Simulations of the Magneto-rotational Instability in Core-Collapse Supernovae

We assess the importance of the magneto-rotational instability in core-collapse supernovae by an analysis of the growth rates of unstable modes in typical post-collapse systems and by numerical simulations of simplified models. The interplay of differential rotation and thermal stratification defines different instability regimes which we confirm in our simulations. We investigate the termination of the growth of the MRI by parasitic instabilities, establish scaling laws characterising the termination amplitude, and study the long-term evolution of the saturated turbulent state.Comment: 6 pages, 1 figure. To appear in Proceedings of 4th International Conference on Numerical Modeling of Space Plasma Flows (Chamonix 2009

A lower bound in Nehari's theorem on the polydisc

By theorems of Ferguson and Lacey (d=2) and Lacey and Terwilleger (d>2), Nehari's theorem is known to hold on the polydisc D^d for d>1, i.e., if H_\psi is a bounded Hankel form on H^2(D^d) with analytic symbol \psi, then there is a function \phi in L^\infty(\T^d) such that \psi is the Riesz projection of \phi. A method proposed in Helson's last paper is used to show that the constant C_d in the estimate \|\phi\|_\infty\le C_d \|H_\psi\| grows at least exponentially with d; it follows that there is no analogue of Nehari's theorem on the infinite-dimensional polydisc

Effect of reservoir tillage on rainwater harvesting and soil erosion control under a developed rainfall simulator.

Soil erosion is a serious environmental threat in the Mediterranean region due to torrential rainfalls, and it contributes to the degradation of agricultural land. Techniques such as rainwater harvesting may improve soil water storage and increase agricultural productivity, which could result in more effective land usage. Reservoir tillage is an effective system of harvesting rainwater, but it has not been scientifically evaluated like other tillage systems. Its suitability for the conditions in Spain has not been determined. To investigate and quantify water storage from reservoir tillage and how it could be adapted to improve infiltration of harvested rainwater, a laboratory-scale rainfall simulator was developed. Rainfall characteristics, including rainfall intensity, spatial uniformity and raindrop size, confirm that natural rainfall conditions are simulated with sufficient accuracy. The simulator was auto-controlled by a solenoid valve and three pressure nozzles were used to spray water corresponding to five rainfall intensities ranging from 36 to 112 mm h-1 for 3 to 101-year return period with uniformity coefficients between 83 and 94%. In order to assess the reservoir tillage method under surface slopes of 0, 5, and 10%, three soil scooping devices with identical volume were used to make depressions in the following forms: a) truncated square pyramid, b) triangular prism, and c) truncated cone. These depressions were compared to a control soil surface with no depression. For the loam soil used in this study, results show that reservoir tillage was able to reduce soil erosion and surface runoff and significantly increase infiltration. There was significant difference between the depressions and the control. Compared to the control, depression (a) reduced surface runoff by about 61% and the sediment yield concentration by about 79%

Interpolation of families

We identify the intermédiate space of a complex interpolation family - in the sense of Coifman, Cwikel, Rochberg, Sagher and Weissof LP spaces with change of measure, for the complex interpolation method associated to an analytic functional

Els models d’escolarització a Mallorca: les relacions entre l’escola pública i l’escola privada

En aquest article abordam la relació entre escola pública i escola privada, i apuntam una sèrie de tendències de la gestió escolar a Mallorca. En un primer moment, es presenta una fonamentació teòrica, en la qual es revisen els factors condicionants de l’escolarització, l’evolució de l’educació i la societat a les Illes Balears i la construcció d’un sistema escolar modern. En un segon moment, s’analitzen les dades recents sobre l’escolarització a Mallorca, en els nivells educatius obligatoris i l’educació infantil, aprofundint en la relació existent entre el tipus de titularitat (pública o privada-concertada) i les característiques dels municipis: el seu caràcter rural-urbà, l’activitat econòmica predominant, la ubicació o la dimensió territorial.En este artículo se aborda la relación entre la escuela pública y la escuela privada y se apuntan una serie de tendencias de la gestión escolar en Mallorca. En un primer momento se presenta una fundamentación teórica, en la que se revisan los factores condicionantes de la escolarización así como la evolución de la educación y la sociedad en las Islas Baleares y la construcción de un sistema escolar moderno. En un segundo momento, se analizan los datos recientes sobre la escolarización en Mallorca en los niveles educativos obligatorios y la educación infantil, profundizando en la relación existente entre el tipo de titularidad (pública o privada-concertada) y las características de los municipios: su carácter rural-urbano, la actividad económica predominante, la ubicación o la dimensión territorial

Equidistribution of the Fekete points on the sphere

The Fekete points are the points that maximize a Vandermonde-type determinant that appears in the polynomial Lagrange interpolation formula. They are well suited points for interpolation formulas and numerical integration. We prove the asymptotic equidistribution of the Fekete points in the sphere. The way we proceed is by showing their connection with other array of points, the Marcinkiewicz-Zygmund arrays and the interpolating arrays, that have been studied recently