Related papers: The Physics of the Vicsek Model
These are lecture notes for a series of lectures given at the Les Houches Summer School on Integrability in Atomic and Condensed Matter Physics, 30 July to 24 August 2018. The same series of lectures has also been given at the Tokyo…
We present existence, uniqueness and continuous dependence results for some kinetic equations motivated by models for the collective behavior of large groups of individuals. Models of this kind have been recently proposed to study the…
The classic Vicsek model [Phys.Rev.Lett. {\bf75},1226(1995)] is studied in the regime of very low noise intensities, which is shown to be characterized by a cluster (MC) that contains a macroscopic fraction of the system particles. It is…
We study a system of self-propelled particles whose alignment with neighbors depends on the degree of local alignment. We show that such a local conformity interaction naturally yields a Vicsek-type model with pairwise and three-body…
The aim of this paper is to calculate the time dependence of the mean position (and orientation) of a fluid particle when a fluid system at thermodynamic equilibrium is submitted to a mechanical action. The starting point of this novel…
This is a series of four lectures presented at the 2015 Enrico Fermi summer school in Varenna. The aim of the lectures is to give an introduction to the hydrodynamics of active matter concentrating on low Reynolds number examples such as…
In this paper, we review recent developments on the derivation and properties of macroscopic models of collective motion and self-organization. The starting point is a model of self-propelled particles interacting with its neighbors through…
The goal of these lecture notes is to present in a unified way various models for the dynamics of aligning self-propelled rigid bodies at different scales and the links between them. The models and methods are inspired from [12,13], but, in…
The standard model of particle physics represents the cornerstone of our understanding of the microscopic world. In these lectures we review its contents and structure, with a particular emphasis on the central role played by symmetries and…
We consider the dynamics of the system of self propelling particles modeled via the Vicsek algorithm in continuum time limit. It is shown that the alignment process for the velocities can be subdivided into two regimes: "fast" kinetic and…
Active particles contain internal degrees of freedom with the ability to take in and dissipate energy and, in the process, execute systematic movement. Examples include all living organisms and their motile constituents such as molecular…
An Ising-type Vicsek model is proposed for collective motion and sudden direction change in a population of self-propelled particles. Particles move on a linear lattice with velocity +1 or -1 in the one-dimensional model. The probability of…
The objective of statistical physics is to understand macroscopic behavior of a many-body system from the interactions of the constituents of that system. When many-body systems reach critical states, simple universal and scaling behaviors…
Three-dimensional simulations with fully resolved hydrodynamics are performed to study the collective motion of model swimmers in confinement. We show that certain swimming mechanisms can lead to traveling wave-like collective motion even…
The generalized transport equations for a consistent description of kinetic and hydrodynamic processes in dense gases and liquids are considered. The inner structure of the generalized transport kernels for these equations is established.…
A new methodology is developed to integrate numerically the equations of motion for classical many-body systems in molecular dynamics simulations. Its distinguishable feature is the possibility to preserve, independently on the size of the…
We present a detailed description of the generalized geometric cluster algorithm for the efficient simulation of continuum fluids. The connection with well-known cluster algorithms for lattice spin models is discussed, and an explicit full…
In these lecture notes from the Les Houches School, we discuss collective motion in model experiments of active systems. We specifically discuss walking grains and colloidal rollers experiments. In both cases, we focus on the theoretical…
We discuss several ways of illustrating fundamental concepts in statistical and thermal physics by considering various models and algorithms. We emphasize the importance of replacing students' incomplete mental images by models that are…
We develop a general hydrodynamic theory describing a system of interacting actively propelling particles of arbitrary shape suspended in a viscous fluid. We model the active part of the particle motion using a slip velocity prescribed on…