How to capture active Marangoni surfers.

Surfers at the air-water interface form a large subset of the domain of active matter systems. They range from the water strider in the biological world to soluto-capillary effect driven artificial boats. In this work, we propose a general protocol to capture soluto-capillary effect driven interfacial surfers. By locally modifying the air-water interface using the perturbation from a micro-air-pump, these boats are reliably captured in the region of influence (ROI) of the perturbation. The surfers begin to explore the available space freely again once the perturbation is switched off. This method is successfully generalized to a couple of distinct surface-active chemicals used as fuel for the boats. Control experiments involving passive particles validate the results as being significantly better than purely mechanical "herding" of the particles. A possible mechanism behind the observed "trapping" is proposed.

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.

A memory-based approach to model glorious uncertainties of love.

We propose a minimal yet intriguing model for a relationship between two individuals. The feeling of an individual is modeled by a complex variable and, hence, has two degrees of freedom [Jafari et al., Nonlinear Dyn. 83, 615-622 (2016)]. The effect of memory of the other individual's behavior in the past has now been incorporated via a conjugate coupling between each other's feelings. A region of parameter space exhibits multi-stable solutions wherein trajectories with different initial conditions end up in different aperiodic trajectories. This aligns with the natural observation that most relationships are aperiodic and unique not only to themselves but, more importantly, to the initial conditions too. Thus, the inclusion of memory makes the task of predicting the trajectory of a relationship hopelessly impossible.

Modes of synchrony in self-propelled pentanol drops.

We report various modes of synchrony observed for a population of two, three and four pentanol drops in a rectangular channel at the air-water interface. Initially, the autonomous oscillations of a single 1-pentanol drop were studied in a ferroin DI water solution pre-mixed with some volume of pentanol. A pentanol drop performs continuous motion on the air-water interface due to Marangoni forces. A linear channel was prepared to study the uniaxial movement of the drop(s). Thereafter, a systematic study of the self-propelled motion of a 1-pentanol drop was reported as a function of the drop volume. Subsequently, the coupled dynamics were studied for two, three and four drops, respectively. We observed anti-phase oscillations in a pair of pentanol drops. In the case of three drops, relay synchronization was observed, wherein consecutive pairs of drops were exhibiting out-of-phase oscillations and alternate drops were performing in-phase oscillations. Four pentanol drops showed two different modes of synchrony: one was relay synchrony and the other was out-of-phase oscillations between two pairs of drops (within a pair, the drops exhibit in-phase oscillations).

Interventions and their efficacy in controlling the spread of an epidemic: A numerical study.

The effect of interventions on the progression of an epidemic is studied by numerically modeling attributes, such as lockdowns and vaccinations within a stochastic, highly connected, mobile community using an agent-based model. Based on real life assumptions, we are able to gauge the effectiveness of various strategies to contain the spread of a disease through a population. The fine-tuning of control parameters makes the model coherent with real life scenarios and robust from a policy-maker's perspective.

Independent-noise provoked spiking, synchronized via coupling.

We report experimental and numerical evidence of synchronized spiking phenomena provoked by the interaction of two bidirectionally coupled electrochemical systems subjected to independent stochastic input signals. To this end, the anodic potentials of two such systems were diffusively coupled. The corresponding anodic currents of these systems exhibited excitable fixed point behavior in the vicinity of a homoclinic bifurcation. Following this, the anodic potentials were perturbed by independent noise signals. The invoked oscillatory dynamics are analyzed using normalized variance and cross-correlation coefficient. By systematically varying the coupling strength between the systems and the level of external noise, regions exhibiting synchronized spiking behavior were identified.

An alternate approach to simulate the dynamics of perturbed liquid drops.

Liquid drops when subjected to external periodic perturbations can execute polygonal oscillations. In this work, a simple model is presented that demonstrates these oscillations and their characteristic properties. The model consists of a spring-mass network such that masses are analogous to liquid molecules and the springs correspond to intermolecular links. Neo-Hookean springs are considered to represent these intermolecular links. The restoring force of a neo-Hookean spring depends nonlinearly on its length such that the force of a compressed spring is much higher than the force of the spring elongated by the same amount. This is analogous to the incompressibility of liquids, making these springs suitable to simulate the polygonal oscillations. It is shown that this spring-mass network can imitate most of the characteristic features of experimentally reported polygonal oscillations. Additionally, it is shown that the network can execute certain dynamics, which so far have not been observed in a perturbed liquid drop. The characteristics of dynamics that are observed in the perturbed network are polygonal oscillations, rotation of network, numerical relations (rational and irrational) between the frequencies of polygonal oscillations and the forcing signal, and that the shape of the polygons depends on the parameters of perturbation.

Electrical coupling of individual electrocatalytic oscillators.

The catalytic electro-oxidation of some small organic molecules is known to display kinetic instabilities, which reflect on potential and/or current oscillations. Under oscillatory conditions, those systems can be considered electrocatalytic oscillators and, therefore, can be described by their amplitude, frequency, and waveform. Just like mechanical oscillators, the electrocatalytic ones can be coupled and their dynamics can be changed by setting different coupling parameters. In the present work, we study the unidirectional coupling of electrocatalytic oscillators, namely, those comprehending the catalytic electro-oxidation of methanol and formic acid on polycrystalline platinum in acidic media under potentiostatic control. Herein, we explore two different scenarios (the coupling of compositionally identical and non-identical oscillators) and investigate the effects of the master's identity and of the coupling constant on the slave's dynamics. For the master (methanol)-slave (methanol) coupling, the oscillators exhibited phase lag synchronization and complete phase synchronization. On the other hand, for the master (formic acid)-slave (methanol) coupling, the oscillators exhibited complete phase synchronization with phase-locking with a 2:3 ratio, complete phase synchronization with phase-locking with a 1:2 ratio, phase lag synchronization, and complete phase synchronization. The obtained results suggest that both the master's identity and the coupling constant (sign and magnitude) are parameters that play an important role on the coupled systems, in such a way that even for completely different systems, synchronization could emerge by setting a suitable coupling constant. To the best of our knowledge, this is the first report concerning the electrical coupling of hidden N-shaped-negative differential resistance type systems.

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.

Phase coalescence in a population of heterogeneous Kuramoto oscillators.

Phase coalescence (PC) is an emerging phenomenon in an ensemble of oscillators that manifests itself as a spontaneous rise in the order parameter. This increment in the order parameter is due to the overlaying of oscillator phases to a pre-existing system state. In the current work, we present a comprehensive analysis of the phenomenon of phase coalescence observed in a population of Kuramoto phase oscillators. The given population is divided into responsive and non-responsive oscillators depending on the position of the phases of the oscillators. The responsive set of oscillators is then reset by a pulse perturbation. This resetting leads to a temporary rise in a macroscopic observable, namely, order parameter. The provoked rise thus induced in the order parameter is followed by unprovoked increments separated by a constant time τPC. These unprovoked increments in the order parameter are caused due to a temporary gathering of the oscillator phases in a configuration similar to the initial system state, i.e., the state of the network immediately following the perturbation. A theoretical framework corroborating this phenomenon as well as the corresponding simulation results are presented. Dependence of τPC and the magnitude of spontaneous order parameter augmentation on various network parameters such as coupling strength, network size, degree of the network, and frequency distribution are then explored. The size of the phase resetting region would also affect the magnitude of the order parameter at τPC since it directly affects the number of oscillators reset by the perturbation. Therefore, the dependence of order parameter on the size of the phase resetting region is also analyzed.

Competitive interplay of repulsive coupling and cross-correlated noises in bistable systems.

The influence of noise on synchronization has potential impact on physical, chemical, biological, and engineered systems. Research on systems subject to common noise has demonstrated that noise can aid synchronization, as common noise imparts correlations on the sub-systems. In our work, we revisit this idea for a system of bistable dynamical systems, under repulsive coupling, driven by noises with varying degrees of cross correlation. This class of coupling has not been fully explored, and we show that it offers new counter-intuitive emergent behavior. Specifically, we demonstrate that the competitive interplay of noise and coupling gives rise to phenomena ranging from the usual synchronized state to the uncommon anti-synchronized state where the coupled bistable systems are pushed to different wells. Interestingly, this progression from anti-synchronization to synchronization goes through a domain where the system randomly hops between the synchronized and anti-synchronized states. The underlying basis for this striking behavior is that correlated noise preferentially enhances coherence, while the interactions provide an opposing drive to push the states apart. Our results also shed light on the robustness of synchronization obtained in the idealized scenario of perfectly correlated noise, as well as the influence of noise correlation on anti-synchronization. Last, the experimental implementation of our model using bistable electronic circuits, where we were able to sweep a large range of noise strengths and noise correlations in the laboratory realization of this noise-driven coupled system, firmly indicates the robustness and generality of our observations.

Ill-matched timescales in coupled systems can induce oscillation suppression.

We explore the behavior of two coupled oscillators, considering combinations of similar and dissimilar oscillators, with their intrinsic dynamics ranging from periodic to chaotic. We first investigate the coupling of two different real-world systems, namely, the chemical mercury beating heart oscillator and the electronic Chua oscillator, with the disparity in the timescales of the constituent oscillators. Here, we are considering a physical situation that is not commonly addressed: the coupling of sub-systems whose characteristic timescales are very different. Our findings indicate that the oscillations in coupled systems are quenched to oscillation death (OD) state, at sufficiently high coupling strength, when there is a large timescale mismatch. In contrast, phase synchronization occurs when their timescales are comparable. In order to further strengthen the concept, we demonstrate this timescale-induced oscillation suppression and phase synchrony through numerical simulations, with the disparity in the timescales serving as a tuning or control parameter. Importantly, oscillation suppression (OD) occurs for a significantly smaller timescale mismatch when the coupled oscillators are chaotic. This suggests that the inherent broad spectrum of timescales underlying chaos aids oscillation suppression, as the temporal complexity of chaotic dynamics lends a natural heterogeneity to the timescales. The diversity of the experimental systems and numerical models we have chosen as a test-bed for the proposed concept lends support to the broad generality of our findings. Last, these results indicate the potential prevention of system failure by small changes in the timescales of the constituent dynamics, suggesting a potent control strategy to stabilize coupled systems to steady 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.

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

We experimentally study the stochastic transport of a self-propelled camphor boat, driven by Marangoni forces, through a crowd of passive paper discs floating on water. We analyze the statistics of the first passage times of the active particle to travel from the center of a circular container to its boundary. While the mean times rise monotonically as a function of the covered area fraction φ of the passive paper discs, their fluctuations show a non-monotonic behavior - being higher at low and high value of φ compared to intermediate values. The reason is traced to an interplay of two distinct sources of fluctuations - one intrinsic to the dynamics, while the other due to the crowding.

Predictive modeling of disease propagation in a mobile, connected community using cellular automata.

We present numerical results obtained from the modeling of a stochastic, highly connected, and mobile community. The spread of attributes like health and disease among the community members is simulated using cellular automata on a planar two-dimensional surface. With remarkably few assumptions, we are able to predict the future course of propagation of such a disease as a function of time and the fine-tuning of parameters related to interactions among the automata.

Velocity controlled pattern writing: An application of stochastic resonance.

In the present work, the concept of stochastic resonance is employed for pattern fabrication. In particular, the interplay of noise amplitudes and intrinsic system time scales is investigated. This interplay enabled us to obtain preordained patterns. Experiments were performed galvanostatically in a two electrode electrochemical cell onto a n-type Si substrate using a coherent wavelength laser source of 5 mW intensity. A focused laser beam was swept along the silicon substrate unidirectionally by moving the electrochemical cell at different velocities. By systematic tuning of the velocity, we have observed a unimodal variation in the contrast of the pattern. This indicates the occurrence of the stochastic resonance phenomena. Corresponding numerical simulations, performed on a spatial array of diffusively coupled FitzHugh-Nagumo oscillators in the presence of external noise, reveal good agreement with the experimental observations.

Entrainment of aperiodic and periodic oscillations in the Mercury Beating Heart system using external periodic forcing.

We report experimental results indicating entrainment of aperiodic and periodic oscillatory dynamics in the Mercury Beating Heart (MBH) system under the influence of superimposed periodic forcing. Aperiodic oscillations in MBH were controlled to generate stable topological modes, namely, circle, ellipse, and triangle, evolving in a periodic fashion at different parameters of the forcing signal. These periodic dynamics show 1:1 entrainment for circular and elliptical modes, and additionally the controlled system exhibits 1:2 entrainment for elliptical and triangular modes at a different set of parameters. The external periodic forcing of the periodic MBH system reveals the existence of domains of entrainment (1:1, 1:2, 1:3, and 1:4) represented in the Arnold tongue structures. Moreover, Devil's staircase is obtained when the amplitude-frequency space of parameters of the applied signal is scanned.

Control, synchronization, and enhanced reliability of aperiodic oscillations in the Mercury Beating Heart system.

Experiments involving the Mercury Beating Heart (MBH) oscillator, exhibiting irregular (aperiodic) dynamics, are performed. In the first set of experiments, control over irregular dynamics of the MBH oscillator was obtained via a superimposed periodic voltage signal. These irregular (aperiodic) dynamics were recovered once the control was switched off. Subsequently, two MBH oscillators were coupled to attain synchronization of their aperiodic oscillations. Finally, two uncoupled MBH oscillators were subjected, repeatedly, to a common stochastic forcing, resulting in an enhancement of their mutual phase correlation.

Provoking predetermined aperiodic patterns in human brainwaves.

In the present work, electroencephalographic recordings of healthy human participants were performed to study the entrainment of brainwaves using a variety of stimuli. First, the periodic entrainment of the brainwaves was studied using two different stimuli in the form of periodic auditory and visual signals. The entrainment with the periodic visual stimulation was consistently observed, whereas the auditory entrainment was inconclusive. Hence, a photic (visual) stimulus, where two frequencies were presented to the subject simultaneously, was used to further explore the bifrequency entrainment of human brainwaves. Subsequently, the evolution of brainwaves as a result of an aperiodic stimulation was explored, wherein an entrainment to the predetermined aperiodic pattern was observed. These results suggest that the aperiodic entrainment could be used as a tool for guided modification of brainwaves. This could find possible applications in processes such as epilepsy suppression and biofeedback.

Electrical resonance of Amphotericin B channel activity in lipidic membranes.

In our previous work [J. Membrane Biol. 237, 31 (2010)], we showed the dependence of the time average conductance of Nystatin channels as a function of the applied potential. Specifically, it was observed that greater potential induced enhanced channel activity. This indicates that the supramolecular structure could be stabilized by a large field, possibly by giving a preferential orientation to the monomers. In the present work, we entertain the notion that the process of pore formation in the lipidic membranes has an underlying deterministic component. To verify this hypothesis, experiments were performed under potentio-dynamic conditions, i.e., a square train of pulses of different frequencies (0.05-2 Hz) were applied to a 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine membrane having 30 mol. % cholesterol and the presence of 35 µM Amphotericin B. An emergence of a resonant frequency, in the present experiments, is tantamount to observing fingerprints of determinism in the activity of these channels in lipidic membranes.