A fractional porous medium equation

We develop a theory of existence, uniqueness and regularity for a porous medium equation with fractional diffusion, $\frac{\partial u}{\partial t} + (-\Delta)^{1/2} (|u|^{m-1}u)=0$ in $\mathbb{R}^N$, with $m>m_*=(N-1)/N$, $N\ge1$ and $f\in L^1(\mathbb{R}^N)$. An $L^1$-contraction semigroup is constructed and the continuous dependence on data and exponent is established. Nonnegative solutions are proved to be continuous and strictly positive for all $x\in\mathbb{R}^N$, $t>0$

Numerical control matrix rotation for the LINC-NIRVANA Multi-Conjugate Adaptive Optics system

LINC-NIRVANA will realize the interferometric imaging focal station of the Large Binocular Telescope. A double Layer Oriented multi-conjugate adaptive optics system assists the two arms of the interferometer, supplying high order wave-front correction. In order to counterbalance the field rotation, mechanical derotation for the two ground wave-front sensors, and optical derotators for the mid-high layers sensors fix the positions of the focal planes with respect to the pyramids aboard the wave-front sensors. The derotation introduces pupil images rotation on the wavefront sensors: the projection of the deformable mirrors on the sensor consequently change. The proper adjustment of the control matrix will be applied in real-time through numerical computation of the new matrix. In this paper we investigate the temporal and computational aspects related to the pupils rotation, explicitly computing the wave-front errors that may be generated.Comment: 6 pages, 2 figures, presented at SPIE Symposium "Astronomical Telescopes and Instrumentation'' conference "Adaptive Optics Systems II'',Sunday 27 June 2010, San Diego, California, US

Sensing and control of segmented mirrors with a pyramid wavefront sensor in the presence of spiders

The segmentation of the telescope pupil (by spiders & the segmented M4) create areas of phase isolated by the width of the spiders on the wavefront sensor (WFS), breaking the spatial continuity of the wavefront. The poor sensitivity of the Pyramid WFS (PWFS) to differential piston leads to badly seen and therefore uncontrollable differential pistons. In close loop operation, differential pistons between segments will settle around integer values of the average sensing wavelength. The differential pistons typically range from one to ten times the sensing wavelength and vary rapidly over time, leading to extremely poor performance. In addition, aberrations created by atmospheric turbulence will contain large amounts of differential piston between the segments. Removing piston contribution over each of the DM segments leads to poor performance. In an attempt to reduce the impact of unwanted differential pistons that are injected by the AO correction, we compare three different approaches. We first limit ourselves to only use the information measured by the PWFS, in particular by reducing the modulation. We show that using this information sensibly is important but will not be sufficient. We discuss possible ways of improvement by using prior information. A second approach is based on phase closure of the DM commands and assumes the continuity of the correction wavefront over the entire unsegmented pupil. The last approach is based on the pair-wise slaving of edge actuators and shows the best results. We compare the performance of these methods using realistic end-to-end simulations. We find that pair-wise slaving leads to a small increase of the total wavefront error, only adding between 20-45 nm RMS in quadrature for seeing conditions between 0.45-0.85 arcsec. Finally, we discuss the possibility of combining the different proposed solutions to increase robustness.Comment: 12 pages, 15 figures, AO4ELT5 Proceedings, Adaptive Optics for Extremely Large Telescopes 5, Conference Proceeding, Tenerife, Canary Islands, Spain, June 25-30, 201

Sistema de información y gestión de proyectos de grado.

Este documento es el informe final de trabajo de grado, requisito para obtener el título de Ingeniero de Sistemas de la Universidad Libre que ha dado origen al método de investigación pedagógico para el desarrollo del proyecto, Sistema de Información y gestión de proyectos de grado. El objetivo del proyecto es desarrollar un prototipo de sistema de gestión para controlar y administrar de manera ordenada las entregas de los trabajos de grado para la universidad Libre, Facultad de Ingeniería, Programa Ingeniería de Sistemas. Se basa en fundamentos teóricos enmarcados en las tecnologías de la información, modelos de prototipos y en el conocimiento del manejo actual del proceso que se lleva a cabo en la gestión de los trabajos de grado de la coordinación de la Facultad de Ingeniería. Uno de los aspectos destacados dentro del desarrollo, es el uso de la investigación cuantitativa, ya que a través de sus técnicas de recolección y análisis de datos, utilizando las características de deducción, verificación, enumeración (a manera de razonamiento mediante la observación, factor tiempo) se logra adquirir conocimientos fundamentales y la elección del modelo más adecuado que nos permita ver la realidad de manera imparcial para recoger y analizar los datos a través de los conceptos y variables. Por último, gracias a las fuentes bibliográficas e investigaciones realizadas se puede demostrar el impacto y la usabilidad que este nuevo prototipo generara en los procesos que se llevan actualmente, impulsando así el desarrollo de nuevos métodos que permitan generan grandes avances en nuestra universidad