Piezoelectricity and valley Chern number in inhomogeneous hexagonal 2D crystals

Conversion of mechanical forces to electric signal is possible in non-centrosymmetric materials due to linear piezoelectricity. The extraordinary mechanical properties of two-dimensional materials and their high crystallinity make them exceptional platforms to study and exploit the piezoelectric effect. Here, the piezoelectric response of non-centrosymmetric hexagonal two-dimensional crystals is studied using the modern theory of polarization and ${\bm k} \cdot {\bm p}$ model Hamiltonians. An analytical expression for the piezoelectric constant is obtained in terms of topological quantities such as the {\it valley Chern number}. The theory is applied to semiconducting transition metal dichalcogenides and hexagonal Boron Nitride. We find good agreement with available experimental measurements for MoS$_2$. We further generalise the theory to study the polarization of samples subjected to inhomogeneous strain (e.g.~nanobubbles). We obtain a simple expression in terms of the strain tensor, and show that charge densities $\gtrsim 10^{11} {\rm cm}^{-2}$ can be induced by realistic inhomogeneous strains, $\epsilon \approx 0.01 - 0.03$.Comment: 14 pages, 3 figure

Estudio de caso : aplicación del concepto -Cadenas de abastecimiento dinámicas-, en una empresa colombiana

El mundo empresarial actual, es un mundo competitivo donde el servicio prestado y la atención al cliente son las premisas más importantes para ser reconocido y lograr una excelente participación en el mercado con una alta rentabilidad. Esto hace evidente la necesidad de ir más allá de los productos o servicios ofrecidos para pensar en el cliente y encontrar las maneras para satisfacer sus necesidades individuales de la mejor manera. Realizar revisiones constantes en las personas, el equipo y los procedimientos es el primer paso para mantener los procesos internos acordes con lo que el cliente necesita, de manera que lo esencial de la prestación de servicios se convierte en cómo se llega a satisfacer una necesidad y al cumplimiento de metas más que sólo cumplirlas. Sin embargo, el modelo que se utiliza actualmente en las empresas no se preocupa por su funcionamiento interno ni por los mecanismos para conseguir los productos y servicios de calidad.Ingeniero (a) IndustrialPregrad

Screening and plasmons in pure and disordered single- and bilayer black phosphorus

We study collective plasmon excitations and screening of disordered single- and bilayer black phosphorus beyond the low energy continuum approximation. The dynamical polarizability of phosphorene is computed using a tight-binding model that properly accounts for the band structure in a wide energy range. Electron-electron interaction is considered within the Random Phase Approximation. Damping of the plasmon modes due to different kinds of disorder, such as resonant scatterers and long-range disorder potentials, is analyzed. We further show that an electric field applied perpendicular to bilayer phosphorene can be used to tune the dispersion of the plasmon modes. For sufficiently large electric field, the bilayer BP enters in a topological phase with a characteristic plasmon spectrum, which is gaped in the armchair direction.Comment: 9 pages, 9 figure

Landau Level Spectrum of ABA- and ABC-stacked Trilayer Graphene

We study the Landau level spectrum of ABA- and ABC-stacked trilayer graphene. We derive analytic low energy expressions for the spectrum, the validity of which is confirmed by comparison to a \pi -band tight-binding calculation of the density of states on the honeycomb lattice. We further study the effect of a perpendicular electric field on the spectrum, where a zero-energy plateau appears for ABC stacking order, due to the opening of a gap at the Dirac point, while the ABA-stacked trilayer graphene remains metallic. We discuss our results in the context of recent electronic transport experiments. Furthermore, we argue that the expressions obtained can be useful in the analysis of future measurements of cyclotron resonance of electrons and holes in trilayer graphene.Comment: 10 pages, 8 figure

The shaping of Spanish CLIL

ELT in Spain is witnessing the arrival of CLIL and English is changing from a goal-oriented school subject to a medium of instruction for content subjects. What is taking place in our system is influenced by what has previously happened elsewhere. Two research episodes have contributed to it: the Bangalore Project in India and the Canadian Immersion Program originated at the St Lambert School in Montreal. From the first one we learnt about the notion of task, as an innovative element for curriculum design at that time, and, consequently, about a new type of syllabus: the process syllabus. Task-based approaches and project-work founded its pedagogical principles on this type of syllabus. The Canadian Immersion Program has provided us with, at least, two psycho-pedagogical principles that are paramount in bilingual education: (a) the distinction between BICS and CALP, and b) the principle of common underlying proficiency.La aparición de CLIL (AICLE, en español), como enfoque y metodología alternativa a las tradicionales clases de lengua extranjera está suponiendo un cambio radical en el sistema educativo español. Sin embargo, buscar parte de sus fundamentos psicopedagógicos nos lleva a prestar especial atención al Proyecto Bangalore y al programa de Inmersión Canadiense. Del primero hemos aprendido el concepto de tarea, como el elemento que articula todo el diseño curricular de tipo procedimental. La distinción entre los términos BICS y CALP y sus consecuencias metodológicas, así como la idea de la competencia común subyacente son los dos principios teóricos que apoyan nuestro aprendizaje de contenidos a través de las lenguas

The shaping of Spanish CLIL

ELT in Spain is witnessing the arrival of CLIL and English is changing from a goal-oriented school subject to a medium of instruction for content subjects. What is taking place in our system is influenced by what has previously happened elsewhere. Two research episodes have contributed to it: the Bangalore Project in India and the Canadian Immersion Program originated at the St Lambert School in Montreal. From the first one we learnt about the notion of task, as an innovative element for curriculum design at that time, and, consequently, about a new type of syllabus: the process syllabus. Task-based approaches and project-work founded its pedagogical principles on this type of syllabus. The Canadian Immersion Program has provided us with, at least, two psycho-pedagogical principles that are paramount in bilingual education: (a) the distinction between BICS and CALP, and b) the principle of common underlying proficiency.La aparición de CLIL (AICLE, en español), como enfoque y metodología alternativa a las tradicionales clases de lengua extranjera está suponiendo un cambio radical en el sistema educativo español. Sin embargo, buscar parte de sus fundamentos psicopedagógicos nos lleva a prestar especial atención al Proyecto Bangalore y al programa de Inmersión Canadiense. Del primero hemos aprendido el concepto de tarea, como el elemento que articula todo el diseño curricular de tipo procedimental. La distinción entre los términos BICS y CALP y sus consecuencias metodológicas, así como la idea de la competencia común subyacente son los dos principios teóricos que apoyan nuestro aprendizaje de contenidos a través de las lenguas

Verificación de algoritmos en Escher

Trabajo Fin de Grado en Grado de Ingeniería Informática , Facultad de Informática UCM, Departamento de Sistemas Informáticos y Computación, Curso 2018/2019This project borns from the growing need not only for quality programs but programs that never fail. Nowadays software is several orders of magnitude greater than just a few decades ago and critical software has become even more relevant, since if it fails, enormous, complex infrastructures fall with it, damaging machines, companies or even human lives. When software testing is not enough, it is imperative to use formal verification of algorithms and data structures. Since it is a meticulous, large task, we need computer-aided program verification to help us to speed up and get confidence on the process. This project aims to assay and understand a tool created for this purpose: Escher C Verifier, made for enabling the development of formally-verifiable sofware in a subset of C. By verifying some known algorithms, we want to study its aptness as an academic tool.Este trabajo nace de la creciente necesidad no solo de programas de calidad, sino de programas que nunca fallen. Actualmente el software es varios órdenes de magnitud más grande que hace tan solo unas décadas y el software crítico se ha vuelto más importante aún, dado que si falla, enormes y complejas infraestructuras caen con él, dañando máquinas, empresas o incluso vidas humanas. Cuando el testing de software no es suficiente, es necesario emplear la verificación formal de algoritmos y estructuras de datos. Puesto que es una tarea meticulosa y extensa, requerimos de la verificación asistida de programas para ayudarnos a acelerar y ganar confianza en el proceso. Este proyecto apunta a analizar y comprender una herramienta creada para este propósito: Escher C Verifier, hecha para permitir el desarrollo de software formalmente verificable en un subconjunto de C. A partir de la verificación de algunos algoritmos conocidos, queremos estudiar su aptitud como una herramienta académica.Depto. de Sistemas Informáticos y ComputaciónFac. de InformáticaTRUEunpu