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 timescale in the acoustic pressure fluctuations, as indicated by its loss of multifractality. Such emergence of order from chaos is intriguing.

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.

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

Real-world complex systems such as the earth's 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.

Tipping in complex systems under fast variations of parameters.

Abrupt changes in the state of a system are often undesirable in natural and human-made systems. Such transitions occurring due to fast variations of system parameters are called rate-induced tipping (R-tipping). While a quasi-steady or sufficiently slow variation of a parameter does not result in tipping, a continuous variation of the parameter at a rate greater than a critical rate results in tipping.

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 is accompanied by a power law leading to finite-time singularity. As a crucial discovery of the system dynamics approaching LBO, we unravel the existence of the discrete scale invariance (DSI).

Extreme COVID-19 waves reveal hyperexponential growth and finite-time singularity.

Coronavirus disease 2019 (COVID-19) has rapidly spread throughout our planet, bringing human lives to a standstill. Understanding the early transmission dynamics of a wave helps plan intervention strategies such as lockdowns that mitigate further spread, minimizing the adverse impact on humanity and the economy. Exponential growth of infections was thought to be the defining feature of an epidemic in its initial growth phase.

Convolutional neural networks to predict the onset of oscillatory instabilities in turbulent systems.

Many fluid dynamic systems exhibit undesirable oscillatory instabilities due to positive feedback between fluctuations in their different subsystems. Thermoacoustic instability, aeroacoustic instability, and aeroelastic instability are some examples. When the fluid flow in the system is turbulent, the approach to such oscillatory instabilities occurs through a universal route characterized by a dynamical regime known as intermittency.

Deep learning for early warning signals of tipping points.

Many natural systems exhibit tipping points where slowly changing environmental conditions spark a sudden shift to a new and sometimes very different state. As the tipping point is approached, the dynamics of complex and varied systems simplify down to a limited number of possible "normal forms" that determine qualitative aspects of the new state that lies beyond the tipping point, such as whether it will oscillate or be stable. In several of those forms, indicators like increasing lag-1 autocorrelation and variance provide generic early warning signals (EWS) of the tipping point by detecting how dynamics slow down near the transition.

Effect of rate of change of parameter on early warning signals for critical transitions.

Many dynamical systems exhibit abrupt transitions or tipping as the control parameter is varied. In scenarios where the parameter is varied continuously, the rate of change of the control parameter greatly affects the performance of early warning signals (EWS) for such critical transitions. We study the impact of variation of the control parameter with a finite rate on the performance of EWS for critical transitions in a thermoacoustic system (a horizontal Rijke tube) exhibiting subcritical Hopf bifurcation.

Universality in spectral condensation.

Self-organization is the spontaneous formation of spatial, temporal, or spatiotemporal patterns in complex systems far from equilibrium. During such self-organization, energy distributed in a broadband of frequencies gets condensed into a dominant mode, analogous to a condensation phenomenon. We call this phenomenon spectral condensation and study its occurrence in fluid mechanical, optical and electronic systems.

Recurrence analysis of slow-fast systems.

Many complex systems exhibit periodic oscillations comprising slow-fast timescales. In such slow-fast systems, the slow and fast timescales compete to determine the dynamics. In this study, we perform a recurrence analysis on simulated signals from paradigmatic model systems as well as signals obtained from experiments, each of which exhibit slow-fast oscillations.

Dynamical systems approach to study thermoacoustic transitions in a liquid rocket combustor.

Liquid rockets are prone to large amplitude oscillations, commonly referred to as thermoacoustic instability. This phenomenon causes unavoidable developmental setbacks and poses a stern challenge to accomplish the mission objectives. Thermoacoustic instability arises due to the nonlinear interaction between the acoustic and the reactive flow subsystems in the combustion chamber.