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

Explosive synchronization in a turbulent reactive flow system

The occurrence of abrupt dynamical transitions in the macroscopic state of a system has received growing attention. We present experimental evidence for abrupt transition via explosive synchronization in a real-world complex system, namely, a turbulent reactive flow system. In contrast to the paradigmatic continuous transition to a synchronized state from an initially desynchronized state, the system exhibits a discontinuous synchronization transition with a hysteresis. We consider the fluctuating heat release rate from the turbulent flames at each spatial location as locally coupled oscillators that are coupled to the global acoustic field in the confined system. We analyze the synchronization between these two subsystems during the transition to a state of oscillatory instability and discover that explosive synchronization occurs at the onset of oscillatory instability. Further, we explore the underlying mechanism of interaction between the subsystems and construct a mathematical model of the same.

Synchronization modes of triple flickering buoyant diffusion flames: Experimental identification and model interpretation

The synchronization modes of a nonlinear oscillator system consisting of three identical flickering buoyant diffusion flames in isosceles triangles were studied experimentally and theoretically. Five synchronization modes, such as the in-phase, flickering death, partially flickering death, partially in-phase, and rotation modes, were experimentally observed and identified by systematically adjusting the flame distance and fuel flow rates. Two toy models were adopted to interpret the experimentally identified dynamical modes: one is the classical Kuramoto model, and the other is a complexified Stuart-Landau model, which was proposed through the introduction of the complex coupling term. The theoretical results show that the Kuramoto model successfully interpreted the dynamical modes except for those associated with amplitude death, and the complexified Stuart-Landau model well interpreted all the dynamical modes identified in our experiment. Remarkably, the proposed complexified Stuart-Landau model breaks a new path in the investigation of globally coupled nonlinear dynamical systems with identical oscillators, especially for the study of amplitude death mode.

Mathematical modeling for the synchronization of two interacting active rotors

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.

Tea-derived carbon dots with two ratiometric fluorescence channels for the independent detection of Hg2+ and H2O

Ratiometric fluorescence carbon dots (CDs) that serve as probes have attracted more attention on account of their unique optical properties, low toxicity, anti-interference, and internal reference. However, the facile fabrication of CDs with the aim of detecting multiple targets through mutually independent response channels is always a challenge. Herein, multifunctional label-free N-doped ratiometric fluorescence CDs (N-CDs) are developed from tea leaves extract and o-phenylenediamine by a mild solvothermal method. The prepared N-CDs are tailored with nitrogen- and oxygen-containing functional groups on the surface and contribute to splendid hydrophilia. Two completely independent ratiometric fluorescence channels of N-CDs, respectively, respond to Hg²⁺ and H₂O in a mutually independent manner. Based on the interactions of N-Hg and O-Hg, N-CDs achieve an excellently sensitive and selective detection for Hg²⁺ in the channel of I_{387 nm}/I_{351 nm}, giving a linear relationship in the range of 0-50 μM. Also, a wide range of Hg²⁺ concentration (0-100 μM) is linear to A_{374 nm} through UV-vis assay. Otherwise, the linear determination of H₂O content (0-30%) is realized in another channel (I_green/I_blue). The good performance in the independent testing of Hg²⁺ and H₂O, demonstrate that the proposed N-CDs have potential in multifunctional detection.

Phase switching phenomenon in a system of three coupled DC glow discharge plasmas

We report the first experimental observations of phase switching in a system of three coupled plasma sources. Two of the plasma sources are inductively coupled to each other while the third one is directly coupled to one of them. The coupled system acquires a frequency pulling synchronized state following which a transition occurs to a frequency entrainment state with an increase in the frequency of the directly coupled system. We also observe a sudden jump from a lower to a higher frequency entrainment state and a concomitant phase switching between the oscillations of the two directly coupled sources while the phase difference between the inductively coupled sources remains constant. These experimental findings are established using various diagnostic tools, such as the Fourier spectra, frequency bifurcation plots, Lissajous plots, and Hilbert transforms of the data. The experimental results are qualitatively modeled using three coupled van der Pol equations, in which two of them are environmentally coupled while the third one is directly coupled with one of them.

Occasional coupling enhances amplitude death in delay-coupled oscillators

This paper aims to study amplitude death in time delay coupled oscillators using the occasional coupling scheme that implies intermittent interaction among the oscillators. An enhancement of amplitude death regions (i.e., an increment of the width of the amplitude death regions along the control parameter axis) can be possible using the occasional coupling in a pair of delay-coupled oscillators. Our study starts with coupled limit cycle oscillators (Stuart-Landau) and coupled chaotic oscillators (Rössler). We further examine coupled horizontal Rijke tubes, a prototypical model of thermoacoustic systems. Oscillatory states are highly detrimental to thermoacoustic systems such as combustors. Consequently, a state of amplitude death is always preferred. We employ the on-off coupling (i.e., a square wave function), as an occasional coupling scheme, to these coupled oscillators. On monotonically varying the coupling strength (as a control parameter), we observe an enhancement of amplitude death regions using the occasional coupling scheme compared to the continuous coupling scheme. In order to study the contribution of the occasional coupling scheme, we perform a detailed linear stability analysis and analytically explain this enhancement of the amplitude death region for coupled limit cycle oscillators. We also adopt the frequency ratio of the oscillators and the time delay between the oscillators as the control parameters. Intriguingly, we obtain a similar enhancement of the amplitude death regions using the frequency ratio and time delay as the control parameters in the presence of the occasional coupling. Finally, we use a half-wave rectified sinusoidal wave function (motivated by practical reality) to introduce the occasional coupling in time delay coupled oscillators and get similar results.

Dynamical states and bifurcations in coupled thermoacoustic oscillators

The emergence of rich dynamical phenomena in coupled self-sustained oscillators, primarily synchronization and amplitude death, has attracted considerable interest in several fields of science and engineering. Here, we present a comprehensive theoretical study on the manifestation of these exquisite phenomena in a reduced-order model of two coupled Rijke tube oscillators, which are prototypical thermoacoustic oscillators. We characterize the dynamical behaviors of two such identical and non-identical oscillators by varying both system parameters (such as the uncoupled amplitudes and the natural frequencies of the oscillators) and coupling parameters (such as the coupling strength and the coupling delay). The present model captures all the dynamical phenomena-namely, synchronization, phase-flip bifurcation, amplitude death, and partial amplitude death-observed previously in experiments on coupled Rijke tubes. By performing numerical simulations and deriving approximate analytical solutions, we systematically decipher the conditions and the bifurcations underlying the aforementioned phenomena. The insights provided by this study can be used to understand the interactions between multiple cans in gas turbine combustors and develop control strategies to avert undesirable thermoacoustic oscillations in them.

Rijke tube: A nonlinear oscillator

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.

Unravelling the highly efficient synthesis of individual carbon nanodots from casein micelles and the origin of their competitive constant-blue-red wavelength shift luminescence mechanism for versatile applications

Synthesis of casein-derived carbon nanodots (CND) using a microwave-assisted approach, giving a high product yield (25%), is reported. Casein was used as a sustainable carbon source, and polyvinylpyrrolidone was used as a stabilizer for the nanodots. The size of the prepared amorphous CND corresponds to individual casein coils, which were only partially carbonized. They were obtained due to the disintegration of casein micelles and submicelles within the microwave-assisted solvothermal process. The resulting nanodots had bright photoluminescence, and their electronic structure and optical properties were investigated. A novel competitive model of their luminescence mechanism was introduced to explain a phenomenon beyond the standard models. The synthesized carbon nanodots were used as luminescent ink for anticounterfeit applications. A polymer matrix nanocomposite was prepared by dispersing the nanodots in a flexible and robust poly(styrene-ethylene-butylene-styrene) tri-block copolymer (SEBS) using the solution cast method. For the first time, the effect of CND on the luminescence and mechanical properties of the SEBS/CND self-supporting films was studied. The film was also studied as a phosphor for light-emitting diodes, with a unique experimental setup to avoid self-absorption, which results in low efficiency and eliminates the excess UV transmitted. Because of their high luminescence, photostability, and mechanical properties, these CND could be used as luminescent labels in the packaging and optoelectronics industries.

Synthesis of individual casein based CND with a discrete luminescence mechanism.

Bifurcation structure of the flame oscillation

A flame exhibits a limit-cycle oscillation, which is called "flame flickering" or "puffing," in a certain condition. We investigated the bifurcation structure of the flame oscillation in both simulation and experiment. We performed a two-dimensional hydrodynamic simulation by employing the flame sheet model. We reproduced the flame oscillation and investigated the parameter dependencies of the amplitude and frequency on the fuel-inlet diameter. We also constructed an experimental system, in which we could finely vary the fuel-inlet diameter, and we investigated the diameter-dependencies of the amplitude and frequency. In our simulation, we observed the hysteresis and bistability of the stationary and oscillatory states. In our experiments, we observed the switching between the stationary and oscillatory states. As fluctuations can induce the switching in the bistable system, switching observed in our experiments suggested the bistability of the two states. Therefore, we concluded that the oscillatory state appeared from the stationary state through the subcritical Andronov-Hopf bifurcation in both the simulation and experiment. The amplitude was increased and the frequency was decreased as the fuel-inlet diameter was increased. In addition, we visualized the vortex structure in our simulation and discussed the effect of the vortex on the flame dynamics.

Steady-state statistics, emergent patterns and intermittent energy transfer in a ring of oscillators

Networks of coupled nonlinear oscillators model a broad class of physical, chemical and biological systems. Understanding emergent patterns in such networks is an ongoing effort with profound implications for different fields. In this work, we analytically and numerically study a symmetric ring of N coupled self-oscillators of van der Pol type under external stochastic forcing. The system is proposed as a model of the thermo- and aeroacoustic interactions of sound fields in rigid enclosures with compact source regions in a can-annular combustor. The oscillators are connected via linear resistive coupling with nonlinear saturation. After transforming the system to amplitude-phase coordinates, deterministic and stochastic averaging is performed to eliminate the fast oscillating terms. By projecting the potential of the slow-flow dynamics onto the phase-locked quasi-limit cycle solutions, we obtain a compact, low-order description of the (de-)synchronization transition for an arbitrary number of oscillators. The stationary probability density function of the state variables is derived from the Fokker-Planck equation, studied for varying parameter values and compared to time series simulations. We leverage our analysis to offer explanations for the intermittent energy transfer between Bloch waves observed in acoustic pressure spectrograms observed of real-world gas turbines.

Effects of frequency mismatch on amplitude death in delay-coupled oscillators

The present paper analytically reveals the effects of frequency mismatch on the stability of an equilibrium point within a pair of Stuart-Landau oscillators coupled by a delay connection. By analyzing the roots of the characteristic function governing the stability, we find that there exist four types of boundary curves of stability in a coupling parameters space. These four types depend only on the frequency mismatch. The analytical results allow us to design coupling parameters and frequency mismatch such that the equilibrium point is locally stable. We show that, if we choose appropriate frequency mismatches and delay times, then it is possible to induce amplitude death with strong stability, even by weak coupling. In addition, we show that parts of these analytical results are valid for oscillator networks with complete bipartite topologies.

Effect of gravity on synchronization of two coupled buoyancy-induced turbulent flames

We study the effect of gravity on the synchronization of two coupled buoyancy-induced turbulent flames by recurrence-based analysis and machine learning. A significant change from nearly complete synchronization in the near field to partial synchronization appears in the far field under low gravity. The synchronized state is gradually lost with increasing gravity level. These results are clearly identified from cross recurrence plots and symbolic recurrence plots and by reservoir computing.

Experimental investigation on the susceptibility of minimal networks to a change in topology and number of oscillators

Understanding the global dynamical behavior of a network of coupled oscillators has been a topic of immense research in many fields of science and engineering. Various factors govern the resulting dynamical behavior of such networks, including the number of oscillators and their coupling schemes. Although these factors are seldom significant in large populations, a small change in them can drastically affect the global behavior in small populations. In this paper, we perform an experimental investigation on the effect of these factors on the coupled behavior of a minimal network of candle-flame oscillators. We observe that strongly coupled oscillators exhibit the global behavior of in-phase synchrony and amplitude death, irrespective of the number and the topology of oscillators. However, when they are weakly coupled, their global behavior exhibits the intermittent occurrence of multiple stable states in time. We report the experimental discovery of partial amplitude death in a network of candle-flame oscillators, in addition to the observation of other dynamical states including clustering, chimera, and weak chimera. We also show that closed-loop networks tend to hold global synchronization for longer duration as compared to open-loop networks.

Flickering candle flames and their collective behavior

Oscillation and collective behavior of diffusion flames is a fascinating phenomena. Considering candle bundles with different sizes in variable oxygen concentration, the flickering dynamics of the flames are experimentally and theoretically investigated. Trends for the flickering frequency as a function of the candle number in the bundle and oxygen concentration is revealed for various topologies of the candles packing. The collective behavior of the flames as a function of their separation distance is studied by measuring an appropriate synchronization order parameter and through the common oscillation frequency. In agreement with previous results we find a discontinuous phase transition between an in-phase synchronized state at small separation distance and a counter-phase synchronized state at larger separation distances. A previously used dynamical model is modified in order to accommodate our experimental findings.

Synchronization route to weak chimera in four candle-flame oscillators

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.

Oscillation quenching and phase-flip bifurcation in coupled thermoacoustic systems

Oscillatory instabilities, although ubiquitous in nature, are undesirable in many situations such as biological systems, swaying of bridges and skyscrapers, aero-acoustic flutter, prey-predator and disease spread models, and thermoacoustic systems, where they exhibit large amplitude periodic oscillations. In the present study, we aim to study the suppression mechanism of such undesired oscillations in a pair of thermoacoustic oscillators, also known as horizontal Rijke tubes. These oscillators are coupled through a connecting tube whose length and diameter are varied as coupling parameters. With the variation of these parameters, we show the first experimental evidence of rich dynamical phenomena such as synchronization, amplitude death, and phase-flip bifurcation in coupled identical thermoacoustic oscillators. We discover that when frequency and amplitude mismatch are introduced between these oscillators, quenching of oscillations in one or both the oscillators occurs with further ease, through the mechanisms of amplitude death and partial amplitude death. Finally, we show that the effectiveness of coupling is sensitive to the dimensions of the connecting tube which can be directly correlated with the time delay and coupling strength of the system.

Facile synthesis of graphene-tin oxide nanocomposite derived from agricultural waste for enhanced antibacterial activity against Pseudomonas aeruginosa

Antibacterial screening of graphene-tin oxide nanocomposites synthesized from carbonized wood and coconut shell is investigated against Pseudomonas aeruginosa for the first time. Efficient and facile one step hydrothermal process adopted in the present work for the synthesis of graphene-tin oxide nanoparticles provides an ideal method for the economic large-scale production of the same. Graphene-tin oxide nanocomposites derived from wood charcoal possess a spherical morphology whereas rod like structures are seen in the case of coconut shell derivatives. An excitation independent fluorescence response is observed in graphene-tin oxide nanohybrids while graphene oxide nanostructures exhibited an excitation dependent behavior. These hydrophilic nanostructures are highly stable and exhibited no sign of luminescence quenching or particle aggregation even after a storage of 30 months. Bactericidal effects of the nanostructures obtained from coconut shell is found to be relatively higher compared to those procured from wood. This variation in antibacterial performance of the samples is directly related to their morphological difference which in turn is heavily influenced by the precursor material used. MIC assay revealed that coconut shell derived graphene-tin oxide composite is able to inhibit the bacterial growth at a lower concentration (250 μg/mL) than the other nanostructures. Nanocomposites synthesized from agro-waste displayed significantly higher antimicrobial activity compared to the precursor and graphene oxide nanostructures thereby making them excellent candidates for various bactericidal applications such as disinfectants, sanitary agents etc.