Suspensions of the aerobic bacteria {\it Bacilus subtilis} develop patterns and flows from the interplay of motility, chemotaxis and buoyancy.In sessile drops, such bioconvectively driven flows carry plumes down the slanted meniscus and concentrate cells at the drop edge, while in pendant drops such self-concentration occurs at the bottom.These dynamics are explained quantitatively by a mathematical model consisting of oxygen diffusion and consumption, chemotaxis, and viscous fluid dynamics.Concentrated regions in both geometries comprise nearly close-packed populations, forming the collective ``Zooming BioNematic'' (ZBN) phase.This state exhibits large-scale orientational coherence, analogous to the molecular alignment of nematic liquid crystals, coupled with remarkable spatial and temporal correlations of velocity and vorticity, as measured by both novel and standard applications of particle imaging velocimetry.To probe mechanisms leading to this phase, response of individual cells to steric stress was explored, finding that they can reverse swimming direction at spatial constrictions without turning the cell body.The consequences of this propensity to flip the flagella are quantified, showing that "forwards" and "backwards" motion are dynamically and morphologically indistinguishable.Finally, experiments and mathematical modeling show that complex flows driven by previously unknown bipolar flagellar arrangements are induced when {\it B. subtilis} are confined in a thin layer of fluid, between asymmetric boundaries.The resulting driven flow circulates around the cell body ranging over several cell diameters, in contrast to the more localized flows surrounding free swimmers.This discovery extends our knowledge of the dynamic geometry of bacteria and their flagella, and reveals new mechanisms for motility-associated molecular transport and inter-cellular communication.

This thesis investigates several phenomena that are associated with (self-)thermophoretic Janus particles with hemispheres made from different materials serving as a paradigm for active propul- sion on the microscale. (i) The dynamics of a single Janus sphere in the external temperature field created by an immobilized heat source is studied. I show that the particle’s angular velocity is solely determined by the temperature profile on the equator between the Janus particle’s hemispheres and their phoretic mobility contrast. (ii) The distinct polarization-density patterns observed for active-particle suspensions in activity landscapes are addressed. The results of my approximate theoretical model agree well with exact numerical and measurement data for a thermophoretic microswimmer, and can serve as a template for more complex applications. The essential physics behind the formal results is robustly captured and elucidated by a schematic two-species “run- and-tumble” model. (iii) I investigate coarse-grained models of suspended self-thermo- phoretic microswimmers. Starting from atomistic molecular dynamics simulations, the coarse-grained de- scription of the fluid in terms of a local molecular temperature field is verified, and effective nonequilibrium temperatures characterizing the particle’s so called hot Brownian motion are mea- sured from simulations. They are theoretically shown to remain relevant for any further spatial coarse-graining towards a hydrodynamic description of the entire suspension as a homogeneous complex fluid. / In dieser Arbeit untersuche ich mehrere Phänomene, die im Zusammenhang mit (selbst-)thermo- phoretischen Janusteilchen auftreten. Diese Teilchen bestehen aus zwei Halbkugeln mit unter- schiedlichen Materialeigenschaften und dienen in dieser Arbeit als Musterbeispiel für aktive Fort- bewegung auf der Mikroskala. (i) Die Dynamik eines einzelnen Janusteilchens im externen Temper- aturfeld einer ortsfesten Heizquelle wird untersucht. Es wird gezeigt, dass die Winkelgeschwindigkeit des Teilchens ausschließlich durch das Temperaturprofil am Äquator zwischen den Hemisphären des Janusteilchens und dem Unterschied ihrer phoretischen Mobilitäten bestimmt wird. (ii) Ich befasse mich mit den charakteristischen Polarisations- und Dichteprofilen, die für aktive Teilchen in Aktivitätslandschaften beobachtet werden. Die Ergebnisse meines approximativen theoretis- chen Modells stimmen gut mit exakten numerischen Lösungen und Messdaten für einen ther- mophoretischen Mikroschwimmer überein und können als Vorlage für komplexere Anwendungen dienen. Die wesentliche Physik hinter den formalen Ergebnissen wird durch ein schematisches Zwei-Spezies-“Run-and-Tumble”-Modell erfasst und erklärt. (iii) Ich untersuche Coarse-Graining- Modelle von suspendierten selbst-thermophoretischen Mikroschwimmern. Ausgehend von atom- istischen molekulardynamischen Simulationen wird die grobkörnige (coarse-grained) Beschreibung des Fluids in Form eines lokalen molekularen Temperaturfeldes verifiziert. Anschließend berechne ich effektive Nichtgleichgewichtstemperaturen, die die sogenannte heiße Brownsche Bewegung der Teilchen charakterisieren, und vergleiche diese mit Simulationsdaten. Es wird gezeigt, dass diese effektiven Temperaturen für jede weitere räumliche Vergröberung hin zu einer hydrodynamischen Beschreibung der gesamten Suspension als homogenes komplexes Fluid relevant bleiben.

Animal groups often exhibit highly coordinated collective motion in a variety of situations. For example, bird flocks, schools of fish, a flock of sheep being herded by a dog and highly efficient traffic on an ant trail. Although these phenomena can be observed every day all over the world our knowledge of what rules the individual's in such groups use is very limited. Questions of this type has been studied using so called self-propelled particle (SPP) models, most of which assume that collective motion arises from individuals aligning with their neighbors. Here we introduce and analyze a SPP-model based on attraction alone. We find that it produces all the typical groups seen in alignment-based models and some novel ones. In particular, a group that exhibits collective motion coupled with non-trivial internal dynamics. Groups that have this property are rarely seen in SPP-models and we show that even when a repulsion term is added to the attraction only model such groups are still present. These findings suggest that an interplay between attraction and repulsion may be the main driving force in real flocks and that the alignment rule may be superfluous. We then proceed to model two different experiments using the SPP-model approach. The first is a shepherding algorithm constructed primarily to model experiments where a sheepdog is herding a flock of sheep. We find that in addition to modeling the specific experimental situation well the algorithm has some properties which may make it useful in more general shepherding situations. The second is a traffic model for leaf-cutting ants bridges. Based on earlier experiments a set of traffic rules for ants on a very narrow bridge had been suggested. We show that these are sufficient to produce the observed traffic dynamics on the narrow bridge. And that when extended to a wider bridge by replacing 'Stop' with 'Turn' the new rules are sufficient to produce several key characteristics of the dynamics on the wide bridge, in particular three-lane formation.

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. / 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.

La première partie de ma thèse est consacrée à l’étude de l’auto-organisation de souches génétiquement modifiées de bactéries Escherichia coli. Ce projet, réalisé en collaboration avec des biologistes synthétiques de l’Université de Hong Kong, a pour objectif l’exploration et le décryptage d’un nouveau mécanisme d’auto-organisation dans des colonies bactériennes multi-espèces. Cela a été inspiré par la question fascinante de comment les écosystèmes bactériens comprenant plusieurs espèces de bactéries peuvent s’auto-organiser dans l’espace. En considérant des systèmes dans lesquels deux souches de bactéries régulent mutuellement leurs motilités, j’ai pu montrer que le contrôle de densité réciproque est une voie générique de formation de motifs: si deux souches tendent à faire augmenter mutuellement leur motilité (la souche A se déplace plus vite quand la souche B est présent, et vice versa), ils subissent un processus de formation de motifs conduisant à la démixtion entre les deux souches. Inversement, l’inhibition mutuelle de la motilité conduit à la formation de motifs avec colocalisation. Ces résultats ont étévalidés expérimentalement par nos collaborateurs biologistes. Par la suite, j’ai étendu mon étude à des systèmes composés de plus de deux espèces en interaction, trouvant des règles simples permettant de prédire l’auto-organisation spatiale d’un nombre arbitraire d’espèces dont la motilité est sous contrôle mutuel. Cette partie de ma thèse ouvre une nouvelle voie pour comprendre l’auto-organisation des colonies bactériennes avec des souches concurrentes, ce qui est une question importante pour comprendre la dynamique des biofilms ou des écosystèmes bactériens dans les sols. Le deuxième problème traité dans ma thèse est inspiré par le comportement collectif des moteurs moléculaires se déplaçant le long des microtubules dans le cytoplasme des cellules eucaryotes. Un modèle pertinent pour le mouvement des moteurs moléculaires est donné par un système paradigmatique de non-équilibre appelé Processus Asymmetrique d’Exclusion Simple, en anglais Asymmetric Simple Exclusion Process (ASEP). Dans ce modèle sur réseau unidimensionnel, les particules se déplacent dans les sites voisins vides à des taux constants, avec un biais gauche-droite qui déséquilibre le système.Lorsqu’il est connecté à ses extrémités à des réservoirs de particules, l’ASEP est un exemple prototypique de transitions de phase unidimensionnelles guidées par les conditions aux limites. Les exemples réalistes, cependant, impliquent rarement une seule voie:les microtubules sont constitués de plusieurs pistes de tubuline auxquelles les moteurs peuvent s’attacher. Dans ma thèse, j’explique comment on peut théoriquement prédire le comportement de phase de systèmes à plusieurs voies complexes, dans lesquels les particules peuvent également sauter entre des voies parallèles. En particulier, je montre que la transition de phase unidimensionnelle vue dans l’ASEP survit cette complexité supplémentaire mais implique de nouvelles caractéristiques telles que des courants transversaux stables non-nulles et une localisation de cisaillement. / The first part of my thesis is devoted to studying the self-organization of engineered strains of run-and-tumble bacteria Escherichia coli. This project, carried out in collaboration with synthetic biologists at Hong Kong University, has as its objective the exploration and decipherment of a novel self-organization mechanism in multi-species bacterial colonies. This was inspired by the fascinating question of how bacterial ecosystems comprising several species of bacteria can self-organize in space. By considering systems in which two strains of bacteria mutually regulate their motilities, I was able to show that reciprocal density control is a generic pattern-formation pathway: if two strains tend tomutually enhance their motility (strain A moves faster when strain B is present, and conversely),they undergo a pattern formation process leading to demixing between the two strains. Conversely, mutual inhibition of motility leads to pattern formation with colocalization. These results were validated experimentally by our biologist collaborators. Subsequently, I extended my study to systems composed of more than two interacting species, finding simple rules that can predict the spatial self-organization of an arbitrary number of species whose motility is under mutual control. This part of my thesis opens up a new route to understand the self-organization of bacterial colonies with competing strains, which is an important question to understand the dynamics of biofilms or bacterial ecosystems in soils.The second problem treated in my thesis is inspired by the collective behaviour ofmolecular motorsmoving along microtubules in the cytoplasm of eukaryotic cells. A relevant model for the molecularmotors’ motion is given by a paradigmatic non-equilibrium system called Asymmetric Simple Exclusion Process (ASEP). In this one-dimensional lattice- based model, particles hop on empty neighboring sites at constant rates, with a leftright bias that drives the systemout of equilibrium. When connected at its ends to particle reservoirs, the ASEP is a prototypical example of one-dimensional boundary driven phase transitions. Realistic examples, however, seldom involve only one lane: microtubules are made of several tubulin tracks to which the motors can attach. In my thesis, I explained how one can theoretically predict the phase behaviour of complex multilane systems, in which particles can also hop between parallel lanes. In particular, I showed that the onedimensional phase transition seen in the ASEP survives this additional complexity but involves new features such as non-zero steady transverse currents and shear localization.

Made available in DSpace on 2015-05-14T12:14:00Z (GMT). No. of bitstreams: 1 parte1.pdf: 2310445 bytes, checksum: 3cfca25ce861a7301fea8d5aa8526310 (MD5) Previous issue date: 2011-02-28 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this work, we study the collective behaviour of living systems whose aggregates form organized groups such as flocks of birds, herds of mamals and schools of fishes. Through numerical simulations, we model the collective movement of a school of fishes using behavioural rules similar to the ones proposed by Couzin et al. [23], that investigates the spatial dynamics of animals groups. The model presents three interaction zones: repulsion, orientation and attraction. Our results for the distributions of nearest neighbour distance, the diference of orientation between the velocities of neighbour fishes and the cooperativeness of the school are in good agreement with experimental measurements. A simpler way to describe the collective motion of several groups of organisms was introduced by Vicsek et al. [10]. This model presents only one interaction region, called orientation zone and considers point particles moving off lattice at constant speed adjusting their direction of motion to that of the average velocity of their neighbors, being subject to some noisy term. A second-order transition between an ordered state and a disordered regime was found. However, Gregoire and Chate [12] contest the nature of such phase transition as being of first order. Indeed, this transition is related to the way of introducing the noise into the system. In this sense, we present a comparative study on noise in two system of self-propelled particle (Vicsek model and Gregoire model) with the aim of understanding the role of the noise on some observables such as polarization, distributions of the nearest neighbour distances, difference of orientations between neighbour particles, the order parameter and the Binder cumulant. / Neste trabalho, estudamos o comportamento coletivo de sistemas vivos cujos agregados formam grupos organizados tais como bandos de pássaros, rebanhos de mamíferos e cardumes de peixes. Através de simulações numéricas, modelamos o movimento coletivo de cardumes de peixes usando regras comportamentais similares áquelas propostas por Cousin et al.[23], que investigam a dinâmica espacial de grupos de animais. O modelo apresenta três zonas de interação: repulsão, orientação e atração. Nossos resultados para as distribuições das distâncias entre vizinhos mais próximos, a diferença de orientação entre as velocidades de peixes vizinhos e a cooperatividade do cardume estão de bom acordo com medidas experimentais. Uma maneira mais simples para descrever o movimento coletivo de vários grupos de organismos foi introduzido por Vicsek et al. [10]. Este modelo apresenta somente uma região de interação, chamada zona de orientação e considera partículas pontuais movendo na rede com uma velocidade constante ajustando sua direção de movimento à velocidade média de seus vizinhos, estando sujeita a algum termo ruidoso. Uma transição de segunda ordem entre um estado ordenado e um regime desordenado foi encontrado. Porém, Gregoire e Chaté [12] contestam a natureza da transição de fase como sendo de primeira ordem. Na verdade, está transição está relacionada à forma de introduzir o ruído no sistema. Neste sentido, apresentamos um estudo comparativo sobre o ruído em dois sistemas de partículas auto-propelidas (modelo de Vicsek e modelo de Gregoire) com o objetivo de compreender o papel do ruído em alguns observáveis tais como a polarização, distribuições das distâncias entre vizinhos mais próximos, diferença de orientação entre partículas vizinhas, o parâmetro de ordem e o cumulante de Binder.