Related papers: The coalescing colony model: mean-field, scaling, …

We study reaction-diffusion particle systems with several interaction mechanisms. As the number of particles tends to infinity, the system admits a mean-field limit describing the bulk behaviour. We focus on determining the propagation…

Kingman's model describes the evolution of a one-locus haploid population of infinite size and discrete generations under the competition of selection and mutation. A random generalisation has been made in a previous paper which assumes all…

Predicting urban growth is important for practical reasons, and also for the challenge it presents to theoretical frameworks for cluster dynamics. Recently, the model of diffusion limited aggregation (DLA) has been applied to describe urban…

Agglomeration processes occur in many different realms of science such as colloid and aerosol formation or formation of bacterial colonies. We study the influence of primary particle density in agglomerate structure using…

Oscillating population model realistic situations in different contexts.We examine this situation with reasonable mathematical models and come to interesting conclusions,such as for example,that the population at most points of the cycle…

Initiation and development of a malignant tumor is a complex phenomenon that has critical stages determining its long time behavior. This phenomenon is mathematically described by means of various models: from simple heuristic models to…

Analysis of the urban population fraction data for sixteen populous countries over the last fifty years reveals a universal increase in urbanization, exhibiting four qualitatively distinct temporal patterns: (i) continuously accelerating…

Developing a scientific understanding of cities in a fast urbanizing world is essential for planning sustainable urban systems. Recently, it was shown that income and wealth creation follow increasing returns, scaling superlinearly with…

Thomas Schelling proposed an influential simple spatial model to illustrate how, even with relatively mild assumptions on each individual's nearest neighbor preferences, an integrated city would likely unravel to a segregated city, even if…

This paper presents a new derivation of the Generalized Poisson distribution. This distribution provides a good fit to the evolved, counts-in-cells distribution measured in numerical simulations of hierarchical clustering from Poisson…

As a population grows, spreading to new environments may favor specialization. In this paper, we introduce and explore a model for specialization at the front of a colony expanding synchronously into new territory. We show through numerical…

In mathematical population genetics, it is well known that one can represent the genealogy of a population by a tree, which indicates how the ancestral lines of individuals in the population coalesce as they are traced back in time. As the…

We prove a mean-field equation for the dynamics of quorum-sensing microbial populations. In the stochastic many-particle process, individuals of a population produce public good molecules to different degrees. Individual production is…

We discuss two cases that can be connected to the dynamics of interacting populations: (I.) density waves for the case or negligible random fluctuations of the populations densities, and (II.) probability distributions connected to the…

We introduce two models of biological aggregation, based on randomly moving particles with individual stochasticity depending on the perceived average population density in their neighbourhood. In the first-order model the location of each…

In this paper a relative number density parameter, called the neighborhood function, is introduced so that the crowded nature of the neighborhood of individual sources can be described. With this parameter one can determine the probability…

We study the effect of mutations in a simple model of colonization, based on Montecarlo simulations. When the population colonizes the whole available habitat, a maximum population density is reached, which depends on the mutation rate.…

The diffusion of particles in complex media has gained significant interest due to its dual relevance: probing the viscoelastic properties of materials via microrheology and assessing the extent of particle displacement over time. In this…

We model an enclosed system of bacteria, whose motility-induced phase separation is coupled to slow population dynamics. Without noise, the system shows both static phase separation and a limit cycle, in which a rising global population…

Spatial models where growth is limited to the edge of the expansions have been instrumental to understand the population dynamics and the clone size distribution in growing cellular populations, such as microbial colonies and avascular…