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Manoj K, Pawar SA, Kurths J, Sujith RI. Rijke tube: A nonlinear oscillator. CHAOS (WOODBURY, N.Y.) 2022; 32:072101. [PMID: 35907738 DOI: 10.1063/5.0091826] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/17/2022] [Accepted: 06/16/2022] [Indexed: 06/15/2023]
Abstract
Dynamical systems theory has emerged as an interdisciplinary area of research to characterize the complex dynamical transitions in real-world systems. Various nonlinear dynamical phenomena and bifurcations have been discovered over the decades using different reduced-order models of oscillators. Different measures and methodologies have been developed theoretically to detect, control, or suppress the nonlinear oscillations. However, obtaining such phenomena experimentally is often challenging, time-consuming, and risky mainly due to the limited control of certain parameters during experiments. With this review, we aim to introduce a paradigmatic and easily configurable Rijke tube oscillator to the dynamical systems community. The Rijke tube is commonly used by the combustion community as a prototype to investigate the detrimental phenomena of thermoacoustic instability. Recent investigations in such Rijke tubes have utilized various methodologies from dynamical systems theory to better understand the occurrence of thermoacoustic oscillations and their prediction and mitigation, both experimentally and theoretically. The existence of various dynamical behaviors has been reported in single and coupled Rijke tube oscillators. These behaviors include bifurcations, routes to chaos, noise-induced transitions, synchronization, and suppression of oscillations. Various early warning measures have been established to predict thermoacoustic instabilities. Therefore, this review article consolidates the usefulness of a Rijke tube oscillator in terms of experimentally discovering and modeling different nonlinear phenomena observed in physics, thus transcending the boundaries between the physics and the engineering communities.
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Affiliation(s)
- Krishna Manoj
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Samadhan A Pawar
- Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai 600036, India
| | - Jürgen Kurths
- Potsdam Institute for Climate Impact Research, Potsdam 14473, Germany
| | - R I Sujith
- Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai 600036, India
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Sebek M, Kawamura Y, Nott AM, Kiss IZ. Anti-phase collective synchronization with intrinsic in-phase coupling of two groups of electrochemical oscillators. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2019; 377:20190095. [PMID: 31656145 PMCID: PMC6833994 DOI: 10.1098/rsta.2019.0095] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 09/05/2019] [Indexed: 05/02/2023]
Abstract
The synchronization of two groups of electrochemical oscillators is investigated during the electrodissolution of nickel in sulfuric acid. The oscillations are coupled through combined capacitance and resistance, so that in a single pair of oscillators (nearly) in-phase synchronization is obtained. The internal coupling within each group is relatively strong, but there is a phase difference between the fast and slow oscillators. The external coupling between the two groups is weak. The experiments show that the two groups can exhibit (nearly) anti-phase collective synchronization. Such synchronization occurs only when the external coupling is weak, and the interactions are delayed by the capacitance. When the external coupling is restricted to those between the fast and the slow elements, the anti-phase synchronization is more prominent. The results are interpreted with phase models. The theory predicts that, for anti-phase collective synchronization, there must be a minimum internal phase difference for a given shift in the phase coupling function. This condition is less stringent with external fast-to-slow coupling. The results provide a framework for applications of collective phase synchronization in modular networks where weak coupling between the groups can induce synchronization without rearrangements of the phase dynamics within the groups. This article is part of the theme issue 'Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences'.
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Affiliation(s)
- Michael Sebek
- Department of Chemistry, Saint Louis University, 3501 Laclede Avenue, St Louis, MO 63103, USA
| | - Yoji Kawamura
- Center for Mathematical Science and Advanced Technology, Japan Agency for Marine-Earth Science and Technology, 236-0001 Yokohama, Japan
| | - Ashley M. Nott
- Department of Chemistry, Saint Louis University, 3501 Laclede Avenue, St Louis, MO 63103, USA
| | - István Z. Kiss
- Department of Chemistry, Saint Louis University, 3501 Laclede Avenue, St Louis, MO 63103, USA
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Blaha KA, Huang K, Della Rossa F, Pecora L, Hossein-Zadeh M, Sorrentino F. Cluster Synchronization in Multilayer Networks: A Fully Analog Experiment with LC Oscillators with Physically Dissimilar Coupling. PHYSICAL REVIEW LETTERS 2019; 122:014101. [PMID: 31012653 DOI: 10.1103/physrevlett.122.014101] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/14/2018] [Indexed: 06/09/2023]
Abstract
We investigate cluster synchronization in experiments with a multilayer network of electronic Colpitts oscillators, specifically a network with two interaction layers. We observe and analytically characterize the appearance of several cluster states as we change coupling in the layers. In this study, we innovatively combine bifurcation analysis and the computation of transverse Lyapunov exponents. We observe four kinds of synchronized states, from fully synchronous to a clustered quasiperiodic state-the first experimental observation of the latter state. Our work is the first to study fundamentally dissimilar kinds of coupling within an experimental multilayer network.
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Affiliation(s)
- Karen A Blaha
- Department of Mechanical Engineering, University of New Mexico, Albuquerque, New Mexico 87131, USA
| | - Ke Huang
- Department of Electrical and Computer Engineering, University of New Mexico, Albuquerque, New Mexico 87131, USA
| | - Fabio Della Rossa
- Department of Mechanical Engineering, University of New Mexico, Albuquerque, New Mexico 87131, USA
- Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
| | - Louis Pecora
- U.S. Naval Research Laboratory, Washington, DC 20375, USA
| | - Mani Hossein-Zadeh
- Department of Electrical and Computer Engineering, University of New Mexico, Albuquerque, New Mexico 87131, USA
| | - Francesco Sorrentino
- Department of Mechanical Engineering, University of New Mexico, Albuquerque, New Mexico 87131, USA
- Department of Electrical and Computer Engineering, University of New Mexico, Albuquerque, New Mexico 87131, USA
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Omel'chenko OE, Sebek M, Kiss IZ. Universal relations of local order parameters for partially synchronized oscillators. Phys Rev E 2018; 97:062207. [PMID: 30011585 DOI: 10.1103/physreve.97.062207] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/02/2018] [Indexed: 11/07/2022]
Abstract
Interactions among discrete oscillatory units (e.g., cells) can result in partially synchronized states when some of the units exhibit phase locking and others phase slipping. Such states are typically characterized by a global order parameter that expresses the extent of synchrony in the system. Here we show that such states carry data-rich information of the system behavior, and a local order parameter analysis reveals universal relations through a semicircle representation. The universal relations are derived from thermodynamic limit analysis of a globally coupled Kuramoto-type phase oscillator model. The relations are confirmed with the partially synchronized states in numerical simulations with a model of circadian cells and in laboratory experiments with chemical oscillators. The application of the theory allows direct approximation of coupling strength, the natural frequency of oscillations, and the phase lag parameter without extensive nonlinear fits as well as a self-consistency check for presence of network interactions and higher harmonic components in the phase model.
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Affiliation(s)
| | - Michael Sebek
- Department of Chemistry, Saint Louis University, 3501 Laclede Avenue, St. Louis, Missouri 63103, USA
| | - István Z Kiss
- Department of Chemistry, Saint Louis University, 3501 Laclede Avenue, St. Louis, Missouri 63103, USA
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Liu Y, Sebek M, Mori F, Kiss IZ. Synchronization of three electrochemical oscillators: From local to global coupling. CHAOS (WOODBURY, N.Y.) 2018; 28:045104. [PMID: 31906643 DOI: 10.1063/1.5012520] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
We investigate the formation of synchronization patterns in an oscillatory nickel electrodissolution system in a network obtained by superimposing local and global coupling with three electrodes. We explored the behavior through numerical simulations using kinetic ordinary differential equations, Kuramoto type phase models, and experiments, in which the local to global coupling could be tuned by cross resistances between the three nickel wires. At intermediate coupling strength with predominant global coupling, two of the three oscillators, whose natural frequencies are closer, can synchronize. By adding even a relatively small amount of local coupling (about 9%-25%), a spatially organized partially synchronized state can occur where one of the two synchronized elements is in the center. A formula was derived for predicting the critical coupling strength at which full synchronization will occur independent of the permutation of the natural frequencies of the oscillators over the network. The formula correctly predicts the variation of the critical coupling strength as a function of the global coupling fraction, e.g., with local coupling the critical coupling strength is about twice than that required with global coupling. The results show the importance of the topology of the network on the synchronization properties in a simple three-oscillator setup and could provide guidelines for decrypting coupling topology from identification of synchronization patterns.
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Affiliation(s)
- Yifan Liu
- Department of Chemistry, Saint Louis University, 3501 Laclede Avenue, St. Louis, Missouri 63103, USA
| | - Michael Sebek
- Department of Chemistry, Saint Louis University, 3501 Laclede Avenue, St. Louis, Missouri 63103, USA
| | - Fumito Mori
- Theoretical Biology Laboratory, RIKEN, Wako 351-0198, Japan
| | - István Z Kiss
- Department of Chemistry, Saint Louis University, 3501 Laclede Avenue, St. Louis, Missouri 63103, USA
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Synchronization of current oscillations in a dual-anode dissolution reaction in the presence of a common cathode electrode. Electrochim Acta 2017. [DOI: 10.1016/j.electacta.2017.08.153] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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Tajima S, Singh H, Nakabayashi S, Singla T, Parmananda P. The emergence of synchrony behavior in weakly coupled electrochemical oscillators via a ‘metallic plate’. J Electroanal Chem (Lausanne) 2016. [DOI: 10.1016/j.jelechem.2016.03.004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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Sebek M, Tönjes R, Kiss IZ. Complex Rotating Waves and Long Transients in a Ring Network of Electrochemical Oscillators with Sparse Random Cross-Connections. PHYSICAL REVIEW LETTERS 2016; 116:068701. [PMID: 26919024 DOI: 10.1103/physrevlett.116.068701] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/14/2015] [Indexed: 06/05/2023]
Abstract
We perform experiments and phase model simulations with a ring network of oscillatory electrochemical reactions to explore the effect of random connections and nonisochronicity of the interactions on the pattern formation. A few additional links facilitate the emergence of the fully synchronized state. With larger nonisochronicity, complex rotating waves or persistent irregular phase dynamics can derail the convergence to global synchronization. The observed long transients of irregular phase dynamics exemplify the possibility of a sudden onset of hypersynchronous behavior without any external stimulus or network reorganization.
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Affiliation(s)
- Michael Sebek
- Department of Chemistry, Saint Louis University, 3501 Laclede Avenue, St. Louis, Missouri 63103, USA
| | - Ralf Tönjes
- Institute of Physics and Astronomy, Potsdam University, 14476 Potsdam-Golm, Germany
| | - István Z Kiss
- Department of Chemistry, Saint Louis University, 3501 Laclede Avenue, St. Louis, Missouri 63103, USA
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Wickramasinghe M, Kiss IZ. Spatially organized partial synchronization through the chimera mechanism in a network of electrochemical reactions. Phys Chem Chem Phys 2015; 16:18360-9. [PMID: 25069401 DOI: 10.1039/c4cp02249a] [Citation(s) in RCA: 61] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023]
Abstract
Detailed experimental and numerical results are presented about the pattern formation mechanism of spatially organized partially synchronized states in a networked chemical system with oscillatory metal dissolution. Numerical simulations of the reaction system are used to identify experimental conditions (heterogeneity, network topology, and coupling time-scale) under which the chemical reactions, which take place in a network, are split into coexisting coherent and incoherent domains through the chimera mechanism. Experiments are carried out with a network of twenty electrodes arranged in a ring with seven nearest neighbor couplings in both directions along the ring. The patterns are characterized by analyzing the oscillation frequencies and entrainments to the mean field of the phases of oscillations. The chimera state forms from two domains of elements: the chimera core in which the elements have identical frequencies and are entrained to their corresponding mean field and the chimera shell where the elements exhibit desynchrony with each other and the mean field. The experiments point out the importance of low level of heterogeneities (e.g., surface conditions) and optimal level of coupling strength and time-scale as necessary components for the realization of the chimera state. For systems with large heterogeneities, a 'remnant' chimera state is identified where the pattern is strongly affected by the presence of frequency clusters. The exploration of dynamical features with networked reactions could open up ways for identification of novel types of patterns that cannot be observed with reaction diffusion systems (with localized interactions) or with reactions under global constraints, coupling, or feedback.
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Affiliation(s)
- Mahesh Wickramasinghe
- Department of Chemistry, Saint Louis University, 3501 Laclede Avenue, St Louis, MO 63103, USA.
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Szabo E. Oregonator generalization as a minimal model of quorum sensing in Belousov–Zhabotinsky reaction with catalyst confinement in large populations of particles. RSC Adv 2015. [DOI: 10.1039/c5ra12841b] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023] Open
Abstract
The Oregonator demonstrates that quorum sensing in populations of Belousov–Zhabotinsky oscillators arises from modification of the stoichiometry by catalyst confinement.
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Affiliation(s)
- E. Szabo
- Department of Earth and Planetary Sciences
- Harvard University
- Cambridge
- USA
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Zhong ZY, Zhang WM, Meng G, Wang MY. Thermoelastic damping in optical waveguide resonators with the bolometric effect. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:063203. [PMID: 25019905 DOI: 10.1103/physreve.89.063203] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/12/2013] [Indexed: 06/03/2023]
Abstract
Incorporating the bolometric effect, the thermoelastic damping in a nanowaveguide resonator driven by an optical gradient force is investigated in this paper. Based on the Euler-Bernoulli beam theory, the governing equation of the optowaveguide resonator is derived by considering the complex distribution of injected optical power, which has significant influence on the thermoelastic damping. By solving the heat diffusion equation, the theoretical model of the thermoelastic damping is presented. In this model, the effects of injected optical power, representative temperatures, waveguide material, and geometries on the thermoelastic damping are studied and discussed respectively. The results show that the peak value of thermoelastic damping increases as the injected optical power is increasing within a low range. Hardly any changes exist for the intrinsic energy dissipation of different materials at higher injected optical power. When the environmental temperature falls in the range of 293-500 K, the thermoelastic damping increases slowly, and then drops down quickly as a function of the dimensionless frequency. However, the thermoelastic damping monotonically decreases when the representative temperature drops to lower than 293 K. In addition, the thermoelastic damping is found to be scale dependent, particularly with the effect of injected optical power.
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Affiliation(s)
- Zuo-Yang Zhong
- State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China and State Key Laboratory of Disaster Prevention and Mitigation of Explosion and Impact, College of Field Engineering, PLA University of Science and Technology, Nanjing, Jiangsu 210007, China
| | - Wen-Ming Zhang
- State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China
| | - Guang Meng
- State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China
| | - Ming-Yang Wang
- State Key Laboratory of Disaster Prevention and Mitigation of Explosion and Impact, College of Field Engineering, PLA University of Science and Technology, Nanjing, Jiangsu 210007, China
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