The constructal law: From man-made flow systems to pedestrian flows. Comment on "The emergence of design in pedestrian dynamics: locomotion, self-organization, walking paths and constructal law" by A.F. Miguel

Abstract

In a very interesting review paper, Miguel presents an extensive and critical review of research of our currentunderstanding of pedestrian dynamics, with a particular emphasis on the advances made possible by the applicationof constructal law. The author describes in detail the major theories and models associated with pedestrian dynamics,namely the Langevin-like formulation which formulation for pedestrians are the social force model and centrifugalforce model. Also, this work presents some new and relevant results: a theoretical demonstration of the experimentalresult that says the Froude number for the walkrun transition is ~0.5; that the Froude number that characterizesthe comfortable walking speed is ~0.33 and new equations to model the optimal geometry of the bifurcated walkways.This last result is very important to design safe routes for pedestrian evacuation.The problem of pedestrian flows has attracted interest from the early days of the previous century, but it was onlysince the 1950's that this topic became the subject of more systematic study, by several researchers. The publisheddata indicate that an increase of pedestrian densities lead to a reduction of the walking speeds. Walking is the mostbasic form of transportation and a good understanding of pedestrian dynamics is an important challenge for modernsocieties, namely in the planning and design of street networks, public transport stations, airports, events organizationand crowd control. So, a central problem in pedestrian dynamics is to find efficient flow configurations.The constructal law was developed by Bejan in the context of optimizing the access to flow of man-madesystems, but it is not limited to these systems. Over the last decade the constructal theory has been successfullyapplied to different topics designed porous media for heat transfer, vascularized networks, solar energy-based systemsfor buildings, atmospheric circulation, the morphology of the respiratory tree, urban design, pedestrian motion,etc.The fundamental idea, of this law, is that everything that moves (animate or inanimate) is a flow system; and aflow system wants to flow more efficiently, and over time will shape itself to do so. Constructal law shows that a single law of physics governs the design behind everything that moves. According to this law, shapes and structuresarise because they facilitate movement, in animal design, river basin design, traffic patterns, social dynamics, andtechnology and sports evolution. However, it is important to be in mind that the constructal law is not about whatflows, but about the physics phenomenon of how any flow system acquires its evolving.The constructal law provides a unifying theory of evolution and the physics definition of life. Accordingto constructal theory, the flow architecture emerges in time such that it provides progressively greater access to itscurrents. The emergence of flow architecture in nature is analogous to emergence of configuration in man-made flowsystems, and that features of materialization of design can be predicted based on the constructal theory.In conclusion, this work brings a useful quantitative perspective into the study of the pedestrian flows, by thesimplest means possible. The constructal law states that every flow system evolves in time so that it develops the flowarchitecture that maximizes flow access under the constraints posed to the flow.