Inevitability of Plate Tectonics on Super-Earths

The recent discovery of super-Earths (masses less or equal to 10 earth-masses) has initiated a discussion about conditions for habitable worlds. Among these is the mode of convection, which influences a planet's thermal evolution and surface conditions. On Earth, plate tectonics has been proposed as a necessary condition for life. Here we show, that super-Earths will also have plate tectonics. We demonstrate that as planetary mass increases, the shear stress available to overcome resistance to plate motion increases while the plate thickness decreases, thereby enhancing plate weakness. These effects contribute favorably to the subduction of the lithosphere, an essential component of plate tectonics. Moreover, uncertainties in achieving plate tectonics in the one earth-mass regime disappear as mass increases: super-Earths, even if dry, will exhibit plate tectonic behaviour.Comment: 13 pages, 2 figures and 1 table; in press in ApJ

Bulk Composition of GJ 1214b and other sub-Neptune exoplanets

GJ1214b stands out among the detected low-mass exoplanets, because it is, so far, the only one amenable to transmission spectroscopy. Up to date there is no consensus about the composition of its envelope although most studies suggest a high molecular weight atmosphere. In particular, it is unclear if hydrogen and helium are present or if the atmosphere is water dominated. Here, we present results on the composition of the envelope obtained by using an internal structure and evolutionary model to fit the mass and radius data. By examining all possible mixtures of water and H/He, with the corresponding opacities, we find that the bulk amount of H/He of GJ1214b is at most 7% by mass. In general, we find the radius of warm sub-Neptunes to be most sensitive to the amount of H/He. We note that all (Kepler-11b,c,d,f, Kepler-18b, Kepler-20b, 55Cnc-e, Kepler-36c and Kepler-68b) but two (Kepler-11e and Kepler-30b) of the discovered low-mass planets so far have less than 10% H/He. In fact, Kepler-11e and Kepler-30b have 10-18% and 5-15% bulk H/He. Conversely, little can be determined about the H2O or rocky content of sub-Neptune planets. We find that although a 100% water composition fits the data for GJ1214b, based on formation constraints the presence of heavier refractory material on this planet is expected, and hence, so is a component lighter than water required. A robust determination by transmission spectroscopy of the composition of the upper atmosphere of GJ1214b will help determine the extent of compositional segregation between the atmosphere and envelope.Comment: Updated the masses and radii of the Kepler-11 system, added Kepler-30b as well in the analysis. Accepted in ApJ, 39 pages, 9 figure

El conocimiento, los usos y la apropiación del computador como herramienta multimedial en los educandos del colectivo "Ciberinquietos.ITM" del Instituto Técnico Marillac del municipio de Santa Rosa de Cabal

Este ejercicio investigativo se enfoca en la descripción del estado en cuanto a conocimiento, usos y apropiación del computador como herramienta multimedial que tienen los educandos pertenecientes al colectivo "Ciberinquietos.ITM" del Instituto Técnico Marillac del municipio de Santa Rosa de Cabal. En este orden de ideas, se reconocen, describen e identifican los principales usos, grados de conocimiento y apropiación que adquieren los educandos al interactuar con el computador, caracterizando a éste como agente de trasformación e innovación en los procesos de aprendizaje.This research exercise focuses on the description of the state in terms of knowledge, uses and ownership of the computer as a multimedia tool with students from "Ciberinquietos.ITM" collective of the InstitutoTécnico Marillac of the municipality of Santa Rosa de Cabal. Consequently, this project recognize, describe and identify the main uses, ownership and knowledge levels acquired by students to interact with the computer, characterizing it as an agent of transformation and innovation in the learning process

Differential Calculus Teaching through Virtual Learning Objects in the Field of Management Sciences

AbstractThis paper examines the use of Virtual Learning Objects (VLO) in the teaching of differential calculus in the area of Management Sciences as a teaching strategy to improve the assimilation of the theoretical knowledge acquired in the classroom courses. This is accomplished by the construction of virtual pedagogical practices concerning to optimization problems through GeoGebra. It is free software that generates VLOs with an adequate contrast between the theoretical mathematical knowledge and its practical application in Management Sciences. Thus, different dynamic, algorithmic and heuristic processes are encouraged, being useful for logic and constructivist student training. The proposed methodology is based on the construction of VLOs (Virtual Learning Objects). It allows choosing variables in the GeoGebra software where students can interact with the formulation of mathematical problems applied to their curricula. So, they strengthen their knowledge and have a greater autonomy in the analysis of optimization problems in financial and management field. The results show how these teaching strategies facilitate the assimilation of the concepts of differential calculus in Management Sciences students. This allows a greater development of student skills in front of the understanding of the geometric behaviour of a curve

[Propuesta para el diseño de un plan de negocios con productores de plátano en el corregimiento de quebrada negra, Calarcá Quindío]

El corregimiento de Quebrada Negra ubicado en el municipio de Calarcá en el departamento del Quindío, cuenta actualmente con varias asociaciones campesinas, organizadas alrededor de actividades productivas tales como el cultivo de la guadua, la piscicultura, los frutales, plantas aromáticas y medicinales, caña panelera, entre otros. En medio de esto aparece en el escenario un grupo de productores de plátano organizados bajo la figura asociativa con el nombre de "ASOPLAQC"; esta iniciativa surge a principios del año 2007 con el fin de dar salida a la problemática generada por la comercialización con intermediarios, con el objetivo de ser ellos los autores del proceso productivo así como el de comercialización con los distribuidores finales. Este trabajo pretendía acompañar la consolidación del proceso de conformación organizativa de la asociación en torno a un Plan de Negocios. Con la intervención se logró en primera instancia la realización de un diagnóstico de los aspectos socio-económicos de los productores vinculados, la formulación de la base administrativa misión, visión, objetivos y el fortalecimiento del modelo organizacional, organigrama y distribución de funciones; igualmente se consultó otra experiencia que ayudó al igual que otras actividades legitimar relaciones de producción y comercialización alternativas al interior de la asociación