Articles written in Indian Academy of Sciences Conference Series
Volume 2 All articles Published: 16 September 2019 Article ID 0022 Special
The prediction of the critical point of a phase transition is a topic of great current interest, and is of utility in many practical contexts. Therefore, the identification of precursors, or early warning signals of the critical point, has become the focus of current interest. Recent model studies have shown that a series of small transitions, which have been called microtransitions, act as precursors to the percolation transition. Here, we identify the existence of microtransitions in two distinct networks, for two distinct processes. The first case is the process of avalanche transmission on branching hierarchical networks. Here, typical realizations of the original lattice of this network exhibit a second order transition.We note that microtransitions in the variance of the order parameter are seen in this case. Additionally, the positions of the microtransitions follow ascaling relation. The scaling relation can be used to calculate the position of the critical point, which is seen to be in agreement with the observed result.We also introduce this method of identifying the microtransitions occurring before the tipping point to a complex real world system, the climate system. We analyse the discontinuous first order phase transition occurring in the climate networks. We apply the percolation framework to these networks to analyse the structural changes in the network and construct an order parameter and a susceptibility. Microtransitions can be found in the behaviour of the susceptibility. These can be used to predict the tipping point in the system. We discuss possible applicationsof this.