Urban pollution, air quality, the demand for new infrastructure, the spread of epidemics, the structure of the city or economic conditions are some of the issues that can benefit from the study of human mobility. From a theoretical point of view, there are two approaches that have been used for the most part for the analysis of mobility: the "opportunity" models, in which certain closed areas represent an attraction for agents, or the gravitational ones, in which the most attractive points are established and whose interest declines with distance as we move away from them. The gravitational model is inspired by Newton's classic laws, with the working population acting as a mass so that mobility is attracted to urban nuclei.
A study carried out by researchers from IFISC (UIB-CSIC) and published in the journal Nature Communications proposes studying daily home-work mobility with a vector field. The existence of the field and its characteristics have been corroborated in large cities around the world with data from both the census and Twitter. In fact, a very definite pattern emerges oriented towards the central nucleus of cities. This field, thanks to the mathematical properties observed empirically (irrotationality), derives from a scalar potential that characterizes pendulum mobility in cities. Such potential, like gravitational potentials, can have one or more centers depending on how the flows are organized. Among its advantages is the fact that it admits an analytical treatment under slight simplifications.
The shape of the defined fields allows obtaining a faithful representation of how the mobility of the labour force is organised in the cities, finding the points with the greatest attraction and redefining the limits of the metropolitan area. It is even possible to observe how groups of "small cities" form gravitational systems analogous to the binary or ternary systems that can be observed in astrophysics. Similarly, there are equilibrium points (called Lagrange points) in which the sum of the attraction vectors is zero. These points play an important role in the theoretical analysis of the proposal.
This study opens the doors to the development of deeper techniques that allow a more analytical understanding of recurrent human mobility.
Mazzoli, Mattia; Molas, Àlex; Bassolas, Aleix; Lenormand, Maxime; Colet, Pere i Ramasco, José J. (2019). Field theory for recurrent mobility. Nature Communications, 2019. 10:38965. https://doi.org/10.1038/s41467-019-11841-2