Related papers: Scaling limits for a population model with growth,…
We introduce a simple geometric model which describes the kinetics of fragmentation of d-dimensional objects. In one dimension our model coincides with the random scission model and show a simple scaling behavior in the long-time limit. For…
To model the morphogenesis of rod-shaped bacterial micro-colony, several individual-based models have been proposed in the biophysical literature. When studying the shape of micro-colonies, most models present interaction forces such as…
Mathematical models of biological populations commonly use discrete structure classes to capture trait variation among individuals (e.g. age, size, phenotype, intracellular state). Upscaling these discrete models into continuum descriptions…
We consider the speed of propagation of a {continuous-time continuous-space} branching random walk with the additional restriction that the birth rate at any spatial point cannot exceed $1$. The dispersion kernel is taken to have density…
We use probabilistic methods to study properties of mean-field models, arising as large-scale limits of certain particle systems with mean-field interaction. The underlying particle system is such that $n$ particles move forward on the real…
There is a widespread recent interest in using ideas from statistical physics to model certain types of problems in economics and finance. The main idea is to derive the macroscopic behavior of the market from the random local interactions…
The dynamics of a population undergoing selection is a central topic in evolutionary biology. This question is particularly intriguing in the case where selective forces act in opposing directions at two population scales. For example, a…
We introduce a solvable model of randomly growing systems consisting of many independent subunits. Scaling relations and growth rate distributions in the limit of infinite subunits are analysed theoretically. Various types of scaling…
In this work we investigate the behaviour of a human crowd in a cross-flow. We first analyse the results of a set of controlled experiments in which subjects were divided into two groups, in such a way to explore different density settings,…
We introduce a high dimensional symplectic map, modeling a large system consisting of weakly interacting chaotic subsystems, as a toy model to analyze the interplay between single-particle chaotic dynamics and particles interactions in…
In this study, spatial stochastic and logistic model (SSLM) describing dynamics of a population of a certain species was analysed. The behaviour of the extinction threshold as a function of model parameters was studied. More specifically,…
Cluster growth in a coagulating system of active particles (such as microswimmers in a solvent) is studied by theory and simulation. In contrast to passive systems, the net velocity of a cluster can have various scalings dependent on the…
We study the interplay of population growth and evolutionary dynamics using a stochastic model based on birth and death events. In contrast to the common assumption of an independent population size, evolution can be strongly affected by…
The analysis of the size distribution of droplets condensing on a substrate (breath figures) is a test ground for scaling theories. Here, we show that a faithful description of these distributions must explicitly deal with the growth…
Starting from a particle model we derive a macroscopic aggregation-diffusion equation for the evolution of slime mold under the assumption of propagation of chaos in the large particle limit. We analyze properties of the macroscopic model…
In this work, we present a multiscale kinetic framework for consensus-based image segmentation. By interpreting an image as a system of interacting particles, each pixel is characterised by its spatial position and an internal feature…
The growth of cities has traditionally been studied from a population perspective, while urban expansion-its spatial growth-has often been approached qualitatively. However, characterizing and modeling this spatial expansion is crucial,…
We deal with the problem of bridging the gap between two scales in neuronal modeling. At the first (microscopic) scale, neurons are considered individually and their behavior described by stochastic differential equations that govern the…
We introduce an interacting particle system that models the spread of an epidemic in terms of heterogeneous diffusive dynamics, rather than exogenous contact and transmission rates at the population level as in classical compartmental…
Scaling limits are analyzed for stochastic continuous opinion dynamics systems, also known as gossip models. In such models, agents update their vector-valued opinion to a convex combination (possibly agent- and opinion-dependent) of their…