Related papers: A deterministic model of competitive cluster growt…
Vegetation patterns are a ubiquitous feature of water-deprived ecosystems. Despite the competition for the same limiting resource, coexistence of several plant species is commonly observed. We propose a two-species reaction-diffusion model…
We propose a stochastic model for evolution. Births and deaths of species occur with constant probabilities. Each new species is associated with a fitness sampled from the uniform distribution on [0,1]. Every time there is a death event…
We classify and predict the asymptotic dynamics of a class of swarming models. The model consists of a conservation equation in one dimension describing the movement of a population density field. The velocity is found by convolving the…
The processes and mechanisms underlying the origin and maintenance of biological diversity have long been of central importance in ecology and evolution. The competitive exclusion principle states that the number of coexisting species is…
We study a size-structured model proposed in [1] C. Barril, \`A. Calsina, O. Diekmann, J. Z. Farkas, On competition through growth reduction, e-print arXiv:2303.02981, to describe the dynamics of trees growth in the forest. Our approach to…
We probe the evolution of globular clusters that could form in giant molecular clouds within high-redshift galaxies. Numerical simulations demonstrate that the large and dense enough gas clouds assemble naturally in current hierarchical…
The emergence and prevalence of cooperative behavior within a group of selfish individuals remains a puzzle for \text{evolutionary game theory} precisely because it conflicts directly with the central idea of natural selection. Accordingly,…
We propose a new model of cluster growth according to which the probability that a new unit is placed in a point at a distance $r$ from the city center is a Gaussian with mean equal to the cluster radius and variance proportional to the…
A bi-disperse granular gas in a compartmentalized system is experimentally found to cluster competitively: Depending on the shaking strength, the clustering can be directed either towards the compartment initially containing mainly small…
How stellar clusters disrupt, and over what timescales, is intimately linked with how they form. Here, we review the theory and observations of cluster disruption, both the suggested initial rapid dissolution phase (infant mortality) and…
A model of interacting random walkers is presented and shown to give rise to patterns consisting in periodic arrangements of fluctuating particle clusters. The model represents biological individuals that die or reproduce at rates depending…
The evolution of marginally bound supercluster-like objects in an accelerating LambdaCDM Universe is followed, by means of cosmological simulations, from the present time to an expansion factor a = 100. The objects are identified on the…
We introduce and analyse a class of fragmentation-coalescence processes defined on finite systems of particles organised into clusters. Coalescent events merge multiple clusters simultaneously to form a single larger cluster, while…
Spatial distribution of the human population is distinctly heterogeneous, e.g. showing significant difference in the population density between urban and rural areas. In the historical perspective, i.e. on the timescale of centuries, the…
By generalizing a class of models recently introduced to account for protracted transients in biological systems, we identify a novel mechanism for hyperuniformity. In this model, competition of particles over a shared resource guides the…
Unlike coffee and cream that homogenize when stirred, growing micro-organisms (e.g., bacteria, baker's yeast) can actively kill each other and avoid mixing. How do such antagonistic interactions impact the growth and survival of competing…
The persistence probability, $P_C(t)$, of a cluster to remain unaggregated is studied in cluster-cluster aggregation, when the diffusion coefficient of a cluster depends on its size $s$ as $D(s) \sim s^\gamma$. In the mean-field the problem…
We study a generic reaction-diffusion model for single-species population dynamics that includes reproduction, death, and competition. The population is assumed to be confined in a refuge beyond which conditions are so harsh that they lead…
Three-dimensional molecular dynamics simulations of dissipative particles (~ 10^6) are carried out for studying the clustering kinetics of granular media during cooling. The inter-connected high particle density regions are identified,…
We study the stochastic dynamics of coupled states with transition probabilities depending on local persistence, this is, the time since a state has changed. When the population has a preference to adopt older states the system orders…