On the nature of nonequilibrium phase transition in a complex system.

The transition from a chaotic to a periodic oscillatory state can be smooth or abrupt in real-world complex systems. We study smooth and abrupt transitions in a turbulent reactive flow system. The turbulent reactive flow system consists of the flame, the acoustic field, and the hydrodynamic field interacting nonlinearly. Generally, as the Reynolds number is increased, a laminar flow becomes turbulent, and the range of time scales associated with the flow broadens. Yet, as the Reynolds number is increased in a turbulent reactive flow system, a single dominant time scale emerges in the acoustic pressure oscillations. By varying the Reynolds number at different rates, we observe smooth and abrupt transitions from chaos to order. For such smooth and abrupt transitions, we study the evolution of correlated (conformists and contrarians) and uncorrelated (disordered) dynamics between the acoustic pressure and the heat release rate oscillations in the spatiotemporal domain of the turbulent reactive flow system. We discover that the spatial extent of the disordered dynamics plays a critical role in deciding the abruptness of the transition. During the smooth transition, we observe a significant presence of disordered dynamics in the spatial domain. In contrast, abrupt transitions are accompanied by the abrupt disappearance of disordered dynamics from the spatial domain.