Network design: From steady-state optimization to unsteady dynamics

This work presents a comprehensive framework to analyze the design and dynamics of branching flow networks, guided by the constructal law. The model is validated against the functionally diverse vascular systems of the liver, kidney, and lungs. Results demonstrate that the architecture of these vital organs consistently aligns with a design that minimizes steady-state impedance under a constant volume constraint. This governing principle is remarkably robust, showing little sensitivity to the non-linear rheological properties of blood, which justifies using a simplified linear model for dynamic analysis. While steady-state models accurately predict mean flow, the framework's unsteady analysis is essential for capturing the true dynamics of unsteady flow systems. This framework, validated on biological systems, provides a tool for both reverse-engineering natural designs and forward-engineering manufactured networks.