Narrow-escape time and sorting of active particles in circular domains

Narrow escape for active camphor particles: facilitated escape and aging

In this work, we experimentally investigate the narrow escape problem using self-propelled camphor-infused discs, which have the possibility to escape from a bounded circular domain through an opening in the boundary. To analyze the statistical properties of the escape problem, we proposed two experimental protocols: first, a control setup within a closed circular domain where the disc encounters a target simulating an opening on the boundary, and a second setup where a real opening is placed on the boundary of the circular domain. These two setups allow us to compare how the statistical properties of escape differ between simulated (or fictitious) escape and the actual escape of camphor particles. Our results suggest that the presence of an actual opening in the wall alters the interactions between the particle and the boundary. Notably, we observe the counterintuitive phenomenon that introducing a real door in the boundary makes less accessible the escape from the domain. We further contrast and analyze several qualitative and quantitative properties of the system, including chiral flips, bouncing behavior, arrival angle distribution, as well as first passage time and exit time distributions, among other dynamical properties.

Stochastic migrations of Marangoni surfers between two lobes of a dumbbell-shaped confinement

We report an experimental investigation on the stochastic migration dynamics of Marangoni surfers (camphor-infused paper disks) between the two lobes of a dumbbell-shaped chamber. We characterize the migration dynamics using survival analysis of a configuration, wherein a configuration represents a distinct distribution of disks between the lobes. We observe that a configuration's stability decreases with increasing pairwise interactions. Consequently, the configuration with equal partitioning of disks between the lobes-that is exactly one-half of disks in each lobe for even-numbered systems but with one extra disk in either of the lobes for odd-numbered systems-has the lowest pairwise interactions, thus is always the most stable configuration. Furthermore, all configurations exhibit a stretched exponential decay with time, which is ascribed to a disk's activity decay with time or "aging"-a phenomenon validated by modeling a camphor disk as a chiral active particle (CAP) as initially proposed by Cruz et al.

Machine learning assisted sorting of active microswimmers

Active matter systems, being in a non-equilibrium state, exhibit complex behaviors, such as self-organization, giving rise to emergent phenomena. There are many examples of active particles with biological origins, including bacteria and spermatozoa, or with artificial origins, such as self-propelled swimmers and Janus particles. The ability to manipulate active particles is vital for their effective application, e.g., separating motile spermatozoa from nonmotile and dead ones, to increase fertilization chance. In this study, we proposed a mechanism-an apparatus-to sort and demix active particles based on their motility values (Péclet number). Initially, using Brownian simulations, we demonstrated the feasibility of sorting self-propelled particles. Following this, we employed machine learning methods, supplemented with data from comprehensive simulations that we conducted for this study, to model the complex behavior of active particles. This enabled us to sort them based on their Péclet number. Finally, we evaluated the performance of the developed models and showed their effectiveness in demixing and sorting the active particles. Our findings can find applications in various fields, including physics, biology, and biomedical science, where the sorting and manipulation of active particles play a pivotal role.

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.

Optimal escapes in active matter

The out-of-equilibrium character of active particles, responsible for accumulation at boundaries in confining domains, determines not-trivial effects when considering escape processes. Non-monotonous behavior of exit times with respect to tumbling rate (inverse of mean persistent time) appears, as a consequence of the competing processes of exploring the bulk and accumulate at boundaries. By using both 1D analytical results and 2D numerical simulations of run-and-tumble particles with different behaviours at boundaries, we scrutinize this very general phenomenon of active matter, evidencing the role of accumulation at walls for the existence of optimal tumbling rates for fast escapes.

Selecting active matter according to motility in an acoustofluidic setup: self-propelled particles and sperm cells

Active systems - including sperm cells, living organisms like bacteria, fish, birds, or active soft matter systems like synthetic "microswimmers" - are characterized by motility, i.e., the ability to propel using their own "engine". Motility is the key feature that distinguishes active systems from passive or externally driven systems. In a large ensemble, motility of individual species can vary in a wide range. Selecting active species according to their motility represents an exciting and challenging problem. We propose a new method for selecting active species based on their motility using an acoustofluidic setup where highly motile species escape from the acoustic trap. This is demonstrated in simulations and in experiments with self-propelled Janus particles and human sperm. The immediate application of this method is selecting highly motile sperm for medically assisted reproduction (MAR). Due to the tunable acoustic trap, the proposed method is more flexible than the existing passive microfluidic methods. The proposed selection method based on motility can also be applied to other active systems that require selecting highly motile species or removing immotile species.

Survival probabilities and first-passage distributions of self-propelled particles in spherical cavities

A model of self-propelled motion in a closed compartment containing simple or complex fluids is formulated in this paper in terms of the dynamics of a point particle moving in a spherical cavity under the action of random thermal forces and exponentially correlated noise. The particle's time evolution is governed by a generalized Langevin equation (GLE) in which the memory function, connected to the thermal forces by a fluctuation-dissipation relation, is described by Jeffrey's model of viscoelasticity (which reduces to a model of ordinary viscous dynamics in a suitable limit). The GLE is transformed exactly to a Fokker-Planck equation that in spherical polar coordinates is in turn found to admit of an exact solution for the particle's probability density function under absorbing boundary conditions at the surface of the sphere. The solution is used to derive an expression (that is also exact) for the survival probability of the particle in the sphere, starting from its center, which is then used to calculate the distribution of the particle's first-passage times to the boundary. The behavior of these quantities is investigated as a function of the Péclet number and the persistence time of the athermal forces, providing insight into the effects of nonequilibrium fluctuations on confined particle motion in three dimensions.

Escape dynamics of a self-propelled nanorod from circular confinements with narrow openings

We perform computer simulations to explore the escape dynamics of a self-propelled (active) nanorod from circular confinements with narrow opening(s). Our results clearly demonstrate how the persistent and directed motion of the nanorod helps it to escape. Such escape events are absent if the nanorod is passive. To quantify the escape dynamics, we compute the radial probability density function (RPDF) and mean first escape time (MFET) and show how the activity is responsible for the bimodality of RPDF, which is clearly absent if the nanorod is passive. Broadening of displacement distributions with activity has also been observed. The computed mean first escape time decreases with activity. In contrast, the fluctuations of the first escape times vary in a non-monotonic way. This results in high values of the coefficient of variation and indicates the presence of multiple timescales in first escape time distributions and multimodality in uniformity index distributions. We hope our study will help in differentiating activity-driven escape dynamics from purely thermal passive diffusion in confinement.

Survival strategies of artificial active agents

Artificial cells can be engineered to display dynamics sharing remarkable features in common with the survival behavior of living organisms. In particular, such active systems can respond to stimuli provided by the environment and undertake specific displacements to remain out of equilibrium, e.g. by moving towards regions with higher fuel concentration. In spite of the intense experimental activity aiming at investigating this fascinating behavior, a rigorous definition and characterization of such "survival strategies" from a statistical physics perspective is still missing. In this work, we take a first step in this direction by adapting and applying to active systems the theoretical framework of Transition Path Theory, which was originally introduced to investigate rare thermally activated transitions in passive systems. We perform experiments on camphor disks navigating Petri dishes and perform simulations in the paradigmatic active Brownian particle model to show how the notions of transition probability density and committor function provide the pivotal concepts to identify survival strategies, improve modeling, and obtain and validate experimentally testable predictions. The definition of survival in these artificial systems paves the way to move beyond simple observation and to formally characterize, design and predict complex life-like behaviors.

A microfluidic method for passive trapping of sperms in microstructures

Sperm motility is a prerequisite for male fertility. Enhancing the concentration of motile sperms in assisted reproductive technologies - for human and animal reproduction - is typically achieved through aggressive methods such as centrifugation. Here, we propose a passive technique for the amplification of motile sperm concentration, with no externally imposed forces or flows. The technique is based on the disparity between probability rates, for motile cells, of entering and escaping from complex structures. The effectiveness of the technique is demonstrated in microfluidic experiments with microstructured devices, comparing the trapping power in different geometries. In these micro-traps, we observe an enhancement of cells' concentration close to 10, with a contrast between motile and non-motile cells increased by a similar factor. Simulations of suitable interacting model sperms in realistic geometries reproduce quantitatively the experimental results, extend the range of observations and highlight the components that are key to the optimal trap design.

Narrow Pore Crossing of Active Particles under Stochastic Resetting

We propose a two-dimensional model of biochemical activation process, whereby self-propelling particles of finite correlation times are injected at the center of a circular cavity with constant rate equal to the inverse of their lifetime; activation is triggered when one such particle hits a receptor on the cavity boundary, modeled as a narrow pore. We numerically investigated this process by computing the particle mean-first exit times through the cavity pore as a function of the correlation and injection time constants. Due to the breach of the circular symmetry associated with the positioning of the receptor, the exit times may depend on the orientation of the self-propelling velocity at injection. Stochastic resetting appears to favor activation for large particle correlation times, where most of the underlying diffusion process occurs at the cavity boundary.

Correlated escape of active particles across a potential barrier

We study the dynamics of one-dimensional active particles confined in a double-well potential, focusing on the escape properties of the system, such as the mean escape time from a well. We first consider a single-particle both in near and far-from-equilibrium regimes by varying the persistence time of the active force and the swim velocity. A non-monotonic behavior of the mean escape time is observed with the persistence time of the activity, revealing the existence of an optimal choice of the parameters favoring the escape process. For small persistence times, a Kramers-like formula with an effective potential obtained within the unified colored noise approximation is shown to hold. Instead, for large persistence times, we developed a simple theoretical argument based on the first passage theory, which explains the linear dependence of the escape time with the persistence of the active force. In the second part of the work, we consider the escape on two active particles mutually repelling. Interestingly, the subtle interplay of active and repulsive forces may lead to a correlation between particles, favoring the simultaneous jump across the barrier. This mechanism cannot be observed in the escape process of two passive particles. Finally, we find that in the small persistence regime, the repulsion favors the escape, such as in passive systems, in agreement with our theoretical predictions, while for large persistence times, the repulsive and active forces produce an effective attraction, which hinders the barrier crossing.

Escape kinetics of self-propelled particles from a circular cavity

We numerically investigate the mean exit time of an inertial active Brownian particle from a circular cavity with single or multiple exit windows. Our simulation results witness distinct escape mechanisms depending on the relative amplitudes of the thermal length and self-propulsion length compared to the cavity and pore sizes. For exceedingly large self-propulsion lengths, overdamped active particles diffuse on the cavity surface, and rotational dynamics solely governs the exit process. On the other hand, the escape kinetics of a very weakly damped active particle is largely dictated by bouncing effects on the cavity walls irrespective of the amplitude of self-propulsion persistence lengths. We show that the exit rate can be maximized for an optimal self-propulsion persistence length, which depends on the damping strength, self-propulsion velocity, and cavity size. However, the optimal persistence length is insensitive to the opening windows' size, number, and arrangement. Numerical results have been interpreted analytically based on qualitative arguments. The present analysis aims at understanding the transport controlling mechanism of active matter in confined structures.