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

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.

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

Testing Composite Null Hypothesis Based on SS-Divergences

We present a robust test for composite null hypothesis based on the general $S$-divergence family. This requires a non-trivial extension of the results of Ghosh et al.~(2015). We derive the asymptotic and theoretical robustness properties of the resulting test along with the properties of the minimum $S$-divergence estimators under parameter restrictions imposed by the null hypothesis. An illustration in the context of the normal model is also presented.Comment: 13 page