Counting colorings on varieties

We present a combinatorial mechanism for counting certain objects associated to a variety over a finite field. The basic example is that of counting conjugacy classes of the general linear group. We discuss how the method applies to counting these and also to counting unipotent matrices and pairs of commuting matrices

Vortex-glass transition in superconducting Nb/Cu superlattices

Nb/Cu superconducting superlattices have been fabricated by dc magnetron sputtering. This system shows a vortex glass transition with critical exponents similar to high temperatures superconductors exponents. The transition dymensionality is governed by the superconducting coupling regime. The vortex glass transition shows a pure two dimensional behavior in decoupled superlattices and a quasi-two dimensional behavior in the superlattice coupling regime.Comment: 9 pages, 3 figure

Shape Optimization of 2D parametric models based on geometric weighting and evolutionary rules

En este trabajo se presenta un método para la optimización de forma de modelos bidimensionales sometidos a casos de carga simple o múltiple. La optimización se realiza aplicando iterativamente reglas evolutivas, basadas en el nivel de esfuerzos. Dichas reglas determinan zonas de la frontera en las que el material es subutilizado o sobreutilizado con el objetivo de que el modelo evolucione a un modelo más ligero y con un nivel de esfuerzos alto y homogéneo. La evolución se lleva a cabo modificando la frontera del modelo lentamente. Dado que la frontera se define con curvas paramétricas B-spline los cambios generados resultan en una frontera suave. La principal propuesta del método es que la modificación de la frontera está dada por un conjunto de desplazamientos que toman en cuenta, en su magnitud y dirección, la información geométrica de la vecindad, a diferencia de otros métodos que simplemente generan desplazamientos perpendiculares a la frontera. Al final del trabajo se presenta el diseño de un marco de bicicleta para mostrar el buen desempeño del método.This paper presents a method for shape optimization of two-dimensional models subjected to simple or multiple load cases. The optimization is performed iteratively using evolutionary rules, based on the stress level. These rules determine regions on the boundary where the material is underused or overused; the objective is that the model evolves to a minimum weight model with a high and homogeneous stress level. The evolution is performed by modifying the boundary of the model slowly. Since the boundary is defined by parametric B-spline curves, generated changes result in a smooth boundary. The main proposal of the method is that boundary modifications are given by a set of displacements that, its magnitude and direction, take into account the geometrical information of the neighborhood, unlike other methods that simply generate displacement perpendicular to the boundary. Finally, the paper presents the design of a frame bike in order to show the good performance of the method.Peer Reviewe