Monogenous algebras. Back to Kronecker

In this note we develop some properties of those algebras (called here locally simple) which can be generated by a single element after, if need be, a faithfully flat extension. For finite algebras, this is shown to be in fact a property of the geometric fibers. Morphisms between rings of algebraic integers are locally simple. Expanding an idea introduced by Kronecker we show that much of the properties (in particular local simplicity) of a finite and locally free A-algebra B can be read through the characteristic polynomial of the generic element of B.Comment: Note ecrite en septembre 2003. 13 page

Multi-tap Digital Canceller for Full-Duplex Applications

We identify phase noise as a bottleneck for the performance of digital self-interference cancellers that utilize a single auxiliary receiver---single-tap digital cancellers---and operate in multipath propagation environments. Our analysis demonstrates that the degradation due to phase noise is caused by a mismatch between the analog delay of the auxiliary receiver and the different delays of the multipath components of the self-interference signal. We propose a novel multi-tap digital self-interference canceller architecture that is based on multiple auxiliary receivers and a customized Normalized-Least-Mean-Squared (NLMS) filtering for self-interference regeneration. Our simulation results demonstrate that our proposed architecture is more robust to phase noise impairments and can in some cases achieve 10~dB larger self-interference cancellation than the single-tap architecture.Comment: SPAWC 201

Strain in crystalline core-shell nanowires

The strain configuration induced by the lattice mismatch in a core-shell nanowire is calculated analytically, taking into account the crystal anisotropy and the difference in stiffness constants of the two materials. The method is applied to nanowires with the wurtzite structure or the zinc-blende structure with the hexagonal / trigonal axis along the nanowire, and the results are compared to available numerical calculations and experimental data. It is also applied to multishell nanowires, and to core-shell nanowires grown along the $$ axis of cubic semiconductors

Parametric studies of cosmic ray acceleration in supernova remnants

We present a library of numerical models of cosmic-ray accelerating supernova remnants (SNRs) evolving through a homogeneous ambient medium. We analyse distributions of the different energy components and diffusive shock acceleration time-scales for the models in various conditions. The library comprises a variety of SNR evolutionary scenarios and is used to map remnants with sufficiently known properties. This mapping constrains the respective ambient medium properties and the acceleration efficiency. Employing the library, we derive the ambient medium density, ambient magnetic field strength and the cosmic-ray acceleration efficiency for models of Tycho and SN 1006 remnants and refine the ages of SNR 0509-67.5 and SNR 0519-69.0.Comment: 13 pages, 9 figures, MNRAS accepte

MARCOS, a numerical tool for the simulation of multiple time-dependent non-linear diffusive shock acceleration

We present a new code aimed at the simulation of diffusive shock acceleration (DSA), and discuss various test cases which demonstrate its ability to study DSA in its full time-dependent and non-linear developments. We present the numerical methods implemented, coupling the hydrodynamical evolution of a parallel shock (in one space dimension) and the kinetic transport of the cosmic-rays (CR) distribution function (in one momentum dimension), as first done by Falle. Following Kang and Jones and collaborators, we show how the adaptive mesh refinement technique (AMR) greatly helps accommodating the extremely demanding numerical resolution requirements of realistic (Bohm-like) CR diffusion coefficients. We also present the paral lelization of the code, which allows us to run many successive shocks at the cost of a single shock, and thus to present the first direct numerical simulations of linear and non-linear multiple DSA, a mechanism of interest in various astrophysical environments such as superbubbles, galaxy clusters and early cosmological flows.Comment: accepted for publication in MNRAS by the Royal Astronomical Society and Blackwell Publishin