Comment on "Flocking without Alignment Interactions in Attractive Active Brownian Particles [arXiv:2303.07746]"

In a recent Letter, Caprini and L\"owen argue that attractive active Brownian particles can flock even in the absence of explicit aligning interactions of their velocities. In this comment, I show that the phenomenology described in [Phys. Rev. Lett. {\bf 130}, 148202 (2023)] in fact lacks several defining features of flocking, such as long-range correlations and large-scale directed motion

Long-Range Nematic Order in Two-Dimensional Active Matter

Working in two space dimensions, we show that the orientational order emerging from self-propelled polar particles aligning nematically is quasi-long-ranged beyond $\ell_{\rm r}$, the scale associated to induced velocity reversals, which is typically extremely large and often cannot even be measured. Below $\ell_{\rm r}$, nematic order is long-range. We construct and study a hydrodynamic theory for this de facto phase and show that its structure and symmetries differ from conventional descriptions of active nematics. We check numerically our theoretical predictions, in particular the presence of $\pi$-symmetric propagative sound modes, and provide estimates of all scaling exponents governing long-range space-time correlations.Comment: 6 pages, 2 figures, comments welcome

Bose-Einstein-like Condensation due to Diffusivity Edge under Periodic Confinement

A generic class of scalar active matter, characterized at the mean field level by the diffusivity vanishing above some threshold density, was recently introduced [Golestanian R 2019 Phys. Rev. E 100 010601(R)]. In the presence of harmonic confinement, such 'diffusivity edge' was shown to lead to condensation in the ground state, with the associated transition exhibiting formal similarities with Bose-Einstein condensation (BEC). In this work, the effect of a diffusivity edge is addressed in a periodic potential in arbitrary dimensions, where the system exhibits coexistence between many condensates. Using a generalized thermodynamic description of the system, it is found that the overall phenomenology of BEC holds even for finite energy barriers separating each neighbouring pair of condensates. Shallow potentials are shown to quantitatively affect the transition, and introduce non-universality in the values of the scaling exponents.Comment: 13 pages, 3 figures. Comments welcom

Dynamical theory of topological defects I: the multivalued solution of the diffusion equation

Point-like topological defects are singular configurations that occur in a variety of in and out of equilibrium systems with two-dimensional orientational order. As they are associated with a nonzero circuitation condition, the presence of defects induces a long-range perturbation of the orientation landscape around them. The effective dynamics of defects is thus generally described in terms of quasi-particles interacting through the orientation field they produce, whose evolution in the simplest setting is governed by the diffusion equation. Due to the multivalued nature of the orientation field, its expression for a defect moving with an arbitrary trajectory cannot be obtained straightforwardly and is often evaluated in the quasi-static approximation. Here, we instead propose an approach that allows to derive the exact expression for the orientation created by multiple moving defects, which we find to depend on their past trajectories and thus to be nonlocal in time. Performing various expansions in relevant regimes, we show how improved approximations with respect to the quasi-static defect solution can be obtained. Moreover, our results lead to so far unnoticed structures in the orientation field of moving defects which we discuss in light of existing experimental results.Comment: 24 page

Optimal navigation of microswimmers in complex and noisy environments

We design new navigation strategies for travel time optimization of microscopic self-propelled particles in complex and noisy environments. In contrast to strategies relying on the results of optimal control theory, these protocols allow for semi-autonomous navigation as they do not require control over the microswimmer motion via external feedback loops. Although the strategies we propose rely on simple principles, they show arrival time statistics strikingly similar to those obtained from stochastic optimal control theory, as well as performances that are robust to environmental changes and strong fluctuations. These features, as well as their applicability to more general optimization problems, make these strategies promising candidates for the realization of optimized semi-autonomous navigation

Dynamical theory of topological defects II: Universal aspects of defect motion

We study the dynamics of topological defects in continuum theories governed by a free energy minimization principle, building on our recently developed framework [Romano J, Mahault B and Golestanian R 2023 J. Stat. Mech.: Theory Exp. 083211]. We show how the equation of motion of point defects, domain walls, disclination lines and any other singularity can be understood with one unifying mathematical framework. For disclination lines, this also allows us to study the interplay between the internal line tension and the interaction with other lines. This interplay is non-trivial, allowing defect loops to expand, instead of contracting, due to external interaction. We also use this framework to obtain an analytical description of two long-lasting problems in point defect motion, namely the scale dependence of the defect mobility and the role of elastic anisotropy in the motion of defects in liquid crystals. For the former, we show that this dependence is strongly problem-dependent, but it can be computed with high accuracy for a pair of annihilating defects. For the latter, we show that at the first order in perturbation theory anisotropy causes a non-radial force, making the trajectory of annihilating defects deviate from a straight line. At higher orders, it also induces a correction in the mobility, which becomes non-isotropic for the $+1/2$ defect. We argue that, due to its generality, our method can help to shed light on the motion of singularities in many different systems, including driven and active non-equilibrium theories.Comment: 33 pages, 6 figure

Energetic cost of microswimmer navigation: the role of body shape

We study the energetic efficiency of navigating microswimmers by explicitly taking into account the geometry of their body. We show that, as their shape transitions from prolate to oblate, non-steering microswimmers rotated by flow gradients naturally follow increasingly time-optimal trajectories. At the same time, they also require larger dissipation to swim. The coupling between body geometry and hydrodynamics thus leads to a generic trade-off between the energetic costs associated with propulsion and navigation, which is accompanied by the selection of a finite optimal aspect ratio. We derive from optimal control theory the steering policy ensuring overall minimum energy dissipation, and characterize how navigation performances vary with the swimmer shape. Our results highlight the important role of the swimmer geometry in realistic navigation problems

Magnetic microswimmers exhibit Bose-Einstein-like condensation

We study an active matter system comprised of magnetic microswimmers confined in a microfluidic channel and show that it exhibits a new type of self-organized behavior. Combining analytical techniques and Brownian dynamics simulations, we demonstrate how the interplay of non-equilibrium activity, external driving, and magnetic interactions leads to the condensation of swimmers at the center of the channel via a non-equilibrium phase transition that is formally akin to Bose-Einstein condensation. We find that the effective dynamics of the microswimmers can be mapped onto a diffusivity-edge problem, and use the mapping to build a generalized thermodynamic framework, which is verified by a parameter-free comparison with our simulations. Our work reveals how driven active matter has the potential to generate exotic classical non-equilibrium phases of matter with traits that are analogous to those observed in quantum systems

Dynamical pattern formation without self-attraction in quorum-sensing active matter: the interplay between nonreciprocity and motility

We study a minimal model involving two species of particles interacting via quorum-sensing rules. Combining simulations of the microscopic model and linear stability analysis of the associated coarse-grained field theory, we identify a mechanism for dynamical pattern formation that does not rely on the standard route of intra-species effective attractive interactions. Instead, our results reveal a highly dynamical phase of chasing bands induced only by the combined effects of self-propulsion and nonreciprocity in the inter-species couplings. Turning on self-attraction, we find that the system may phase separate into a macroscopic domain of such chaotic chasing bands coexisting with a dilute gas. We show that the chaotic dynamics of bands at the interfaces of this phase-separated phase results in anomalously slow coarsening.Comment: Supplemental movies are available on reques