Is a hyperchaotic attractor superposition of two multifractals?

In the context of chaotic dynamical systems with exponential divergence of nearby trajectories in phase space, hyperchaos is defined as a state where there is divergence or stretching in at least two directions during the evolution of the system. Hence the detection and characterization of a hyperchaotic attractor is usually done using the spectrum of Lyapunov Exponents (LEs) that measure this rate of divergence along each direction. Though hyperchaos arise in different dynamical situations and find several practical applications, a proper understanding of the geometric structure of a hyperchaotic attractor still remains an unsolved problem. In this paper, we present strong numerical evidence to suggest that the geometric structure of a hyperchaotic attractor can be characterized using a multifractal spectrum with two superimposed components. In other words, apart from developing an extra positive LE, there is also a structural change as a chaotic attractor makes a transition to the hyperchaotic phase and the attractor changes from a simple multifractal to a dual multifractal, equivalent to two inter-mingled multifractals. We argue that a cross-over behavior in the scaling region for computing the correlation dimension is a manifestation of such a structure. In order to support this claim, we present an illustrative example of a synthetically generated set of points in the unit interval (a Cantor set with a variable iteration scheme) displaying dual multifractal spectrum. Our results are also used to develop a general scheme to generate both hyperchaotic as well as high dimensional chaotic attractors by coupling two low dimensional chaotic attractors and tuning a time scale parameter.Comment: 21 pages, 9 figures, To appear in Chaos Solitons & Fractal

Nonlinear time series anaysis of the light curves from the black hole system GRS1915+105

GRS 1915+105 is a prominent black hole system exhibiting variability over a wide range of time scales and its observed light curves have been classified into 12 temporal states. Here we undertake a complete analysis of these light curves from all the states using various quantifiers from nonlinear time series analysis, such as, the correlation dimension (D_2), the correlation entropy (K_2), singular value decomposition (SVD) and the multifractal spectrum ($f(\alpha)$ spectrum). An important aspect of our analysis is that, for estimating these quantifiers, we use algorithmic schemes which we have proposed recently and tested successfully on synthetic as well as practical time series from various fields. Though the schemes are based on the conventional delay embedding technique, they are automated so that the above quantitative measures can be computed using conditions prescribed by the algorithm and without any intermediate subjective analysis. We show that nearly half of the 12 temporal states exhibit deviation from randomness and their complex temporal behavior could be approximated by a few (3 or 4) coupled ordinary nonlinear differential equations. These results could be important for a better understanding of the processes that generate the light curves and hence for modelling the temporal behavior of such complex systems. To our knowledge, this is the first complete analysis of an astrophysical object (let alone a black hole system) using various techniques from nonlinear dynamics.Comment: Accepted for publication in RA

Computing the multifractal spectrum from time series: An algorithmic approach

We show that the existing methods for computing the f(\alpha) spectrum from a time series can be improved by using a new algorithmic scheme. The scheme relies on the basic idea that the smooth convex profile of a typical f(\alpha) spectrum can be fitted with an analytic function involving a set of four independent parameters. While the standard existing schemes [16, 18] generally compute only an incomplete f(\alpha) spectrum (usually the top portion), we show that this can be overcome by an algorithmic approach which is automated to compute the Dq and f(\alpha) spectrum from a time series for any embedding dimension. The scheme is first tested with the logistic attractor with known f(\alpha) curve and subsequently applied to higher dimensional cases. We also show that the scheme can be effectively adapted for analysing practcal time series involving noise, with examples from two widely different real world systems. Moreover, some preliminary results indicating that the set of four independant parameters may be used as diagnostic measures is also included.Comment: 10 pages, 16 figures, submitted to CHAO

Large Magnetoresistance and Jahn Teller effect in Sr2_2FeCoO6_6

Neutron diffraction measurement on the spin glass double perovskite Sr$_2$FeCoO$_6$ reveals site disorder as well as Co$^{3+}$ intermediate spin state. In addition, multiple valence states of Fe and Co are confirmed through M\"{o}ssbauer and X-ray photoelectron spectroscopy. The structural disorder and multiple valence lead to competing ferromagnetic and antiferromagnetic interactions and subsequently to a spin glass state, which is reflected in the form of an additional $T$-linear contribution at low temperatures in specific heat. A clear evidence of Jahn-Teller distortion at the Co$^{3+}$-O$_6$ complex is observed and incorporating the physics of Jahn-Teller effect, the presence of localized magnetic moment is shown. A large, negative and anomalous magnetoresistance of $\approx$ 63% at 14K in 12T applied field is observed for Sr$_2$FeCoO$_6$. The observed magnetoresistance could be explained by applying a semi-empirical fit consisting of a negative and a positive contribution and show that the negative magnetoresistance is due to spin scattering of carriers by localized magnetic moments in the spin glass phase

Streamer evolution arrest governed amplified AC breakdown strength of graphene and CNT colloids

The present article experimentally explores the concept of large improving the AC dielectric breakdown strength of insulating mineral oils by the addition of trace amounts of graphene or CNTs to form stable dispersions. The nano-oils infused with these nanostructures of high electronic conductance indicate superior AC dielectric behaviour in terms of augmented breakdown strength compared to the base oils. Experimental observations of two grades of synthesized graphene and CNT nano-oils show that the nanomaterials not only improve the average breakdown voltage but also significantly improve the reliability and survival probabilities of the oils under AC high voltage stressing. Improvement of the tune of ~ 70-80 % in the AC breakdown voltage of the oils has been obtained via the present concept. The present study examines the reliability of such nano-colloids with the help of two parameter Weibull distribution and the oils show greatly augmented electric field bearing capacity at both standard survival probability values of 5 % and 63.3 %. The fundamental mechanism responsible for such observed outcomes is reasoned to be delayed streamer development and reduced streamer growth rates due to effective electron scavenging by the nanostructures from the ionized liquid insulator. A mathematical model based on the principles of electron scavenging is proposed to quantify the amount of electrons scavenged by the nanostructures. The same is then employed to predict the enhanced AC breakdown voltage and the experimental values are found to match well with the model predictions. The present study can have strong implications in efficient, reliable and safer operation of real life AC power systems