Early warnings of tipping in a non-autonomous turbulent reactive flow system: efficacy, reliability, and warning times

Real-world complex systems such as the climate, ecosystems, stock markets, and combustion engines are prone to dynamical transitions from one state to another, with catastrophic consequences. State variables of such systems often exhibit aperiodic fluctuations, either chaotic or stochastic in nature. Often, the parameters describing a system vary with time, showing time dependency. Constrained by these effects, it becomes difficult to be warned of an impending critical transition, as such effects contaminate the precursory signals of the transition. Therefore, a need for efficient and reliable early-warning signals (EWS) in such complex systems is in pressing demand. Motivated by this fact, in the present work, we analyze various EWS in the context of a non-autonomous turbulent thermoacoustic system. In particular, we investigate the efficacy of different EWS in forecasting the onset of thermoacoustic instability (TAI) and their reliability with respect to the rate of change of the control parameter. We consider the Reynolds number (Re) as the control parameter, which is varied linearly with time at finite rates. The considered EWS are derived from critical slowing down, spectral properties, and fractal characteristics of the system variables. The state of TAI is associated with large amplitude acoustic pressure oscillations that could lead thermoacoustic systems to break down. Our analysis shows that irrespective of the rate of variation of the control parameter, the Hurst exponent and variance of autocorrelation coefficients warn of an impending transition well in advance and are more reliable than other EWS measures. We also investigate the variation of amplitudes of the most significant modes of acoustic pressure oscillations with the Hurst exponent. Such variations lead to scaling laws which could be significant in prediction and devising control actions to mitigate TAI

Imprints of log-periodicity in thermoacoustic systems close to lean blowout

In the context of statistical physics, critical phenomena are accompanied by power laws having a singularity at the critical point where a sudden change in the state of the system occurs. In this work, we show that lean blowout (LBO) in a turbulent thermoacoustic system can be viewed as a critical phenomenon. As a crucial discovery of the system dynamics approaching LBO, we unravel the existence of the discrete scale invariance (DSI). In this context, we identify the presence of log-periodic oscillations in the temporal evolution of the amplitude of dominant mode of low-frequency oscillations $(A_f)$ exist in pressure fluctuations preceding LBO. The presence of DSI indicates the recursive development of blowout. Additionally, we find that $A_f$ shows a faster than exponential growth and becomes singular when blowout occurs. We then present a model that depicts the evolution of $A_f$ based on log-periodic corrections to the power law associated with its growth. Using the model, we find that blowout can be predicted even several seconds earlier. The predicted time of LBO in good agreement with the actual time of occurrence of LBO obtained from the experiment.Comment: 15 pages, 10 figure

Abrupt transitions in turbulent thermoacoustic systems

Abrupt transitions to the state of thermoacoustic instability (TAI) in gas turbine combustors are a significant challenge plaguing the development of next-generation low-emission aircraft and power generation engines. In this paper, we present the observation of abrupt transition in three disparate turbulent thermoacoustic systems: an annular combustor, a swirl-stabilized combustor, and a preheated bluff-body stabilized combustor. Using a low-order stochastic thermoacoustic model, we show that the reported abrupt transitions occur when an initially stable, supercritical limit cycle becomes unstable, leading to a secondary bifurcation to a large amplitude limit cycle solution. The states of combustion noise and intermittency observed in these turbulent combustors are well captured by the additive stochastic noise in the model. Through amplitude reduction, we analyze the underlying potential functions affecting the stability of the observed dynamical states. Finally, we make use of the Fokker-Planck equation, educing the effect of stochastic fluctuations on subcritical and secondary bifurcation. We conclude that a high enough intensity of stochastic fluctuations which transforms a subcritical bifurcation into an intermittency-facilitated continuous transition may have little effect on the abrupt nature of secondary bifurcation. Our findings imply the high likelihood of abrupt transitions in turbulent combustors possessing higher-order nonlinearities where turbulence intensities are disproportionate to the large amplitude limit cycle solution

Emergence of order from chaos through a continuous phase transition in a turbulent reactive flow system

As the Reynolds number is increased, a laminar fluid flow becomes turbulent, and the range of time and length scales associated with the flow increases. Yet, in a turbulent reactive flow system, as we increase the Reynolds number, we observe the emergence of a single dominant time scale in the acoustic pressure fluctuations, as indicated by its loss of multifractality. Such emergence of order from chaos is intriguing and has hardly been studied. We perform experiments in a turbulent reactive flow system consisting of flame, acoustic, and hydrodynamic subsystems interacting nonlinearly. We study the evolution of short-time correlated dynamics between the acoustic field and the flame in the spatiotemporal domain of the system. The order parameter, defined as the fraction of the correlated dynamics, increases gradually from zero to one. We find that the susceptibility of the order parameter, correlation length, and correlation time diverge at a critical point between chaos and order. Our results show that the observed emergence of order from chaos is a continuous phase transition. Moreover, we provide experimental evidence that the critical exponents characterizing this transition fall in the universality class of directed percolation. Our study demonstrates how a real-world complex, non-equilibrium turbulent reactive flow system exhibits universal behavior near a critical point

Optimal state space reconstruction via Monte Carlo decision tree search

A novel idea for an optimal time delay state space reconstruction from uni- and multivariate time series is presented. The entire embedding process is considered as a game, in which each move corresponds to an embedding cycle and is subject to an evaluation through an objective function. This way the embedding procedure can be modeled as a tree, in which each leaf holds a specific value of the objective function. By using a Monte Carlo ansatz, the proposed algorithm populates the tree with many leafs by computing different possible embedding paths and the final embedding is chosen as that particular path, which ends at the leaf with the lowest achieved value of the objective function. The method aims to prevent getting stuck in a local minimum of the objective function and can be used in a modular way, enabling practitioners to choose a statistic for possible delays in each embedding cycle as well as a suitable objective function themselves. The proposed method guarantees the optimization of the chosen objective function over the parameter space of the delay embedding as long as the tree is sampled sufficiently. As a proof of concept, we demonstrate the superiority of the proposed method over the classical time delay embedding methods using a variety of application examples. We compare recurrence plot-based statistics inferred from reconstructions of a Lorenz-96 system and highlight an improved forecast accuracy for map-like model data as well as for palaeoclimate isotope time series. Finally, we utilize state space reconstruction for the detection of causality and its strength between observables of a gas turbine type thermoacoustic combustor

Effect of nurse culture on inducing division of isolated pollen protoplasts of Hevea brasiliensis

Haploids are of great relevance in crop improvement of Hevea, a highly heterozygous tree species with a long breeding cycle. The isolation and culture of pollen protoplasts may be a viable proposition for raising haploid plants/ homozygous lines in Hevea. The present work envisages the development of a method for the isolation and culture of pollen protoplasts of Hevea. Effect of different nurse cultures on the development of cultured protoplasts has been studied. Intact pollen grains were isolated from mature male flowers of Hevea prior to opening. Viable protoplasts in high yield could be isolated from these pollen grains when exposed to a mixture of 0.5 per cent cellulase and 0.05 per cent pectolyase in the presence of the osmotic stabilizers 0.6 M mannitol and 0.3 M sorbitol. These protoplasts were partially purified and cultured in the nutrient medium with three different nurse cultures namely embryogenic calli from Hevea, tobacco and carrot. Division of the cultured protoplasts leading to the formation of a few micro-colonies was observed in the medium containing 0.8 mg l-1 2, 4-D and 0.5 mg l-1 BA and enriched with Hevea nurse culture. Cultures with micro-colonies are dark incubated for further development. This is the first report of division of pollen protoplasts and micro-colony formation in Hevea brasiliensis

Indoor Positioning of Workers and Monitoring Climatology in Mines Using FM with RSSI

Location based services are becoming a most useful technology in our day-to-day life. Wide utilization of Global Positioning System (GPS) in devices like mobile phones combined with Wi-Fi and cellular networks have solved the problem of outdoor positioning or localization and emerged as a market trend. This, however, is the case only for outdoors. There are many areas, which require the knowledge of user position in indoors. Awareness of user’s location is important in such areas as smart environments, assisted daily living, behaviour analysis studies. The main objective of this thesis was A Dedicated RF Frequency Carrier with Modulated Signal is used for mapping the Movement of Object or Human being. The performance of indoor localization using FM transmitter and receivers are compared with Wi-Fi based indoor positioning which has significantly lower Frequency range when compared to FM

Spontaneous bilateral adrenal hemorrhage of pregnancy

Spontaneous adrenal hemorrhage of pregnancy is an acute hemorrhage into the adrenal gland in pregnancy in the absence of trauma, tumor or decoagulant therapy. This can have catastrophic consequences on the mother and the baby and if the hemorrhage involves both the adrenal glands the risk is aggravated because of the high incidence of resulting adrenal insufficiency. We report a case of spontaneous bilateral adrenal hemorrhage in pregnancy resulting in adrenal crisis. A 26 year old primigravida presented at 32 weeks of gestation initially with right sided infrascapular pain and one month later with similar pain in the left side associated with high blood pressure. Imaging with ultrasound and MRI was suggestive of bilateral adrenal mass probably hemorrhage; 2 days following the second episode of pain she developed drowsiness and hypotension and a diagnosis of primary adrenal insufficiency was confirmed by a low serum cortisol and high ACTH. She stabilized with hydrocortisone therapy and the fetus was closely monitored. At 37 weeks she had a normal vaginal delivery under steroid cover. Repeat MRI abdomen 3 months after delivery showed resolution of the hemorrhage but biochemically she continued to be cortisol insufficient at 1 year of follow up. Prompt diagnosis of adrenal hemorrhage in pregnancy and treatment of adrenal insufficiency along with close fetal monitoring usually results in good perinatal outcome in spontaneous adrenal hemorrhage of pregnancy

Universality in the emergence of oscillatory instabilities in turbulent flows

Spontaneous emergence of periodic oscillations due to self-organization is ubiquitous in turbulent flows. The emergence of such oscillatory instabilities in turbulent fluid mechanical systems is often studied in different system-specific frameworks. We uncover the existence of a universal scaling behaviour during self-organization in turbulent flows leading to oscillatory instability. Our experiments show that the spectral amplitude of the dominant mode of oscillations scales inversely with the Hurst exponent of a fluctuating state variable following an inverse power law relation. Interestingly, we observe the same power law behaviour with a constant exponent near -2 across various turbulent systems such as aeroacoustic, thermoacoustic and aeroelastic systems.Comment: 5 pages, 4 figures and supplementary informatio