On the Capacity Achieving Covariance Matrix for Frequency Selective MIMO Channels Using the Asymptotic Approach

In this contribution, an algorithm for evaluating the capacity-achieving input covariance matrices for frequency selective Rayleigh MIMO channels is proposed. In contrast with the flat fading Rayleigh cases, no closed-form expressions for the eigenvectors of the optimum input covariance matrix are available. Classically, both the eigenvectors and eigenvalues are computed numerically and the corresponding optimization algorithms remain computationally very demanding. In this paper, it is proposed to optimize (w.r.t. the input covariance matrix) a large system approximation of the average mutual information derived by Moustakas and Simon. An algorithm based on an iterative water filling scheme is proposed, and its convergence is studied. Numerical simulation results show that, even for a moderate number of transmit and receive antennas, the new approach provides the same results as direct maximization approaches of the average mutual information.Comment: presented at ISIT 2010 Conference, Austin, Texas, June 13-18, 2010 (5 pages, 1 figure, 2 tables

Second-order hyperbolic Fuchsian systems. Gowdy spacetimes and the Fuchsian numerical algorithm

This is the second part of a series devoted to the singular initial value problem for second-order hyperbolic Fuchsian systems. In the first part, we defined and investigated this general class of systems, and we established a well-posedness theory in weighted Sobolev spaces. This theory is applied here to the vacuum Einstein equations for Gowdy spacetimes admitting, by definition, two Killing fields satisfying certain geometric conditions. We recover, by more direct and simpler arguments, the well-posedness results established earlier by Rendall and collaborators. In addition, in this paper we introduce a natural approximation scheme, which we refer to as the Fuchsian numerical algorithm and is directly motivated by our general theory. This algorithm provides highly accurate, numerical approximations of the solution to the singular initial value problem. In particular, for the class of Gowdy spacetimes under consideration, various numerical experiments are presented which show the interest and efficiency of the proposed method. Finally, as an application, we numerically construct Gowdy spacetimes containing a smooth, incomplete, non-compact Cauchy horizon.Comment: 22 pages. A shortened version is included in: F. Beyer and P.G. LeFloch, Second-order hyperbolic Fuchsian systems and applications, Class. Quantum Grav. 27 (2010), 24501

Mechanical alloying of Cu and Fe induced by severe plastic deformation of a Cu-Fe composite

A filamentary composite elaborated by cold drawing was processed by High Pressure Torsion (HPT). The nanostructure resulting from this severe plastic deformation (SPD) was investigated thanks to scanning electron microscopy, transmission electron microscopy, X-ray diffraction and 3D atom probe. Although the mutual solubility of Cu and Fe is extremely low at room temperature in equilibrium conditions, it is shown that nanoscaled Fe clusters dissolve in the Cu matrix. The non-equilibrium copper supersaturated solid solutions contain up to 20at.% Fe. The driving force of the dissolution is attributed to capillary pressures and mechanisms which could enhanced the atomic mobility during HPT are discussed. We conclude that the interdiffusion is the result of a dramatic increase of the vacancy concentration during SPD.Comment: 20 page