Synchronization and chimera are examples of collective behavior observed in an ensemble of coupled nonlinear oscillators. Recent studies have focused on their discovery in systems with least possible number of oscillators. Here we present an experimental study revealing the synchronization route to weak chimera via quenching, clustering, and chimera states in a single system of four coupled candle-flame oscillators. We further report the discovery of multiphase weak chimera along with experimental evidence of the theoretically predicted states of in-phase chimera and antiphase chimera. © 2019 American Physical Society.

R. I. Sujith

Department of Aerospace Engineering

Krishna Manoj

Samadhan A. Pawar

Suraj Dange

ANTIPHASE

CANDLE FLAME

Collective behavior

COUPLED NONLINEAR OSCILLATORS

Experimental evidence

In-phase

Synchronization

IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

Physical Review E

Synchronization route to weak chimera in four candle-flame oscillators

We investigate the coupled behaviour of two oscillatory flames produced by separate bundles of candles, referred to as candle-flame oscillators, as the distance between them is varied. Each bundle consists of four candles whose individual flames are fused so that the resultant flame produces self-sustained limit cycle oscillations. The recent study by Manoj et al. [Scientific Reports 8, 11626 (2018)] has reported the occurrence of four different modes of coupled behaviour, which include in-phase synchronization, amplitude death, anti-phase synchronization, and desynchronization by observing the flame dynamics of such coupled candle-flame oscillators. Here, we investigate the physical mechanism behind the occurrence of these different dynamical modes. Towards this purpose, we perform simultaneous measurements of the flow field around the candle flames using high-speed shadowgraph and of the reaction zone of each flame using high-speed CH ∗ chemiluminescence imaging. We notice that these modes are distinguished by the distinct features of the flame dynamics and the corresponding buoyancy-induced flows surrounding the flames. We observe that the difference in the interaction of vortices, formed due to the instability of buoyancy-induced flows around each flame at various distances, plays a significant role in inducing different modes of coupled dynamics between the oscillators. Furthermore, we find that the change in the length scales of vortices shed around the flames is a contributing factor in increasing the frequency of the oscillators during the transition from in-phase to anti-phase mode of synchronization. © 2019 Author(s).

Fulltext

AIP Advances

Role of buoyancy-driven vortices in inducing different modes of coupled behaviour in candle-flame oscillators

Nonlinear phenomena emerging from the coupled behaviour of a pair of oscillators have attracted considerable research attention over the years, of which, amplitude death (AD) and phase-flip bifurcation (PFB) are two noteworthy examples. Although theoretical research has postulated the coexistence of AD and PFB upon variation of different control parameters, such an occurrence has not been reported in practical systems. Here, we provide the first experimental evidence of the coexistence of AD and PFB in a physical system, comprising of a coupled pair of candle-flame oscillators. As the strength of coupling between the oscillators is increased, we report a decrease in the span of AD region between the states of in-phase and anti-phase oscillations, leading up to a point of PFB. Understanding such a switching of phenomena between AD and PFB helps us to evade their undesirable occurrences such as AD in neuron and brain cells, oscillatory state in prey-predator systems, oscillatory spread of epidemics and so forth. © 2018, The Author(s).

Scientific Reports

Experimental Evidence of Amplitude Death and Phase-Flip Bifurcation between In-Phase and Anti-Phase Synchronization

Thermoacoustic systems with a turbulent reactive flow, prevalent in the fields of power and propulsion, are highly susceptible to oscillatory instabilities. Recent studies showed that such systems transition from combustion noise to thermoacoustic instability through a dynamical state known as intermittency, where bursts of large-amplitude periodic oscillations appear in a near-random fashion in between regions of low-amplitude aperiodic fluctuations. However, as these analyses were in the temporal domain, this transition remains still unexplored spatiotemporally. Here, we present the spatiotemporal dynamics during the transition from combustion noise to limit cycle oscillations in a turbulent bluff-body stabilized combustor. To that end, we acquire the pressure oscillations and the field of heat release rate oscillations through high-speed chemiluminescence images of the reaction zone. With a view to get an insight into this complex dynamics, we compute the instantaneous phases between acoustic pressure and local heat release rate oscillations. We observe that the aperiodic oscillations during combustion noise are phase asynchronous, while the large-amplitude periodic oscillations seen during thermoacoustic instability are phase synchronous. We find something interesting during intermittency: patches of synchronized periodic oscillations and desynchronized aperiodic oscillations coexist in the reaction zone. In other words, the emergence of order from disorder happens through a dynamical state wherein regions of order and disorder coexist, resembling a chimera state. Generally, mutually coupled chaotic oscillators synchronize but retain their dynamical nature; the same is true for coupled periodic oscillators. In contrast, during intermittency, we find that patches of desynchronized aperiodic oscillations turn into patches of synchronized periodic oscillations and vice versa. Therefore, the dynamics of local heat release rate oscillations change from aperiodic to periodic as they synchronize intermittently. The temporal variations in global synchrony, estimated through the Kuramoto order parameter, echoes the breathing nature of a chimera state. © 2016 Cambridge University Press.

Journal of Fluid Mechanics

Onset of thermoacoustic instability in turbulent combustors: An emergence of synchronized periodicity through formation of chimera-like states

Thermoacoustic instability is the result of a positive coupling between the acoustic field in the duct and the heat release rate fluctuations from the flame. Recently, in several turbulent combustors, it has been observed that the onset of thermoacoustic instability is preceded by intermittent oscillations, which consist of bursts of periodic oscillations amidst regions of aperiodic oscillations. Quantitative analysis of the intermittency route to thermoacoustic instability has been performed hitherto using the pressure oscillations alone. We perform experiments on a laboratory-scale bluff-body-stabilized turbulent combustor with a backward-facing step at the inlet to obtain simultaneous data of acoustic pressure and heat release rate fluctuations. With this, we show that the onset of thermoacoustic instability is a phenomenon of mutual synchronization between the acoustic pressure and the heat release rate signals, thus emphasizing the importance of the coupling between these non-identical oscillators. We demonstrate that the stable operation corresponds to desynchronized aperiodic oscillations, which, with an increase in the mean velocity of the flow, transition to synchronized periodic oscillations. In between these states, there exists a state of intermittent phase synchronized oscillations, wherein the two oscillators are synchronized during the periodic epochs and desynchronized during the aperiodic epochs of their oscillations. Furthermore, we discover two different types of limit cycle oscillations in our system. We notice a significant increase in the linear correlation between the acoustic pressure and the heat release rate oscillations during the transition from a lower-amplitude limit cycle to a higher-amplitude limit cycle. Further, we present a phenomenological model that qualitatively captures all of the dynamical states of synchronization observed in the experiment. Our analysis shows that the times at which vortices that are shed from the inlet step reach the bluff body play a dominant role in determining the behaviour of the limit cycle oscillations. © 2017 Cambridge University Press.

Journal	Data powered by TypesetPhysical Review E
Publisher	Data powered by TypesetAmerican Physical Society
ISSN	24700045
Open Access	No