Metastability of Constant-Density Flocks

We study numerically the Toner-Tu field theory where the density field is maintained constant, a limit case of "Malthusian" flocks for which the asymptotic scaling of correlation functions in the ordered phase is known exactly. While we confirm these scaling laws, we also show that such constant-density flocks are metastable to the nucleation of a specific defect configuration, and are replaced by a globally disordered phase consisting of asters surrounded by shock lines that constantly evolves and remodels itself. We demonstrate that the main source of disorder lies along shock lines, rendering this active foam fundamentally different from the corresponding equilibrium system. We thus show that in the context of active matter also, a result obtained at all orders of perturbation theory can be superseded by nonperturbative effects, calling for a different approach.

Flocking in one dimension: Asters and reversals

We study the one-dimensional active Ising model in which aligning particles undergo diffusion biased by the signs of their spins. The phase diagram obtained varying the density of particles, their hopping rate, and the temperature controlling the alignment shows a homogeneous disordered phase but no homogeneous ordered one, as well as two phases with localized dense structures. In the flocking phase, large ordered aggregates move ballistically and stochastically reverse their direction of motion. In what we termed the "aster" phase, dense immobile aggregates of opposite magnetization face each other, exchanging particles, without any net motion of the aggregates. Using a combination of numerical simulations and mean-field theory, we study the evolution of the shapes of the flocks, the statistics of their reversal times, and their coarsening dynamics. Solving exactly for the zero-temperature dynamics of an aster allows us to understand their coarsening, which shows extremal dynamics, while mean-field equations account for their shape.

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.

Dynamic clustering of passive colloids in dense suspensions of motile bacteria

Mixtures of active and passive particles are predicted to exhibit a variety of nonequilibrium phases. Here we report a dynamic clustering phase in mixtures of colloids and motile bacteria. We show that colloidal clustering results from a balance between bond breaking due to persistent active motion and bond stabilization due to torques that align active particle velocity tangentially to the passive particle surface. Furthermore, dynamic clustering spans a broad regime between diffusivity-based and motility-induced phase separation that subsumes typical bacterial motility parameters.

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.

Self-Organized Critical Coexistence Phase in Repulsive Active Particles

We revisit motility-induced phase separation in two models of active particles interacting by pairwise repulsion and uncover new qualitative features: the resulting dense phase contains gas bubbles distributed algebraically up to a typically extremely large cutoff scale. At large enough system size and/or global density, all the gas may be contained inside the bubbles, at which point the system is microphase separated with a finite cutoff bubble scale. We further observe that the ordering is clearly anomalous, with different dynamics for the coarsening of the dense phase and of the gas bubbles. This self-organized critical phenomenology is reproduced by a "reduced bubble model" that implements the basic idea of reverse Ostwald ripening put forward in Tjhung et al. [Phys. Rev. X 8, 031080 (2018)PRXHAE2160-330810.1103/PhysRevX.8.031080].

The 2020 motile active matter roadmap

Activity and autonomous motion are fundamental in living and engineering systems. This has stimulated the new field of 'active matter' in recent years, which focuses on the physical aspects of propulsion mechanisms, and on motility-induced emergent collective behavior of a larger number of identical agents. The scale of agents ranges from nanomotors and microswimmers, to cells, fish, birds, and people. Inspired by biological microswimmers, various designs of autonomous synthetic nano- and micromachines have been proposed. Such machines provide the basis for multifunctional, highly responsive, intelligent (artificial) active materials, which exhibit emergent behavior and the ability to perform tasks in response to external stimuli. A major challenge for understanding and designing active matter is their inherent nonequilibrium nature due to persistent energy consumption, which invalidates equilibrium concepts such as free energy, detailed balance, and time-reversal symmetry. Unraveling, predicting, and controlling the behavior of active matter is a truly interdisciplinary endeavor at the interface of biology, chemistry, ecology, engineering, mathematics, and physics. The vast complexity of phenomena and mechanisms involved in the self-organization and dynamics of motile active matter comprises a major challenge. Hence, to advance, and eventually reach a comprehensive understanding, this important research area requires a concerted, synergetic approach of the various disciplines. The 2020 motile active matter roadmap of Journal of Physics: Condensed Matter addresses the current state of the art of the field and provides guidance for both students as well as established scientists in their efforts to advance this fascinating area.

Nonequilibrium forces following quenches in active and thermal matter

Nonequilibrium systems with conserved quantities like density or momentum are known to exhibit long-ranged correlations. This, in turn, leads to long-ranged fluctuation-induced (Casimir) forces, predicted to arise in a variety of nonequilibrium settings. Here, we study such forces, which arise transiently between parallel plates or compact inclusions in a gas of particles, following a change ("quench") in temperature or activity of the medium. Analytical calculations, as well as numerical simulations of passive or active Brownian particles, indicate two distinct forces: (i) The immediate effect of the quench is adsorption or desorption of particles of the medium to the immersed objects, which in turn initiates a front of relaxing (mean) density. This leads to time-dependent density-induced forces. (ii) A long-term effect of the quench is that density fluctuations are modified, manifested as transient (long-ranged) (pair-)correlations that relax diffusively to their (short-ranged) steady-state limit. As a result, transient fluctuation-induced forces emerge. We discuss the properties of fluctuation-induced and density-induced forces as regards universality, relaxation as a function of time, and scaling with distance between objects. Their distinct signatures allow us to distinguish the two types of forces in simulation data. Our simulations also show that a quench of the effective temperature of an active medium gives rise to qualitatively similar effects to a temperature quench in a passive medium. Based on this insight, we propose several scenarios for the experimental observation of the forces described here.

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.