First passage of an active particle in the presence of passive crowders

Can self-propelled objects escape from compression stimulation?

We studied circular papers impregnated with camphor (CPs) and CPs with magnets (MCPs) as self-propelled objects floating on water under the compression of the water surface as an inanimate system for evacuation in an emergency. Two water chambers-Cin and Cout-were connected via a plastic gate, and eight CPs or eight MCPs were placed on Cin. We monitored the movement of the CPs or MCPs from Cin to Cout when the gate was opened and the area of Cin (Ain) was decreased using a barrier. When Ain was large, CPs moved stochastically from Cin to Cout while exhibiting random motion. The escape probability from Cin to Cout (P) at time t = 20 s increased with a decrease in Ain, and the rate of increase in P increased depending on the width of the gate (Wg). By contrast, clustering was observed for MCPs. Consequently, P of MCPs was lower than that of CPs. The difference in the surface tension between Cin and Cout (Δγ) increased with a decrease in Ain. P is discussed in relation to Δγ as the driving force for emergencies and the repulsive forces between CPs or attractive forces between MCPs. These results suggest that the repulsive force enhances the self-propulsion of objects towards the gate, that is, as a result, higher values of P are obtained.

Active chiral dynamics and boundary accumulation phenomenon in confined camphor particles

In this work, we perform experimental and numerical investigations on the dynamics of camphor-infused discs, well-established as active particles in their behavior. Our analysis focuses on examining the individual dynamics of these discs within a confined circular domain, revealing that they exhibit characteristics akin to active chiral particles. To characterize this behavior effectively, we introduce a methodology for estimating key model parameter values from our experiments, including linear velocity, angular velocity, and angular noise intensity. To validate our findings, we compare our experimental results with numerical simulations of the model. Our results demonstrate a striking phenomenon associated with camphor-infused discs: a pronounced accumulation of particles along the boundary. This intriguing observation suggests the occurrence of an attractive interaction between the active particles and the boundary, resulting in a kind of adsorption effect. The latter results in the confinement of the camphor disc along the Petri dish wall, which we refer to as sliding dynamics. We empirically determine the velocity of the particle along the Petri dish wall as well as its fluctuations, properties whose behavior notably deviates from the bulk dynamics.

Pathway selection by an active droplet

We report the movement of an active 1-pentanol drop within a closed Y-shaped channel subjected to geometrical and chemical asymmetry. A Y-shaped channel was configured with an angle of 120° between any two arms, which serves as the closed area of movement for the active drop. The arm where the 1-pentanol drop is introduced in the beginning is considered the source arm, and the center of the Y-shaped structure is the decision region. The drop always selects a specific route to move away from the decision region. The total probability of pathway selection excludes the possibility of the drop choosing the source channel. Remarkably, the active drop exhibits a strong sense of navigation for both geometrically and chemically asymmetric environments with accuracy rates of 80% and 100%, respectively. The pathway selection in a chemically asymmetric channel is a demonstration of the artificial negative chemotaxis, where the extra confined drop acts as a chemo-repellent. To develop a better understanding of our observations, a numerical model is constructed, wherein the particle is subjected to a net force which is a combined form of - (i) Yukawa-like repulsive interaction force (acting between the drop and the walls), (ii) a self-propulsion force, (iii) a drag, and (iv) a stochastic force. The numerics can capture all the experimental findings both qualitatively and quantitatively. Finally, a statistical analysis validates conclusions derived from both experiments and numerics.

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.

In-phase and mixed-phase measure synchronization of camphor rotors

The numerical, analytical, and experimental analyses are presented for synchronizing two rotors under the Yukawa interaction. We report that the rotors exhibit in-phase and mixed-phase measure synchronizations for a pair of coupled rotors. Here, the analytical condition for synchronization is derived, tested numerically, and confirmed experimentally using coupled camphor infused rotors as a test bed. Moreover, the concept of measure synchronization is discussed. We report that, in conservative systems, not only the critical coupling parameter but initial conditions also play an essential role for estimating the measure synchronization region.

Phase-flip transition in volume-mismatched pairs of coupled 1-pentanol drops

We have explored a variety of synchronization domains and observed phase-flip transition in a pair of coupled 1-pentanol drops as a function of the volume mismatch. Both experimental observations and numerical studies are presented. The experiments were carried out in a rectangular channel in a ferroin deionized water solution premixed with some volume of pentanol. A single pentanol drop (≥ 3μL) performs back and forth oscillations along the length of the channel due to the well-known Marangoni forces. In the present work, for a pair of drops, the drop 1 volume was changed from 3 to 5 μL in steps of 1μL, whereas the drop 2 volume was varied from 1 to 3 μL in steps of 0.5μL. A systematic investigation of all the possible combinations of the drop volumes showed the presence of three different types of synchrony-in-phase, antiphase, and phase-switched. In-phase synchronization was robust for a volume mismatch of >3.0μL between the two drops. On the other hand, antiphase synchronization was robust when the volume mismatch was <2.0μL. The phase-switched state is a synchronized state involving a phase-flip transition in the time domain. This state was observed for the intermediate range of volume mismatch. Numerically, the system has been investigated using two Stuart-Landau oscillators interacting via a coupling function in the form of Lennard-Jones potential. The numerical results suitably capture both in-phase and antiphase oscillations for a pair of volume-mismatched pentanol drops.

Generation of aperiodic motion due to sporadic collisions of camphor ribbons

We present numerical and experimental results for the generation of aperiodic motion in coupled active rotators. The numerical analysis is presented for two point particles constrained to move on a unit circle under the Yukawa-like interaction. Simulations exhibit that the collision among the rotors results in chaotic motion of the rotating point particles. Furthermore, the numerical model predicts a route to chaotic motion. Subsequently, we explore the effect of separation between the rotors on their chaotic dynamics. The numerically calculated fraction of initial conditions which led to chaotic motion shed light on the observed effects. We reproduce a subset of the numerical observations with two self-propelled ribbons rotating at the air-water interface. A pinned camphor rotor moves at the interface due to the Marangoni forces generated by surface tension imbalance around it. The camphor layer present at the common water surface acts as chemical coupling between two ribbons. The separation distance of ribbons (L) determines the nature of coupled dynamics. Below a critical distance (L_{T}), rotors can potentially, by virtue of collisions, exhibit aperiodic oscillations characterized via a mixture of co- and counterrotating oscillations. These aperiodic dynamics qualitatively matched the chaotic motion observed in the numerical model.

Aperiodic bursting dynamics of active rotors

We report experiments on an active camphor rotor. A camphor rotor is prepared by infusing camphor on a regular rectangular paper strip. It performs self-propelled motion at the air-water interface due to Marangoni driven forces. After some transient (periodic) dynamics, the rotor enters into the aperiodic bursting regime, which is characterized as an irregularly repeated rest (halt) and run (motion) of the rotor. Subsequently, this aperiodic (irregular) rotor is entrained to a periodic (regular) regime with the help of a suitable external periodic forcing. Furthermore, we conducted experiments on two such coupled aperiodic camphor rotors. In this set of experiments, synchronized bursting was observed. During this bursting motion, one rotor follows the movement of the other rotor. A numerical point particle model, incorporating excitable underlying equations, successfully replicated experimentally observed aperiodic bursting.

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.

Alternate Route Selection of Self-Propelled Filter Papers Impregnated with Camphor for Two-Branched Water Channels

The route selection of self-propelled filter papers impregnated with camphor for two-branched water channels was investigated. The two-branched water channel was composed of a stem channel and two branch channels, and the branch channels were connected to the stem channel at a junction. When a single camphor paper reached the junction from the stem channel, it selected one of the two routes equivalently. Three or five camphor papers which were placed on a stem channel exhibited either alternate or random route selection depending on the characteristic length between the leading and following papers, L_c. That is, the alternate route selection of the camphor papers for the two-branched water channels was observed at L_c ≤ 25 mm. By contrast, the alternate route selection was broken at L_c > 25 mm. The physicochemical meaning of the threshold value, L_th ∼ 26 mm, between the alternate and random route selections was discussed based on the experimental results. In addition, the distribution length of camphor molecules developed from the leading camphor paper and the change in the spatial gradient of surface tension around the junction supports the value of L_th. These results suggest that autonomous phenomena using inanimate self-propelled objects are important to understand collective motion in living organisms.

Revealing the deterministic components in active avalanche-like dynamics

Avalanche dynamics in an ensemble of self-propelled camphor boats are studied. The self-propelled agents are camphor infused circular paper disks moving on the surface of water. The ensemble exhibits bursts of activity in the autonomous state triggered by stochastic fluctuations. This type of dynamics has been previously reported in a slightly different system (J. Phys. Soc. Jpn., 2015, 84, 034802). Fourier analysis of the autonomous ensemble's average speed reveals a unimodal spectrum, indicating the presence of a preferred time scale in the dynamics. We therefor, entrain such an ensemble by external forcing by using periodic air perturbations on the surface of the water. This forcing is able to replace the stochastic fluctuations which trigger a burst in the autonomous ensemble, thus entraining the system. Upon varying the periodic forcing frequency, an optimal frequency is revealed at which the quality of entrainment of the ensemble by the forcing is augmented. This optimal frequency is found to be in the vicinity of the Fourier spectrum peak of the autonomous ensemble's average speed. This indicates the existence of an underlying deterministic component in the apparent aperiodic bursts of motion of the autonomous ensemble of active particles. A qualitative reasoning for the observed phenomenon is presented.

Oscillatory Motion of a Camphor Object on a Surfactant Solution

The mode bifurcation between oscillatory motion and no motion of a camphor object floating on surfactant aqueous solution was investigated. The camphor and surfactant were used as the sources of driving and suppressing forces, respectively. A circular plastic sheet was attached to the center of the bottom of a camphor disk, which served as the self-propelled object; further, the contact area between the disk and the solution (S) was varied to control the amount of camphor molecules from the disk that dissolved in the solution. Motion features, that is, the maximum speed, frequency of oscillatory motion, and mode bifurcation, varied depending on S. We discussed the relationship between these motion features and the kinetics of camphor and surfactant molecules around the object. The results suggest that the nature of the oscillatory motion depends on the amount of camphor molecules accumulated at the base of the self-propelled object.

Capture of a diffusive prey by multiple predators in confined space

The first passage search of a diffusing target (prey) by multiple searchers (predators) in confinement is an important problem in the stochastic process literature. While the analogous problem in open space has been studied in some detail, a systematic study in confined space is still lacking. In this paper, we study the first passage times for this problem in one, two, and three dimensions. Due to confinement, the survival probability of the target takes a form ∼e^{-t/τ} at large times t. The characteristic capture timescale τ associated with the rare capture events are rather challenging to measure. We use a computational algorithm that allows us to estimate τ with high accuracy. We study in detail the behavior of τ as a function of the system parameters, namely, the number of searchers N, the relative diffusivity r of the target with respect to the searcher, and the system size. We find that τ deviates from the ∼1/N scaling seen in the case of a static target, and this deviation varies continuously with r and the spatial dimensions.

Chimeralike states in a minimal network of active camphor ribbons

A chimeralike state is the spatiotemporal pattern in an ensemble of homogeneous coupled oscillators, described as the emergence of coexisting coherent (synchronized) and incoherent (unsynchronized) groups. We demonstrate the existence of these states in three active camphor ribbons, which are camphor infused rectangular pieces of paper. These pinned ribbons rotate on the surface of the water due to Marangoni effect driven forces generated by the surface tension gradients. The ribbons are coupled via a camphor layer on the surface of the water. In the minimal network of globally coupled camphor ribbons, chimeralike states are characterized by the coexistence of two synchronized and one unsynchronized ribbons. We present a numerical model, simulating the coupling between ribbons as repulsive Yukawa interactions, which was able to reproduce these experimentally observed states.

Periodic oscillations in a string of camphor infused disks

The rhythmic beating motion of autonomously motile filaments has many practical applications. Here, we present an experimental study on a filament made of camphor infused paper disks, stitched together adjacent to each other using nylon thread. The filament displays spontaneous translatory motion when it is placed on the surface of water due to the surface tension gradients created by camphor molecules on the water surface. When this filament is clamped on one end, we obtain regular oscillatory motion instead of translation. The filament shows qualitatively different dynamics at different activity levels, which is controlled by the amount of camphor infused into the paper disks. For a better physical understanding of the filament dynamics, we develop a minimal numerical model involving a semi-flexible filament made of active polar disks, where the polarity is coupled to the instantaneous velocity of the particle. This model qualitatively reproduces different oscillatory modes of the filament. Moreover, our model reveals a rich dynamical state diagram of the system, as a function of filament activity and the coupling strength.

Protein hourglass: Exact first passage time distributions for protein thresholds

Protein thresholds have been shown to act as an ancient timekeeping device, such as in the time to lysis of Escherichia coli infected with bacteriophage λ. The time taken for protein levels to reach a particular threshold for the first time is defined as the first passage time (FPT) of the protein synthesis system, which is a stochastic quantity. The first few moments of the distribution of first passage times were known earlier, but an analytical expression for the full distribution was not available. In this work, we derive an analytical expression for the first passage times for a long-lived protein. This expression allows us to calculate the full distribution not only for cases of no self-regulation, but also for both positive and negative self-regulation of the threshold protein. We show that the shape of the distribution matches previous experimental data on λ-phage lysis time distributions. We also provide analytical expressions for the FPT distribution with non-zero degradation in Laplace space. Furthermore, we study the noise in the precision of the first passage times described by coefficient of variation (CV) of the distribution as a function of the protein threshold value. We show that under conditions of positive self-regulation, the CV declines monotonically with increasing protein threshold, while under conditions of linear negative self-regulation, there is an optimal protein threshold that minimizes the noise in the first passage times.