Related papers: Kinetic equations and self-organized band formatio…
The Vicsek-BGK equation is a kinetic model for alignment of particles moving with constant speed between stochastic reorientation events with sampling from a von Mises distribution. The spatially homogeneous model shows a steady state…
In this paper, we begin by reviewing a certain number of mathematical challenges posed by the modelling of collective dynamics and self-organization. Then, we focus on two specific problems, first, the derivation of fluid equations from…
A variant of the well known Vicsek model of the collective motion of a group of agents has been studied where the range of interactions are spatially quenched and non-overlapping. To define such interactions, the underlying two dimensional…
The emergence of organized multiscale patterns resulting from convection is ubiquitous, observed throughout different cloud types. The reproduction of such patterns by general circulation models remains a challenge due to the complex nature…
We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis on nonlinear and stochastic dynamics of…
We study the behaviour of interacting self-propelled particles, whose self-propulsion speed decreases with their local density. By combining direct simulations of the microscopic model with an analysis of the hydrodynamic equations obtained…
We study analytically and numerically a model metabolic cycle composed of an arbitrary number of species of catalytically active particles. Each species converts a substrate into a product, the latter being used as the substrate by the next…
We describe a generic theoretical framework, denoted as the Boltzmann-Ginzburg-Landau approach, to derive continuous equations for the polar and/or nematic order parameters describing the large scale behavior of assemblies of point-like…
We introduce a model for self-organized dynamics which, we argue, addresses several drawbacks of the celebrated Cucker-Smale (C-S) model. The proposed model does not only take into account the distance between agents, but instead, the…
How large ecosystems can create and maintain the remarkable biodiversity we see in nature is probably one of the biggest open questions in science, attracting attention from different fields, from Theoretical Ecology to Mathematics and…
It is shown how to explicitly coarse-grain the microscopic dynamics of the Vicsek model for self-propelled agents. The macroscopic transport equations are derived by means of an Enskog-type kinetic theory. Expressions for all transport…
We consider several systems of nonlinear hyperbolic conservation laws describing the dynamics of nonlinear waves in presence of phase transition phenomena. These models admit under-compressive shock waves which are not uniquely determined…
A phenomenological description for active bundles of polar filaments is presented. The activity of the bundle results from crosslinks, that induce relative displacements between the aligned filaments. Our generic description is based on…
We analyze the continuous time evolution of a $d$-dimensional system of $N$ self propelled particles with a kinematic constraint on the velocities inspired by the original Vicsek's one \cite{VCB-JCS}. Interactions among particles are…
Here we provide a detailed analysis, along with some extensions and additonal investigations, of a recently proposed self-organised model for the evolution of complex networks. Vertices of the network are characterised by a fitness variable…
In the present work we have studied collectives of active disks with an energy depot, moving in the two-dimensional plane and interacting via excluded volume. The energy depot accounts for the extraction of energy taking place at the level…
In this study we formulate a theoretical approach, based on a Boltzmann-like kinetic equation, to describe pattern formation in two-dimensional mixtures of microtubular filaments and molecular motors. Following the previous work by Aranson…
The physics of active biological matter, such as bacterial colonies and bird flocks, exhibiting interesting self-organizing dynamical behavior has gained considerable importance in recent years. Recent theoretical advances use techniques…
Spatial self-organization emerges in distributed systems exhibiting local interactions when nonlinearities and the appropriate propagation of signals are at work. These kinds of phenomena can be modeled with different frameworks, typically…
Systems of dynamical interactions between competing species can be used to model many complex systems, and can be mathematically described by {\em random} networks. Understanding how patterns of activity arise in such systems is important…