Model of Active Solids: Rigid Body Motion and Shape-Changing Mechanisms.

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.

Traveling fronts in vibrated polar disks: At the crossroad between polar ordering and jamming.

We investigate experimentally the collective motion of polar vibrated disks in an annular geometry, varying both the packing fraction and the amplitude of the angular noise. For low enough noise and large enough density, an overall collective motion takes place along the tangential direction. The spatial organization of the flow reveals the presence of polar bands of large density, as expected from the commonly accepted picture of the transition to collective motion in systems of aligning polar active particles. However, in our case, the low density phase is also polar, consistent with what is observed when jamming takes place in a very high density flock. Interestingly, while in that case the particles in the high density bands are arrested, resulting in an upstream propagation at a constant speed, in our case the bands travel downstream with a density-dependent speed. We demonstrate from local measurements of the packing fraction, alignment, and flow speeds that the bands observed here result both from a polar ordering process and a motility induced phase separation mechanism.

Noise-induced collective actuation in active solids.

Collective actuation describes the spontaneous synchronized oscillations taking place in active solids when the elasto-active feedback, which 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 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 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.

Reconfiguration, Interrupted Aging, and Enhanced Dynamics of a Colloidal Gel Using Photoswitchable Active Doping.

We study quasi-2D gels made of a colloidal network doped with Janus particles activated by light. Following the gel formation, we monitor both the structure and dynamics before, during, and after the activation period. Before activity is switched on, the gel is slowly aging. During the activation, the mobility of the passive particles exhibits a characteristic scale-dependent response, while the colloidal network remains connected, and the gel maintains its structural integrity. Once activity is switched off, the gel stops aging and 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 softer gel, with frozen dynamics, but with more space for thermal fluctuations. The above conclusions remain valid long after the activity period.

Morphological computation and decentralized learning in a swarm of sterically interacting robots.

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 Morphobots, a robotic swarm platform developed to implement embodied computation through a morpho-functional design. By engineering a three-dimensional printed exoskeleton, we encode a reorientation 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 motility and stability and also allows encoding of 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. Experimenting with physical swarms (of up to 64 robots) and simulated swarms (of up to 8192 agents) shows that the effect of morphological computation increases with growing swarm size.

Steering self-organisation through confinement.

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 is an action over a system that limits its units' translational and rotational degrees of freedom, thus also influencing the system's phase space probability density; it can function as either a catalyst or inhibitor of self-organisation. Confinement 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 and perspective for future research, we examine the role of confinement in the self-organisation of soft-matter systems and identify overarching scientific challenges that need to be addressed to harness its full scientific and technological potential in soft matter and related fields. By drawing analogies with other disciplines, this framework will accelerate a common deeper understanding of self-organisation and trigger the development of innovative strategies to steer it using confinement, with impact on, e.g., the design of smarter materials, tissue engineering for biomedicine and in guiding active matter.

Discontinuous Tension-Controlled Transition between Collective Actuations in Active Solids.

The recent finding of collective actuation in active solids-solids embedded with active units-is a new promise for the design of multifunctional materials with genuine autonomy, and a better understanding of dense biological systems. Here, we combine the experimental study of centimetric model active solids, the numerical study of an agent-based model, and theoretical arguments to reveal a new form of collective actuation and how mechanical tension can serve as a general mechanism for transitioning between different collective actuation regimes. The presence of hysteresis when varying tension back and forth highlights the nontrivial selectivity of collective actuations.

Linear Instability of Turbulent Channel Flow.

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 wave vector of the modulation at onset.

Polymer-chain configurations in active and passive baths.

The configurations taken by polymers embedded in out-of-equilibrium baths may have broad implications 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 agree with 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.

Kinetic Monte Carlo Algorithms for Active Matter Systems.

We study kinetic Monte Carlo (KMC) descriptions of active particles. We show that, when they rely on purely persistent, active steps, 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 then show how, under an appropriate scaling, mixing passive steps with active ones leads to a well-defined continuous-time limit that however differs from standard active dynamics. Finally, we propose new KMC algorithms whose continuous-time limits lead to the dynamics of active Ornstein-Uhlenbeck, active Brownian, and run-and-tumble particles.

Elastoplasticity Mediates Dynamical Heterogeneity Below the Mode Coupling Temperature.

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-ranged, 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.

Swimming droplets in 1D geometries: an active Bretherton problem.

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 used to explore even higher confinement. The lubrication layer around the droplet then takes a non-uniform thickness which constitutes a significant difference to 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 in the droplet's behavior under confinement. We then propose an analytical formulation by integrating the interface activity and the swollen micelle 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 micelle concentration along the interface, which would explain the divergence of the lubrication layer thickness for long enough droplets, eventually leading to spontaneous droplet division.

Flow Statistics in the Transitional Regime of Plane Channel Flow.

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.

Speed-dispersion-induced alignment: A one-dimensional model inspired by swimming droplets experiments.

We investigate the collective dynamics of self-propelled droplets, confined in a one-dimensional microfluidic channel. On the one hand, neighboring droplets align and form large trains of droplets moving in the same direction. On the other hand, the droplets condensate, 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.

Velocity and Speed Correlations in Hamiltonian Flocks.

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.

Attractive versus truncated repulsive supercooled liquids: The dynamics is encoded in the pair correlation function.

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.

Interrupted Motility Induced Phase Separation in Aligning Active Colloids.

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. Our large scale quantification of the phase separation kinetics in active colloids points towards the new physics observed when both alignment and short-range repulsions are present.

Ferromagnetism-induced phase separation in a two-dimensional spin fluid.

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 with the liquid-vapor 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 thus becomes 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 semianalytical low-density approach.

Dynamics of a Self-Propelled Particle in a Harmonic Trap.

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 a finite distance from the trap center. In the first state, also found in other systems, the particle points radially outward from 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 overdamped limit or when the particle is confined by a curved hard wall.