Related papers: Non-mean-field Vicsek-type models for collective b…
In this paper the normal collision of spherical particles is investigated. The particle interaction is modelled in a macroscopic way using the Hertzian contact force with additional linear damping. The goal of the work is to develop an…
We consider systems of agents interacting through topological interactions. These have been shown to play an important part in animal andhuman behavior. Precisely, the system consists of a finite number of particles characterized by their…
Active agents with time-delayed interactions arise naturally in various real-world systems, such as biological systems, transportation networks and robotic swarms. Such systems are typically modeled as Delay Differential Equations (DDEs)…
We present a mathematical model based on a system of partial differential equations (PDEs) with cross-diffusion and reaction terms to describe ecological interactions between multiple bacterial species and substrates within microaggregates,…
When particles move at a constant speed and have the tendency to align their directions of motion, ordered large scale movement can emerge despite significant levels of noise. Many variants of this model of self-propelled particles have…
In this article we study the convergence of a stochastic particle system that interacts through threshold hitting times towards a novel equation of McKean-Vlasov type. The particle system is motivated by an original model for the behavior…
Biological systems are non-linear, include unobserved variables and the physical principles that govern their dynamics are partly unknown. This makes the characterization of their behavior very challenging. Notably, their activity occurs on…
We introduce a system of self-propelled agents (active Brownian particles) with velocity alignment in two spatial dimensions and derive a mean-field theory from the microscopic dynamics via a nonlinear Fokker-Planck equation and a moment…
The Vicsek model is a very popular individual based model which describes collective behavior among animal societies. A macroscopic version of the Vicsek model has been derived from a large scale limit of this individual based model…
We derive macroscopic dynamics for self-propelled particles in a fluid. The starting point is a coupled Vicsek-Stokes system. The Vicsek model describes self-propelled agents interacting through alignment. It provides a phenomenological…
We propose a particle system of diffusion processes coupled through a chain-like network structure described by an infinite-dimensional, nonlinear stochastic differential equation of McKean-Vlasov type. It has both (i) a local chain…
Suspensions of swimming particles exhibit complex collective behaviors driven by hydrodynamic interactions, showing persistent large-scale flows and long-range correlations. While heavily studied, it remains unclear how such structures…
Usage, manipulation, transport, delivery, and mixing of granular or particulate media, comprised of spherical or polyhedral particles, is commonly encountered in industrial sectors of construction (cement and rock fragments), pharmaceutics…
We present a study of pedestrian motion along a corridor in a non-panic regime (e.g., schools, hospitals or airports). Such situations have been discussed so far within the Social Force Model (SFM). We suggest to enrich this model by…
Many vesicles have a spherical resting shape and exposure to fluid flows induces an exchange between sub-optical area and visible (systematic) deformation, while the total area is conserved. The dynamics which controls the exchange between…
Persistence of motion is the tendency of an object to maintain motion in a direction for short time scales without necessarily being biased in any direction in the long term. One of the most appropriate mathematical tools to study this…
We introduce a Vicsek-like flocking model with a minimal form of time-delayed orientational interactions, in which the delays occur on a time scale that is well-separated from other time scales in the model. We achieve this by implementing…
The thermodynamics and the dynamics of particle systems with infinite-range coupling display several unusual and new features with respect to systems with short-range interactions. The Hamiltonian Mean Field (HMF) model represents a…
Studying systems where many individual bodies in motion interact with one another is a complex and interesting area. Simple mechanisms that may be determined for biological, chemical, or physical reasons can lead to astonishingly complex…
We consider an infinite system of coupled stochastic differential equations (SDE) describing dynamics of the following infinite particle system. Each partricle is characterised by its position $x\in \mathbb{R}^{d}$ and internal parameter…