Related papers: The coalescing colony model: mean-field, scaling, …
In mean-field theory, the non-local state of fluid molecules can be taken into account using a statistical method. The molecular model combined with a density expansion in Taylor series of the fourth order yields an internal energy value…
We introduce a simple model of active transport for an ensemble of particles driven by an external shear flow. Active refers to the fact that the flow of the particles is modified by the distribution of particles itself. The model consists…
In this paper we make an attempt to increase our understanding of the urban scaling phenomenon. We investigate how superlinear scaling emerges if a network increases in size and how this scaling depends on the occurrence of elements that…
This paper studies the bounded confidence model on growing fully-mixed populations. In this model, in addition to the usual opinion clusters, significant secondary clusters of smaller size appear systematically, while those secondary…
While worldwide census data provide statistical evidence that firmly link the population density with several indicators of social welfare, the precise mechanisms underlying these observations are largely unknown. Here we study the impact…
We study a scaling limit associated to a model of planar aggregation. The model is obtained by composing certain independent random conformal maps. The evolution of harmonic measure on the boundary of the cluster is shown to converge to the…
We study a one-dimensional spatial population model where the population sizes at each site are chosen according to a translation invariant and ergodic distribution and are uniformly bounded away from 0 and infinity. We suppose that the…
From the exact single step evolution equation of the two-point correlation function of a particle distribution subjected to a stochastic displacement field $\bu(\bx)$, we derive different dynamical regimes when $\bu(\bx)$ is iterated to…
We propose a class of evolutionary models that involves an arbitrary exchangeable process as the breeding process and different selection schemes. In those models, a new genome is born according to the breeding process, and then a genome is…
Applying the mean surface density of companions, Sigma(r), to the dynamical evolution of star clusters is an interesting approach to quantifying structural changes in a cluster. It has the advantage that the entire density structure,…
In this paper, we propose a tumor growth model to incorporate and investigate the spatial effects of autophagy. The cells are classified into two phases: normal cells and autophagic cells, whose dynamics are also coupled with the nutrients.…
We study an evolution cross-diffusion problem with mutualistic Lotka-Volterra reaction term to modelize the long-term spatial distribution of labor and capital. The mutualistic behavior is deduced from the gradient flow associated to…
Nucleation on top of two-dimensional islands with step edge barriers is investigated using scaling arguments. The nucleation rate is expressed in terms of three basic time scales: The time interval between deposition events, the residence…
In this paper we study some mathematical models describing evolution of population density and spread of epidemics in population systems in which spatial movement of individuals depends only on the departure and arrival locations and does…
Microbial colonies are experimental model systems for studying the colonization of new territory by biological species through range expansion. We study a generalization of the two-species Eden model, which incorporates local…
We consider the general character of the spatial distribution of a population that grows through reproduction and subsequent local resettlement of new population members. We present several simple one and two-dimensional point placement…
Swarming behavior, where coherent motion emerges from the interactions of many mobile agents, is ubiquitous in physics and biology. Moreover, there are many efforts to replicate swarming dynamics in mobile robotic systems which take…
The scaling relations between city attributes and population are emergent and ubiquitous aspects of urban growth. Quantifying these relations and understanding their theoretical foundation, however, is difficult due to the challenge of…
We consider a flocking system confined transversally between two infinite reflecting parallel walls separated by a distance $L_\perp$. Infinite or periodic boundary conditions are assumed longitudinally to the direction of collective…
This paper concerns the long term behaviour of a growth model describing a random sequential allocation of particles on a finite cycle graph. The model can be regarded as a reinforced urn model with graph-based interactions. It is motivated…