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The Physics of the City

A. Bazzani, O. Bernardi, M. Brambilla, M. Capriotti, L. Cattelani, B. Giorgini, G. Melchiorre, S. Rambaldi, Servizi, G. Turchetti, F. Zanlungo.

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The state of art

The city is certainly a complex object evolving in a non linear way. The urban space-time topology is built up by the melting of aesthetics, biology, physics and sociology, planning and information theory. Moreover in metropolitan territories different citizen populations are mixing, sometime in an harmonic way, sometime conflicting each other.
Since the 60s some mathematical models have tried to describe and/or to explain the urban systems evolutions. In some cases they hoped to be able to predict the effects of planning and/or of the urban transformations, economic, social ones etc.
The first models were statics and/or stationary, with equilibrium or quasi-equilibrium solutions.
One of the most important application of mathematical modelling was on road traffic. Generally it was modelled like an hydrodynamics flux or by Origin-Destination (O-D) matrices, where the origin and the destination are well determined and precisely known in time and spatially.
Obviously when the situation is rapidly evolving and higly dynamical by these models we can't obtain solutions fitting with the observed phenomena. Further the asystematic (brownian) mobility in principle can not dealt with the O-D matrices.
The exponential growth of computing power, the developing of the information theory (automatons and artificial intelligences) and the complex system physics can set up a tools collection for microscopic and dynamic modelling.


City Physics Group is working on a physical-mathematical model in order to study the metropolitan mobility. This model is implemented on a computer giving birth to Mobilis, a virtual system which is able to simulate the individual mobility, in particular the asystematic one:
a) in different scales from a pedestrian town centre to a metropolitan area (from few meters to many kilometres);
b) with different transport means (by foot, bike, public transportation, car, etc).
Until now Mobilis has been applied to:
1. the quarter of Les Halles in Paris during the collaboration with the RATP (Régie Autonome des Transports Parisiens) and the Politecnico di Milano (2002);
2.the town centre of Rimini during the collaboration with the Ordine degli Architetti e l'ufficio Mobilità del Comune, (pedestrian mobility and public transportation, 2003) ;
3.the campus of Milano-Bicocca University during the collaboration with the group of Sociology (Prof. Guido Martinotti) (pedestrian mobility and public transportation, 2004);
4.the train station of Rimini in agreement with Regione Emilia-Romagna, Agenzia TRAM and the collaboration with TrenItalia e RFI (pedestrian mobility and the interchanging transportation junctions, 2005 work in progress);
5.the Senigallia town in agreement with the town administration (private car mobility, public transports in the winter time and in the summer time when there is a strong presence of tourists and holiday makers, 2005 work in progress).
In all these cases the empirical data were in a good agreement with the simulation results.

The Mobilis Physics

We are talking about a set of elementary/individual components moving according dynamics and statistical laws on an urban chronotopic topology. We define "chronotopoi" the primigenius agent of the urban timing activity. For examples University, Hospital, public offices, business centres, business farms ... .
The dynamics is divided into two main fields.
The first one is physics with forces (non Newtonian), interactions, energies, brownian movements, molecular kinematics etc.. In this case for one version of the model which is analytically solving, the mean field solutions are in good agreement with the simulations.
The second one is intentional/decisional dynamics and it is built up by the Bayes-de Finetti probability and by the Markov chains. The individuals are equipped by memory, information, vision. These properties constitute the "intelligence" of the system elementary component. The simulations show emerging self-organization structures and features. Finally we are studying the the von Neumann automata thermodynamics.

Further documentation

Rome: traffic flows on may 2010

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