Related papers: Aggregation-diffusion phenomena: from microscopic …
Given a large ensemble of interacting particles, driven by nonlocal interactions and localized repulsion, the mean-field limit leads to a class of nonlocal, nonlinear partial differential equations known as aggregation-diffusion equations.…
The complicated dynamics of the contact line of a moving droplet on a solid substrate often hamper the efficient modeling of microfluidic systems. In particular, the selection of the effective boundary conditions, specifying the contact…
The transition from a microscopic model for the movement of many particles to a macroscopic continuum model for a density flow is studied. The microscopic model for the free flow is completely deterministic, described by an interaction…
Aggregation-diffusion equations are foundational tools for modelling biological aggregations. Their principal use is to link the collective movement mechanisms of organisms to their emergent space use patterns in a concrete mathematical…
A new diffuse interface model for a two-phase flow of two incompressible fluids with different densities is introduced using methods from rational continuum mechanics. The model fulfills local and global dissipation inequalities and is also…
A new diffuse interface model for a two-phase flow of two incompressible fluids with different densities is introduced using methods from rational continuum mechanics. The model fulfills local and global dissipation inequalities and is…
We consider a random diffusion dynamics for an infinite system of hard spheres of two different sizes evolving in $\mathbb{R}^d$, its reversible probability measure, and its projection on the subset of the large spheres. The main feature is…
Over the past decades, nonlocal models have been widely used to describe aggregation phenomena in biology, physics, engineering, and the social sciences. These are often derived as mean-field limits of attraction-repulsion agent-based…
Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial…
We consider a congested aggregation model that describes the evolution of a density through the competing effects of nonlocal Newtonian attraction and a hard height constraint. This provides a counterpoint to existing literature on…
Diffusion in an evolving environment is studied by continuos-time Monte Carlo simulations. Diffusion is modelled by continuos-time random walkers on a lattice, in a dynamic environment provided by bubbles between two one-dimensional…
This article is an invitation. It is, first, an invitation to consider as a subject worthy of attention the wide range of situations where small discrete elements, either bubbles, droplets or solid particles, are embedded in turbulent…
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…
We present a model for cell growth, division and packing under soft constraints that arise from the deformability of the cells as well as of a membrane that encloses them. Our treatment falls within the framework of diffuse interface…
Reversible diffusion limited cluster aggregation of hard spheres with rigid bonds was simulated and the self diffusion coefficient was determined for equilibrated systems. The effect of increasing attraction strength was determined for…
There are three fundamental physical processes that gives rise to the morphology of a surface: deposition, surface diffusion and desorption. The characteristics of the interfaces generated by the combination of deposition and surface…
We study an aggregation PDE with competing attractive and repulsive forces on a sphere of arbitrary dimension. In particular, we consider the limit of strongly localized repulsion with a constant attraction term. We prove convergence of…
A simple three-dimensional model of a fluid whose constituent particles interact via a short range attractive and long range repulsive potential is used to model the aggregation into large spherical-like clusters made up of hundreds of…
We study colloidal particle dynamics of a model glass system using confocal and fluorescence microscopy as the sample evolves from a hard-sphere glass to a liquid with attractive interparticle interactions. The transition from hard-sphere…
In this paper we propose and validate a multiscale model for the description of particle diffusion in presence of trapping boundaries. We start from a drift-diffusion equation in which the drift term describes the effect of bubble traps,…