Dry Active Matter Research Articles

Correlations between two vortices in dry active matter

It was recently shown that wet active matter can form synchronized rotating vortices in a square lattice, similar to an antiferromagnetic Ising model (by considering rotation direction as spin projection). In this study, we investigate whether such a correlated state occurs for a model of dry active matter. We achieve that by numerically simulating the dynamics of a system of active particles in the presence of two identical circular obstacles. Then, we measure the angular velocity correlation function of both vortices as a function of the obstacle diameter, their shortest separation (gap), and the particle density. When the correlation function is negative, both vortices rotate in contrary directions. They maintain this state by exchanging particles through the region between them, analogously to synchronized cogs. On the other hand, with a positive correlation function, a single rotating cluster emerges, and the particles move around the whole structure, similar to a belt strapped around the obstacles. Additionally, we observe the emergence of uncorrelated states at the transition between correlated states, in which only a single vortex is present, or in the large gap regime, in which the vortices are nearly independent on each other.

Fluctuation-induced first order transition to collective motion

The nature of the transition to collective motion in assemblies of aligning self-propelled particles remains a long-standing matter of debate. In this article, we focus on dry active matter and show that weak fluctuations suffice to generically turn second-order mean-field transitions into a ‘discontinuous’ coexistence scenario. Our theory shows how fluctuations induce a density-dependence of the polar-field mass, even when this effect is absent at mean-field level. In turn, this dependency on density triggers a feedback loop between ordering and advection that ultimately leads to an inhomogeneous transition to collective motion and the emergence of inhomogeneous travelling bands. Importantly, we show that such a fluctuation-induced first order transition is present in both metric models, in which particles align with neighbors within a finite distance, and in ‘topological’ ones, in which alignment is based on more complex constructions of neighbor sets. We compute analytically the noise-induced renormalization of the polar-field mass using stochastic calculus, which we further back up by a one-loop field-theoretical analysis. Finally, we confirm our analytical predictions by numerical simulations of fluctuating hydrodynamics as well as of topological particle models with either k-nearest neighbors or Voronoi alignment.

First Order Alignment Transition in an Interfaced Active Nematic Fluid.

We investigate experimentally the dynamic phase transition of a two-dimensional active nematic layer interfaced with a passive liquid crystal. Under a temperature ramp that leads to the transition of the passive liquid into a highly anisotropic lamellar smectic-A phase, and in the presence of a magnetic field, the coupled active nematic reorganizes its flow and orientational patterns from the turbulent into a quasilaminar regime aligned perpendicularly to the field. Remarkably, while the phase transition of the passive fluid is known to be continuous, or second order, our observations reveal intermittent dynamics of the order parameter and the coexistence of aligned and turbulent regions in the active nematic, a signature of discontinuous, or first order, phase transitions, similar to what is known to occur in relation to flocking in dry active matter. Our results suggest that alignment transitions in active systems are intrinsically discontinuous, regardless of the symmetry and momentum-damping mechanisms.

Dependency of active pressure and equation of state on stiffness of wall

Autonomous motion and motility are hallmarks of active matter. Active agents, such as biological cells and synthetic colloidal particles, consume internal energy or extract energy from the environment to generate self-propulsion and locomotion. These systems are persistently out of equilibrium due to continuous energy consumption. It is known that pressure is not always a state function for generic active matter. Torque interaction between active constituents and confinement renders the pressure of the system a boundary-dependent property. The mechanical pressure of anisotropic active particles depends on their microscopic interactions with a solid wall. Using self-propelled dumbbells confined by solid walls as a model system, we perform numerical simulations to explore how variations in the wall stiffness influence the mechanical pressure of dry active matter. In contrast to previous findings, we find that mechanical pressure can be independent of the interaction of anisotropic active particles with walls, even in the presence of intrinsic torque interaction. Particularly, the dependency of pressure on the wall stiffness vanishes when the stiffness is above a critical level. In such a limit, the dynamics of dumbbells near the walls are randomized due to the large torque experienced by the dumbbells, leading to the recovery of pressure as a state variable of density.

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.

Uncovering novel phase transitions in dense dry polar active fluids using a lattice Boltzmann method

The dynamics of dry active matter have implications for a diverse collection of biological phenomena spanning a range of length and time scales, such as animal flocking, cell tissue dynamics, and swarming of inserts and bacteria. Uniting these systems are a common set of symmetries and conservation laws, defining dry active fluids as a class of physical system. Many interesting behaviours have been observed at high densities, which remain difficult to simulate due to the computational demand. Here, we show how two-dimensional dry active fluids in a dense regime can be studied using a simple modification of the lattice Boltzmann method. We apply our method on a model that exhibits motility-induced phase separation, and an active model with contact inhibition of locomotion, which has relevance to collective cell migration. For the latter, we uncover multiple novel phase transitions: two first-order and one potentially critical. We further support our simulation results with an analytical treatment of the hydrodynamic equations obtained via a Chapman–Enskog coarse-graining procedure.

Landau kinetic equation for dry aligning active models

The Landau equation is a kinetic equation based on the weak coupling approximation of the interaction between the particles. In the framework of dry active matter this new kinetic equation relies on the weak coupling approximation of both the alignment strength and the magnitude of the angular noise, instead of the hypothesis of diluteness. Therefore, it is a kinetic equation bridging between the Boltzmann (Bertin et al 2006 Phys. Rev. E 74 022101), and the Smoluchowski (Baskaran et al 2010 J. Stat. Mech. P04019) approximations, and allowing analytical descriptions at moderate densities. The form of the equation presents non-linear and density dependent diffusions and advections fully derived by the microscopic equations of motions. Finally, implementing the BGL procedure (Peshkov et al 2014 Eur. Phys. J. Spec. Top. 223 1315–44), the parameters of the Toner–Tu equations are derived showing the appearance of linearly stable homogeneous ordered solutions and mimicking the results obtained from the Boltzmann approach.

Computational models for active matter

Active matter, which ranges from molecular motors to groups of animals, exists at different length scales and timescales, and various computational models have been proposed to describe and predict its behaviour. The diversity of the methods and the challenges in modelling active matter primarily originate from the out-of-equilibrium character, lack of detailed balance and of time-reversal symmetry, multiscale nature, nonlinearity and multibody interactions. Models exist for both dry active matter and active matter in fluids, and can be agent-based or continuum-level descriptions. They can be generic, emphasizing universal features, or detailed, capturing specific features. We compare various modelling approaches and numerical techniques to illuminate the innovations and challenges in understanding active matter. Active matter consists of energy-consuming units, which self-propel, exert forces on their neighbours and act collectively, resulting in emergent non-equilibrium behaviour. This Review surveys computational models that describe a wide range of active systems, from synthetic microswimmers to animal herds.

Quantitative Assessment of the Toner and Tu Theory of Polar Flocks.

We present a quantitative assessment of the Toner and Tu theory describing the universal scaling of fluctuations in polar phases of dry active matter. Using large-scale simulations of the Vicsek model in two and three dimensions, we find the overall phenomenology and generic algebraic scaling predicted by Toner and Tu, but our data on density correlations reveal some qualitative discrepancies. The values of the associated scaling exponents we estimate differ significantly from those conjectured in 1995. In particular, we identify a large crossover scale beyond which flocks are only weakly anisotropic. We discuss the meaning and consequences of these results.

Deriving hydrodynamic equations from dry active matter models in three dimensions

We derive hydrodynamic equations from Vicsek-style dry active matter models in three dimensions (3D), building on our experience on the 2D case using the Boltzmann–Ginzburg–Landau approach. The hydrodynamic equations are obtained from a Boltzmann equation expressed in terms of an expansion in spherical harmonics. All their transport coefficients are given with explicit dependences on particle-level parameters. The linear stability analysis of their spatially-homogeneous solutions is presented. While the equations derived for the polar case (original Vicsek model with ferromagnetic alignment) and their solutions do not differ much from their 2D counterparts, the active nematics case exhibits remarkable differences: we find a true discontinuous transition to order with a bistability region, and cholesteric solutions whose stability we discuss.

Mechanical pressure and momentum conservation in dry active matter**This article belongs to the special issue: Emerging Talents (https://iopscience.iop.org/journal/1751-8121/page/Emerging-Talents), which features invited work from the best early-career researchers working within the scope of J. Phys. A. This project is part of the Journal of Physics series’ 50th anniversary celebrations in 2017. Julien Tailleur was selected by the Editorial Board of J.

We relate the breakdown of equations of states (EOS) for the mechanical pressure of generic dry active systems to the lack of momentum conservation in such systems. We show how net sources and sinks of momentum arise generically close to confining walls. These typically depend on the interactions of the container with the particles, which makes the mechanical pressure a container-dependent quantity. We show that an EOS is recovered if the dynamics of the propulsive forces of the particles are decoupled from other degrees of freedom and lead to an apolar bulk steady-state. This recovery of an EOS stems from the mean steady-state active force density being the divergence of the flux of ‘active impulse’, an observable which measures the mean momentum particles will receive from the substrate in the future.

An Active Approach to Colloidal Self-Assembly.

In this review, we discuss recent advances in the self-assembly of self-propelled colloidal particles and highlight some of the most exciting results in this field, with a specific focus on dry active matter. We explore this phenomenology through the lens of the complexity of the colloidal building blocks. We begin by considering the behavior of isotropic spherical particles. We then discuss the case of amphiphilic and dipolar Janus particles. Finally, we show how the geometry of the colloids and/or the directionality of their interactions can be used to control the physical properties of the assembled active aggregates, and we suggest possible strategies for how to exploit activity as a tunable driving force for self-assembly. The unique properties of active colloids lend promise to the design of the next generation of functional, environment-sensing microstructures able to perform specific tasks in an autonomous and targeted manner.

Stabilization of active matter by flow-vortex lattices and defect ordering.

Active systems, from bacterial suspensions to cellular monolayers, are continuously driven out of equilibrium by local injection of energy from their constituent elements and exhibit turbulent-like and chaotic patterns. Here we demonstrate both theoretically and through numerical simulations, that the crossover between wet active systems, whose behaviour is dominated by hydrodynamics, and dry active matter where any flow is screened, can be achieved by using friction as a control parameter. Moreover, we discover unexpected vortex ordering at this wet–dry crossover. We show that the self organization of vortices into lattices is accompanied by the spatial ordering of topological defects leading to active crystal-like structures. The emergence of vortex lattices, which leads to the positional ordering of topological defects, suggests potential applications in the design and control of active materials.

Hydrodynamic theory of dry active matter

In this paper we shortly review theoretical progress in the field of active matter, focusing on the continuum theory of dry systems, in which momentum of active particles is not conserved due to the interaction between the particles and a substrate or medium. In particular, we review the phenomenological way of deriving hydrodynamic equations for both polar and apolar systems, and the predictions of these theories such as long-ranged orientational order in two-dimensional polar systems and giant number fluctuations. The comparisons among theoretical predictions, numerical results, and experimental evidence are also summarized.

Vibrated polar disks: spontaneous motion, binary collisions, and collective dynamics

We study the spontaneous motion, binary collisions, and collective dynamics of “polar disks”, i.e. specially designed particles which, when vibrated between two horizontal plates, move coherently along a direction strongly correlated to their intrinsic polarity. The motion of our particles, although nominally three-dimensional and complicated, is well accounted for by a two-dimensional persistent random walk. Their binary collisions are spatiotemporally extended events during which multiple actual collisions happen, yielding a weak average effective alignment. We show that this well-controlled, “dry active matter” system can display collective motion with orientationally-ordered regions of the order of the system size. We provide evidence of strong number density fluctuations in the most ordered regimes observed. These results are discussed in the light of the limitations of our system, notably those due to the inevitable presence of walls.