Author: David Martin

Publisher:

Published: 2021

Total Pages: 0

ISBN-13:

Active Matter deals with the study of colloidal systems for which Brownian motion is replaced by a persistent self-propulsion. The main motivation of Active Matter is to provide a theoretical framework describing ensembles of interacting living entities. Such an approach has already led to breakthroughs in our understanding of living systems, be it in bacterial dynamics or for the analysis of bird flocks. But the successes of active matter extend beyond living matter. The field has inspired a wealth of experiments dealing with artificial materials: Quincke rollers, Janus colloids, or shaken grains among other examples. In these setups, the active entities are synthetic units whose self-propulsion relies on a physical rather than biological mechanism. This manuscript contributes to the active matter roadmap along four axes: the exact study of a workhorse model of active dynamics, the characterization of the order in the flocking transition, the study of the interplay between flocks and jams, and the presentation of anisotropy-induced long-ranged correlations. As a starting point, I present in chapter 2 an exact perturbative analysis of the nonequilibrium model called Active Ornstein Uhlenbeck Particles (AOUPs). Using it, I derive analytically the steady-state distribution of an AOUP and quantify its departure from equilibrium through the characterization of three signatures: the deviation from Boltzmann distribution, the ratchet current, and the entropy production rate. I then generalize these results to the case of a particle experiencing both active and passive noises. The interplay between the two types of fluctuations leads to a rich phenomenology for the ratchet current and the entropy production rate when the temperature is varied: decline or non-monotonicity, divergence or decay at high T. Finally, I discuss the extension of these results to the case of N active particles in dimension d. In the third chapter, I revisit the transition to collective motion according to the type of microscopic alignment at play. Be it so-called metric or topological interactions, I show that the emergence of flocking generically remains discontinuous. To achieve this result, I present the notion of Fluctuation-Induced First Order Phase Transition (FIFOT) and apply it to models of collective motion. In the fourth chapter, I study the outbreak of Motility-Induced Phase Separation (MIPS) in flocking models. To this aim, I report the appearance of jams in dense assemblies of Quincke rollers. At the transition, which we dubbed active solidification, the jams propagate upstream the homogeneous flock of rollers. I then establish a theoretical model for active solidification which allows me to explore the rich phenomenology emerging from the interplay between MIPS and collective motion. By varying relevant 1 parameters, I predict the existence of a phase where flocking bands coexist with active jams. In the fifth chapter, I study long-ranged fluctuations in an active system. Starting from a microscopic dynamics only endowed with short-ranged anisotropic interactions, I show the emergence of macroscopic long-ranged density correlations. I then assess the effect of these correlations on the pressure exerted by the system in order to probe for a possible Casimir-like behaviour. Finally, in the last chapter, I conclude this manuscript by summarizing the contributions developed in the four previous chapters. For each of these works, I propose a possible future research direction. 2.