Related papers: Modelling pattern formation through differential r…
Discrete particle simulation methods have been used to study axial segregation in a horizontal rotating cylinder that is partially filled with a mixture of two different kinds of granular particles. Under suitable conditions segregation was…
Dynamics of two particles with short range repulsive or attractive interaction is studied numerically in the Harper model. It is shown that interaction leads to appearance of localized states and pure-point spectrum component in the case…
We prove the existence of solutions of a cross-diffusion parabolic population problem. The system of partial differential equations is deduced as the limit equations satisfied by the densities corresponding to an interacting particles…
Extensive simulations are performed of the diffusion-limited reaction A$+$B$\to 0$ in one dimension, with initially separated reagents. The reaction rate profile, and the probability distributions of the separation and midpoint of the…
We consider a collection of weakly interacting diffusion processes moving in a two-scale locally periodic environment. We study the large deviations principle of the empirical distribution of the particles' positions in the combined limit…
We numerically examine binary-sized granular mixtures confined between two parallel walls subjected to vertical vibration using the discrete element method. For a size ratio of $3$ between large and small particles, we study the structure…
We reveal that the mechanical pulsation of locally synchronised particles is a generic route to propagate deformation waves. We consider a model of dense repulsive particles whose activity drives periodic change in size of each individual.…
During drying of colloidal suspensions, colloidal particles can form concentrated particle layers beneath the receding free surface. The drying rate can gradually decrease with the growth of the particle layers. We construct a model to…
Repulsion between individuals within a finite radius is encountered in numerous applications, including cell exclusion, i.e. avoidance of overlapping cells, bird flocks, or microscopic pedestrian models. We define such individual based…
This paper deals with the derivation of a collective model of cell populations out of an individual-based description of the underlying physical particle system. By looking at the spatial distribution of cells in terms of time-evolving…
Turing's mechanism is often invoked to explain periodic patterns in nature, although direct experimental support is scarce. Turing patterns form in reaction-diffusion systems when the activating species diffuse much slower than the…
This paper is a first step to chase the ambitious objective of developing a mathmatical theory of living systems. The contents refer modeling large systems of interacting living entities with the aim of describing their collective behaviors…
In this work, we consider a diffusive two-species d-dimensional model and study it in great details. Two types of particles, with hard-core, diffuse symmetrically and cross each other. For arbitrary dimensions, we obtain the exact density,…
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…
Recently, we proposed a self-propelled particle model with competing alignment interactions: nearby particles tend to align their velocities whereas they anti-align their direction of motion with particles which are further away [R.…
Colloidal particles of two types, driven in opposite directions, can segregate into lanes [Vissers et al. Soft Matter 7, 2352 (2011)]. This phenomenon can be reproduced by two-dimensional Brownian dynamics simulations of model particles…
Pattern formation often occurs in confined systems, yet how boundaries shape patterning dynamics is unclear. We develop techniques to analyze confinement effects in nonlocal advection-diffusion equations, which generically capture the…
Cell cortex contraction is essential for shaping cells, enabling movement, ensuring proper division, maintaining tissue integrity, guiding development, and responding to mechanical signals - all critical for the life and health of…
A molecule traveling in a realistic propagation environment can experience stochastic interactions with other molecules and the environment boundary. The statistical behavior of some isolated phenomena, such as dilute unbounded molecular…
Segregation patterns of size-bidisperse particle mixtures in a fully-three-dimensional flow produced by alternately rotating a spherical tumbler about two perpendicular axes are studied over a range of particle sizes and volume ratios using…