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.

Asymptotic Properties of Minimum S-Divergence Estimator for Discrete Models

Robust inference based on the minimization of statistical divergences has proved to be a useful alternative to the classical techniques based on maximum likelihood and related methods. Recently Ghosh et al. (2013) proposed a general class of divergence measures, namely the S-Divergence Family and discussed its usefulness in robust parametric estimation through some numerical illustrations. In this present paper, we develop the asymptotic properties of the proposed minimum S-Divergence estimators under discrete models.Comment: Under review, 24 page

Higher Efficiency In Prediction Of TIBO Activity By Evolutionary Neural Network

The treatment of acquired immunodeficiency syndrome (AIDS) is a challenging medical problem. TIBO is a nonnucleoside reverse transcriptase inhibitor, which binds non-competitively to the hydrophobic pocket on the p66 subunit of RT enzyme. We used a dataset consisting of physicochemical properties and reverse transcriptase inhibitor activities of 88 set of 4,5,6,7-tetrahydro-y-imidazo-[4,5,1-jk][1,4]-x-benzodiazepin-2-(1h)one derivatives that are variously substituted by halogens, alkyl groups. The dataset was taken from the BIOBYTE database at (www.davidhoekman.com). The concentration of the compound leading to 50% effect has been measured and expressed as IC50. The logarithm of the inverse of this parameter has been used as biological end points (log 1/C) in the QSAR studies. The evolutionary neural network (ENN) is a new system for modeling multivariate data. The strengths of ENN’s are that they can extract insignificant predictors, choose the size of the hidden layers and nodes and fine tune the parameters needed in training the network. We have used an ENN to predict the biological activities of Reverse Transcriptase Inhibitors. We have found out that Evolutionary Neural networks are better predictor of activity values than Multiple linear regression and Multilayered Perceptrons. We have calculated the correlation coefficient of each of the methods where we have found ENNs are the best

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