Thermodynamic and Geometric Optimization of Systems with Flow Irreversibilities

该项目在几个新的方向上扩展了优化点和体之间树形流动的热力学几何形状的方法。流动结构的几何细节将从受全局约束的全局热力学性能（例如，总体流动阻力）的最大化中推导出来。例如，树形网络在一个区域内收集和分配水和电力。该方法也将扩展到经济学，其中流动由商品组成，全球目标是收入最大化。在生物传热领域，该方法将应用于存在于血管化组织中的流体树（动脉和静脉）对。树木形状的流动在自然系统中随处可见，有生命的和无生命的（如肺、河流、照明）。它们在工程、经济和社会领域也很普遍。这个项目的目标是从最大化被水流渗透的系统的整体性能的原则中推断出树状流的最佳几何结构。例如，在城市地区的水和电力分布的树形网络中，全局目标是最小的流动阻力和最小的成本。在经济学中，在一个地区内分配或收集货物时，目标是收入最大化。在皮肤下的血管化组织中，动脉和静脉成双成对地逆流排列，目的是尽量减少流动阻力和身体热量损失。所有这些流动结构都将从基于全局热力学优化的几何优化的角度进行生成和研究。

This project extends in several new directions the method of optimizing thermodynamically the geometry of tree-shaped flows between points and volumes. The geometric details of the flow structure will be deduced from the maximization of global thermodynamic performance (e.g., overall flow resistance) subject to global constraints. Examples are the tree-shaped networks that collect and distribute water and electric power over a territory. The method will also be extended to economics, where the flow consists of goods, and the global objective is revenue maximization. In the field of bioheat transfer, the method will be applied to the pairs of fluid trees (arteries and veins) that are present in vascularized tissues. Flows that are shaped as trees are found everywhere in natural systems, animate and inanimate (e.g., lungs, rivers, lighting). They are also prevalent in engineering, economics and society. The objective of this project is to deduce the optimal geometric structure of tree-shaped flows from the principle of maximizing the global performance of the system permeated by the flow. For example, in a tree network for the distribution of water and electric power over an urban area the global objective is minimum flow resistance and minimum cost. In economics, in the distribution or collection of goods over a territory, the objective is the maximization of revenue. In vascularized tissues under the skin, where trees of arteries and veins are arranged in pairs and in counterflow, the objective is the minimization of flow resistance and body heat loss. All these flow structures will be generated and studied from the point of view of geometric optimization based on global thermodynamic optimization.