Confinement and Collective Escape of Active Particles

The narrow escape problem of a chiral active particle (CAP): an optimal scheme

We report a simulation study on the narrow escape kinetics of a chiral active particle (CAP) confined to a circular domain with a narrow escape opening. The study's main objective is to optimize the CAP's escape chances as a function of the relevant parameters, such as translational and rotational speeds of the CAP, domain size, etc. We identified three regimes in the escape kinetics, namely the noise-dominated regime, the optimal regime, and the chiral activity-dominated regime. In particular, the optimal regime is characterized by an escape scheme that involves a direct passage to the domain boundary at first and then a unidirectional drift along the boundary towards the exit. Furthermore, we propose a non-dimensionalization approach to optimize the escape performance across microorganisms with varying motile characteristics. Additionally, we explore the influence of the translational and rotational noise on the CAP's escape kinetics.

Local control for the collective dynamics of self-propelled particles

Utilizing a paradigmatic model for the motion of interacting self-propelled particles, we demonstrate that local accelerations at the level of individual particles can drive transitions between different collective dynamics, leading to a control process. We find that the ability to trigger such transitions is hierarchically distributed among the particles and can form distinctive spatial patterns within the collective. Chaotic dynamics occur during the transitions, which can be attributed to fractal basin boundaries mediating the control process. The particle hierarchies described in this paper offer decentralized capabilities for controlling artificial swarms.

Deterministic active particles in the overactive limit

We consider two models of deterministic active particles in an external potential. In the limit where the speed of a particle is fixed, both models nearly coincide and can be formulated as a Hamiltonian system, but only if the potential is time-independent. If the particles are identical, their interaction via a potential force leads to conservative dynamics with a conserved phase volume. In contrast, the phase volume is shown to shrink for non-identical particles even if the confining potential is time-independent.

Noise-induced escape of a self-propelled particle from metastable orbits

Active particles, like motile microorganisms and active colloids, are often found in confined environments where they can be arrested in a persistent orbital motion. Here, we investigate noise-induced switching between different coexisting orbits of a confined active particle as a stochastic escape problem. We show that, in the low-noise regime, this problem can be formulated as a least-action principle, which amounts to finding the most probable escape path from an orbit to the basin of attraction of another coexisting orbit. The corresponding action integral coincides with the activation energy, a quantity readily accessible in experiments and simulations via escape rate data. To illustrate how this approach can be used to tackle specific problems, we calculate optimum escape paths and activation energies for noise-induced transitions between clockwise and counterclockwise circular orbits of an active particle in radially symmetric confinement. We also investigated transitions between orbits of different topologies (ovals and lemniscates) coexisting in elliptic confinement. In all worked examples, the calculated optimum paths and minimum actions are in excellent agreement with mean-escape-time data obtained from direct numerical integration of the Langevin equations.

Sensitivity of nonequilibrium relaxation to interaction potentials: Timescales of response from Boltzmann's H function

We investigate, by simulations and analytic theory, the sensitivity of nonequilibrium relaxation to interaction potential and dimensionality by using Boltzmann's H function H(t). We evaluate H(t) for three different intermolecular potentials in all three dimensions and find that the well-known H theorem is valid and that the H function exhibits rather strong sensitivity to all these factors. The relaxation of H(t) is long in one dimension, but short in three dimensions, longer for the Lennard-Jones potential than for the hard spheres. The origin of the ultraslow approach to the equilibrium of H(t) in one-dimensional systems is discussed. Importantly, we obtain a closed-form analytic expression for H(t) using the solution of the Fokker-Planck equation for velocity space probability distribution and compare its predictions with the simulation results. Interestingly, H(t) is found to exhibit a linear response when vastly different initial nonequilibrium conditions are employed. The microscopic origin of this linear response is discussed. The oft-quoted relation of H function with Clausius's entropy theorem is discussed.

Collective vortical motion and vorticity reversals of self-propelled particles on circularly patterned substrates

The collective behavior of self-propelled particles (SPPs) under the combined effects of a circularly patterned substrate and circular confinement is investigated through coarse-grained molecular dynamics simulations of polarized and disjoint ring polymers. The study is performed over a wide range of values of the SPPs packing fraction ϕ[over ¯], motility force F_{D}, and area fraction of the patterned region. At low packing fractions, the SPPs are excluded from the system's center and exhibit a vortical motion that is dominated by the substrate at intermediate values of F_{D}. This exclusion zone is due to the coupling between the driving force and torque induced by the substrate, which induces an outward spiral motion of the SPPs. For high values of F_{D}, the SPPs exclusion from the center is dominated by the confining boundary. At high values of ϕ[over ¯], the substrate pattern leads to reversals in the vorticity, which become quasiperiodic with increasing ϕ[over ¯]. We also found that the substrate pattern is able to separate SPPs based on their motilities.

Coexisting orbits and chaotic dynamics of a confined self-propelled particle

We investigate theoretically the dynamics of a confined active swimmer with velocity and orientation axis coupled to each other via a self-alignment torque. For an isotropic harmonic potential, this system is known to exhibit two distinct dynamical phases: a climbing one, where the particle is oriented radially and undergoes angular Brownian motion, and a circularly orbiting phase. Here we show that for nonradially symmetric confinement an assortment of complex phenomena emerge. For an elliptic harmonic potential the orbiting phase splits into several periodic orbits with a diversity of shapes: ovals, lemniscates, and generalized lemniscates with multiple lobes. These orbits can coexist in the parameter space and decay into one another induced by noise. For anharmonic confining potentials, we report transitions from periodic to chaotic dynamics, as one changes the intensity of the self-alignment torque and noise-induced complex orbits. These results demonstrate that the combination of the shape of the trapping potential and self-alignment torque can induce a rich variety of nontrivial dynamical states of a confined active particle.