arXiv subjects
Publications and source records attributed to Olivier Dauchot.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.