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Journal ArticleDOI

Condensation in the phase space and network topology during transition from chaos to order in turbulent thermoacoustic systems.

19 Apr 2021-Chaos (AIP Publishing LLC AIP Publishing)-Vol. 31, Iss: 4, pp 043126-043126
TL;DR: The use of network centrality measures derived from cycle networks are proposed as a novel means to characterize the number and stability of periodic orbits in the phase space and to study the topological transformations in thephase space during the emergence of order from chaos in the combustors.
Abstract: The emergence of oscillatory dynamics (order) from chaotic fluctuations is a well-known phenomenon in turbulent thermoacoustic, aero-acoustic, and aeroelastic systems and is often detrimental to the system. We study the dynamics of two distinct turbulent thermoacoustic systems, bluff-body and swirl-stabilized combustors, where the transition occurs from the state of combustion noise (chaos) to thermoacoustic instability (order) via the route of intermittency. Using unweighted complex networks built from phase space cycles of the acoustic pressure oscillations, we characterize the topology of the phase space during various dynamical states in these combustors. We propose the use of network centrality measures derived from cycle networks as a novel means to characterize the number and stability of periodic orbits in the phase space and to study the topological transformations in the phase space during the emergence of order from chaos in the combustors. During the state of combustion noise, we show that the phase space consists of several unstable periodic orbits, which influence the phase space trajectory. As order emerges in the system dynamics, the number of periodic orbits decreases and their stability increases. At the onset of oscillatory dynamics, the phase space consists of a stable periodic orbit. We also use network centrality measures to identify the onset of thermoacoustic instability in both the combustors. Finally, we propose that the onset of oscillatory instabilities in turbulent systems is analogous to Bose-Einstein condensation transition observed for bosons, if we define phase space cycles as particles and the periodic orbits as energy levels.
Citations
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Journal ArticleDOI
TL;DR: In this paper, the authors highlight the importance of the inherent fluctuations in the system in providing early warning signals for critical transitions and highlight the challenges faced while detecting oscillatory instabilities in practical systems.
Abstract: Many complex systems undergo critical transitions. A thermoacoustic system is one such system which exhibits a catastrophic transition to a state of oscillatory instability known as thermoacoustic instability. So far, several early warning signals have been devised to detect the transition from stable operation to thermoacoustic instability in both laminar and turbulent systems. We focus on these early warning signals, and the challenges faced while detecting oscillatory instabilities in practical systems. In contrast to the transition from a fixed point to limit cycle oscillations in laminar systems, turbulent systems exhibit a transition from a chaotic state to limit cycle via a state of intermittency. In this review, we highlight the importance of the inherent fluctuations in the system in providing early warning signals for critical transitions.

16 citations

Journal ArticleDOI
TL;DR: In this article , the authors provide a brief introduction to network science and an overview of the progress on network-based strategies to study the complex dynamics of fluid flows, with a particular emphasis on interactive dynamics.

4 citations

Journal ArticleDOI
TL;DR: In this paper , a Rijke tube system with a premixed methane-air laminar flame was used to trigger the self-excited thermoacoustic oscillations with varied equivalence ratios (Φ), and time domain analysis methods including phase difference, Recurrence Plot (RP) and Recurrence quantification analysis (RQA) were applied to obtain the characteristics of system nonlinearities.

3 citations

Journal ArticleDOI
TL;DR: In this paper , the authors introduced a framework of complex networks to analyze the particle dynamics through a Lagrangian perspective and observed an emergence of a giant component through a continuous phase transition as particles cluster in the flow field, thus providing novel insight into the spatiotemporal dynamics of particles such as the rate of clustering.
Abstract: Studying particle-laden flows is essential for understanding diverse physical processes such as rain formation in clouds, pathogen transmission, and pollutant dispersal. This work introduces a framework of complex networks to analyze the particle dynamics through a Lagrangian perspective. To illustrate this method, we study the clustering of inertial particles (small heavy particles) in Taylor–Green flow, where the dynamics depend on the particle Stokes number ( St). Using complex networks, we can obtain the instantaneous local and global clustering characteristics simultaneously. Furthermore, from the complex networks derived from the particle locations, we observe an emergence of a giant component through a continuous phase transition as particles cluster in the flow field, thus providing novel insight into the spatiotemporal dynamics of particles such as the rate of clustering. Finally, we believe that complex networks have a great potential for analyzing the spatiotemporal dynamics of particle-laden flows.

1 citations

Journal ArticleDOI
01 Aug 2022-Chaos
TL;DR: In this paper , the authors numerically examined the gravitational effect on the nonlinear dynamics of a buoyant turbulent flame utilizing analytical methods based on complex networks and dynamical systems, showing that a dense (sparse) network structure is formed in the near (far) field in low gravity, as shown by the degree and cluster coefficient in the spatial network.
Abstract: This study numerically examines the gravitational effect on the nonlinear dynamics of a buoyant turbulent flame utilizing analytical methods based on complex networks and dynamical systems. A dense (sparse) network structure is formed in the near (far) field in low gravity, as shown by the degree and cluster coefficient in the spatial network. The global dynamics of the vertical flow velocity fluctuations in the intermittent luminous zone is synchronous with that of the temperature fluctuations in low gravity. The synchronized state disappears as the gravity level is increased, leading to a desynchronized state. These behaviors are clearly identified by the symbolic recurrence plots.

1 citations

References
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Journal ArticleDOI
04 Jun 1998-Nature
TL;DR: Simple models of networks that can be tuned through this middle ground: regular networks ‘rewired’ to introduce increasing amounts of disorder are explored, finding that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs.
Abstract: Networks of coupled dynamical systems have been used to model biological oscillators, Josephson junction arrays, excitable media, neural networks, spatial games, genetic control networks and many other self-organizing systems. Ordinarily, the connection topology is assumed to be either completely regular or completely random. But many biological, technological and social networks lie somewhere between these two extremes. Here we explore simple models of networks that can be tuned through this middle ground: regular networks 'rewired' to introduce increasing amounts of disorder. We find that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs. We call them 'small-world' networks, by analogy with the small-world phenomenon (popularly known as six degrees of separation. The neural network of the worm Caenorhabditis elegans, the power grid of the western United States, and the collaboration graph of film actors are shown to be small-world networks. Models of dynamical systems with small-world coupling display enhanced signal-propagation speed, computational power, and synchronizability. In particular, infectious diseases spread more easily in small-world networks than in regular lattices.

39,297 citations

Journal ArticleDOI
TL;DR: The major concepts and results recently achieved in the study of the structure and dynamics of complex networks are reviewed, and the relevant applications of these ideas in many different disciplines are summarized, ranging from nonlinear science to biology, from statistical mechanics to medicine and engineering.

9,441 citations

Journal ArticleDOI
01 Mar 1977
TL;DR: A family of new measures of point and graph centrality based on early intuitions of Bavelas (1948) is introduced in this paper, which define centrality in terms of the degree to which a point falls on the shortest path between others and there fore has a potential for control of communication.
Abstract: A family of new measures of point and graph centrality based on early intuitions of Bavelas (1948) is introduced. These measures define centrality in terms of the degree to which a point falls on the shortest path between others and there fore has a potential for control of communication. They may be used to index centrality in any large or small network of symmetrical relations, whether connected or unconnected.

8,026 citations

Journal ArticleDOI
TL;DR: In this paper, a critical review of particle-hopping models of vehicular traffic is presented, focusing on the results obtained mainly from the so-called "particle hopping" models, particularly emphasizing those formulated in recent years using the language of cellular automata.

2,211 citations

Journal ArticleDOI

2,136 citations