Related papers: Localisation in a growth model with interaction
Originally motivated by the morphogenesis of bacterial microcolonies, the aim of this article is to explore models through different scales for a spatial population of interacting, growing and dividing particles. We start from a microscopic…
Granular convergence is a property of a granular pack as it is repeatedly sheared in a cyclic, quasistatic fashion, as the packing configuration changes via discrete events. Under suitable conditions the set of microscopic configurations…
As data-driven methods are deployed in real-world settings, the processes that generate the observed data will often react to the decisions of the learner. For example, a data source may have some incentive for the algorithm to provide a…
We introduce a stochastic agent-based model for the flocking dynamics of self-propelled particles that exhibit velocity-alignment interactions with neighbours within their field of view. The stochasticity in the dynamics of the model arises…
We consider a stochastic model, describing the growth of two competing infections on $\mathbb{R}^d$. The growth takes place by way of spherical outbursts in the infected region, an outburst in the type 1 (2) infected region causing all…
We provide a numerical study of the macroscopic model of [3] derived from an agent-based model for a system of particles interacting through a dynamical network of links. Assuming that the network remodelling process is very fast, the…
We study the spatial patterns formed by a system of interacting particles where the mobility of any individual is determined by the population crowding at two different spatial scales. In this way we model the behavior of some biological…
We investigate a system of interacting clusters evolving through mass exchange and supplemented by input of small clusters. Three possibilities depending on the rate of exchange generically occur when input is homogeneous: continuous…
Understanding the influence of an environment on the evolution of its resident population is a major challenge in evolutionary biology. Great progress has been made in homogeneous population structures while heterogeneous structures have…
In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a…
The morphology of urban agglomeration is studied here in the context of information exchange between different spatio-temporal scales. Cities are multidimensional non-linear phenomena, so understanding the relationships and connectivity…
The cell cycle duration is a variable cellular phenotype that underlies long-term population growth and age structures. By analyzing the stationary solutions of a branching process with heritable cell division times, we demonstrate…
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…
Growing graphs describe a multitude of developing processes from maturing brains to expanding vocabularies to burgeoning public transit systems. Each of these growing processes likely adheres to proliferation rules that establish an…
An investigation of the effect of surface diffusion in random deposition model is made by analytical methods and reasoning. For any given site, the extent to which a particle can diffuse is decided by the morphology in the immediate…
Relationships between sediment flux and geomorphic processes are combined with statements of mass conservation, in order to create continuum models of hillslope evolution. These models have parameters which can be calibrated using available…
Random intersection graphs containing an underlying community structure are a popular choice for modelling real-world networks. Given the group memberships, the classical random intersection graph is obtained by connecting individuals when…
We study survival among two competing types in two settings: a planar growth model related to two-neighbour bootstrap percolation, and a system of urns with graph-based interactions. In the planar growth model, uncoloured sites are given a…
The adoption of agroecological practices will be crucial to address the challenges of climate change and biodiversity loss. Such practices favor the cultivation of plants in complex mixtures with layouts differing from the monoculture…
The spread of ideas, behaviors, and technologies generally depends on feedback mechanisms operating across multiple scales. Previous studies have extensively examined pairwise transmission and local reinforcement. However, the role of…