Calculation of the incremental stress-strain relation of a polygonal packing

The constitutive relation of the quasi-static deformation on two dimensional packed samples of polygons is calculated using molecular dynamic simulations. The stress values at which the system remains stable are bounded by a failure surface, that shows a power law dependence on the pressure. Below the failure surface, non linear elasticity and plastic deformation are obtained, which are evaluated in the framework of the incremental linear theory. The results shows that the stiffness tensor can be directly related to the micro-contact rearrangements. The plasticity obeys a non-associated flow rule, with a plastic limit surface that does not agree with the failure surface.Comment: 11 pages, 20 figur

Non-grey dimming events of KIC 8462852 from GTC spectrophotometry

We report ground-based spectrophotometry of KIC 8462852, during its first dimming events since the end of the Kepler mission. The dimmings show a clear colour-signature, and are deeper in visual blue wavelengths than in red ones. The flux loss' wavelength dependency can be described with an \AA ngstr\"om absorption coefficient of $2.19\pm0.45$, which is compatible with absorption by optically thin dust with particle sizes on the order of 0.0015 to 0.15 $\mu$m. These particles would be smaller than is required to be resistant against blow-out by radiation pressure when close to the star. During occultation events, these particles must be replenished on time-scales of days. If dust is indeed the source of KIC 8462852's dimming events, deeper dimming events should show more neutral colours, as is expected from optically thick absorbers.Comment: 5 pages, accepted for A&A letter

Encoding algebraic power series

Algebraic power series are formal power series which satisfy a univariate polynomial equation over the polynomial ring in n variables. This relation determines the series only up to conjugacy. Via the Artin-Mazur theorem and the implicit function theorem it is possible to describe algebraic series completely by a vector of polynomials in n+p variables. This vector will be the code of the series. In the paper, it is then shown how to manipulate algebraic series through their code. In particular, the Weierstrass division and the Grauert-Hironaka-Galligo division will be performed on the level of codes, thus providing a finite algorithm to compute the quotients and the remainder of the division.Comment: 35 page

Double exchange model for RuSr_2(Eu,Gd)Cu_2O_8

We propose a double exchange model to describe the RuO_2 planes of RuSr_2(Eu,Gd)Cu_2O_8. The Ru^+5 ions are described by localized spins, and additional electrons provided by the superconducting CuO_2 planes are coupled ferromagnetically to them by Hund rules coupling. We calculate the spin structure factor, magnetic susceptibility and magnetization as a function of magnetic field and temperature, using a Monte Carlo algorithm in which the Ru^+5 spins are treated as classical. Several experiments which seemed in contradiction with one another are explained by the theory.Comment: 3 pages, 3 figs., submitted to LAW3M conferenc

Entanglement Polygon Inequality in Qubit Systems

We prove a set of tight entanglement inequalities for arbitrary $N$-qubit pure states. By focusing on all bi-partite marginal entanglements between each single qubit and its remaining partners, we show that the inequalities provide an upper bound for each marginal entanglement, while the known monogamy relation establishes the lower bound. The restrictions and sharing properties associated with the inequalities are further analyzed with a geometric polytope approach, and examples of three-qubit GHZ-class and W-class entangled states are presented to illustrate the results.Comment: 8 pages, 4 figure