Decaying magnetohydrodynamics: effects of initial conditions

We study the effects of homogenous and isotropic initial conditions on decaying Magnetohydrodynamics (MHD). We show that for an initial distribution of velocity and magnetic field fluctuations, appropriately defined structure functions decay as power law in time. We also show that for a suitable choice of initial cross-correlations between velocity and magnetic fields even order structure functions acquire anomalous scaling in time where as scaling exponents of the odd order structure functions remain unchanged. We discuss our results in the context of fully developed MHD turbulence.Comment: To appear in Phys. Rev.

Dynamo mechanism: Effects of correlations and viscosities

We analyze the effects of the background velocity and the initial magnetic field correlations, and viscosities on the turbulent dynamo and the \alpha-effect. We calculate the \alpha-coefficients for arbitrary magnetic and fluid viscosities, background velocity and the initial magnetic field correlations. We explicitly demonstrate that the general features of the initial growth and late-time saturation of the magnetic fields due to the non-linear feedback are qualitatively independent of these correlations. We also examine the hydrodynamic limit of the magnetic field growth in a renormalization group framework and discuss the possibilities of suppression of the dynamo growth below a critical rotation. We demonstrate that for Kolmogorov- (K41) type of spectra the Ekman number M >1/2 for dynamo growth to occur.Comment: To appear in EPJB (2004

The Minimum S-Divergence Estimator under Continuous Models: The Basu-Lindsay Approach

Robust inference based on the minimization of statistical divergences has proved to be a useful alternative to the classical maximum likelihood based techniques. Recently Ghosh et al. (2013) proposed a general class of divergence measures for robust statistical inference, named the S-Divergence Family. Ghosh (2014) discussed its asymptotic properties for the discrete model of densities. In the present paper, we develop the asymptotic properties of the proposed minimum S-Divergence estimators under continuous models. Here we use the Basu-Lindsay approach (1994) of smoothing the model densities that, unlike previous approaches, avoids much of the complications of the kernel bandwidth selection. Illustrations are presented to support the performance of the resulting estimators both in terms of efficiency and robustness through extensive simulation studies and real data examples.Comment: Pre-Print, 34 page

Robust Bounded Influence Tests for Independent Non-Homogeneous Observations

Experiments often yield non-identically distributed data for statistical analysis. Tests of hypothesis under such set-ups are generally performed using the likelihood ratio test, which is non-robust with respect to outliers and model misspecification. In this paper, we consider the set-up of non-identically but independently distributed observations and develop a general class of test statistics for testing parametric hypothesis based on the density power divergence. The proposed tests have bounded influence functions, are highly robust with respect to data contamination, have high power against contiguous alternatives, and are consistent at any fixed alternative. The methodology is illustrated by the simple and generalized linear regression models with fixed covariates.Comment: To appear in Statistica Sinica (2017