## A Physical - Mathematical *Model*

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:

- in different scales from a pedestrian town centre to a metropolitan area (from few meters to many kilometres);
- with different transport means (by foot, bike, public transportation, car, etc)

## The *Simulator*

Mobilis: the name comes from "Mobilis in Mobile" definition given by Captain Nemo to its submarine Nautilus in "Twenty thousands leagues under the sea" of Jules Verne. It is a simulator based on a mathematical-physics model of asystematic mobility, implemented in C++ with a graphics interface for the program user interactions and based on probabilistic decision processes. It is based on a microscopic description of mobility where pedestrians, cyclists and private vehicles are intelligent automata moving on a network and therefore a model of complex system, capable of describing not only phase transitions but also emerging properties and self organization phenomena.

The simulator has been used to describe the asystematic mobility in the historical center of Rimini. Some characteristics are: discrete space time with time step equal to 1 minute for the pedestrians motion, representation of the citizens as autonomous agents whose dynamics is determined by the daily schedule, by the network of streets, by the public transportation, by the presence of chronotopoi, by the incoming and outgoing fluxes in the historical center.

## About the Simulator *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, etc.

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.

## Urban Dynamics *Simulation Videos*

We present some animations showing the mobility model applied to:

- The Rome's street system traffic flow
- The Rimini's historical centre (See: Pedestrian Mobility)
- A general crossing network with traffic lights (See also: Vehicles Mobility)

Rome: traffic flows on may 2010

Vehicles mobility model applied to a regular crossing network with traffic lights and precedence rules

Rimini: population density on the grid's nodes

Rimini: Resident citizen moving

Rimini: "Foreign" citizen moving

Rimini: population density

Rimini: Non resident student going to University and downtown

Rimini: Resident citizen going to the Mail Office

Rimini: Citizen coming from parking and going (by feet and bus) to the market