Fire ants link their legs and jaws together to form functional structures called self- assemblages. Examples include floating rafts, towers, bridges, and bivouacs. We investigate these self-assemblages of fire ants. Our studies are motivated in part by the vision of providing guidance for programmable robot swarms. The goal for such systems is to develop a simple programmable element from which complex patterns or behaviors emerge on the collective level. Intelligence is decentralized, as is the case with social insects such as fire ants. In this combined experimental and theoretical study, we investigate the construction of two fire ant self-assemblages that are critical to the colony’s survival: the raft and the tower. Using time-lapse photography, we record the construction processes of rafts and towers in the laboratory. We identify and characterize individual ant behaviors that we consistently observe during assembly, and incorporate these behaviors into mathematical models of the assembly process. Our models accurately predict both the assemblages’ shapes and growth patterns, thus providing evidence that we have identified and analyzed the key mechanisms for these fire ant self-assemblages. We also develop novel techniques using scanning electron microscopy and micro-computed tomography scans to visualize and quantify the internal structure and packing properties of live linked fire ants. We compare our findings to packings of dead ants and similarly shaped granular material packings to understand how active arranging affects ant spacing and orientation. We find that ants use their legs to increase neighbor spacing and hence reduce their packing density by one-third compared to packings of dead ants. Also, we find that live ants do not align themselves in parallel with nearest neighbors as much as dead ants passively do. Our main contribution is the development of parsimonious mathematical models of how the behaviors of individuals result in the collective construction of fire ant assemblages. The models posit only simple observed behaviors based on local information, yet their mathe- matical analysis yields accurate predictions of assemblage shapes and construction rates for a wide range of ant colony sizes.

[pt] Organismos vivos têm seus próprios meios de locomoção e são capazes de se reproduzir. Além disto, o habitat no qual os organismos estão inseridos é tipicamente heterogêneo, de modo que as condições ambientais variam no tempo e no espaço. Nesta tese, são propostos e investigados modelos teóricos para compreender o comportamento coletivo de organismos vivos, visando responder questões relevantes sobre a organização e preservação da população utilizando técnicas analíticas e numéricas. Inicialmente, considerando um habitat homogêneo, em que as propriedades estatísticas das condições ambientais são independentes do tempo e do espaço, estudamos como padrões espaço-temporais podem emergir na distribuição da população devido a interações não-locais e investigamos o papel das flutuações ambientais neste processo. Em seguida, assumindo um meio ambiente heterogêneo, analisamos o caso de um único domínio de habitat. Considerando uma classe de equações não lineares, introduzindo flutuações temporais e interações entre os organismos, fornecemos uma perspectiva geral da estabilidade de populações neste caso, desafiando os conceitos ecológicos anteriores. Em um segundo passo, assumindo uma paisagem complexa fragmentada, consideramos que os indivíduos têm acesso a informações sobre a estrutura espacial do meio. Mostramos que os indivíduos sobrevivem quando as regiões espaciais viáveis estão suficientemente aglomeradas e observamos que o tamanho da população é maximizado quando os indivíduos utilizam parcialmente a informação do meio ambiente. Finalmente, como resultados exatos analíticos não são factíveis em muitas situações importantes, propomos uma abordagem efetiva para interpretar os dados experimentais. Assim, somos capazes de conectar a heterogeneidade do ambiente e a persistência da população, caracterizada pela distribuição de probabilidade para os tempos de vida. / [en] Living entities have their own means of locomotion and are capable of reproduction. Furthermore, the habitat in which organisms are embedded is typically heterogeneous, such that environment conditions vary in time and space. In this thesis, theoretical models to understand the collective dynamics of living beings have been proposed and investigated aiming to address relevant questions such as population organization and persistence in the environment, using analytical and numerical techniques. Initially, considering an homogeneous habitat, in which the statistical properties of the environmental conditions are time and space independent, we study how spatiotemporal order can emerge in the population distribution due to nonlocal interactions and investigate the role of environment fluctuations in the self-organization process. Further, we continue our investigation assuming an heterogeneous environment, starting with the simplest case of a single habitat domain, and we obtain the critical conditions for population survival for different population dynamics. Considering a class of nonlinear equations, introducing temporal oscillations and interactions among the organisms, we are able to provide a general picture of population stability in a single habitat domain, challenging previous ecological concepts. At last, assuming a fragmented complex landscape, resembling realistic properties observed in nature, we additionally assume that individuals have access to information about the spatial structure. We show that individuals survive when patches of viable regions are clustered enough and, counter-intuitively, observe that population size is maximized when individuals have partial information about the habitat. Finally, since, analytical exact results are not feasible in many important situations, we propose an effective approach to interpret experimental data. This way we are able to connect environment heterogeneity and population persistence.

Originalmente introduzidas por T. Vicksek et al. [Phys. Rev. Lett. 75, 1226 (1995)], partÂıculas auto-propelidas (PAP) possuem uma velocidade intrÂınseca constante que sofre variaÂcËoes em sua direÂcËao como resultados de perturbaÂcËoes externas (outras partÂıculas ou meio) e sËao usadas para modelar sistemas que apresentam efeitos de aglomeraÂcËao. O conceito de PAP Âe aplicado para descrever e entender efeitos dinËamicos de aglomeraÂcËao em sistemas naturais, tais como microorganismos vivos (bactÂerias, vÂırus, etc) e colËonias de indivÂıduos de que se movem em bandos (peixes, ovelhas, abelhas, etc) ou, produzidos artificialmente, como sistemas coloidais especialmente preparadas em laboratÂorio. O estudo de PAP tem sua relevËancia em diversas Âareas do conhecimento, tais como engenharia de materiais, medicina e ciËencias da natureza (fÂısica, quÂımica e biologia). Na maioria dos casos, o movimento coletivo tem um comportamento bastante diferenciado dos movimentos individuais dos componentes de um dado sistema. Assim, o movimento de um certo indivÂıduo Âe influenciado pela presenÂca dos outros constituintes do sistema, alterando o seu comportamento geral, como consequËencia da interaÂcËao direta entre eles. Desta forma, vemos a importËancia da investigaÂcËao e entendimento do comportamento coletivo das PAP. Nesta dissertaÂcËao, estudamos um sistema bidimensional binÂario de PAP na presenÂca de obstÂaculos rÂıgidos com geometria anisotrÂopica (semi-cÂırculos) distribuÂıdos na forma de uma rede quadrada. AlÂem das interaÂcËoes partÂıcula-partÂıcula e partÂıcula-obstÂaculo, o movimento individual de cada PAP sofre influËencia de um ruÂıdo branco. O objetivo Âe caracterizar o transporte de PAP atravÂes do substrato bidimensional na ausËencia de uma forÂca externa propulsora. Apresentamos um estudo sistemÂatico do movimento coletivo das PAP em funÂcËao das velocidades das partÂıculas, da intensidade do ruÂıdo que define o movimento estocÂastico das PAP, do tamanho dos obstÂaculos, da densidade de PAP e da separaÂcËao entre os obstÂaculos. Devido a anisotropia dos obstÂaculos, surge um movimento coletivo espontËaneo e ordenado na direÂcËao normal `a superfÂıcie plana dos obstÂaculos, caracterizado por uma velocidade mÂedia nËao-nula para cada tipo de PAP na ausËencia de forÂca externa e que Âe influenciado pelos parËametros do sistema / Originally introduced by T. Vicksek et al. [Phys. Rev. Lett. 75, 1226 (1995)], Self Propelled Particles (SPP) have an intrinsic constant speed which suffer variations ins its direction as results of external perturbations (another particles or system) and are used to model systems that shows agglomeration effects. The concept of SPP is applied to describe and understand dynamic effects of agglomeration in natural systems, such as living micro-organisms (bacteria, virus, etc.) and colonies of individuals which move in flocks (fishes, sheep, bees) or, artificially produced, as colloidal systems especially prepared in laboratory. The study of SPP has its relevance in several areas of knowledge, such as material engineering, medicine and sciences of nature (physics, chemistry and biology). In most of cases, the collective motion has an well-differentiated behaviour of the individual motion of the components of a given system. So, the movement of a certain individual is affected by the presence of the other elements of the system, changing its general behaviour, as direct consequences of the direct interaction between them. In this way, we see the importance of investigation and understanding of collective motion of the SPP. Especially in this dissertation, we study a binary two-dimensional system of SPP subject to the presence of rigid obstacles with anisotropic geometry (semi-circles) distributed neatly in form of a square web. Beyond the particle-particle and particleobstacle interaction, the individual movement of each SPP suffers influence of an white noise. The objective is characterize the transport of SPP trough the two-dimensional substratum in absence of an propeller external force. We present and systematic study of collective motion of SPP in function of the speed of the particles, of the noise intensity which defines the stochastic movement of SPP, of the size of the obstacles, of the SPP density e the separation between the obstacles. Due the anisotropy of the obstacles, arise an spontaneous and ordered collective motion in normal direction of the plane surface of the obstacles, characterized by an non-null mean speed for each type of SPP in absence of an external force which in affected by the system parameters.

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.

No description available.

In tissue development, wound healing and aberrant cancer progression cell–cell interactions drive mixing and segregation of cellular composites. However, the exact nature of these interactions is unsettled. Here we study the dynamics of packed, heterogeneous cellular systems using wound closure experiments. In contrast to previous cell sorting experiments, we find non-universal sorting behavior. For example, monolayer tissue composites with two distinct cell types that show low and high neighbor exchange rates (i.e., MCF-10A & MDA-MB-231) produce segregated domains of each cell type, contrary to conventional expectation that the construct should stay jammed in its initial configuration. On the other hand, tissue compounds where both cell types exhibit high neighbor exchange rates (i.e., MDA-MB-231 & MDA-MB-436) produce highly mixed arrangements despite their differences in intercellular adhesion strength. The anomalies allude to a complex multi-parameter space underlying these sorting dynamics, which remains elusive in simpler systems and theories merely focusing on bulk properties. Using cell tracking data, velocity profiles, neighborhood volatility, and computational modeling, we classify asymmetric interfacial dynamics. We indicate certain understudied facets, such as the effects of cell death & division, mechanical hindrance, active nematic behavior, and laminar & turbulent flow as their potential drivers. Our findings suggest that further analysis and an update of theoretical models, to capture the diverse range of active boundary dynamics which potentially influence self-organization, is warranted.

Development of a single-cell embryo into an adult multi-cellular organism features the establishment of upto three anatomical body axes - anteroposterior, dorsoventral and left-right. It has been observed in many organisms that these body axes can consistently orient relative with respect to the geometric features of the embryo in many organisms. One such example is observed in the model organism Caenorhabditis elegans (C. elegans), where the Anteroposterior (AP) axis coincides with the geometric long axis of the ellipsoidal embryo -- the shape being imposed by the surrounding eggshell. In C. elegans, the Anteroposterior axis is established at the one-cell stage via its polarization by PAR polarity proteins. This cell polarization proceeds via a self-organized mechanochemical feedback between the PAR proteins and mechanical flows in the actomyosin cortex, resulting in the formation of two mutually exclusive domains of Anterior PAR and Posterior PAR proteins on the cortex denoting the future anterior and posterior end of the embryo -- and thus establishing the Anteroposterior axis. The initial orientation of the Anteroposterior axis is determined by the site of sperm entry at fertilization. However, the nascent Anteroposterior axis that forms after fertilization is observed to actively re-orient -- indicated by the movement of the PAR domains and concurrent migration (here termed posteriorisation) of the sperm-donated male pronucleus -- such that it aligns with the long axis of the ellipsoidal embryo, if it is not already aligned. In effect, the site of sperm entry only determines which half of the embryo becomes the posterior half of the embryo. This phenomenon of active re-orientation of the Anteroposterior axis, that ensures that the Anteroposterior axis aligns with the long axis of the embryo, is termed Anteroposterior axis alignment. The work described in this thesis investigates the mechanism of this Anteroposterior axis alignment in the C. elegans embryo. Anterior-directed flows in the actomyosin cortex observed during Anteroposterior axis establishment have also been found to be essential for Anteroposterior axis alignment. In this thesis, two possible mechanisms of Anteroposterior axis alignment are considered, both of which are consequences of these cortical flows. Cortical flows at the embryo surface can drive flows in the bulk cytoplasm in the embryo, generating cytoplasmic flows which point towards the sperm-donated male pronucleus as it posteriorises. Previous studies have proposed that these cytoplasmic flows could push onto the male pronucleus, and due to the ellipsoidal geometry of the embryo, drive it towards the closest tip of the embryo. This proposed mechanism is referred to as the cytoplasmic flow-dependent mechanism in this thesis. Another mechanism proposed in this thesis postulates that the reorientation of the Anteroposterior axis occurs via the repositioning of the pseudocleavage furrow. The pseudocleavage furrow is a contractile ring-like structure that forms at the boundary of the two PAR domains during Anteroposterior axis establishment. The pseudocleavage furrow forms as a result of compressive alignment of actin filaments in the actomyosin cortex due to cortical flows. In cases where the Anteroposterior axis is not aligned with the long axis of the embryo, the pseudocleavage furrow is not perpendicular to the long axis of the embryo. In such cases, active anisotropic stresses generated in the actomyosin cortex could force the rotation of the pseudocleavage furrow akin to an elastic rubber-band on an ellipsoid, and cause the Anteroposterior axis to re-orient towards the long axis of the embryo. This proposed mechanism is referred to as the pseudocleavage furrow-dependent mechanism in this thesis. This thesis investigates the role played by the two mechanisms in Anteroposterior axis alignment. This is accomplished in the following way: a theoretical model of the Anteroposterior axis alignment is introduced, consisting of a description of the actomyosin cortex as an active nematic fluid present on the 2D surface of a fixed ellipsoid representing the embryo. This description of the cortex incorporates both the cytoplasmic flow-dependent mechanism and the pseudocleavage furrow-dependent mechanism. RNAi experiments in the C. elegans embryo that remove the pseudocleavage furrow, in conjuction with numerical simulations using the theoretical model, show that the pseudocleavage furrow-dependent mechanism is the predominant mechanism that drives Anteroposterior axis alignment, while cytoplasmic flow-dependent mechanism plays only a minor role. RNAi experiments that modify the geometry of the C. elegans embryo -- specifically, generate rounder embyros -- show that embryo geometry can influence the rate of re-orientation of the Anteroposterior axis during Anteroposterior axis alignment -- with slower Anteroposterior axis alignment in rounder embryos. Such an relation between embryo geometry and Anteroposterior axis alignment is found to be consistent with pseudocleavage furrow-dependent mechanism, both via predictions made using the theoretical model and using a simplified effective model of a contractile ring (or elastic rubber-band) on a fixed ellipsoid. Altogether, the work presented in this thesis shows Anteroposterior axis alignment observed in the C. elegans embryo is driven primarily by the anisotropic stresses in the actomyosin cortex that generate the pseudocleavage furrow. The work here also shows that the Anteroposterior axis alignment process is sensitive to the geometry of the embryo. In effect, active mechanical flows in the actomyosin cortex translate the ellipsoidal geometry of the embryo into a robust orientation of the Anteroposterior axis of the C. elegans embryo. Mechanical flows such as these are not exclusive to C. elegans, nor are specific orientations of the body axes with respect to the embryo geometry. The results in this thesis thus point towards a possibly general role of the interactions between mechanical flows and embryo geometry to properly orient the body axes of the developing embryos of many multi-cellular organisms.:Contents Abbreviations iii Abstract iv 1 Introduction 1 1.1 Cytoskeleton 3 1.1.1 Main constituents of the cytoskeleton 3 1.1.2 Actomyosin cortex 7 1.2 Hydrodynamic theory of active fluids 8 1.2.1 Conservation Laws 9 1.2.2 Continuously broken symmetries 11 1.2.3 Irreversible thermodynamics of active fluids 13 1.2.4 Constitutive equations of active nematic fluids 19 1.3 C. elegans as a model organism 21 1.3.1 Early embryogenesis in C. elegans 22 1.4 AP axis establishment in C. elegans 24 1.4.1 PAR polarity system . 24 1.4.2 Mechanism of AP axis establishment 26 1.4.3 AP axis alignment 27 1.5 Overview 29 2 A theoretical model for AP axis alignment 30 2.1 A model of AP axis establishment in C. elegans 30 2.1.1 Turing-like system for PAR polarity system 31 2.1.2 Active isotropic description of actomyosin cortex 33 2.1.3 Guiding cues for AP axis establishment 34 2.1.4 Full model of AP axis establishment in [1] 35 2.2 A model of pseudocleavage furrow formation in C. elegans 36 2.2.1 Dynamics of Actin alignment 37 2.2.2 Active stress generated by alignment of actin filaments 38 2.3 A model of AP axis alignment in C. elegans 39 2.3.1 A thin film active nematic description of the cortex 40 2.3.2 Description of the Cytoplasm and Male pronucleus 46 2.3.3 Numerical simulations of the theoretical model 48 3 Materials and Methods 52 3.1 Culture conditions, strains and worm handling 52 3.2 Genetic perturbations by RNAi 53 3.3 Time-lapse microscopy 53 3.4 Image analysis 54 3.4.1 Pre-processing 54 3.4.2 Tracking posteriorisation of the male pronucleus 56 3.4.3 Measuring cortical flows 66 3.4.4 Measuring cytoplasmic flows 67 3.5 Data analysis 67 4 Experimental investigation of AP axis alignment 71 4.1 Characterising AP axis alignment in unperturbed embryos 71 4.2 Cortical flows are required for AP axis alignment 76 4.3 Role of Pseudocleavage furrow in AP axis alignment 83 4.3.1 Removing Pseudocleavage furrow via RNAi 83 4.3.2 Comparing numerical simulations to experimental results 88 4.4 Role of embryo geometry in AP axis alignment 99 4.4.1 Rounder embryos show slower AP axis alignment 99 4.4.2 Relation between embryo geometry and AP axis alignment 108 4.5 Additional experiments 118 4.5.1 Exploring relation between embryo geometry and AP axis alignment in ima-3 RNAi embryos 118 4.5.2 Are pseudocleavage furrow-dependent and cytoplasmic flow-dependent mechanisms sufficient to explain AP axis alignment? 121 4.5.3 Role of microtubules in AP axis alignment 127 5 Conclusions and Outlook 134 Appendix 139 Bibliography 142 List of publications 156 Acknowledgements 157

No description available.

Small devices capable of self-propulsion have potential application in areas of nanoscience where autonomous locomotion and programmability are needed. The specific base-pairing interactions that arise from DNA hybridisation permit the programmed assembly of matter and also the creation of controllable dynamical systems. The aim of this thesis is to use the tools of DNA nanotechnology to design synthetic active matter at the micro and nano scales. In the first section, DNA was used as an active medium capable of transporting information faster than diffusion in the form of chemical waves. DNA waves were generated experimentally using a DNA autocatalytic reaction in a microfluidic channel. The propagation velocity of DNA chemical waves was slowed down by creating concentration gradients that changed the reaction kinetics in space. The second section details the synthesis of chemically-propelled particles and the use of DNA as a 'programmable glue' to mediate their interactions. Janus micromotors were fabricated by physical vapour deposition and a wet-chemical approach was demonstrated to synthesise asymmetrical catalytic Pt-Au nanoparticles that function as nanomotors. Dynamic light scattering measurements showed nanomotor activity that depends on H₂O₂ concentration, consistent with chemical propulsion. Gold nanoparticles/Origami hybrids were assembled in 2D lattices of different symmetries arranged by DNA linkers. The third section details the design process and synthesis of nanomotors using DNA as a structural scaffold. 3D DNA Origami rectangular prisms were functionalised site-specifically with bioconjugated catalysts, i.e. Pt nanoparticles and catalase. Enzymatic nanomotors were also conjugated to various cargoes and their motor activity was demonstrated by Fluorescence Correlation Spectroscopy. In the final section, control mechanisms for autonomous nanomotors are studied, which includes the conformational change of DNA aptamers in response to chemical signals, as well as a design for an adaptive dynamical system based on DNA/enzyme reaction networks.

Nous étudions le comportement collectif d'une assemblée de colloïdes Janus, des sphères d'or de 1µm dont une moitié est recouverte de platine. Lorsqu'ils sont immergés dans une solution d'eau oxygénée, ils se déplacent à des vitesses de l'ordre de 5µm/s, contrôlable par la concentration en peroxyde. Individuellement, ces colloïdes suivent une marche aléatoire persistante ; Ils interagissent par effets phorétiques, formant des clusters dynamiques de quelques dizaines de colloïdes. Ces clusters, mobiles, échangent continuellement des colloïdes, se divisent et se fusionnent, formant une phase stationnaire. Nous avons développés ces colloïdes, ainsi qu'un système d'acquisition pour détecter et reconstituer les trajectoires des colloïdes. La taille moyenne des clusters augmente linéairement avec l'activité, définie comme la vitesse moyenne des colloïdes en dehors des clusters. La fonction densité de probabilité de la taille des clusters est une loi de puissance d'exposant -2. Nous quantifions les vitesses de translation et de rotation des clusters. Pour réaliser une étude thermodynamique, nous réalisons des expériences de sédimentation. Une transition est observée, entre une phase peu dense, un gaz parfait, dans lequel on mesure une température effective, et une phase dense à la dynamique hétérogène. L'équation d'état du système est mesurée, et une forme analytique heuristique est proposée / We study the collective behavior of an assembly of Janus Colloids. These are 1µm gold colloids with one half coated in platinum. When immersed in a peroxide bath, they self-propel, owing to diffusiophoresis and electrophoresis, moving at velocities of order 5µm/s. The velocity can be tune by adjusting the amount of peroxide in the bath. At the single particle level, the colloids undergo a persistent random walk. When in denser groups, the colloids interact through chemical and steric effects. The combination of these interactions, with the colloids activity, leads to collective effects. A dynamic cluster phase is observed, the formation of motile clusters of colloids, formed of up to 100 colloids. The clusters are in a stationary state, constantly moving, and exchanging colloids, they are also colliding, merging and breaking apart. We developed both the colloids, whose synthesis is described, and a high-throughput acquisition and analysis system. We measure the positions, and reconstruct the trajectories of thousands of colloids for a few minutes. From the trajectories, we extract statistical observables. We show that the sizes of clusters increases linearly as a function of the activity of the colloids. The probability distribution functions of sizes are power laws. As the density increases, a jamming transition is observed. The dense phase heterogeneous dynamics is characterized. We study the transition from the dense phase to a low density assembly with sedimentation experiments. The low density phase behaves as an ideal gas, allowing the definition of an effective temperature. We measure an equation of state for the system, and propose a heuristic collapse