Optimal long-distance transport systems in nature: control and applications

Abstract

Long-distance conducting systems in high plants and animals are presented by networks of rigid tubes with porous walls (in plants) or distensible tubes with impermeable walls (in animals). Geometrical relationships between the diameters, lengths and branching angles of separate conducting vessels have been studied and the results of the comparative analysis are presented. It was shown that the principles of construction of the transport systems are similar in animals and plants and correspond to the optimal pipelines with impermeable and permeable walls accordingly. The optimization criterion is the total energy expenses W for the fluid delivery and construction of the system. Global optimality at the systemic level is provided by local optimality conditions in each conducting element. It is shown that complexity of the branching system of the optimal tubes leads to certain regularities in the hydraulic and wave properties of the systems. The obtained regularities and the principles of design of the long-distance transportation networks in Nature can be used in biomedical applications and technique.