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Active solids, more specifically elastic lattices embedded with polar active units, exhibit collective actuation when the elasto-active feedback, generically present in such systems, exceeds some critical value. The dynamics then condensates on a small fraction of the vibrational modes, the selection of which obeys non trivial rules rooted in the nonlinear part of the dynamics. So far the complexity of the selection mechanism has limited the design of specific actuation. Here we investigate numerically how, localizing the activity on a fraction of modes, one can select non-trivial collective actuation. We perform numerical simulations of an agent based model on triangular and disordered lattices and vary the concentration and the localization of the active agents on the lattices nodes. Both contribute to the distribution of the elastic energy across the modes. We then introduce an algorithm, which, for a given fraction of active nodes, evolves the localization of the activity in such a way that the energy distribution on a few targeted modes is maximized -- or minimized. We illustrate on a specific targeted actuation, how the algorithm performs as compared to manually chosen localization of the activity. While, in the case of the ordered lattice, a well educated guess performs better than the algorithm, the latter outperform the manual trials in the case of the disordered lattice. Finally, the analysis of the results in the case of the ordered lattice leads us to introduce a design principle based on a measure of the susceptibility of the modes to be activated along certain activation paths.

We analyze a one-dimensional two-scalar fields reaction advection diffusion model for the globally subcritical transition to turbulence. In this model, the homogeneous turbulent state is disconnected from the laminar one and disappears in a tipping catastrophe scenario. The model however exhibits a linear instability of the turbulent homogeneous state, mimicking the onset of the laminar-turbulent patterns observed in the transitional regime of wall shear flows. Numerically continuing the solutions obtained at large Reynolds numbers, we construct the Busse balloon associated with the multistability of the nonlinear solutions emerging from the instability. In the core of the balloon, the turbulent fluctuations, encoded into a multiplicative noise, select the pattern wavelength. On the lower Reynolds number side of the balloon, the pattern follows a cascade of destabilizations towards larger and larger, eventually infinite wavelengths. In that limit, the periodic limit cycle associated with the spatial pattern hits the laminar fixed point, resulting in a saddle-loop global bifurcation and the emergence of solitary pulse solutions. This saddle-loop scenario predicts a logarithmic divergence of the wavelength, which captures experimental and numerical data in two representative shear flows., Comment: 5 pages, 6 figures

Self-alignment describes the property of a polar active unit to align or anti-align its orientation towards its velocity. In contrast to mutual alignment, where the headings of multiple active units tend to directly align to each other -- as in the celebrated Vicsek model --, self-alignment impacts the dynamics at the individual level by coupling the rotation and displacements of each active unit. This enriches the dynamics even without interactions or external forces, and allows, for example, a single self-propelled particle to orbit in a harmonic potential. At the collective level, self-alignment modifies the nature of the transition to collective motion already in the mean field description, and it can also lead to other forms of self-organization such as collective actuation in dense or solid elastic assemblies of active units. This has significant implications for the study of dense biological systems, metamaterials, and swarm robotics. Here, we review a number of models that were introduced independently to describe the previously overlooked property of self-alignment and identify some of its experimental realizations. Our aim is three-fold: (i)~underline the importance of self-alignment in active systems, especially in the context of dense populations of active units and active solids; (ii)~provide a unified mathematical and conceptual framework for the description of self-aligning systems; (iii)~discuss the common features and specific differences of the existing models of self-alignment. We conclude by discussing promising research avenues in which the concept of self-alignment could play a significant role., Comment: 26 pages, 14 figures, review paper

We extend the study of the inertial effects on the dynamics of active agents to the case where self-alignment is present. In contrast with the most common models of active particles, we find that self-alignment, which couples the rotational dynamics to the translational one, produces unexpected and non-trivial dynamics, already at the deterministic level. Examining first the motion of a free particle, we contrast the role of inertia depending on the sign of the self-aligning torque. When positive, inertia does not alter the steady-state linear motion of an a-chiral self-propelled particle. On the contrary, for a negative self-aligning torque, inertia leads to the destabilization of the linear motion into a spontaneously broken chiral symmetry orbiting dynamics. Adding an active torque, or bias, to the angular dynamics the bifurcation becomes imperfect in favor of the chiral orientation selected by the bias. In the case of a positive self-alignment, the interplay of the active torque and inertia leads to the emergence, out of a saddle-node bifurcation, of truly new solutions, which coexist with the simply biased linear motion. In the context of a free particle, the rotational inertia leaves unchanged the families of steady-state solutions but can modify their stability properties. The situation is radically different when considering the case of a collision with a wall, where a very singular oscillating dynamics takes place which can only be captured if both translational and rotational inertia are present., Comment: 10 pages, 9 figures

Convincing evidence of domain growth in the heating of ultrastable glasses suggests that the equilibration dynamics of super-cooled liquids could be driven by a nucleation and growth mechanism. We investigate this possibility by simulating the equilibration dynamics of a model glass during both heating and cooling between poorly and well-annealed states. Though we do observe the growth of domains during heating, we find that domains are absent during cooling. This absence is inconsistent with classical nucleation theory. By comparing the equilibration dynamics of our glass with that of two models with kinetic constraints, we demonstrate that dynamical facilitation generically leads to heating driven by domain growth and cooling without domains. Our results provide strong evidence that dynamical facilitation, not nucleation and interfacial-tension-driven domain growth, is the driving mechanism for the equilibration dynamics of glass-formers., Comment: 21 pages, 16 figures. Supplemental Movies too large for arXiv. Will provide download link once available. Available on request until then

Collective actuation describes the spontaneous synchronized oscillations taking place in active solids, when the elasto-active feedback, that generically couples the reorientation of the active forces and the elastic stress, is large enough. In the absence of noise, collective actuation takes the form of a strong condensation of the dynamics on a specific pair of modes and their generalized harmonics. Here we report new experiments conducted with centimetric active elastic structures, where collective oscillation takes place along the single lowest energy mode of the system, gapped from the other modes because of the system's geometry. Combining the numerical and theoretical analysis of an agent-based model, we demonstrate that this new form of collective actuation is noise-induced. The effect of the noise is first analyzed in a single-particle toy model that reveals the interplay between the noise and the specific structure of the phase space. We then show that in the continuous limit, any finite amount of noise turns this new form of transition to collective actuation into a bona fide supercritical Hopf bifurcation., Comment: 15 pages, 6 figures

Active solids such as cell collectives, colloidal clusters, and active metamaterials exhibit diverse collective phenomena, ranging from rigid body motion to shape-changing mechanisms. The nonlinear dynamics of such active materials remains however poorly understood when they host zero-energy deformation modes and when noise is present. Here, we show that stress propagation in a model of active solids induces the spontaneous actuation of multiple soft floppy modes, even without exciting vibrational modes. By introducing an adiabatic approximation, we map the dynamics onto an effective Landau free energy, predicting mode selection and the onset of collective dynamics. These results open new ways to study and design living and robotic materials with multiple modes of locomotion and shape-change.

We study light-activated quasi-2d gels made of a colloidal network doped with Janus particles. Following the gel formation, the internal dynamics of the gel are monitored before, during, and after the light activation. We monitor both the structure and dynamics, before, during and after the illumination period. The mobility of the passive particles exhibits a characteristic scale-dependent response. Immediately following light activation, the gel displays large-scale reorganization, followed by progressive, short-scale displacements throughout the activation period. Albeit subtle structural changes (including pore opening and widening and shortening of strands) the colloidal network remains connected, and the gel maintains its structural integrity. Once activity is switched off, the gel keeps the memory of the structure inherited from the active phase. Remarkably, the motility remains larger than that of the gel, before the active period. The system has turned into a genuinely different gel, with frozen dynamics, but with more space for thermal fluctuations. The above conclusions remain valid long after the activity period., Comment: 4 pages, 5 figures

The configurations taken by polymers embedded in out-of-equilibrium baths may have broad effects in a variety of biological systems. As such, they have attracted considerable interest, particularly in simulation studies. Here we analyze the distribution of configurations taken by a passive flexible chain in a bath of hard, self-propelled, vibrated disks and systematically compare it to that of the same flexible chain in a bath of hard, thermal-like, vibrated disks. We demonstrate experimentally that the mean length and mean radius of gyration of both chains obey Flory's Law. However, the Kuhn length associated with the number of correlated monomers is smaller in the case of the active bath, corresponding to a higher effective temperature. Importantly, the active bath does not just simply map on a hot equilibrium bath. Close examination of the chains' configurations indicates a marked bias, with the chain in the active bath more likely assuming configurations with a single prominent bend., Comment: 4 pages, 4 figures

We highlight certain key achievements in experimental work on molecular, colloidal and granular glassformers. This short review considers these three classes of experimental systems and focusses largely on the work of the authors and their coworkers and thus is far from exhaustive. Our goal is rather to discuss particular experimental results from these classes and to explore universality and specificity across the broad range of length- and time-scales they span. We emphasize that a variety of phenomena, not least dynamical heterogeneity, growing lengthscales and a change in structure, albeit subtle, are now well established in these three classes of glassformer. We then review some experimental measurements which depend more specifically on the class of glassformer, such as the Gardner transition and some which have been investigated more in one or two classes than in all, such as configurational entropy and evidence for a dynamical phase transition. We finally put forward some open questions and consider what could be done to fill some of the gaps between theoretical approaches and experiments., Comment: 32 pages, 13 figures

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 tools one can use to relate the knowledge of the dynamics at the particle scale to the large scale physics., Comment: 28 pages, published as Ch3 in Active Matter and Nonequilibrium Statistical Physics Lecture Notes of the Les Houches Summer School: Volume 112, September 2018

We experimentally revisite the flow down an inclined plane of dense granular suspensions, with particles of sizes in the micron range, for which thermal fluctuations cannot be ignored. Using confocal microscopy on a miniaturized set-up, we observe that, in contrast with standard granular rheology, the flow profiles strongly depend on the particles size. Also, suspensions composed of small enough particles flow at infinitesimal inclinations. From the velocity measurements, an effective rheology is extracted in terms of a friction coefficient as a fonction of the dimensionless shear rate (the viscous number), and of the particle pressure normalized by the thermal pressure. Inspired by a previous work [1], a phenomenological model based on the sum of a thermal contribution describing the glass transition and an athermal contribution capturing the jamming transition is developed, which reproduces well the experimental observations. The model predicts the existence of a glassy friction angle lower than the granular athermal friction angle, a signature of the glass transition in the framework of a pressure imposed rheology.

The recent finding of collective actuation in active solids, namely solids embedded with active units, opens the path towards multifunctional materials with genuine autonomy. In such systems, collective dynamics emerge spontaneously and little is known about the way to control or drive them. Here, we combine the experimental study of centimetric model active solids, the numerical study of an agent based model and theoretical arguments to reveal how mechanical tension can serve as a general mechanism for switching between different collective actuation regimes in active solids. We further show the existence of a hysteresis when varying back and forth mechanical tension, highlighting the non-trivial selectivity of collective actuations., Comment: 5 pages, 4 figures

Laminar-turbulent pattern formation is a distinctive feature of the intermittency regime in subcritical plane shear flows. By performing extensive numerical simulations of the plane channel flow, we show that the pattern emerges from a spatial modulation of the turbulent flow, due to a linear instability. We sample over many realizations the linear response of the fluctuating turbulent field to a temporal impulse, in the regime where the turbulent flow is stable, just before the onset of the instability. The dispersion relation is constructed from the ensemble-averaged relaxation rates. As the instability threshold is approached, the relaxation rate of the least damped modes eventually reaches zero. The method allows, despite the presence of turbulent fluctuations and without any closure model, for an accurate estimation of the wavevector of the modulation at onset., Comment: 5 pages, 4 figures

Self-organisation is the spontaneous emergence of spatio-temporal structures and patterns from the interaction of smaller individual units. Examples are found across many scales in very different systems and scientific disciplines, from physics, materials science and robotics to biology, geophysics and astronomy. Recent research has highlighted how self-organisation can be both mediated and controlled by confinement. Confinement occurs through interactions with boundaries, and can function as either a catalyst or inhibitor of self-organisation. It can then become a means to actively steer the emergence or suppression of collective phenomena in space and time. Here, to provide a common framework for future research, we examine the role of confinement in self-organisation and identify overarching scientific challenges across disciplines that need to be addressed to harness its full scientific and technological potential. This framework will not only accelerate the generation of a common deeper understanding of self-organisation but also trigger the development of innovative strategies to steer it through confinement, with impact, e.g., on the design of smarter materials, tissue engineering for biomedicine and crowd management.

Whereas naturally occurring swarms thrive when crowded, physical interactions in robotic swarms are either avoided or carefully controlled, thus limiting their operational density. Here we present a mechanical design rule that allows robots to act in a collision-dominated environment. We introduce the Morphobots -- a robotic swarm platform developed to implement embodied computation through a morpho-functional design. By engineering a 3D-printed exoskeleton we encode a re-orientation response to an external body force (such as gravity) or a surface force (such as a collision). We show that the force-orientation response is generic, and can augment existing swarm-robotic platforms (e.g Kilobots) as well as custom robots even 10 times larger. At the individual level, the exoskeleton improves the motility and stability, and also allows to encode two contrasting dynamical behaviors in response to an external force or a collision (including collision with a wall or a movable obstacle, and on a dynamically tilting plane). This force-orientation response adds a mechanical layer to the robot's sense-act cycle at the swarm level, leveraging steric interactions for collective phototaxis when crowded. Enabling collisions also promotes information flow, facilitating online distributed learning. Each robot runs an embedded algorithm that ultimately optimizes collective performance. We identify an effective parameter that controls the force-orientation response and explore its implications in swarms that transition from dilute to crowded. \green{Experimenting with both physical swarms (of up to 64 robots), and simulated swarms (of up to 8192 agents) show that the effect of morphological-computation increases with growing swarm size., Comment: 21 pages, 12 figures

A type of polar self-propelled particle generates a torque that makes it naturally drawn to higher-density areas. The collective behaviour this induces in assemblies of particles constitutes a new form of phase separation in active fluids., Comment: 3 pages, 1 figure

We investigate experimentally the behavior of self-propelled water-in-oil droplets, confined in capillaries of different square and circular cross-sections. The droplet's activity comes from the formation of swollen micelles at its interface. In straight capillaries the velocity of the droplet decreases with increasing confinement. However at very high confinement, the velocity converges toward a non-zero value, so that even very long droplets swim. Stretched circular capillaries are then used to explore even higher confinement. The lubrication layer around the droplet then takes a non-uniform thickness which constitutes a significant difference with usual flow-driven passive droplets. A neck forms at the rear of the droplet, deepens with increasing confinement, and eventually undergoes successive spontaneous splitting events for large enough confinement. Such observations stress the critical role of the activity of the droplet interface on the droplet's behavior under confinement. We then propose an analytical formulation by integrating the interface activity and the swollen micelles transport problem into the classical Bretherton approach. The model accounts for the convergence of the droplet's velocity to a finite value for large confinement, and for the non-classical shape of the lubrication layer. We further discuss on the saturation of the micelles concentration along the interface, which would explain the divergence of the lubrication layer thickness for long enough droplets, eventually leading to the spontaneous droplet division.

We study kinetic Monte-Carlo (KMC) descriptions of active particles. By relying on large discrete time steps, KMC algorithms accelerate the relaxational dynamics of active systems towards their steady-state. We show, however, that their continuous-time limit is ill-defined, leading to the vanishing of trademark behaviors of active matter such as the motility-induced phase separation, ratchet effects, as well as to a diverging mechanical pressure. We show how mixing passive steps with active ones regularizes this behavior, leading to a well-defined continuous-time limit. We propose new AKMC algorithms whose continuous-time limits lead to the active dynamics of Active-Ornstein Uhlenbeck, Active Brownian, and Run-and-Tumbles particles.

As liquids approach the glass transition temperature, dynamical heterogeneity emerges as a crucial universal feature of their behavior. Dynamic facilitation, where local motion triggers further motion nearby, plays a major role in this phenomenon. Here we show that long-range, elastically-mediated facilitation appears below the mode-coupling temperature, adding to the short-range component present at all temperatures. Our results suggest deep connections between the supercooled liquid and glass states, and pave the way for a deeper understanding of dynamical heterogeneity in glassy systems., Comment: 6 pages, 4 figures. SM included as ancillary

The transitional regime of plane channel flow is investigated {above} the transitional point below which turbulence is not sustained, using direct numerical simulation in large domains. Statistics of laminar-turbulent spatio-temporal intermittency are reported. The geometry of the pattern is first characterized, including statistics for the angles of the laminar-turbulent stripes observed in this regime, with a comparison to experiments. High-order statistics of the local and instantaneous bulk velocity, wall shear stress and turbulent kinetic energy are then provided. The distributions of the two former quantities have non-trivial shapes, characterized by a large kurtosis and/or skewness. Interestingly, we observe a strong linear correlation between their kurtosis and their skewness squared, which is usually reported at much higher Reynolds number in the fully turbulent regime.

In their comment on our work (ArXiv:1912.07056v1), Cavagna \textit{et al.} raise several interesting points on the phenomenology of flocks of birds, and conduct additional data analysis to back up their points. In particular, they question the existence of rigid body rotations in flocks of birds. In this reply, we first clarify the notions of rigid body rotations, and of rigidity itself. Then, we justify why we believe that it is legitimate to wonder about their importance when studying the spatial correlations between speeds in flocks of birds., Comment: 5 pages, 1 figure

We study a $2d$ Hamiltonian fluid made of particles carrying spins coupled to their velocities. At low temperatures and intermediate densities, this conservative system exhibits phase coexistence between a collectively moving droplet and a still gas. The particle displacements within the droplet have remarkably similar correlations to those of birds flocks. The center of mass behaves as an effective self-propelled particle, driven by the droplet's total magnetization. The conservation of a generalized angular momentum leads to rigid rotations, opposite to the fluctuations of the magnetization orientation that, however small, are responsible for the shape and scaling of the correlations., Comment: Main text: 6 pages, 4 figures. Supplementary Information: 13 pages, 5 figures, 2 movies

We investigate the collective dynamics of self-propelled droplets, confined in a one dimensional micro-fluidic channel. On one hand, neighboring droplets align and form large trains of droplets moving in the same direction. On the other hand, the droplets condensates, leaving large regions with very low density. A careful examination of the interactions between two "colliding" droplets demonstrates that local alignment takes place as a result of the interplay between the dispersion of their speeds and the absence of Galilean invariance. Inspired by these observations, we propose a minimalistic 1D model of active particles reproducing such dynamical rules and, combining analytical arguments and numerical evidences, we show that the model exhibits a transition to collective motion in 1D for a large range of values of the control parameters. Condensation takes place as a transient phenomena which tremendously slows down the dynamics, before the system eventually settles into a homogeneous aligned phase., Comment: 5 pages, 5 figures

We compare glassy dynamics in two liquids that differ in the form of their interaction potentials. Both systems have the same repulsive interactions but one has also an attractive part in the potential. These two systems exhibit very different dynamics despite having nearly identical pair correlation functions. We demonstrate that a properly weighted integral of the pair correlation function, which amplifies the subtle differences between the two systems, correctly captures their dynamical differences. The weights are obtained from a standard machine learning algorithm., Comment: 6 pages, 5 figures

Using analytic and numerical methods, we study a $2d$ Hamiltonian model of interacting particles carrying ferro-magnetically coupled continuous spins which are also locally coupled to their own velocities. This model has been characterised at the mean field level in a parent paper. Here, we first obtain its finite size ground states, as a function of the spin-velocity coupling intensity and system size, with numerical techniques. These ground states, namely a collectively moving polar state of aligned spins, and two non moving states embedded with topological defects, are recovered from the analysis of the continuum limit theory and simple energetic arguments that allow us to predict their domains of existence in the space of control parameters. Next, the finite temperature regime is investigated numerically. In some specific range of the control parameters, the magnetisation presents a maximum at a finite temperature. This peculiar behaviour, akin to an order-by-disorder transition, is explained by the examination of the free energy of the system and the metastability of the states of minimal energy. The robustness of our results is checked against the geometry of the boundary conditions and the dimensionality of space., Comment: 26 pages, 10 figures, 1 supplemental animated gif

We present here first-of-a-kind experimental measurements of the flow field around a swimming water droplet, using confocal PIV in three dimensions. The droplet is denser than the continuous oil phase, and swims close and parallel to the bottom wall. The measured flow field is first quantitatively characterized and compared to the flow field obtained for an axisymmetric swimmer in unbounded flow. Important qualitative differences are observed, in particular the emergence of a strong isotropic radial flow field in the planes parallel to the wall. These fundamental differences stress the critical impact of confinement on the flow field around the swimming droplet. We then propose an analytical formulation, based on a reduced order description of the swimming droplet in terms of fundamental hydrodynamic singularities as well as the classical method of images. This model is able to account exactly for the effect of the wall and provides a simplified description of the flow field as the superposition of axisymmetric dipole and quadrupole singularities. We demonstrate that this simplified description quantitatively captures the effect of the wall on the dipolar and quadrupolar components of the flow field. Further including the confinement-induced asymmetry of the concentration field responsible for the droplet's Marangoni propulsion, our model is also able to account for the monopolar contribution to the experimental flow field which drives the dominant far-field signature of the droplet., Comment: 14 pages, 6 figures, 3 appendices

Switching on high activity in a relatively dense system of active Janus colloids, we observe fast clustering, followed by cluster aggregation towards full phase separation. The phase separation process is however interrupted when large enough clusters start breaking apart. Following the cluster size distribution as a function of time, we identify three successive dynamical regimes. Tracking both the particle positions and orientations, we characterize the structural ordering and alignment in the growing clusters and thereby unveil the mechanisms at play in these regimes. In particular, we identify how alignment between the neighboring particles is responsible for the interruption of the full phase separation. This experimental study, which provides the first large scale observation of the phase separation kinetics in active colloids, combined with single particle analysis of the local mechanisms, points towards the new physics observed when both alignment and short-range repulsions are present., Comment: 5 pages, 5 figures

We investigate the flow around an oscillating nearly-spherical particle at low, yet non-vanishing, Reynolds numbers, and the potential resulting locomotion. We analytically demonstrate that no net motion can arise up to order one in Re and order one in the asphericity parameter, regardless of the particle's shape. Therefore, geometry-induced acoustic streaming propulsion, if any, must arise at higher order., Comment: 10 pages, no figures

The dynamics of an active walker in a harmonic potential is studied experimentally, numerically and theoretically. At odds with usual models of self-propelled particles, we identify two dynamical states for which the particle condensates at finite distance from the trap center. In the first state, also found in other systems, the particle points radially outward the trap, while diffusing along the azimuthal direction. In the second state, the particle performs circular orbits around the center of the trap. We show that self-alignment, taking the form of a torque coupling the particle orientation and velocity, is responsible for the emergence of this second dynamical state. The transition between the two states is controlled by the persistence of the particle orientation. At low inertia, the transition is continuous. For large inertia the transition is discontinuous and a coexistence regime with intermittent dynamics develops. The two states survive in the over-damped limit or when the particle is confined by a curved hard wall., Comment: 5 pages, 5 figures

We study the liquid-gas phase separation observed in a system of repulsive particles dressed with ferromagnetically aligning spins, a so-called `spin fluid'. Microcanonical ensemble numerical simulations of finite-size systems reveal that magnetization sets in and induces a liquid-gas phase separation between a disordered gas and a ferromagnetic dense phase at low enough energies and large enough densities. The dynamics after a quench into the coexistence region show that the order parameter associated to the liquid-vapour phase separation follows an algebraic law with an unusual exponent, as it is forced to synchronize with the growth of the magnetization: this suggests that for finite size systems the magnetization sets in along a Curie line, which is also the gas-side spinodal line, and that the coexistence region ends at a tricritical point. This picture is confirmed at the mean-field level with different approximation schemes, namely a Bethe lattice resolution and a virial expansion complemented by the introduction of a self-consistent Weiss-like molecular field. However, a detailed finite-size scaling analysis shows that in two dimensions the ferromagnetic phase escapes the Berezinskii-Kosterlitz-Thouless scenario, and that the long-range order is not destroyed by the unbinding of topological defects. The Curie line becomes thus a magnetic crossover in the thermodynamic limit. Finally, the effects of the magnetic interaction range and those of the interaction softness are characterized within a mean-field semi-analytic low-density approach., Comment: 25 pages, 17 figures, 1 appendix

We propose a macroscopic realization of planar Brownian motion by vertically vibrated disks. We perform a systematic statistical analysis of many random trajectories of individual disks. The distribution of increments is shown to be almost Gaussian, with slight deviations at large increments caused by inter-disk collisions. The velocity auto-correlation function takes both positive and negative values at short lag times but rapidly vanishes. We compare the empirical and theoretical distributions of time averaged mean square displacements and discuss distinctions between its mean and mode. These well-controlled experimental data can serve for validating statistical tools developed for the analysis of single-particle trajectories in microbiology.

We experimentally and numerically study the structure and dynamics of a mono-disperse packing of spontaneously aligning self-propelled hard disks. The packings are such that their equilibrium counterparts form perfectly ordered hexagonal structures. Experimentally, we first form a perfect crystal in an hexagonal arena which respects the same crystalline symmetry. Frustration of the hexagonal order, obtained by removing a few particles, leads to the formation of a rapidly diffusing "droplet". Removing more particles, the whole system spontaneously forms a macroscopic sheared flow, while conserving an overall crystalline structure. This flowing crystalline structure, which we call a "rheo-crystal" is made possible by the condensation of shear along localized stacking faults. Numerical simulations very well reproduce the experimental observations and allow us to explore the parameter space. They demonstrate that the rheo-crystal is induced neither by frustration nor by noise. They further show that larger systems flow faster while still remaining ordered., Comment: 4 pages, 5 figures

We present a novel, self-consistent and robust theoretical model to investigate elastic interactions between topological defects in liquid crystal shells. Accounting for the non-concentric nature of the shell in a simple manner, we are able to successfully and accurately explain and predict the positions of the defects, most relevant in the context of colloidal self-assembly. We calibrate and test our model on existing experimental data, and extend it to all newly observed defects configurations in chiral nematic shells. We perform new experiments to check further and confirm the validity of the present model. Moreover, we are able to obtain quantitative estimates of the energies of $+1$ or $+3/2$ disclination lines in cholesterics, whose intricate nature was only reported recently., Comment: 6 pages, 5 figures

We investigate experimentally and numerically the defect configurations emerging when a cholesteric liquid crystal is confined to a spherical shell. We uncover a rich scenario of defect configurations, some of them non-existent in nematic shells, where new types of defects are stabilized by the helical ordering of the liquid crystal. In contrast to nematic shells, here defects are not simple singular points or lines, but have a large structured core. Specifically, we observe five different types of cholesteric shells. We study the statistical distribution of the different types of shells as a function of the two relevant geometrical dimensionless parameters of the system. By playing with these parameters, we are able to induce transitions between different types of shells. These transitions involve interesting topological transformations in which the defects recombine to form new structures. Surprisingly, the defects do not approach each other by taking the shorter distance route (geodesic), but by following intricate paths., Comment: 10 pages, 8 figures

Analyzing the dynamics of a vibrated bi-dimensional packing of bidisperse granular discs below jamming, we provide evidences of a Gardner phase deep into the glass phase. To do so we perform several independent compression cycles within the same glass and show that the particles select different average vibrational positions at each cycle, while the neighborhood structure remains unchanged. We compute the mean square displacement as a function of the packing fraction and compare it with the average separation between the cages obtained for different compression cycles. Our results are fully compatible with recent numerical observations obtained for a mean field model of glass as well as for hard spheres in finite dimension. We also characterize the distribution of the cage order parameters. Here we note several differences from the numerical results, which could be attributed to activated processes and cage heterogeneities., Comment: 4 pages, 3 figures

We evidence critical fluctuations in the strain-rate of granular flows that are weakly vibrated. Strikingly, the critical point arises at {\em finite} values of the mean strain rate and vibration strength, far away from the yielding critical point at zero flow rate. We show that the global rheology, as well as the amplitude and correlation time of the fluctuations, are consistent with a mean-field, Landau like description, where strain rate and stress act as conjugated variables. We introduce a general model which captures the observed phenomenology, and argue that this type of critical behavior generically arises when self fluidization competes with friction.

We study cholesteric order in liquid crystal shells with planar degenerate anchoring. We observe that the bipolar and radial configurations intensively reported for bulk droplets have a higher degree of complexity when the liquid crystal is confined to a spherical shell. The bipolar configuration is replaced by a structure where the boojums are linked to a stack of disclination rings that spans the shell, while the radial configuration exhibits a double helix structure where two disclinations wind around each other. Our results confirm recent numerical simulations and highlight the complexity of the defect structures arising when cholesteric liquid crystals are confined to spherical geometries. We also show that the position of the boojums is only ruled by the shell geometry, independently of the cholesteric pitch. To understand quantitatively this behavior, we develop a simple yet insightful theoretical framework which captures the essence of the observed phenomenology. We also show that the transition between the two configurations is solely governed by the confinement ratio c = h/p, where h is the average shell thickness and p is the cholesteric pitch. Finally, we perform a dynamical study of this transition, and report a fascinating defect waltz due to a chemical Lehmann effect.

We propose a conservative two-dimensional particle model in which particles carry a continuous and classical spin. The model includes standard ferromagnetic interactions between spins of two different particles, and a nonstandard coupling between spin and velocity of the same particle inspired by the coupling observed in self-propelled hard discs. Because of this coupling Galilean invariance is broken and the conserved linear momentum associated to translation invariance is not proportional to the velocity of the center of mass. Also, the dynamics is not invariant under a global rotation of the spins alone. This, in principle, leaves room for collective motion and thus raises the question whether collective motion can arise in Hamiltonian systems. We study the statistical mechanics of such a system, and show that, in the fully connected (or mean-field) case, a transition to collective motion does exist in spite of momentum conservation. Interestingly, the velocity of the center of mass, which in the absence of Galilean invariance, is a relevant variable, also feeds back on the magnetization properties, as it acts as an external magnetic field that smoothens the transition. Molecular dynamics simulations of finite size systems indeed reveal a rich phase diagram, with a transition from a disordered to a homogeneous polar phase, but also more complex inhomogeneous phases with local order interrupted by topological defects.

We study the effect of thermal fluctuations in the XY-model on a surface with non vanishing mean curvature and zero Gaussian curvature. Unlike Gaussian curvature that typically frustrates orientational order, the extrinsic curvature of the surface can act as a local field that promotes long range order at low temperature. We find numerically that the transition from the high temperature isotropic phase to the true long range ordered phase is characterized by critical exponents consistent with those of the flat space Ising model in two dimensions, up to finite size effects. Our results suggest a versatile strategy to achieve geometric control of liquid crystal order by suitable design of the underlying curvature of a substrate or bounding surface., Comment: Submitted to Soft Matter

We investigate experimentally the mechanical response to shear of a 2D packing of grains across the jamming transition. First, we develop a dedicated experimental setup, together with tracking and photoelastic techniques in order to prepare the packing in a controlled fashion and to quantify the stress and strain tensors at the grain scale. Second, we install a inflating probe (a 2D "balloon"), which shears the packing with a cylindrical symmetry. We probe experimentally stresses and strains for strain amplitudes as low as $10^{-3}$ and for a range of packing fractions within $2\%$ variation around the jamming transition. We observe not only that shear strain induces shear stresses, but also normal stresses. Moreover, we show that both shear and normal stresses behave nonlinearly with the shear strain. Finally, we show by scaling analysis that the constitutive laws are controlled by the Jamming transition., Comment: 10 pages, 8 figures, in french

We show that low density homogeneous phases of self propelled hard disks exhibit a transition from isotropic to polar collective motion, albeit of a qualitatively distinct class from the Vicsek one. In the absence of noise, an abrupt discontinuous transition takes place between the isotropic phase and a fully polar absorbing state. Increasing the noise, the transition becomes continuous at a tri-critical point. We explain all our numerical findings in the framework of Boltzmann theory, on the basis of the binary scattering properties. We show that the qualitative differences observed between the present and the Vicsek model at the level of their phase behavior, take their origin in the complete opposite physics taking place during scattering events. We argue that such differences will generically hold for systems of self-propelled particles with repulsive short range interactions., Comment: 6 pages, 5 figures

We study the spatially homogeneous phases of polar active particles in the low density limit, and specifically the transition from the isotropic phase to collective polar motion. We show that the fundamental quantity of interest for the stability of the isotropic phase is the forward component of the momentum change induced by binary scattering events. Building on the Boltzmann formalism, we introduce an ansatz for the one-particle distribution and derive a closed-form evolution equation for the order parameter. This approach yields a very intuitive and physically meaningful criterion for the destabilization of the isotropic phase, where the ansatz is exact. The criterion also predicts whether the transition is continuous or discontinuous, as illustrated in three different classes of models. The theoretical predictions are in excellent agreement with numerical results., Comment: 20 pages, 6 figures Publised at IOP, Journal of Statistical Mechanics, available at http://dx.doi.org/10.1088/1742-5468/2015/10/P10017

We study the problem of the transformation of a given reactant species into an immiscible product species, as they flow through a chemically active porous medium. We derive the equation governing the evolution of the volume fraction of the species -- in a one-dimensional macroscopic description --, identify the relevant dimensionless numbers, and provide simple models for capillary pressure and relative permeabilities, which are quantities of crucial importance when tackling multiphase flows in porous media. We set the domain of validity of our models and discuss the importance of viscous coupling terms in the extended Darcy's law. We investigate numerically the steady regime and demonstrate that the spatial transformation rate of the species along the reactor is non-monotonous, as testified by the existence of an inflection point in the volume fraction profiles. We obtain the scaling of the location of this inflection point with the dimensionless lengths of the problem. Eventually, we provide key elements for optimization of the reactor., Comment: 13 pages, 10 figures

We report spontaneous motion in a fully bio-compatible system consisting of pure water droplets in an oil-surfactant medium of squalane and monoolein. Water from the droplet is solubilized by the reverse micellar solution, creating a concentration gradient of swollen reverse micelles around each droplet. The strong advection and weak diffusion conditions allow for the first experimental realization of spontaneous motion in a system of isotropic particles at sufficiently large P\'eclet number according to a straightforward generalization of a recently proposed mechanism. Experiments with a highly concentrated solution of salt instead of water, and tetradecane instead of squalane, confirm the above mechanism. The present swimming droplets are able to carry external bodies such as large colloids, salt crystals, and even cells., Comment: 5 pages, 5 figures

We investigate experimentally the mechanical response of a monolayer of bi-disperse frictional grains to an inhomogeneous shear perturbation across the jamming transition. We inflate an intruder inside the packing and use photo-elasticity and tracking techniques to measure the induced shear strain and stresses at the grain scale. We quantify experimentally the constitutive relations for strain amplitudes as low as 0.001 and for a range of packing fractions within 2% variation around the jamming transition. At the transition strong nonlinear effects set in : both the shear modulus and the dilatancy shear-soften at small strain until a critical strain is reached where effective linearity is recovered. The dependencies of the critical strain and the associated critical stresses on the distance from jamming are extracted via scaling analysis. We check that the constitutive laws, when applied to the equations governing mechanical equilibrium, lead to the observed stress and strain profiles. These profiles exhibit a spatial crossover between an effective linear regime close to the inflater and the truly nonlinear regime away from it. The crossover length diverges at the jamming transition., Comment: 5 pages, 5 figures