its relation to the discrete model and its stationary solutions, including discrete network solutions. Moreover, we present an alternative formulation of the mesoscopic model that avoids the explicit presence of the pressure in the energy functional.