Analysis of the Heterogeneous Vectorial Network Model of Collective Motion

We analyze the vectorial network model, a stochastic protocol that describes collective motion of groups of agents, randomly mixing in a planar space. Motivated by biological and technical applications, we focus on a heterogeneous form of the model, where agents have different propensity to interact with others. By linearizing the dynamics about a synchronous state and leveraging an eigenvalue perturbation argument, we establish a closed-form expression for the mean-square convergence rate to the synchronous state in the absence of additive noise. These closed-form findings are extended to study the effect of added noise on the agents' coordination, captured by the polarization of the group. Our results reveal that heterogeneity has a detrimental effect on both the convergence rate and the polarization, which is nonlinearly moderated by the average number of connections in the group. Numerical simulations are provided to support our theoretical findings.</p

Inferring the size of a collective of self-propelled Vicsek particles from the random motion of a single unit

nferring the size of a collective from the motion of a few accessible units is a fundamental problem in network science and interdisciplinary physics. Here, we recognize stochasticity as the commodity traded in the units’ interactions. Drawing inspiration from the work of Einstein-Perrin-Smoluchowski on the discontinuous structure of matter, we use the random motion of one unit to identify the footprint of every other unit. Just as the Avogadro’s number can be determined from the Brownian motion of a suspended particle in a liquid, the size of the collective can be inferred from the random motion of any unit. For self-propelled Vicsek particles, we demonstrate an inverse proportionality between the diffusion coefficient of the heading of any particle and the size of the collective. We provide a rigorous method to infer the size of a collective from measurements of a few units, strengthening the link between physics and collective behavior

Lattice models for granular and active matter fluctuating hydrodynamics

This thesis investigates the common nature of granular and active systems, which is rooted in their intrinsic out-of-equilibrium behavior, with the aim of finding minimal models able to reproduce and predict the complex collective behavior observed in experiments and simulations. Granular and active matter are among the most studied systems in out-of-equilibrium statistical physics. The thesis guides readers through the derivation of a fluctuating hydrodynamic description of granular and active matter by means of controlled and transparent mathematical assumptions made on a lattice model. It also shows how a macroscopic description can be provided from microscopic requirements, leading to the prediction of collective states such as cooling, swarming, clustering and the transitions among them. The analytical and numerical results shed new light on the physical connection between the local, microscopic properties of few particles and the macroscopic collective motion of the whole system

Dynamique collective de particules auto-propulsées : ondes, vortex, essaim, tressage

The emergence of coherent motion at large scale has been widely observed in animal populations (bird flocks, fish schools, bacterial swarms...) and more recently in artificial systems. Such ensembles of self-propelled individuals, capable of aligning their velocities, are commonly referred to as polar active materials. They display unique physical properties, which we investigate in this theoretical thesis.We first describe a population of self-propelled colloids. In strong connection with the experiments, we model the dynamics from the individual level to the macroscopic scale. The theoretical results account for the emergence and the structure of coherent patterns: (i)~transition to collective motion, (ii)~propagation of polar spatial structures, (iii)~damping of density fluctuations in a polar liquid, (iv)~heterogeneous vortex in confined geometries.We then follow a more formal perspective, and study the non-linear excitations which propagate in polar active systems. We analyze the hydrodynamic theories of active matter using a dynamical-system framework. This approach makes it possible to rationalize the experimental and numerical observations reported so far.Finally, we propose a complementary approach to characterize active populations. Combining numerical and analytical results, we study the geometric properties of the individual trajectories and their entanglement within three-dimensional flocks. We suggest that these observables should provide powerful tools to describe animal flocks in the wild.L'émergence de mouvements cohérents à grande échelle a été abondamment observée dans les populations animales (nuées d'oiseaux, bancs de poissons, essaims de bactéries...) et plus récemment au sein de systèmes artificiels. De tels ensembles d'individus auto-propulsés, susceptibles d'aligner leurs vitesses, présentent des propriétés physiques singulières. Cette thèse théorique étudie divers aspects de ces systèmes actifs polaires.Dans un premier temps, nous avons modélisé une population de colloïdes auto-propulsés. En étroite association avec les travaux expérimentaux, nous avons décrit la dynamique du niveau individuel à l'échelle macroscopique. Les résultats théoriques expliquent l'émergence et la structure de motifs cohérents : (i) transition vers le mouvement collectif, (ii) propagation de structures spatiales polarisées, (iii) amortissement des fluctuations de densité dans un liquide polaire, (iv) vortex hétérogène dans des géométries confinées.D'un point de vue plus fondamental, nous avons ensuite étudié les excitations non linéaires qui se propagent dans les systèmes actifs polaires. L'analyse des théories hydrodynamiques de la matière active, à l'aide d'outils issus des systèmes dynamiques, a permis de rationaliser les observations expérimentales et numériques reportées jusqu'ici.Enfin, nous avons proposé une approche complémentaire pour caractériser les populations actives. Associant étude numérique et résultats analytiques, nous avons étudié les propriétés géométriques des trajectoires individuelles, ainsi que leur enchevêtrement au sein de groupes tridimensionnels. Ces observables pourraient permettre de sonder efficacement la dynamique de populations animales

Activity Mediated Interactions in Soft Matter. Structure, Interactions, and Phase Transitions

[eng] In this thesis we asses the phenomena of arising interactions in soft matter in coexistence with soft active matter. As a non-equilibrium bath we introduce ensembles of self-propelled particles, granular shaken beds, and photo active catalytic particles. We start the thesis with a detailed study of the widely used Active Brownian Particle (ABP) model. This model exhibits a non-equilibrium phase transition which has been intensively studied in recent years, we have finally reported that this transition satisfies all features of equilibrium first order phase transitions. Then, we introduce aligning interactions in ABP and characterize the emergent collective phenomena. In parallel, we explore the emergent forces, from mechanical contact forces, in probe particles in suspensions of aligning active particles and horizontally shaken granular beds. We characterize the forces and identify the emergence of long range interactions in both systems, in aligning active particles long range attractive interactions appear as alignment is increased, and in granular shaken media when the pair of particles align in the shaking direction. Finally, we conclude this thesis with the study of emergent interactions in spherically symmetric systems of catalytic active particles. Symmetry does not permit such particles to propell but the symmetry is broken with the addition of neighboring particles. We model the pair interaction in terms of the relative velocity between particles, and proceed to explore the emergent structures in mixtures of catalytic magnetic particles, and passive particles. We have unveiled the formation of clusters of passive particles. The addition of magnetic interactions between active particles leads to the formation of ramified gel-like structures for dense configurations of active particles. In this case, experimentalists have checked the formation of structures with the same morphologies in experiments in the laboratory.[spa] En aquesta tesi abordem el fenomen de les interaccions emergents en matèria tova en coexistència amb matèria tova activa. Com a sistemes de matèria tova activa introduïm col·lectius de partícules autopropulsades, col·loides amb capacitat de catalitzar productes químics i medis granulars agitats. Primer de tot estudiem en detall un model molt estès per a partícules actives, el model de les partícules actives brownianes (ABP). D'aquest model estudiem amb detall una transició de fase de no equilibri i comprovem que la transició satisfà amb les característiques d'una transició en equilibri de primer ordre. Seguidament incorporem interaccions d'alineació en el model de partícules actives i procedim a estudiar les propietats col·lectives de les suspensions de partícules actives amb alineació. Per tal d'abordar l'objectiu de la tesi introduïm partícules de prova en suspensions de partícules actives, i en medis granulars amb forçament periòdic horitzontal, amb diferents paràmetres d'activitat per tal d'estudiar les forces, des d'un punt de vista mecànic, que emergeixen entre les parelles. Hem caracteritzat les forces i hem identificat l'aparició d'interaccions de llarg abast per sistemes de partícules amb alineació i en sistemes granulars en la direcció del forçament. Finalment, tanquem la tesi amb l'estudi i modelització d'interaccions emergents per a partícules catalítiques amb simetria esfèrica. La simetria no permet a les partícules d'autopropulsar-se però la presència de partícules al seu entorn sí que dóna lloc a interaccions, en forma de velocitats induïdes. Amb un model raonable de la interacció a distància hem calibrat la magnitud de la interacció amb sistemes experimentals i procedit a caracteritzar les estructures emergents per a mescles de partícules actives i passives que van des de la formació d'agregats en forma de clústers. L'addició d'interaccions magnètiques entre partícules actives permet la formació d'estructures ramificades de tipus gel. En aquest cas l'equip experimental ha pogut comparar l'aparició d'estructures amb les mateixes característiques al laboratori