arXiv subjects

Giulia Carra

Publications and source records attributed to Giulia Carra.

3 recordsLinked to original sources

arXiv2017

The coalescing colony model: mean-field, scaling, and geometry

We analyze the coalescing model where a `primary' colony grows and randomly emits secondary colonies that spread and eventually coalesce with it. This model describes population proliferation in theoretical ecology, tumor growth and is also of great interest for modeling the development of cities. Assuming the primary colony to be always spherical of radius $r(t)$ and the emission rate proportional to $r(t)^θ$ where $θ>0$, we derive the mean-field equations governing the dynamics of the primary colony, calculate the scaling exponents versus $θ$ and compare our results with numerical simulations. We then critically test the validity of the circular approximation and show that it is sound for a constant emission rate ($θ=0$). However, when the emission rate is proportional to the perimeter, the circular approximation breaks down and the roughness of the primary colony can not be discarded, thus modifying the scaling exponents.

q-bio.PE↗

arXiv2016

The fundamental diagram of urbanization

The process of urbanization is one of the most important phenomenon of our societies and it is only recently that the availability of massive amounts of geolocalized historical data allows us to address quantitatively some of its features. Here, we discuss how the number of buildings evolves with population and we show on different datasets (Chicago, $1930-2010$; London, $1900-2015$; New York City, $1790-2013$; Paris, $1861-2011$) that this `fundamental diagram' evolves in a possibly universal way with three distinct phases. After an initial pre-urbanization phase, the first phase is a rapid growth of the number of buildings versus population. In a second regime, where residences are converted into another use (such as offices or stores for example), the population decreases while the number of buildings stays approximatively constant. In another subsequent phase, the number of buildings and the population grow again and correspond to a re-densification of cities. We propose a stochastic model based on these simple mechanisms to reproduce the first two regimes and show that it is in excellent agreement with empirical observations. These results bring evidences for the possibility of constructing a minimal model that could serve as a tool for understanding quantitatively urbanization and the future evolution of cities.

physics.soc-ph↗

arXiv2016

Modeling the relation between income and commuting distance

We discuss the distribution of commuting distances and its relation to income. Using data from Denmark, the UK, and the US, we show that the commuting distance is (i) broadly distributed with a slow decaying tail that can be fitted by a power law with exponent $γ\approx 3$ and (ii) an average growing slowly as a power law with an exponent less than one that depends on the country considered. The classical theory for job search is based on the idea that workers evaluate the wage of potential jobs as they arrive sequentially through time, and extending this model with space, we obtain predictions that are strongly contradicted by our empirical findings. We propose an alternative model that is based on the idea that workers evaluate potential jobs based on a quality aspect and that workers search for jobs sequentially across space. We also assume that the density of potential jobs depends on the skills of the worker and decreases with the wage. The predicted distribution of commuting distances decays as $1/r^{3}$ and is independent of the distribution of the quality of jobs. We find our alternative model to be in agreement with our data. This type of approach opens new perspectives for the modeling of mobility.

physics.soc-ph↗