10 papers
Invasion with size-dependent dispersion range
Ulysse Marquis
The coalescing colony model provides a minimal framework for biological invasions with long-range dispersion. In its standard formulation, the dispersion range is assumed independe…
Spectral properties of non-Hermitian real random matrices with long-range correlations
Ulysse Marquis
We investigate the spectral properties of non-Hermitian real random matrices whose entries exhibit long-range correlations decaying as~. We find a progressive breakdow…
FKPP fronts in quenched random media
Ulysse Marquis, Henri Berestycki, Marc Barthelemy
We study numerically the evolution of one-dimensional FKPP fronts initiated from steep initial conditions in the presence of a quenched random growth rate. Compared to both the hom…
Beyond dynamic scaling: rare events break universality
Ulysse Marquis, Riccardo Gallotti, Marc Barthelemy
Surface growth driven by non-monomeric deposition has remained largely unexplored. We investigate a model based on the deposition of blobs with a power-law size distribution $P(s)\…
Mathematical modeling of urban sprawl
Marc Barthelemy, Ulysse Marquis
Urban land cover doubled between 1985 and 2015, yet the spatial dynamics of urban form remain under-quantified, despite its importance for sustainability, infrastructure planning,…
On the Meaning of Urban Scaling
Ulysse Marquis, Marc Barthelemy
Cities are often compared through scaling laws, usually expressed as power-law relations between population size and aggregate urban quantities related to infrastructure, socioecon…