Ball milling of an equiatomic sigma--feV alloy in vacuum.

A coarse-grained tetragonal sigma phase Fe47.4V52.6 at% alloy was ground in vacuum in a vibratory mill. The sigma phase transforms into a bcc alpha phase. A concomitant partial amorphization of the bcc phase occurs. The near-equiatomic FeV alloys are concluded to behave in the same way as the related FeCr alloys when they are ball-milled in vacuum in similar milling conditions. In the stationary state of milling, about half of the iron atoms are contained in an amorphous phase both for sigma-FeCr and for sigma-FeV.

Superferromagnetism in mechanically alloyed fcc Fe(23)Cu(77) with bimodal cluster size distribution.

Magnetic measurements, x-ray diffraction and Mössbauer spectroscopy were used to characterize a nanostructured fcc Fe(23)Cu(77) at.% alloy prepared by high-energy ball-milling, addressing in particular the effect of clustering on the nature of the interacting magnetic entities. The interpretation of magnetization measurements leads to the conclusion that grains, whose mean size is ∼16 nm, contain two populations of magnetic Fe-rich nanoclusters with a bimodal size distribution. These two sets of clusters contain about 14 and 400 Fe atoms and have magnetic moments of 30 µ(B) and 860 µ(B), respectively. The inter-cluster ferromagnetic interactions that lead to superferromagnetism with a Curie temperature T(C)∼220 K can be described by a mean field determined by the smaller clusters only, which account for 90% of the magnetization.

1/falpha noise in the fluctuations of the spectra of tridiagonal random matrices from the beta-Hermite ensemble.

The 1/falpha noise displayed by the fluctuation of the n th unfolded eigenvalue, where n plays the role of a discrete time, was recently characterized for the classical Gaussian ensembles of NxN random matrices. It is investigated here for the beta-Hermite ensemble by wavelet analysis of Monte Carlo simulated series both as a function of beta and of N. When beta decreases from 1 to 0, for a given and large enough N, the evolution from a 1/f noise at beta=1 Gaussian orthogonal ensemble (GOE) to a 1/f2 noise at beta=0 Gaussian diagonal ensemble (GDE) is heterogeneous with a approximately 1/f2 noise at the finest scales and an approximately 1/f noise at the coarsest ones.

Distribution of the determinant of a random real-symmetric matrix from the gaussian orthogonal ensemble

The Mellin transform of the probability density of the determinant of NxN random real-symmetric matrices from the Gaussian orthogonal ensemble is calculated. The determinant probability density is given by a single Meijer G function for odd N. The distribution of the potential at the origin, within the Coulomb gas interpretation, is investigated from the Mellin transform of the determinant distribution and is shown to be asymptotically Gaussian.

Some consequences of exchangeability in random-matrix theory.

Properties of infinite sequences of exchangeable random variables result directly in explicit expressions for calculating asymptotic densities of eigenvalues rho(infinity)(lambda) of any ensemble of random matrices H whose distribution depends only on tr(H+H), where H+ is the Hermitian conjugate of H. For real symmetric matrices and for Hermitian matrices, the densities rho(infinity)(lambda) are constructed by summing up Wigner semicircles with varying radii and weights as confirmed by Monte Carlo simulations. Extensions to more general matrix ensembles are also considered.