![]() ![]() Recent GPS technology has made it possible to trace detailed trajectories of millions of people, macroscopic approaches such as the gravity law for human flow between cities and microscopic approaches of individual origin-destination distributions are attracting much attention. Owing to the big data the extension of physical laws on nonmaterial has seen numerous successes, and human mobility is one of the scientific frontier topics. The potential landscape provides an easy-to-use visualisation tool for showing the attractive places of human flow and will help in a variety of applications such as commerce, urban design, and epidemic spreading. We then determine how well the commuting flow is described by the potential, by evaluating the percentage of the gradient component for metropolitan areas in the USA and show that the gradient component is almost 100% in several areas in other areas, however, the curl component is dominant, indicating the importance of circular flow along with triangles of places. We depict the potential landscapes in cities resulting from commuting flow and reveal how the landscapes have either changed or remained unchanged by years or methods of transportation. In this case, we use Hodge–Kodaira decomposition, which uniquely decomposes a matrix into a potential-driven (gradient) flow and a curl flow. However, the definition of such a potential in terms of the origin-destination flow matrix and its feasibility remain unresolved. Scalar potential is a mathematical concept that, when properly applied, can provide an intuitive view of human flow. ![]() Human flow in cities indicates social activity and can reveal urban spatial structures based on human behaviours for relevant applications. Such a non-systematic view will lead us to leave outside many relevant papers, and for this we must apologise. Instead, we will only provide a brief taste of some of these above-mentioned aspects, which could serve as an introduction to the collection ‘Cities as Complex Systems’. All these topics have been addressed in many works in the literature, and we do not intend to offer here a systematic review. ![]() In the last decade, the introduction of communication and information technologies have enormously facilitated the collection of datasets on these and other questions, making possible a more quantitative approach to city science. There are many different aspects to study in urban systems from a scientific point of view, one can concentrate in demography and population evolution, mobility, economic output, land use and urban planning, home accessibility and real estate market, energy and water consumption, waste processing, health, education, integration of minorities, just to name a few. The advantages brought in terms of agglomeration for economy, innovation, social and cultural advancements have kept them as a major landmark in recent human history. They appear in parallel to the Neolithic revolution a few millennia ago. The same for Paris with a circle (c) and a square (d) centered at the Passage du Grand Cerf in the 2nd ArrondissementĬities are characterized by the presence of a dense population with a high potential for interactions between individuals of diverse backgrounds. In the figure, we show half the side as the x-axis variable to maintain the geographical scales similar to those of the circle radius. b A square perimeter around London with the same center and side 2R. a Results in London for a circle of radius R centered at Waterloo Bridge. In blue, the flux calculated as the surface integral of the vector field W→\documentclass. ![]()
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