Ashok Kumar Mittal

Prediction Rules for Regime Changes and Length in a New Regime for the Lorenz Model

Abstract Despite the widespread use of the Lorenz model as a conceptual model for predictability studies in meteorology, only Evans et al. seem to have studied the prediction of occurrence of regime changes and their duration. In this paper, simpler rules are presented for forecasting regime changes and their lengths, with near-perfect forecasting accuracy. It is found that when |x(t)| is greater than a critical value xc, the current regime will end after it completes the current orbit. Moreover, the length n of the new regime increases monotonically with the maximum value xm of |x(t)| in the previous regime. A best-fit cubic expression provides a very good estimate of n for the next regime, given xm for the previous regime. Similar forecasting rules are also obtained for regime changes in the forced Lorenz model. This model was introduced by Palmer and used as a conceptual model to explore the effects of sea surface temperature on seasonal mean rainfall. It was found that for the forced Lorenz model, the...

An empirical rule for extended range prediction of duration of Indian summer monsoon breaks

Prediction of the duration of the Indian summer monsoon breaks is highly desirable. It will help in planning water resource management, sowing and harvesting. Applicability of the recently discovered regime transition rules for the Lorenz model in predicting the duration of monsoon breaks, is explored in this paper. Using several indices of the observed summer monsoon intraseasonal oscillation (ISO), it is shown that the peak anomaly in an active regime can be used as a predictor for the duration of the subsequent break spell. It is also found that the average growth rate around the threshold to an active condition can be used as a predictor of the peak anomaly in the active spell. Average growth around the threshold to an active condition can give useful prediction of the duration of the following break, on an average, about 23 days (38 days) in advance of its commencement (end).

Fractal and multifractal characteristics of swift heavy ion induced self-affine nanostructured BaF2 thin film surfaces.

Fractal and multifractal characteristics of self-affine surfaces of BaF2 thin films, deposited on crystalline Si ⟨1 1 1⟩ substrate at room temperature, were studied. Self-affine surfaces were prepared by irradiation of 120 MeV Ag(9+) ions which modified the surface morphology at nanometer scale. The surface morphology of virgin thin film and those irradiated with different ion fluences are characterized by atomic force microscopy technique. The surface roughness (interface width) shows monotonic decrease with ion fluences, while the other parameters, such as lateral correlation length, roughness exponent, and fractal dimension, did not show either monotonic decrease or increase in nature. The self-affine nature of the films is further confirmed by autocorrelation function. The power spectral density of thin films surfaces exhibits inverse power law variation with spatial frequency, suggesting the existence of fractal component in surface morphology. The multifractal detrended fluctuation analysis based on the partition function approach is also performed on virgin and irradiated thin films. It is found that the partition function exhibits the power law behavior with the segment size. Moreover, it is also seen that the scaling exponents vary nonlinearly with the moment, thereby exhibiting the multifractal nature.

THE DOUBLE-CUSP MAP FOR THE FORCED LORENZ SYSTEM

It is found that adding constant forcing terms to the Lorenz equations breaks the (x,y)→(-x,-y) symmetry of the system. As a result of the symmetry breaking the consecutive zmax return map (the cusp map) gets split into a double-cusp map. We investigate the double-cusp map for the forced Lorenz system using approximate invariant manifolds about the fixed points and use the double-cusp map to understand the stability of the attractor.

Fractal characterization and wettability of ion treated silicon surfaces

Fractal characterization of surface morphology can be useful as a tool for tailoring the wetting properties of solid surfaces. In this work, rippled surfaces of Si (100) are grown using 200 keV Ar+ ion beam irradiation at different ion doses. Relationship between fractal and wetting properties of these surfaces are explored. The height-height correlation function extracted from atomic force microscopic images, demonstrates an increase in roughness exponent with an increase in ion doses. A steep variation in contact angle values is found for low fractal dimensions. Roughness exponent and fractal dimensions are found correlated with the static water contact angle measurement. It is observed that after a crossover of the roughness exponent, the surface morphology has a rippled structure. Larger values of interface width indicate the larger ripples on the surface. The contact angle of water drops on such surfaces is observed to be lowest. Autocorrelation function is used for the measurement of ripple wavelength.

COMPARISON OF GENERALIZED COMPETITIVE MODES AND RETURN MAPS FOR CHARACTERIZING DIFFERENT TYPES OF CHAOTIC ATTRACTORS IN CHEN SYSTEM

The Chen system of equations exhibits Lorenz, Transition, Chen and Transverse 8 type of chaotic attractors depending on the system parameters. Some authors have proposed a generalized competitive mode (GCM) technique to explain the topological difference between the Lorenz attractor and the Chen attractor. In this paper, we show a range of parameter values for which the nature of the topological attractor for the Chen system is not in accordance with that expected from GCM analysis. Instead, we find that return maps can be used to characterize the transition between different types of attractors more reliably.

Effect of averaging timescale on a forced lorenz model

Abstract The effect of temporal averaging on the forced Lorenz model is studied. It is shown that the duration of temporal averaging affects the regime structure. When temporal averaging is increased beyond the fast timescale of the Lorenz model, regime splitting takes place. The increase in the predictability of the system with an increase in moving time average steps is quantified. Our findings from a conceptual forced Lorenz model are consistent with real world observations.

Characterizing atmospheric surface layer turbulence using chaotic return map analysis

Nonlinear time series analysis methods are used to investigate the dynamics of mechanical and convective turbulences in the atmospheric surface layer flow. Using dynamical invariant analysis (e.g. correlation dimension, Lyapunov exponent and mutual information) along with recurrence quantification analysis (e.g. recurrent rate, determinism, average diagonal length of recurrence plot, etc.) of the vertical wind component data, it is confirmed that a convective turbulence is a lower order manifold in its phase space exhibiting higher degree of organization than a mechanical turbulence. Applying a quasi-one-dimensional chaotic return map technique, the topological differences between the mechanical and convective turbulences are explored. These quasi-one-dimensional return maps are produced using the local maxima of the first principal component of the reconstructed turbulence data. A comparison of the probability distribution of the local maxima of a forced Lorenz model with the turbulence data indicates the possible existence of a stable fixed point for both type of turbulences. Furthermore, dynamically the mechanical turbulence is found to resemble an unforced Lorenz model whereas the convective turbulence resembles a forced Lorenz model.

Short-term predictions by statistical methods in regions of varying dynamical error growth in a chaotic system

In a nonlinear, chaotic dynamical system, there are typically regions in which an infinitesimal error grows and regions in which it decays. If the observer does not know the evolution law, recourse is taken to non-dynamical methods, which use the past values of the observables to fit an approximate evolution law. This fitting can be local, based on past values in the neighborhood of the present value as in the case of Farmer–Sidorowich (FS) technique, or it can be global, based on all past values, as in the case of Artificial Neural Networks (ANN). Short-term predictions are then made using the approximate local or global mapping so obtained. In this study, the dependence of statistical prediction errors on dynamical error growth rates is explored using the Lorenz-63 model. The regions of dynamical error growth and error decay are identified by the bred vector growth rates or by the eigenvalues of the symmetric Jacobian matrix. The prediction errors by the FS and ANN techniques in these two regions are compared. It is found that the prediction errors by statistical methods do not depend on the dynamical error growth rate. This suggests that errors using statistical methods are independent of the dynamical situation and the statistical methods may be potentially advantageous over dynamical methods in regions of low dynamical predictability.

Role of parameter adaptation in chaotic communication

A chaos shift keying (CSK) scheme for secure communication of binary messages is proposed, in which two identical hyper-chaotic systems are synchronised in a time less than the time scale of their chaotic oscillations using complete replacement, feedback control and parameter adaptation. It is shown that this scheme is more secure compared to other similar schemes because coding parameter of the transmitting system changes so rapidly that an intruder cannot infer any information about the attractors corresponding to the two coding parameters. An extended scheme of secure communication based on arbitrary chaotic systems is also presented. This gives the sender a handle for making changes at the transmitting end without having to convey this information to the receiver, thereby significantly enhancing the security. Salient features of standard cryptology are presented and the cryptological aspects of the proposed chaotic communication scheme are analysed.