Rectified Rotational Dynamics of Mobile Inclusions in Two-Dimensional Active Nematics

The 2025 motile active matter roadmap

Activity and autonomous motion are fundamental aspects of many living and engineering systems. Here, the scale of biological agents covers a wide range, from nanomotors, cytoskeleton, and cells, to insects, fish, birds, and people. Inspired by biological active systems, various types of autonomous synthetic nano- and micromachines have been designed, which provide the basis for multifunctional, highly responsive, intelligent active materials. A major challenge for understanding and designing active matter is their inherent non-equilibrium nature due to persistent energy consumption, which invalidates equilibrium concepts such as free energy, detailed balance, and time-reversal symmetry. Furthermore, interactions in ensembles of active agents are often non-additive and non-reciprocal. An important aspect of biological agents is their ability to sense the environment, process this information, and adjust their motion accordingly. It is an important goal for the engineering of micro-robotic systems to achieve similar functionality. Many fundamental properties of motile active matter are by now reasonably well understood and under control. Thus, the ground is now prepared for the study of physical aspects and mechanisms of motion in complex environments, the behavior of systems with new physical features like chirality, the development of novel micromachines and microbots, the emergent collective behavior and swarming of intelligent self-propelled particles, and particular features of microbial systems. The vast complexity of phenomena and mechanisms involved in the self-organization and dynamics of motile active matter poses major challenges, which can only be addressed by a truly interdisciplinary effort involving scientists from biology, chemistry, ecology, engineering, mathematics, and physics. The 2025 motile active matter roadmap of Journal of Physics: Condensed Matter reviews the current state of the art of the field and provides guidance for further progress in this fascinating research area.

Multiparticle collision framework for active polar fluids

Sufficiently dense intrinsically out-of-equilibrium suspensions, such as those observed in biological systems, can be modeled as active fluids characterized by their orientational symmetry. While mesoscale numerical approaches to active nematic fluids have been developed, polar fluids are simulated as either ensembles of microscopic self-propelled particles or continuous hydrodynamic-scale equations of motion. To better simulate active polar fluids in complex geometries or as a solvent for suspensions, mesoscale numerical approaches are needed. In this work, the coarse-graining multiparticle collision dynamics (MPCD) framework is applied to three active particle models to produce mesoscale simulations of polar active fluids. The first active-polar MPCD (AP-MPCD) is a variant of the Vicsek model, while the second and third variants allow the speed of the particles to relax towards a self-propulsion speed subject to Andersen and Langevin thermostats, respectively. Each of these AP-MPCD variants exhibits a flocking transition at a critical activity and banding in the vicinity of the transition point. We leverage the mesoscale nature of AP-MPCD to explore flocking in the presence of external fields, which destroys banding, and anisotropic obstacles, which act as a ratchet that biases the flocking direction. These results demonstrate the capacity of AP-MPCD to capture the known phenomenology of polar active suspensions and its versatility to study active polar fluids in complex scenarios.

Spontaneous flows and quantum analogies in heterogeneous active nematic films

Incorporating the inherent heterogeneity of living systems into models of active nematics is essential to provide a more realistic description of biological processes such as bacterial growth, cell dynamics and tissue development. Spontaneous flow of a confined active nematic is a fundamental feature of these systems, in which the role of heterogeneity has not yet been considered. We therefore determine the form of spontaneous flow transition for an active nematic film with heterogeneous activity, identifying a correspondence between the unstable director modes and solutions to Schrödinger's equation. We consider both activity gradients and steps between regions of distinct activity, finding that such variations can change the signature properties of the flow. The threshold activity required for the transition can be raised or lowered, the fluid flux can be reduced or reversed and interfaces in activity induce shear flows. In a biological context fluid flux influences the spread of nutrients while shear flows affect the behaviour of rheotactic microswimmers and can cause the deformation of biofilms. All the effects we identify are found to be strongly dependent on not simply the types of activity present in the film but also on how they are distributed.

Controlling wall-particle interactions with activity

We theoretically determine the effective forces on hard disks near walls embedded inside active nematic liquid crystals. When the disks are sufficiently close to the wall and the flows are sufficiently slow, we can obtain exact expressions for the effective forces. We find these forces and the dynamics of disks near the wall depend both on the properties of the active nematic and on the anchoring conditions on the disks and the wall. Our results show that the presence of active stresses attract planar anchored disks to walls if the activity is extensile, and repel them if contractile. For normal anchored disks the reverse is true; they are attracted in contractile systems, and repelled in extensile ones. By choosing the activity and anchoring, these effects may be helpful in controlling the self assembly of active nematic colloids.

Active nematics in corrugated channels

Active nematic fluids exhibit complex dynamics in both bulk and in simple confining geometries. However, complex confining geometries could have substantial impact on active spontaneous flows. Using multiparticle collision dynamics simulations adapted for active nematic particles, we study the dynamic behaviour of an active nematic fluid confined in a corrugated channel. The transition from a quiescent state to a spontaneous flow state occurs from a weak swirling flow to a strong coherent flow due to the presence of curved-wall induced active flows. We show that the active nematic fluid flows in corrugated channels can be understood in two different ways: (i) as the result of an early or delayed flow transition when compared with that in a flat-walled channel of appropriate width and (ii) boundary-induced active flows in the corrugations providing an effective slip velocity to the coherent flows in the bulk. Thus, our work illustrates the crucial role of corrugations of the confining boundary in dictating the flow transition and flow states of active fluids.

Active nematic ratchet in asymmetric obstacle arrays

We numerically investigate the effect of an asymmetric periodic obstacle array in a two-dimensional active nematic. We find that activity in conjunction with the asymmetry leads to a ratchet effect or unidirectional flow of the fluid along the asymmetry direction. The directional flow is still present even in the active turbulent phase when the gap between obstacles is sufficiently small. We demonstrate that the dynamics of the topological defects transition from flow mirroring to smectic-like as the gap between obstacles is made smaller, and explain this transition in terms of the pinning of negative winding number defects between obstacles. This also leads to a nonmonotonic ratchet effect magnitude as a function of obstacle size, so that there is an optimal obstacle size for ratcheting at fixed activity.

Anomalous dynamics of a passive droplet in active turbulence

Motion of a passive deformable object in an active environment serves as a representative of both in-vivo systems such as intracellular particle motion in Acanthamoeba castellanii, or in-vitro systems such as suspension of beads inside dense swarms of Escherichia coli. Theoretical modeling of such systems is challenging due to the requirement of well resolved hydrodynamics which can explore the spatiotemporal correlations around the suspended passive object in the active fluid. We address this critical lack of understanding using coupled hydrodynamic equations for nematic liquid crystals with finite active stress to model the active bath, and a suspended nematic droplet with zero activity. The droplet undergoes deformation fluctuations and its movement shows periods of "runs" and "stays". At relatively low interfacial tension, the droplet begins to break and mix with the outer active bath. We establish that the motion of the droplet is influenced by the interplay of spatial correlations of the flow and the size of the droplet. The mean square displacement shows a transition from ballistic to normal diffusion which depends on the droplet size. We discuss this transition in relation to spatiotemporal scales associated with velocity correlations of the active bath and the droplet.

Non-Gaussian Displacements in Active Transport on a Carpet of Motile Cells

We study the dynamics of micron-sized particles on a layer of motile cells. This cell carpet acts as an active bath that propels passive tracer particles via direct mechanical contact. The resulting nonequilibrium transport shows a crossover from superdiffusive to normal-diffusive dynamics. The particle displacement distribution is distinctly non-Gaussian even at macroscopic timescales exceeding the measurement time. We obtain the distribution of diffusion coefficients from the experimental data and introduce a model for the displacement distribution that matches the experimentally observed non-Gaussian statistics. We argue why similar transport properties are expected for many composite active matter systems.

Maximally mixing active nematics

Active nematics are an important new paradigm in soft condensed matter systems. They consist of rodlike components with an internal driving force pushing them out of equilibrium. The resulting fluid motion exhibits chaotic advection, in which a small patch of fluid is stretched exponentially in length. Using simulation, this paper shows that this system can exhibit stable periodic motion when confined to a sufficiently small square with periodic boundary conditions. Moreover, employing tools from braid theory, we show that this motion is maximally mixing, in that it optimizes the (dimensionless) "topological entropy"-the exponential stretching rate of a material line advected by the fluid. That is, this periodic motion of the defects, counterintuitively, produces more chaotic mixing than chaotic motion of the defects. We also explore the stability of the periodic state. Importantly, we show how to stabilize this orbit into a larger periodic tiling, a critical necessity for it to be seen in future experiments.