Self-propelled Disks Research Articles

Extinction and coexistence in a binary mixture of proliferating motile disks.

A binary mixture of two-different-size proliferating motile disks is studied. As growth is space limited, we focus on the conditions such that there is a coexistence of both large and small disks, or dominance of the larger disks. The study involves systematically varying some system parameters, such as diffusivities, growth rates, and self-propulsion velocities. In particular, we demonstrate that diffusing faster confers a competitive advantage, so that larger disks can in the long time coexist or even dominate the smaller ones. In the case of self-propelled disks, a coexistence regime is induced by the activity where the two types of disks show the same spatial distribution: both particles are phase separated or both are homogeneously distributed in the whole system.

Emerging Mesoscale Flows and Chaotic Advection in Dense Active Matter

We study two models of overdamped self-propelled disks in two dimensions, with and without aligning interactions. Both models support active mesoscale flows, leading to chaotic advection and transport over large length scales in their homogeneous dense fluid states, away from dynamical arrest. They form streams and vortices reminiscent of multiscale flow patterns in turbulence. We show that the characteristics of these flows do not depend on the specific details of the active fluids, and result from the competition between crowding effects and persistent propulsions. This observation suggests that dense active suspensions of self-propelled particles present a type of “active turbulence” distinct from collective flows reported in other types of active systems. Published by the American Physical Society 2024

Collective behavior of soft self-propelled disks with rotational inertia

We investigate collective properties of a large system of soft self-propelled inertial disks with active Langevin dynamics simulation in two dimensions. Rotational inertia of the disks is found to favor motility induced phase separation (MIPS), due to increased effective persistence of the disks. The MIPS phase diagram in the parameter space of rotational inertia and disk softness is reported over a range of values of translation inertia and self-propulsion strength of the disks. Our analytical prediction of the phase boundary between the homogeneous (no-MIPS) and MIPS state in the limit of small and large rotational inertia is found to agree with the numerical data over a large range of translational inertia. Shape of the high density MIPS phase is found to change from circular to rectangular one as the system moves away from the phase boundary. Structural and dynamical properties of the system, measured by several physical quantities, are found to be invariant in the central region of the high density MIPS phase, whereas they are found to vary gradually near the peripheral region of the high density phase. Importantly, the width of the peripheral region near the phase boundary is much larger compared to the narrow peripheral region far away from the phase boundary. Rich dynamics of the disks inside the high density MIPS phase is addressed. Spatial correlation of velocity of the disks is found to increase with rotational inertia and disk hardness. However, temporal correlation of the disks’ velocity is found to be a function of rotational inertia, while it is independent of disk softness.

Reentrant phase separation of a sparse collection of nonreciprocally aligning self-propelled disks.

We study a model of aligning self-propelled disks that nonreciprocally reorient the self-propulsion directions along the interparticle separation and towards the other disks. In the limit of small inertia and large softness, where conventional motility-induced phase separation is absent, we demonstrate that the homogeneous system at a small area fraction phase-separates into clusters and a low-density phase that, eventually, reenters the homogeneous phase with a monotonic increase in alignment strength. The disks inside the clusters move with a finite space-dependent speed, constantly shuttling between clusters through the surrounding low-density homogeneous phase while maintaining the hexatic structure properties within the clusters. The area fraction gradually increases from the periphery towards the center of the clusters with a negligible correlation of the velocity and propulsion direction inside the clusters. The novel collective behavior of reentrant phase separation is found to follow from both the limits of hard disks and extremely small inertia, tending towards the overdamped limit. However, important differences in the structural and dynamical properties are shown in the limit of hard disks and extremely small inertia, as compared to that for soft disks at finite inertia. We show that the cluster phase is associated with an effective temperature for a wide range of values of alignment strength, whereas an effective temperature is associated with the specific range of alignment in the low-density phase. We believe that the reentrant phase behavior in the limit of small area fraction and the remarkable properties of the clusters should be useful in understanding a wide range of physics issues, ranging from clogging and unclogging to information exchange and transport, in biological and synthetic self-propelled systems.

On a numerical bifurcation analysis of a particle reaction-diffusion model for a motion of two self-propelled disks

AbstractTheoretical analysis using mathematical models is often used to understand a mechanism of collective motion in a self-propelled system. In the experimental system using camphor disks, several kinds of characteristic motions have been observed due to the interaction of two camphor disks. In this paper, we understand the emergence mechanism of the motions caused by the interaction of two self-propelled bodies by analyzing the global bifurcation structure using the numerical bifurcation method for a mathematical model. Finally, it is also shown that the irregular motion, which is one of the characteristic motions, is chaotic motion and that it arises from periodic bifurcation phenomena and quasi-periodic motions due to torus bifurcation.

Motility-induced phase separation of self-propelled soft inertial disks.

The phase diagram of the phenomenon of motility-induced phase separation (MIPS) for a collection of self-propelled interacting disks over a large inertial range is explored using active Langevin dynamics simulation with particular emphasis on disk softness and effective size. It is shown that the parabola-like phase boundary between the homogeneous and MIPS states in the semi-log space of disk softness and effective size moves towards the hard disk limit with increase in inertia, before complete disappearance in the limit of large inertia. With increase in effective size of the disks, re-entrant phase separation, that is the system phase-separating from a homogeneous phase and eventually re-entering the homogeneous phase, is reported. The structural and the dynamical properties of the different phases are investigated in the considered inertial range. The particular shape of the phase boundary and the re-entrant behavior is explained based on several qualitative and quantitative results. Unlike most of the earlier studies on MIPS, which consider hard particle limits, our findings may be directly applicable to soft active matter for a range of physical and biological systems.

Phase separation of self-propelled disks with ferromagnetic and nematic alignment.

We present a comprehensive study of a model system of repulsive self-propelled disks in two dimensions with ferromagnetic and nematic velocity alignment interactions. We characterize the phase behavior of the system as a function of the alignment and self-propulsion strength, featuring orientational order for strong alignment and motility-induced phase separation (MIPS) at moderate alignment but high enough self-propulsion. We derive a microscopic theory for these systems yielding a closed set of hydrodynamic equations from which we perform a linear stability analysis of the homogenous disordered state. This analysis predicts MIPS in the presence of aligning torques. The nature of the continuum theory allows for an explicit quantitative comparison with particle-based simulations, which consistently shows that ferromagnetic alignment fosters phase separation, while nematic alignment does not alter either the nature or the location of the instability responsible for it. In the ferromagnetic case, such behavior is due to an increase of the imbalance of the number of particle collisions along different orientations, giving rise to the self-trapping of particles along their self-propulsion direction. On the contrary, the anisotropy of the pair correlation function, which encodes this self-trapping effect, is not significantly affected by nematic torques. Our work shows the predictive power of such microscopic theories to describe complex active matter systems with different interaction symmetries and sheds light on the impact of velocity-alignment interactions in motility-induced phase separation.

Learning to control active matter

The study of active matter has revealed novel non-equilibrium collective behaviors, illustrating their potential as a new materials platform. However, most works treat active matter as unregulated systems with uniform microscopic energy input, which we refer to as activity. In contrast, functionality in biological materials results from regulating and controlling activity locally over space and time, as has only recently become experimentally possible for engineered active matter. Designing functionality requires navigation of the high dimensional space of spatio-temporal activity patterns, but brute force approaches are unlikely to be successful without system-specific intuition. Here, we apply reinforcement learning to the task of inducing net transport in a specific direction for a simulated system of Vicsek-like self-propelled disks using a spotlight that increases activity locally. The resulting time-varying patterns of activity learned exploit the distinct physics of the strong and weak coupling regimes. Our work shows how reinforcement learning can reveal physically interpretable protocols for controlling collective behavior in non-equilibrium systems.

Polarity Fluctuation Inhibition by Memory in Collective Cell Motion

Polarity memory often commonly stabilizes a polarity order in eukaryotic cells and self-propelled disks. This seemingly does not hold for dense cases: the polarity memory of dense cells stabilizes ...

Mixing and unmixing induced by active camphor particles

In this experimental study, we report on the mixing properties of interfacial colloidal floaters (glass bubbles) by chemical and hydrodynamical currents generated by self-propelled camphor disks swimming at the air-water interface. Despite reaching a statistically stationary state for the glass bubbles distribution, those floaters always remain only partially mixed. This intermediate state results from a competition between (i) the mixing induced by the disordered motion of many camphor swimmers and (ii) the unmixing promoted by the chemical cloud attached to each individual self-propelled disk. Mixing/unmixing is characterized globally using the standard deviation of concentration and spectra, but also more locally by averaging the concentration field around a swimmer. Besides the demixing process, the system develops a "turbulent-like" concentration spectra, with a large-scale region, an inertial regime and a Batchelor region. We show that unmixing is due to the Marangoni flow around the camphor swimmers, and is associated to compressible effects.

Hidden velocity ordering in dense suspensions of self-propelled disks

The present paper studies the spontaneous velocity alignment and the time-intermittency of the kinetic-energy in dense phases of active matter. The dynamical properties are described by considering the spatial velocity correlations and constructing a non-equilibrium phase diagram of active force and density which explores homogeneous and inhomogeneous phases

Cooperative motion and shear strain correlations in dense 2D systems of self-propelled soft disks

We present a detailed study of cooperative and correlated dynamics in a 2D model system for soft active matter that undergoes motility-induced phase separation (MIPS). Particle displacement correlation functions reveal increasing dynamical heterogeneity with increasing activity. In the phase-separated regime as well as in the truly glassy phase, transverse mean squared displacements as well as shear strain correlations exhibit a regime of long-range behaviour with strain correlations decaying as r−2 on time scales short compared to the rotational diffusion time. We attribute the origin of the r−2 decay to elastic interactions that lead to similar behaviour in passive glass formers.

Reaction processes among self-propelled particles.

We study a system of self-propelled disks that perform run-and-tumble motion, where particles can adopt more than one internal state. One of those internal states can be transmitted to other particle if the particle carrying this state maintains physical contact with another particle for a finite period of time. We refer to this process as a reaction process and to the different internal states as particle species, making an analogy to chemical reactions. The studied system may fall into an absorbing phase, where due to the disappearance of one of the particle species no further reaction can occur, or may remain in an active phase where particles constantly react. By combining individual-based simulations and mean-field arguments, we study the dependency of the equilibrium densities of particle species on motility parameters, specifically the active speed v0 and tumbling frequency λ. We find that the equilibrium densities of particle species exhibit two very distinct, non-trivial scaling regimes, with v0 and λ depending on whether the system is in the so-called ballistic or diffusive regime. Our mean-field estimates lead to an effective renormalization of reaction rates that allow building the phase-diagram v0-λ that separates the absorbing and active phases. We find an excellent agreement between numerical simulations and mean-field estimates. This study is a necessary step towards an understanding of phase transitions into absorbing states in active systems and sheds light on the spreading of information/signaling among moving elements.

Velocity alignment promotes motility-induced phase separation

We study the phase behavior of polar active Brownian particles moving in two-spatial dimensions and interacting through volume exclusion and velocity alignment. We combine particle-based simulations of the microscopic model with a simple mean-field kinetic model to understand the impact of velocity alignment on the motility-induced phase separation of self-propelled disks. We show that, as the alignment strength is increased, approaching the onset of collective motion from below, orientational correlations grow, rendering the diffusive reorientation dynamics slower. As a consequence, the tendency of particles to aggregate into isotropic clusters is enhanced, favoring the complete de-mixing of the system into a low and high-density phase.

Three-body correlations and conditional forces in suspensions of active hard disks.

Self-propelled Brownian particles show rich out-of-equilibrium physics, for instance, the motility-induced phase separation (MIPS). While decades of studying the structure of liquids have established a deep understanding of passive systems, not much is known about correlations in active suspensions. In this work we derive an approximate analytic theory for three-body correlations and forces in systems of active Brownian disks starting from the many-body Smoluchowski equation. We use our theory to predict the conditional forces that act on a tagged particle and their dependence on the propulsion speed of self-propelled disks. We identify preferred directions of these forces in relation to the direction of propulsion and the positions of the surrounding particles. We further relate our theory to the effective swimming speed of the active disks, which is relevant for the physics of MIPS. To test and validate our theory, we additionally run particle-resolved computer simulations, for which we explicitly calculate the three-body forces. In this context, we discuss the modeling of active Brownian swimmers with nearly hard interaction potentials. We find very good agreement between our simulations and numerical solutions of our theory, especially for the nonequilibrium pair-distribution function. For our analytical results, we carefully discuss their range of validity in the context of the different levels of approximation we applied. This discussion allows us to study the individual contribution of particles to three-body forces and to the emerging structure. Thus, our work sheds light on the collective behavior, provides the basis for further studies of correlations in active suspensions, and makes a step towards an emerging liquid state theory.

Active versus Passive Hard Disks against a Membrane: Mechanical Pressure and Instability.

We experimentally study the mechanical pressure exerted by a set of respectively passive isotropic and self-propelled polar disks onto two different flexible unidimensional membranes. In the case of the isotropic disks, the mechanical pressure, inferred from the shape of the membrane, is identical for both membranes and follows the equilibrium equation of state for hard disks. On the contrary, for the self-propelled disks, the mechanical pressure strongly depends on the membrane in use and thus is not a state variable. When self-propelled disks are present on both sides of the membrane, we observe an instability of the membrane akin to the one predicted theoretically for active Brownian particles against a soft wall. In that case, the integrated mechanical pressure difference across the membrane cannot be computed from the sole knowledge of the packing fractions on both sides, further evidence of the absence of an equation of state.

Active-Matter Thermodynamics Under Pressure

Experiments show that, unlike an ideal gas, an active-matter system comprised of self-propelled disks does not have a well-defined mechanical pressure.

Dewetting and spreading transitions for active matter on random pinning substrates.

We show that sterically interacting self-propelled disks in the presence of random pinning substrates exhibit transitions among a variety of different states. In particular, from a phase separated cluster state, the disks can spread out and homogeneously cover the substrate in what can be viewed as an example of an active matter wetting transition. We map the location of this transition as a function of activity, disk density, and substrate strength, and we also identify other phases including a cluster state, coexistence between a cluster and a labyrinth wetted phase, and a pinned liquid. Convenient measures of these phases include the cluster size, which dips at the wetting-dewetting transition, and the fraction of sixfold coordinated particles, which drops when dewetting occurs.

A multi-layer model for self-propelled disks interacting through alignment and volume exclusion

We present an individual-based model describing disk-like self-propelled particles moving inside parallel planes. The disk directions of motion follow alignment rules inside each layer. Additionally, the disks are subject to interactions with those of the neighboring layers arising from volume exclusion constraints. These interactions affect the disk inclinations with respect to the plane of motion. We formally derive a macroscopic model composed of planar self-organized hydrodynamic (SOH) models describing the transport of mass and evolution of mean direction of motion of the disks in each plane, supplemented with transport equations for the mean disk inclination. These planar models are coupled due to the interactions with the neighboring planes. Numerical comparisons between the individual-based and macroscopic models are carried out. These models could be applicable, for instance, to describe sperm-cell collective dynamics.

Bifurcation phenomena of two self-propelled camphor disks on an annular field depending on system length.

Mode selection and bifurcation of a synchronized motion involving two symmetric self-propelled objects in a periodic one-dimensional domain were investigated numerically and experimentally by using camphor disks placed on an annular water channel. Newton's equation of motion for each camphor disk, whose driving force was the difference in surface tension, and a reaction-diffusion equation for camphor molecules on water were used in the numerical calculations. Among various dynamical behaviors found numerically, four kinds of synchronized motions (reversal oscillation, stop-and-move rotation, equally spaced rotation, and clustered rotation) were also observed in experiments by changing the diameter of the water channel. The mode bifurcation of these motions, including their coexistence, were clarified numerically and analytically in terms of the number density of the disk. These results suggest that the present mathematical model and the analysis of the equations can be worthwhile in understanding the characteristic features of motion, e.g., synchronization, collective motion, and their mode bifurcation.