Related papers: Modelling pattern formation through differential r…
We introduce two 2D mechanical models reproducing the evolution of two viscous tissues in contact. Their main property is to model the swirling cell motions while keeping the tissues segregated, as observed during vertebrate embryo…
This chapter focuses on the mathematical modelling of active particles (or agents) in crowded environments. We discuss several microscopic models found in literature and the derivation of the respective macroscopic partial differential…
A model for a monolayer of two types of particles spontaneously forming ordered patterns is studied by a mesoscopic theory and by MC simulations. We assume hard-cores of the same size for both components, short-range attraction long-range…
The phenomena of radial and axial segregation in a horizontal rotating cylinder containing a mixture of granular particles of two different species have been modeled using discrete particle simulation. Space-time plots and detailed imagery…
Segregation of different cell types is a crucial process for the pattern formation in tissues, in particular during embryogenesis. Since the involved cell interactions are complex and difficult to measure individually in experiments,…
A binary mixture of particles interacting with spherically-symmetric potentials leading to microsegregation is studied by theory and molecular dynamics (MD) simulations. We consider spherical particles with equal diameters and volume…
We propose a model of mobile agents to construct social networks, based on a system of moving particles by keeping track of the collisions during their permanence in the system. We reproduce not only the degree distribution, clustering…
This chapter investigates some mechanisms behind pattern formation driven by competitive-only or repelling interactions, and explores how these patterns are influenced by different types of particle movement. Despite competition and…
Macroscopic models for systems involving diffusion, short-range repulsion, and long-range attraction have been studied extensively in the last decades. In this paper we extend the analysis to a system for two species interacting with each…
We present and analyse a model for cell signalling processes in biological tissues. The model includes diffusion and nonlinear reactions on the cell surfaces, and both inter- and intracellular signalling. Using techniques from the theory of…
Accurate interaction potentials between microscopic components such as colloidal particles or cells are crucial to understanding a range of processes, including colloidal crystallization, bacterial colony formation, and cancer metastasis.…
We present a statistical model of non-interacting individual classical particles that may lead to a microscopic implementation of quantum mechanics. The model requires the action of a special type of detector that detects and records…
Interacting populations often create complicated spatiotemporal behavior, and understanding it is a basic problem in the dynamics of spatial systems. We study the two-species case by simulations of a host--parasitoid model. In the case of…
We study segregation of a binary mixture of similarly charged particles under shear using particle-based simulations. We simulate particle dynamics using a discrete-element model including electrostatic interactions and find that particles…
Granular materials segregate spontaneously due to differences in particle size, shape, density and flow behaviour. In this paper we experimentally investigate density-difference-driven segregation for a range of density ratios and a range…
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…
A simple phenomenological model of a binary granular mixture is developed and investigated numerically. We attempt to model the experimental system of [1,2] where a horizontally vibrated binary monolayer was found to exhibit a transition…
We propose a sequential Monte Carlo algorithm for parameter learning when the studied model exhibits random discontinuous jumps in behaviour. To facilitate the learning of high dimensional parameter sets, such as those associated to neural…
Throughout developmental biology and ecology, transport can be driven by nonlocal interactions. Examples include cells that migrate based on contact with pseudopodia extended from other cells, and animals that move based on their vision of…
We propose a new model for the description of complex granular particles and their interaction in molecular dynamics simulations of granular material in two dimensions. The grains are composed of triangles which are connected by deformable…