In an effort to understand the fundamental physics of turbulent transport of particles and heat in a tokamak, the floating potential fluctuations in the the scrape-off layer plasma of ohmically heated ADITYA tokamak are analysed for self-similarity using distribution function approach. It is observed that the distribution function of a sum of n data points converges to a Lévy distribution of scale index, α = 1.111 for n ≤ 40 and α = 2.0 for larger n. In both scaling ranges, the edge fluctuation is self-similar. This observation is backed by several supporting evidences. The results indicate that the small scale fluctuations transport matter and heat dominantly by convection whereas the transport due to large scale fluctuations is by a diffusive process.

Ideas of state space reconstruction of dynamics are combined with nonparametric artificial neural network approach to model sunspot activity. The structural aspects of the model are for the most part determined from the sunspot data. The model gives a very good fit to the data. Further it predicts weaker solar activity in the current (23‐rd) cycle, with a maximum of 144±36.

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ABSTARCTA hybrid approach, incorporating concepts of nonlinear dynamics in artificial neural networks (ANN), is proposed to model time series generated by complex dynamic systems. We introduce well known features used in the study of dynamic systems -time delay τ and embedding dimension d -for ANN modelling of time series. These features provide a theoretical basis for selecting the optimal size for the number of neurons in the input layer. The main outcome of the new approach for such problems is that to a large extent it defines the ANN architecture and leads to better predictions. We illustrate our method by considering computer generated periodic and chaotic time series. The ANN model developed gave excellent quality of fit for the training and test sets as well as for iterative dynamic predictions for future values of the two time series. Further, computer experiments were conducted by introducing Gaussian noise of various degrees in the two time series, to simulate real world effects. We find rather surprising results that upto a limit introduction of noise leads to a smaller network with good generalizing capability.

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We estimate the initial conditions of a multivariable dynamical system from a scalar signal, using a modified Newton-Raphson method incorporating the time evolution. We can estimate initial conditions of periodic and chaotic systems and the required length of scalar signal is very small. We also find that the information flow from one variable to the other has logarithmic dependence on time. An important application of the method is in secure communications. The communication procedure has several advantages as compared to others using dynamical systems.