Related papers: A nonlocal continuum model for biological aggregat…
Understanding the structural evolution of granular systems is a long-standing problem. A recently proposed theory for such dynamics in two dimensions predicts that steady states of very dense systems satisfy detailed-balance. We analyse…
Mathematical modelling of biological population dynamics often involves proposing high fidelity discrete agent-based models that capture stochasticity and individual-level processes. These models are often considered in conjunction with an…
The cohesive collective motion (flocking, swarming) of autonomous agents is ubiquitously observed and exploited in both natural and man-made settings, thus, minimal models for its description are essential. In a model with continuous space…
We investigate methods for modelling metabolism within populations of cells. Typically one represents the interaction of a cloned population of cells with their environment as though it were one large cell. The question is as to whether any…
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…
Inspired by motile cells in tissue formation, we find that active systems of self-aligning adhesive particles undergo ballistic aggregation through a flocking transition. This kinetic regime emerges when the cluster persistence length grows…
Cellular aggregates play a significant role in the evolution of biological systems such as tumor growth, tissue spreading, wound healing, and biofilm formation. Analysis of such biological systems, in principle, includes examining the…
The goal of this paper is to provide mathematically rigorous tools for modelling the evolution of a community of interacting individuals. We model the population by a measure space where the measure determines the abundance of individual…
We study a multilayer SIR model with two levels of mixing, namely a global level which is uniformly mixing, and a local level with two layers distinguishing household and workplace contacts, respectively. We establish the large population…
Numerous problems in development, regeneration, and disease involve simultaneous evolution of both spatial organization and the internal state of the constituents in addition to local interactions and crowding. This motivates us to study a…
We consider N run and tumble particles in one dimension interacting via a linear 1D Coulomb potential, an active version of the rank diffusion problem. It was solved previously for N = 2 leading to a stationary bound state in the attractive…
We introduce a theoretical model for the compaction of granular materials by discrete vibrations which is expected to hold when the intensity of vibration is low. The dynamical unit is taken to be clusters of granules that belong to the…
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…
Flocking refers to collective behavior of a large number of interacting entities, where the interactions between discrete individuals produce collective motion on the large scale. We employ an agent-based model to describe the microscopic…
The stochastic Eden model of charged particles aggregation in two-dimensional systems is presented. This model is governed by two parameters: screening length of electrostatic interaction, $\lambda $, and short range attraction energy, $E$.…
The properties of a hinged floating elastic sheet of finite length under compression are considered. Numerical continuation is used to compute spatially localized buckled states with many spatially localized folds. Both symmetric and…
We report that population dynamics in fluctuating environment accompanies mathematically equivalent structure to steady state thermodynamics. By employing the structure, population growth in fluctuating environment is decomposed into…
There exists a wide variety of works on the dynamics of large populations ranging from simple heuristic modeling to those based on advanced computer supported methods. Their interconnections, however, remain mostly vague, which…
We numerically study a model convection system of a suspension of self-propelled particles, motivated by recent experimental findings of localized and bistable bioconvection pattern, being distinct from classical Rayleigh--B\'{e}nard…
There are many natural, physical, and biological systems that exhibit multiple time scales. For example, the dynamics of a population of ticks can be described in continuous time during their individual life cycle yet discrete time is used…