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Dixit S, Chotalia A, Shukla S, Roy T, Parmananda P. Pathway selection by an active droplet. SOFT MATTER 2023; 19:6844-6850. [PMID: 37655779 DOI: 10.1039/d3sm00610g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/02/2023]
Abstract
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.
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Affiliation(s)
- Shiva Dixit
- Department of Physics, Indian Institute of Technology Bombay, Mumbai, Maharashtra 400 076, India.
| | - Aarsh Chotalia
- Department of Physics, Indian Institute of Technology Bombay, Mumbai, Maharashtra 400 076, India.
| | - Shantanu Shukla
- Department of Mechanical Engineering, Indian Institute of Technology Bombay, Mumbai, Maharashtra 400 076, India
| | - Tanushree Roy
- Department of Physics, Indian Institute of Technology Bombay, Mumbai, Maharashtra 400 076, India.
| | - P Parmananda
- Department of Physics, Indian Institute of Technology Bombay, Mumbai, Maharashtra 400 076, India.
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Mishra A, Saha S, Dana SK. Chimeras in globally coupled oscillators: A review. CHAOS (WOODBURY, N.Y.) 2023; 33:092101. [PMID: 37703474 DOI: 10.1063/5.0143872] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/27/2023] [Accepted: 08/21/2023] [Indexed: 09/15/2023]
Abstract
The surprising phenomenon of chimera in an ensemble of identical oscillators is no more strange behavior of network dynamics and reality. By this time, this symmetry breaking self-organized collective dynamics has been established in many networks, a ring of non-locally coupled oscillators, globally coupled networks, a three-dimensional network, and multi-layer networks. A variety of coupling and dynamical models in addition to the phase oscillators has been used for a successful observation of chimera patterns. Experimental verification has also been done using metronomes, pendula, chemical, and opto-electronic systems. The phenomenon has also been shown to appear in small networks, and hence, it is not size-dependent. We present here a brief review of the origin of chimera patterns restricting our discussions to networks of globally coupled identical oscillators only. The history of chimeras in globally coupled oscillators is older than what has been reported in nonlocally coupled phase oscillators much later. We elaborate the story of the origin of chimeras in globally coupled oscillators in a chronological order, within our limitations, and with brief descriptions of the significant contributions, including our personal experiences. We first introduce chimeras in non-locally coupled and other network configurations, in general, and then discuss about globally coupled networks in more detail.
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Affiliation(s)
- Arindam Mishra
- Department of Physics, National University of Singapore, Singapore 117551
| | - Suman Saha
- Cognitive Brain Dynamics Laboratory, National Brain Research Centre, Gurugram 122051, India
| | - Syamal K Dana
- Centre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, Kolkata 700032, India
- Division of Dynamics, Lodz University of Technology, 90-924 Lodz, Poland
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3
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Jain R, Sharma J, Tiwari I, Gadre SD, Kumarasamy S, Parmananda P, Prasad A. In-phase and mixed-phase measure synchronization of camphor rotors. Phys Rev E 2023; 108:024217. [PMID: 37723774 DOI: 10.1103/physreve.108.024217] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/22/2023] [Accepted: 08/03/2023] [Indexed: 09/20/2023]
Abstract
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.
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Affiliation(s)
- Rishabh Jain
- Kirori Mal College, University of Delhi, Delhi 110007, India
| | - Jyoti Sharma
- Department of Physics, Indian Institute of Technology, Bombay, Powai, Mumbai, Maharashtra 400076, India
| | - Ishant Tiwari
- Department of Physics, Indian Institute of Technology, Bombay, Powai, Mumbai, Maharashtra 400076, India
| | | | - Suresh Kumarasamy
- Centre for Nonlinear Systems, Chennai Institute of Technology, Chennai 600069, India
| | - P Parmananda
- Department of Physics, Indian Institute of Technology, Bombay, Powai, Mumbai, Maharashtra 400076, India
| | - Awadhesh Prasad
- Department of Physics & Astrophysics, University of Delhi, Delhi 110007, India
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Matsuo M, Ejima K, Nakata S. Recursively positive and negative chemotaxis coupling with reaction kinetics in self-organized inanimate motion. J Colloid Interface Sci 2023; 639:324-332. [PMID: 36805757 DOI: 10.1016/j.jcis.2023.02.039] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/04/2022] [Revised: 01/16/2023] [Accepted: 02/08/2023] [Indexed: 02/18/2023]
Abstract
Reconstructing recursive chemotaxis in inanimate self-propelled objects is inevitable in the development of recursively and autonomously artificial mass transport systems. However, the fabrication of inanimately recursive chemotaxis has been extremely challenging because of the difficulty in introducing competitive positive and negative feedback into an inanimate self-propelled object. Herein, a coumarin derivative (coumarin, 4-methylcoumarin (4-MC), or 6-methylcoumarin (6-MC))-based disk floated on water as a self-propelled object exhibited characteristic features of motion; these features include continuous motion, repetition between positive and negative chemotaxis to the Na3PO4 powder as a base stimulus, and oscillatory motion above the Na3PO4 powder depending on the Na3PO4 density of the powder and the functional group of coumarin derivatives. The mechanism of the characteristic features of motion to the base stimulus is discussed in relation to the surface tension of the coumarin derivatives as the driving force of motion and the reaction rate of the hydrolysis between coumarin derivatives and OH- obtained from Na3PO4. This study suggests a novel avenue for developing a recursive chemotactic system coupled with reaction kinetics in self-organized motion.
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Affiliation(s)
- Muneyuki Matsuo
- Graduate School of Integrated Sciences for Life, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8526, Japan
| | - Kaho Ejima
- Graduate School of Integrated Sciences for Life, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8526, Japan
| | - Satoshi Nakata
- Graduate School of Integrated Sciences for Life, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8526, Japan.
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5
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Kitahata H, Koyano Y. Mathematical modeling for the synchronization of two interacting active rotors. Phys Rev E 2023; 107:064607. [PMID: 37464628 DOI: 10.1103/physreve.107.064607] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/27/2023] [Accepted: 06/07/2023] [Indexed: 07/20/2023]
Abstract
We investigate the synchronization of active rotors. A rotor is composed of a free-rotating arm with a particle that releases a surface-active chemical compound. It exhibits self-rotation due to the surface tension gradient originating from the concentration field of the surface-active compound released from the rotor. In a system with two active rotors, they should interact through the concentration field. Thus, the interaction between them does not depend only on the instantaneous positions, but also on the dynamics of the concentration field. By numerical simulations, we show that in-phase and antiphase synchronizations occur depending on the distance between the two rotors. The stability of the synchronization mode is analyzed based on phase reduction theorem through the calculation of the concentration field in the co-rotating frame with the active rotor. We also confirm that the numerical results meet the prediction by theoretical analyses.
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Affiliation(s)
- Hiroyuki Kitahata
- Department of Physics, Graduate School of Science, Chiba University, Chiba 263-8522, Japan
| | - Yuki Koyano
- Department of Human Environmental Science, Graduate School of Human Development and Environment, Kobe University, Kobe 657-0011, Japan
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Tiwari I, Parmananda P. How to capture active Marangoni surfers. SOFT MATTER 2023; 19:2710-2715. [PMID: 36779912 DOI: 10.1039/d2sm01472f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/18/2023]
Abstract
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.
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Affiliation(s)
- Ishant Tiwari
- Department of Physics, Indian Institute of Technology - Bombay, Mumbai, Maharashtra 400076, India.
| | - P Parmananda
- Department of Physics, Indian Institute of Technology - Bombay, Mumbai, Maharashtra 400076, India.
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Kalita H, Khan P, Dutta S. Rotational synchronization of pinned spiral waves. Phys Rev E 2022; 106:034201. [PMID: 36266837 DOI: 10.1103/physreve.106.034201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/20/2022] [Accepted: 08/16/2022] [Indexed: 06/16/2023]
Abstract
Coupled rotors can spontaneously synchronize, giving rise to a plethora of intriguing dynamics. We present here a pair of spiral waves as two synchronizing rotors, coupled by diffusion. The spirals are pinned to unexcitable obstacles, which enables us to modify their frequencies and restrain their drift. In experiments with the Belousov-Zhabotinsky reaction, we show that two counterrotating spiral rotors, pinned to circular heterogeneities, can synchronize in frequency and phase. The nature of the phase synchronization varies depending on the difference in their characteristic frequencies. We observe in-phase and out-of-phase synchronization, lag synchronization, and phase resetting across the experiments. The time required for the two spirals to synchronize is found to depend upon the relative size of their pinning obstacles and the distance separating them. This distance can also modify the phase lag of the two rotors upon synchronization. Our experimental observations are reproduced and explained further on the basis of numerical simulations of an excitable reaction-diffusion model.
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Affiliation(s)
- Hrishikesh Kalita
- Department of Chemistry, Indian Institute of Technology Guwahati, Guwahati 781039, India
| | - Parvej Khan
- Department of Chemistry, Indian Institute of Technology Guwahati, Guwahati 781039, India
| | - Sumana Dutta
- Department of Chemistry, Indian Institute of Technology Guwahati, Guwahati 781039, India
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Jain R, Sharma J, Tiwari I, Gadre SD, Kumarasamy S, Parmananda P, Prasad A. Generation of aperiodic motion due to sporadic collisions of camphor ribbons. Phys Rev E 2022; 106:024201. [PMID: 36109890 DOI: 10.1103/physreve.106.024201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/12/2022] [Accepted: 07/13/2022] [Indexed: 06/15/2023]
Abstract
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.
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Affiliation(s)
- Rishabh Jain
- Kirori Mal College, University of Delhi, Delhi 110007, India
| | - Jyoti Sharma
- Department of Physics, Indian Institute of Technology, Bombay, Powai, Mumbai, Maharashtra 400076, India
| | - Ishant Tiwari
- Department of Physics, Indian Institute of Technology, Bombay, Powai, Mumbai, Maharashtra 400076, India
| | | | - Suresh Kumarasamy
- Centre for Nonlinear Systems, Chennai Institute of Technology, Chennai 600069, India
| | - P Parmananda
- Department of Physics, Indian Institute of Technology, Bombay, Powai, Mumbai, Maharashtra 400076, India
| | - Awadhesh Prasad
- Department of Physics & Astrophysics, University of Delhi, Delhi 110007, India
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Dixit S, Aravind M, Parmananda P. Regulating dynamics through intermittent interactions. Phys Rev E 2022; 106:014203. [PMID: 35974523 DOI: 10.1103/physreve.106.014203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/04/2022] [Accepted: 05/23/2022] [Indexed: 06/15/2023]
Abstract
In this article we experimentally demonstrate an efficient scheme to regulate the behavior of coupled nonlinear oscillators through dynamic control of their interaction. It is observed that introducing intermittency in the interaction term as a function of time or the system state predictably alters the dynamics of the constituent oscillators. Choosing the nature of the interaction, attractive or repulsive, allows for either suppression of oscillations or stimulation of activity. Two parameters Δ and τ, that reign the extent of interaction among subsystems, are introduced. They serve as a harness to access the entire range of possible behaviors from fixed points to chaos. For fixed values of system parameters and coupling strength, changing Δ and τ offers fine control over the dynamics of coupled subsystems. We show this experimentally using coupled Chua's circuits and elucidate their behavior for a range of coupling parameters through detailed numerical simulations.
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Affiliation(s)
- Shiva Dixit
- Department of Physics, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India
| | - Manaoj Aravind
- Department of Physics, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India
| | - P Parmananda
- Department of Physics, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India
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Sharma J, Tiwari I, Parmananda P, Rivera M. Aperiodic bursting dynamics of active rotors. Phys Rev E 2022; 105:014216. [PMID: 35193313 DOI: 10.1103/physreve.105.014216] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/01/2021] [Accepted: 01/10/2022] [Indexed: 06/14/2023]
Abstract
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.
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Affiliation(s)
- Jyoti Sharma
- Department of Physics, Indian Institute of Technology-Bombay, Powai, Mumbai, Maharashtra 400076, India
| | - Ishant Tiwari
- Department of Physics, Indian Institute of Technology-Bombay, Powai, Mumbai, Maharashtra 400076, India
| | - P Parmananda
- Department of Physics, Indian Institute of Technology-Bombay, Powai, Mumbai, Maharashtra 400076, India
| | - M Rivera
- Centro de Investigación en Ciencias-(IICBA), UAEM, Avenida Universidad 1001, 62209 Cuernavaca, Morelos, Mexico
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Kachhara S, Ambika G. Frequency chimera state induced by differing dynamical timescales. Phys Rev E 2021; 104:064214. [PMID: 35030851 DOI: 10.1103/physreve.104.064214] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/06/2021] [Accepted: 12/04/2021] [Indexed: 06/14/2023]
Abstract
We report the occurrence of a self-emerging frequency chimera state in spatially extended systems of coupled oscillators, where the coherence and incoherence are defined with respect to the emergent frequency of the oscillations. This is generated by the local coupling among nonlinear oscillators evolving under differing dynamical timescales starting from random initial conditions. We show how they self-organize to structured patterns with spatial domains of coherence that are in frequency synchronization, coexisting with domains that are incoherent in frequencies. Our study has relevance in understanding such patterns observed in real-world systems like neuronal systems, power grids, social and ecological networks, where differing dynamical timescales is natural and realistic among the interacting systems.
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Affiliation(s)
- Sneha Kachhara
- Indian Institute of Science Education and Research (IISER) Tirupati, Tirupati 517507, India
| | - G Ambika
- Indian Institute of Science Education and Research (IISER) Tirupati, Tirupati 517507, India
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Andrzejak RG. Chimeras confined by fractal boundaries in the complex plane. CHAOS (WOODBURY, N.Y.) 2021; 31:053104. [PMID: 34240923 DOI: 10.1063/5.0049631] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/07/2021] [Accepted: 04/16/2021] [Indexed: 06/13/2023]
Abstract
Complex-valued quadratic maps either converge to fixed points, enter into periodic cycles, show aperiodic behavior, or diverge to infinity. Which of these scenarios takes place depends on the map's complex-valued parameter c and the initial conditions. The Mandelbrot set is defined by the set of c values for which the map remains bounded when initiated at the origin of the complex plane. In this study, we analyze the dynamics of a coupled network of two pairs of two quadratic maps in dependence on the parameter c. Across the four maps, c is kept the same whereby the maps are identical. In analogy to the behavior of individual maps, the network iterates either diverge to infinity or remain bounded. The bounded solutions settle into different stable states, including full synchronization and desynchronization of all maps. Furthermore, symmetric partially synchronized states of within-pair synchronization and across-pair synchronization as well as a symmetry broken chimera state are found. The boundaries between bounded and divergent solutions in the domain of c are fractals showing a rich variety of intriguingly esthetic patterns. Moreover, the set of bounded solutions is divided into countless subsets throughout all length scales in the complex plane. Each individual subset contains only one state of synchronization and is enclosed within fractal boundaries by c values leading to divergence.
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Affiliation(s)
- Ralph G Andrzejak
- Department of Information and Communication Technologies, Universitat Pompeu Fabra, 08018 Barcelona, Catalonia, Spain
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