Nematic Torques in Scalar Active Matter: When Fluctuations Favor Polar Order and Persistence.

We study the impact of nematic alignment on scalar active matter in the disordered phase. We show that nematic torques control the emergent physics of particles interacting via pairwise forces and can either induce or prevent phase separation. The underlying mechanism is a fluctuation-induced renormalization of the mass of the polar field that generically arises from nematic torques. The correlations between the fluctuations of the polar and nematic fields indeed conspire to increase the particle persistence length, contrary to what phenomenological computations predict. This effect is generic and our theory also quantitatively accounts for how nematic torques enhance particle accumulation along confining boundaries and opposes demixing in mixtures of active and passive particles.

Characterization and Control of the Run-and-Tumble Dynamics of Escherichia Coli.

We characterize the full spatiotemporal gait of populations of swimming Escherichia coli using renewal processes to analyze the measurements of intermediate scattering functions. This allows us to demonstrate quantitatively how the persistence length of an engineered strain can be controlled by a chemical inducer and to report a controlled transition from perpetual tumbling to smooth swimming. For wild-type E. coli, we measure simultaneously the microscopic motility parameters and the large-scale effective diffusivity, hence quantitatively bridging for the first time small-scale directed swimming and macroscopic diffusion.

Metastability of Discrete-Symmetry Flocks.

We study the stability of the ordered phase of flocking models with a scalar order parameter. Using both the active Ising model and a hydrodynamic description, we show that droplets of particles moving in the direction opposite to that of the ordered phase nucleate and grow. We characterize analytically this self-similar growth and demonstrate that droplets spread ballistically in all directions. Our results imply that, in the thermodynamic limit, discrete-symmetry flocks-and, by extension, continuous-symmetry flocks with rotational anisotropy-are metastable in all dimensions.

Susceptibility of Polar Flocks to Spatial Anisotropy.

We study the effect of spatial anisotropy on polar flocks by investigating active q-state clock models in two dimensions. In contrast to the equilibrium case, we find that any amount of anisotropy is asymptotically relevant, drastically altering the phenomenology from that of the rotationally invariant case. All of the well-known physics of the Vicsek model, from giant density fluctuations to microphase separation, is replaced by that of the active Ising model, with short-range correlations and complete phase separation. These changes appear beyond a length scale that diverges in the q→∞ limit, so that the Vicsek-model phenomenology is observed in finite systems for weak enough anisotropy, i.e., sufficiently high q. We provide a scaling argument which explains why anisotropy has such different effects in the passive and active cases.

Anomalous Transport of Tracers in Active Baths.

We derive the long-time dynamics of a tracer immersed in a one-dimensional active bath. In contrast to previous studies, we find that the damping and noise correlations possess long-time tails with exponents that depend on the tracer symmetry. For generic tracers, shape asymmetry induces ratchet effects that alter fluctuations and lead to superdiffusion and friction that grows with time when the tracer is dragged at a constant speed. In the singular limit of a completely symmetric tracer, we recover normal diffusion and finite friction. Furthermore, for small symmetric tracers, the active contribution to the friction becomes negative: active particles enhance motion rather than oppose it. These results show that, in low-dimensional systems, the motion of a passive tracer in an active bath cannot be modeled as a persistent random walker with a finite correlation time.

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.

Disorder-Induced Long-Ranged Correlations in Scalar Active Matter.

We study the impact of quenched random potentials and torques on scalar active matter. Microscopic simulations reveal that motility-induced phase separation is replaced in two dimensions by an asymptotically homogeneous phase with anomalous long-ranged correlations and nonvanishing steady-state currents. Using a combination of phenomenological models and a field-theoretical treatment, we show the existence of a lower-critical dimension d_{c}=4, below which phase separation is only observed for systems smaller than an Imry-Ma length scale. We identify a weak-disorder regime in which the structure factor scales as S(q)∼1/q^{2}, which accounts for our numerics. In d=2, we predict that, at larger scales, the behavior should cross over to a strong-disorder regime. In d>2, these two regimes exist separately, depending on the strength of the potential.

Fluctuation-Induced Phase Separation in Metric and Topological Models of Collective Motion.

We study the role of noise on the nature of the transition to collective motion in dry active matter. Starting from field theories that predict a continuous transition at the deterministic level, we show that fluctuations induce a density-dependent shift of the onset of order, which in turn changes the nature of the transition into a phase-separation scenario. Our results apply to a range of systems, including models in which particles interact with their "topological" neighbors that have been believed so far to exhibit a continuous onset of order. Our analytical predictions are confirmed by numerical simulations of fluctuating hydrodynamics and microscopic models.

An alternative mechanism of early nodal clustering and myelination onset in GABAergic neurons of the central nervous system.

In vertebrates, fast saltatory conduction along myelinated axons relies on the node of Ranvier. How nodes assemble on CNS neurons is not yet fully understood. We previously described that node-like clusters can form prior to myelin deposition in hippocampal GABAergic neurons and are associated with increased conduction velocity. Here, we used a live imaging approach to characterize the intrinsic mechanisms underlying the assembly of these clusters prior to myelination. We first demonstrated that their components can partially preassemble prior to membrane targeting and determined the molecular motors involved in their trafficking. We then demonstrated the key role of the protein ß2Nav for node-like clustering initiation. We further assessed the fate of these clusters when myelination proceeds. Our results shed light on the intrinsic mechanisms involved in node-like clustering prior to myelination and unravel a potential role of these clusters in node of Ranvier formation and in guiding myelination onset.

Active depinning of bacterial droplets: The collective surfing of Bacillus subtilis.

How systems are endowed with migration capacity is a fascinating question with implications ranging from the design of novel active systems to the control of microbial populations. Bacteria, which can be found in a variety of environments, have developed among the richest set of locomotion mechanisms both at the microscopic and collective levels. Here, we uncover, experimentally, a mode of collective bacterial motility in humid environment through the depinning of bacterial droplets. Although capillary forces are notoriously enormous at the bacterial scale, even capable of pinning water droplets of millimetric size on inclined surfaces, we show that bacteria are able to harness a variety of mechanisms to unpin contact lines, hence inducing a collective slipping of the colony across the surface. Contrary to flagella-dependent migration modes like swarming, we show that this much faster "colony surfing" still occurs in mutant strains of Bacillus subtilis lacking flagella. The active unpinning seen in our experiments relies on a variety of microscopic mechanisms, which could each play an important role in the migration of microorganisms in humid environment.

Exact Hydrodynamic Description of Active Lattice Gases.

We introduce lattice gas models of active matter systems whose coarse-grained "hydrodynamic" description can be derived exactly. We illustrate our approach by considering two systems exhibiting two of the most studied collective behaviors in active matter: the motility-induced phase separation and the transition to collective motion. In both cases, we derive coupled partial differential equations describing the dynamics of the local density and polarization fields and show how they quantitatively predict the emerging properties of the macroscopic lattice gases.

Optimized Diffusion of Run-and-Tumble Particles in Crowded Environments.

We study the transport of self-propelled particles in dynamic complex environments. To obtain exact results, we introduce a model of run-and-tumble particles (RTPs) moving in discrete time on a d-dimensional cubic lattice in the presence of diffusing hard-core obstacles. We derive an explicit expression for the diffusivity of the RTP, which is exact in the limit of low density of fixed obstacles. To do so, we introduce a generalization of Kac's theorem on the mean return times of Markov processes, which we expect to be relevant for a large class of lattice gas problems. Our results show the diffusivity of RTPs to be nonmonotonic in the tumbling probability for low enough obstacle mobility. These results prove the potential for the optimization of the transport of RTPs in crowded and disordered environments with applications to motile artificial and biological systems.

Impact of a mechanical shear stress on intracellular trafficking.

Intracellular trafficking mainly takes place along the microtubules, and its efficiency depends on the local architecture and organization of the cytoskeletal network. In this work, the cytoplasm of stem cells is subjected to mechanical vortexing at a frequency of up to 1 Hz, by using magnetic chains of endosomes embedded in the cell body, in order to locally perturb the network structure. The consequences are evaluated on the directionality and processivity of the spontaneous motion of endosomes. When the same chains are used both to shear the cell medium and to probe the intracellular traffic, a substantial decrease in transport efficiency is detected after applying the mechanical shear. Interestingly, when using different objects to apply the shear and to probe the spontaneous motion, no alteration of the transport efficiency can be detected. We conclude that shaking the vesicles mainly causes their unbinding from the cytoskeletal tracks, but has little influence on the integrity of the network itself. This is corroborated by active microrheology measurements, performed with chains actuated by a magnetic field, and showing that the mechanical compliance of the cytoplasm is similar before and after slow vortexing.

How Far from Equilibrium Is Active Matter?

Active matter systems are driven out of thermal equilibrium by a lack of generalized Stokes-Einstein relation between injection and dissipation of energy at the microscopic scale. We consider such a system of interacting particles, propelled by persistent noises, and show that, at small but finite persistence time, their dynamics still satisfy a time-reversal symmetry. To do so, we compute perturbatively their steady-state measure and show that, for short persistent times, the entropy production rate vanishes. This endows such systems with an effective fluctuation-dissipation theorem akin to that of thermal equilibrium systems. Last, we show how interacting particle systems with viscous drags and correlated noises can be seen as in equilibrium with a viscoelastic bath but driven out of equilibrium by nonconservative forces, hence providing energetic insight into the departure of active systems from equilibrium.

Active Particles with Soft and Curved Walls: Equation of State, Ratchets, and Instabilities.

We study, from first principles, the pressure exerted by an active fluid of spherical particles on general boundaries in two dimensions. We show that, despite the nonuniform pressure along curved walls, an equation of state is recovered upon a proper spatial averaging. This holds even in the presence of pairwise interactions between particles or when asymmetric walls induce ratchet currents, which are accompanied by spontaneous shear stresses on the walls. For flexible obstacles, the pressure inhomogeneities lead to a modulational instability as well as to the spontaneous motion of short semiflexible filaments. Finally, we relate the force exerted on objects immersed in active baths to the particle flux they generate around them.

From phase to microphase separation in flocking models: the essential role of nonequilibrium fluctuations.

We show that the flocking transition in the Vicsek model is best understood as a liquid-gas transition, rather than an order-disorder one. The full phase separation observed in flocking models with Z(2) rotational symmetry is, however, replaced by a microphase separation leading to a smectic arrangement of traveling ordered bands. Remarkably, continuous deterministic descriptions do not account for this difference, which is only recovered at the fluctuating hydrodynamics level. Scalar and vectorial order parameters indeed produce different types of number fluctuations, which we show to be essential in selecting the inhomogeneous patterns. This highlights an unexpected role of fluctuations in the selection of flock shapes.

Pressure and phase equilibria in interacting active brownian spheres.

We derive a microscopic expression for the mechanical pressure P in a system of spherical active Brownian particles at density ρ. Our exact result relates P, defined as the force per unit area on a bounding wall, to bulk correlation functions evaluated far away from the wall. It shows that (i) P(ρ) is a state function, independent of the particle-wall interaction; (ii) interactions contribute two terms to P, one encoding the slow-down that drives motility-induced phase separation, and the other a direct contribution well known for passive systems; and (iii) P is equal in coexisting phases. We discuss the consequences of these results for the motility-induced phase separation of active Brownian particles and show that the densities at coexistence do not satisfy a Maxwell construction on P.

Emergent spatial structures in flocking models: a dynamical system insight.

We show that hydrodynamic theories of polar active matter generically possess inhomogeneous traveling solutions. We introduce a unifying dynamical-system framework to establish the shape of these intrinsically nonlinear patterns, and show that they correspond to those hitherto observed in experiments and numerical simulation: periodic density waves, and solitonic bands, or polar-liquid droplets both cruising in isotropic phases. We elucidate their respective multiplicity and mutual relations, as well as their existence domain.

Quantitative characterization of run-and-tumble statistics in bulk bacterial suspensions.

We introduce a numerical method to extract the parameters of run-and-tumble dynamics from experimental measurements of the intermediate scattering function. We show that proceeding in Laplace space is unpractical and employ instead renewal processes to work directly in real time. We first validate our approach against data produced using agent-based simulations. This allows us to identify the length and time scales required for an accurate measurement of the motility parameters, including tumbling frequency and swim speed. We compare different models for the run-and-tumble dynamics by accounting for speed variability at the single-cell and population level, respectively. Finally, we apply our approach to experimental data on wild-type Escherichia coli obtained using differential dynamic microscopy.