相关论文: Range expansion by growth and congestion

The mathematical modeling of tumor growth leads to singular stiff pressure law limits for porous medium equations with a source term. Such asymptotic problems give rise to free boundaries, which, in the absence of active motion, are…

Ever since the ground breaking work of Trepat et al. in 2009, we know that cell colonies growing on a substrate can be under tensile mechanical stress. The origin of tension has so far been attributed to cellular motility forces being…

We study the competition and the evolution of nodes embedded in Euclidean restricted spaces. The population evolves by a branching process in which new nodes are generated when up to two new nodes are attached to the previous ones at each…

We consider the well-posedness of models involving age structure and non-linear diffusion. Such problems arise in the study of population dynamics. It is shown how diffusion and age boundary conditions can be treated that depend…

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…

Habitat fragmentation, often driven by human activities, alters ecological landscapes by disrupting connectivity and reshaping species interactions. In such fragmented environments, habitats can be modeled as networks, where individuals…

We study the dynamics of proliferating cell collectives whose microscopic constituents' growth is inhibited by macroscopic growth-induced stress. Discrete particle simulations of a growing collective show the emergence of concentric-ring…

The paper is devoted to a reaction-diffusion equation with doubly nonlocal nonlinearity arising in various applications in population dynamics. One of the integral terms corresponds to the nonlocal consumption of resources while another one…

Simple random coverage models, well studied in Euclidean space, can also be defined on a general compact metric space. By analogy with the geometric models, and with the discrete coupon collector's problem and with cover times for finite…

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…

How are granular details of stochastic growth and division of individual cells reflected in smooth deterministic growth of population numbers? We provide an integrated, multiscale perspective of microbial growth dynamics by formulating a…

We consider a certain lattice branching random walk with on-site competition and in an environment which is heterogeneous at a macroscopic scale $1/\varepsilon$ in space and time. This can be seen as a model for the spatial dynamics of a…

This work is devoted to studying the dynamics of a structured population that is subject to the combined effects of environmental stochasticity, competition for resources, spatio-temporal heterogeneity and dispersal. The population is…

In this paper we study singular limits of congestion-averse growth models, connecting different models describing the effect of congestion. These models arise in particular in the context of tissue growth. The main ingredient of our…

Developing epithelial tissues coordinate cell proliferation and mechanical forces to achieve proper size and shape. As epithelial cells tightly adhere together to form the confluent tissue, the distribution of cell areas significantly…

Essential to each other, growth and exploration are jointly observed in populations, be it alive such as animals and cells or inanimate such as goods and money. But their ability to move, crucial to cope with uncertainty and optimize…

Bacteria regulate their motility through a variety of mechanisms, including quorum sensing (QS) and other density-dependent responses mediated by diffusible signals. While nonlinear density-dependent motility is well known in active-matter…

How far is neuroepithelial cell proliferation in the developing central nervous system a deterministic process? Or, to put it in a more precise way, how accurately can it be described by a deterministic mathematical model? To provide tracks…

A population is said to have an ideal free distribution in a spatially heterogeneous but temporally constant environment if each of its members have chosen a fixed spatial location in a way that optimizes its individual fitness, allowing…

Spatially explicit models have been widely used in today's mathematical ecology and epidemiology to study persistence and extinction of populations as well as their spatial patterns. Here we extend the earlier work--static dispersal between…