Amplification of large-scale magnetic field in nonhelical magnetohydrodynamics

It is typically assumed that the kinetic and magnetic helicities play a crucial role in the growth of large-scale dynamo. In this paper we demonstrate that helicity is not essential for the amplification of large-scale magnetic field. For this purpose, we perform nonhelical magnetohydrodynamic (MHD) simulation, and show that the large-scale magnetic field can grow in nonhelical MHD when random external forcing is employed at scale $1/10$ the box size. The energy fluxes and shell-to-shell transfer rates computed using the numerical data show that the large-scale magnetic energy grows due to the energy transfers from the velocity field at the forcing scales.Comment: 8 pages, 13 figure

Estimation of a Two-component Mixture Model with Applications to Multiple Testing

We consider a two-component mixture model with one known component. We develop methods for estimating the mixing proportion and the unknown distribution nonparametrically, given i.i.d.~data from the mixture model, using ideas from shape restricted function estimation. We establish the consistency of our estimators. We find the rate of convergence and asymptotic limit of the estimator for the mixing proportion. Completely automated distribution-free honest finite sample lower confidence bounds are developed for the mixing proportion. Connection to the problem of multiple testing is discussed. The identifiability of the model, and the estimation of the density of the unknown distribution are also addressed. We compare the proposed estimators, which are easily implementable, with some of the existing procedures through simulation studies and analyse two data sets, one arising from an application in astronomy and the other from a microarray experiment.Comment: 42 pages, 8 figures, 6 table