Student :
Giulia Carra
Institute of Theoretical Physics
Quanturb research team

Site web :

Mots clés :
Statistical physics, Data Analysis, Smart Cities


Evolution of urban systems : a physical approach

Giulia Carra is part of the QuantUrb team, a research team working on various aspects of the emerging science of cities through data analysis and modeling with the tools of statistical physics.  She is a former student of the École Normale Supérieure of Paris and of the University of Rome La Sapienza. She is currently pursuing her PhD at the Institute of Theoretical Physics in Saclay under the supervision of Marc Barthelemy. The main goal of her thesis is to participate to the quantitative understanding of the structure and growth of urban systems.


Most of the individuals in the world are now living in urban areas and this proportion is predicted to increase in the next decades. Understanding what governs the evolution of urban systems has thus become of paramount importance. This renewed interest combined with the availability of large-scale data, allows a glimpse into the dawn of a new science of cities, interdisciplinary and based on data.

The main goal of the thesis is to participate to the quantitative understanding of the structure and growth of urban systems. In particular, recent studies reported empirical observations such as scaling relations with population for various socio-economical indicators (gasoline consumption, total commuting distance, cost of infrastructures, etc.), and despite several attempts, the theoretical understanding of the statistical regularities observed empirically is still missing and we propose here to work on these problems.

We will draw on studies in quantitative geography and spatial economics and will inspect some of the previous models with a new, physical approach. An important aspect is to propose simple models that allow predictions that can be tested against empirical measures. Another important difference with early studies in urban economics, is that we consider cities as being out-of equilibrium systems. Finally, it is clear that cities are complex systems characterized by a large variety of mechanisms occurring over a wide range of time and spatial scales. Whereas traditional models integrate many of these interactions and variables, the aim of the project is to understand the hierarchy of the processes governing the development and the expansion of a city, to distinguish the dominant ones from the irrelevant or of second order ones.

This research will necessarily be interdisciplinary and we are collaborating with geographers, economists, applied mathematicians, and physicists. It will be based on predictions and stylized facts extracted from empirical data (essentially coming from various sources such as the Census Bureau, Eurostat, INSEE, or open data initiatives) and comparison with predictions obtained by analytical methods and simulations of simplified models. We will primarily use tools from statistical physics of networks and disordered systems such as scaling relations, local optimization methods, partial differential equations, etc.

The goal is to provide a simplified, out-of-equilibrium modeling of urban growth, relying on a small number of important mechanisms and which gives quantitative predictions in agreement with empirical data. This project will contribute to the development of tools that could serve as guides in many practical problems by assessing quantitatively the effects of various urban planning decisions.


The fundamental diagram of urbanization
G. Carra, M. Barthelemy

Modeling the relation between income and commuting distance
G. Carra, I. Mulalic, M. Fosgerau, M. Barthelemy
J. R. Soc. Interface 2016 13 20160306 (2016)