Monochromatic Clique Decompositions of Graphs

Let $G$ be a graph whose edges are coloured with $k$ colours, and $\mathcal H=(H_1,\dots , H_k)$ be a $k$-tuple of graphs. A monochromatic $\mathcal H$-decomposition of $G$ is a partition of the edge set of $G$ such that each part is either a single edge or forms a monochromatic copy of $H_i$ in colour $i$, for some $1\le i\le k$. Let $\phi_{k}(n,\mathcal H)$ be the smallest number $\phi$, such that, for every order-$n$ graph and every $k$-edge-colouring, there is a monochromatic $\mathcal H$-decomposition with at most $\phi$ elements. Extending the previous results of Liu and Sousa ["Monochromatic $K_r$-decompositions of graphs", Journal of Graph Theory}, 76:89--100, 2014], we solve this problem when each graph in $\mathcal H$ is a clique and $n\ge n_0(\mathcal H)$ is sufficiently large.Comment: 14 pages; to appear in J Graph Theor

Spin filtering in nanowire directional coupler

The spin transport characteristics of a nanowire directional electronic coupler have been evaluated theoretically via a transfer matrix approach. The application of a gate field in the region of mixing allows for control of spin current through the different leads of the coupler via the Rashba spin-orbit interaction. The combination of spin-orbit interaction and applied gate voltages on different legs of the coupler give rise to a controllable modulation of the spin polarization. Both structural factors and field strength tuning lead to a rich phenomenology that could be exploited in spintronic devices.Comment: 9 pages, 4 figure

ARES v2 - new features and improved performance

Aims: We present a new upgraded version of ARES. The new version includes a series of interesting new features such as automatic radial velocity correction, a fully automatic continuum determination, and an estimation of the errors for the equivalent widths. Methods: The automatic correction of the radial velocity is achieved with a simple cross-correlation function, and the automatic continuum determination, as well as the estimation of the errors, relies on a new approach to evaluating the spectral noise at the continuum level. Results: ARES v2 is totally compatible with its predecessor. We show that the fully automatic continuum determination is consistent with the previous methods applied for this task. It also presents a significant improvement on its performance thanks to the implementation of a parallel computation using the OpenMP library.Comment: 4 pages, 2 Figures; accepted in A&A; ARES Webpage: www.astro.up.pt/~sousasag/are