Phase transitions in number theory: from the birthday problem to Sidon sets

In this work, we show how number theoretical problems can be fruitfully approached with the tools of statistical physics. We focus on g-Sidon sets, which describe sequences of integers whose pairwise sums are different, and propose a random decision problem which addresses the probability of a random set of k integers to be g-Sidon. First, we provide numerical evidence showing that there is a crossover between satisfiable and unsatisfiable phases which converts to an abrupt phase transition in a properly defined thermodynamic limit. Initially assuming independence, we then develop a mean-field theory for the g-Sidon decision problem. We further improve the mean-field theory, which is only qualitatively correct, by incorporating deviations from independence, yielding results in good quantitative agreement with the numerics for both finite systems and in the thermodynamic limit. Connections between the generalized birthday problem in probability theory, the number theory of Sidon sets and the properties of q-Potts models in condensed matter physics are briefly discussed

Surface-Assisted Luminescence: The PL Yellow Band and the EL of n-GaN Devices

Although everybody should know thatmeasurements are never performed directly onmaterials but on devices, this is not generally true. Devices are physical systems able to exchange energy and thus subject to the laws of physics, which determine the information they provide. Hence, we should not overlook device effects in measurements as we do by assuming naively that photoluminescence (PL) is bulk emission free fromsurface effects. By replacing this unjustified assumption with a propermodel forGaN surface devices, their yellow band PL becomes surface-assisted luminescence that allows for the prediction of the weak electroluminescence recently observed in n-GaN devices when holes are brought to their surfaces.

Theoretical and experimental structural studies of historical Latin-American laminated planked timber arches

This article describes a first group of theoretical and experimental works undertaken at the Polytechnic University of Madrid. One major purpose is to obtain a structural model for the assessment of historical Latin-American vertically laminated planked timber arches built by the Spanish, mainly in the XVII and XVIII centuries. Many of those constructions still stand and represent a notable historical heritage. Pedro Hurtado recently presented his Ph. D. thesis on historical and construction topics. A structural study was then undertaken. This step of the structural research focussed on static analysis, most especially the deformation in the connection system. This article describes part of this first structural research. Even though it is still at a basic level, it shows reasonable agreement with the experimental results. Further static analytical models are been now developed and implemented. The next stage will address the dynamic problem, even though improvements will be made also in the constitutive equations.

River Restoration in Spain: Theoretical and Practical Approach in the Context of the European Water Framework Directive.

River restoration is becoming a priority in many countries because of increasing the awareness of environmental degradation. In Europe, the EU Water Framework Directive (WFD) has significantly reinforced river restoration, encouraging the improvement of ecological status for water bodies. To fulfill the WFD requirements, the Spanish Ministry of the Environment developed in 2006 a National Strategy for River Restoration whose design and implementation are described in this paper. At the same time many restoration projects have been conducted, and sixty of them have been evaluated in terms of stated objectives and pressures and implemented restoration measures. Riparian vegetation enhancement, weir removal and fish passes were the most frequently implemented restoration measures, although the greatest pressures came from hydrologic alteration caused by flow regulation for irrigation purposes. Water deficits in quantity and quality associated with uncontrolled water demands seriously affect Mediterranean rivers and represent the main constraint to achieving good ecological status of Spanish rivers, most of them intensively regulated. Proper environmental allocation of in-stream flows would need deep restrictions in agricultural water use which seem to be of very difficult social acceptance. This situation highlights the need to integrate land-use and rural development policies with water resources and river management, and identifies additional difficulties in achieving the WFD objectives and good ecological status of rivers in Mediterranean countries.

Crack width control in RC elements with recycled steel fibres and applications to integral structures : theoretical and experimental study

El presente trabajo trata de elementos reforzados con barras de armadura y Fibras Metálicas Recicladas (FMR). El objetivo principal es mejorar el comportamiento a fisuración de elementos sometidos a flexión pura y a flexión compuesta, aumentando en consecuencia las prestaciones en servicio de aquellas estructuras con requerimientos estrictos con respecto al control de fisuración. Entre éstas últimas se encuentran las estructuras integrales, es decir aquellas estructuras sin juntas (puentes o edificios), sometidas a cargas gravitatorias y deformaciones impuestas en los elementos horizontales debidas a retracción, fluencia y temperatura. Las FMR son obtenidas a partir de los neumáticos fuera de uso, y puesto que el procedimiento de reciclado se centra en el caucho en vez que en el acero, su forma es aleatoria y con longitud variable. A pesar de que la eficacia del fibrorefuerzo mediante FMR ha sido demostrada en investigaciones anteriores, la innovación que representa este trabajo consiste en proponer la acción combinada de barras convencionales y FMR en la mejora del comportamiento a fisuración. El objetivo es por tanto mejorar la sostenibilidad del proyecto de la estructura en HA al utilizar materiales reciclados por un lado, y aumentando por el otro la durabilidad. En primer lugar, se presenta el estado del arte con respecto a la fisuración en elementos de HA, que sucesivamente se amplía a elementos reforzados con barras y fibras. Asimismo, se resume el método simplificado para el análisis de columnas de estructuras sin juntas ya propuesto por Pérez et al., con particular énfasis en aquellos aspectos que son incompatibles con la acción de las fibras a nivel seccional. A continuación, se presenta un modelo para describir la deformabilidad seccional y la fisuración en elementos en HA, que luego se amplía a aquellos elementos reforzados con barras y fibras, teniendo en cuenta también los efectos debidos a la retracción (tension stiffening negativo). El modelo es luego empleado para ampliar el método simplificado para el análisis de columnas. La aportación consiste por tanto en contar con una metodología amplia de análisis para este tipo de elementos. Seguidamente, se presenta la campaña experimental preliminar que ha involucrado vigas a escala reducida sometidas a flexión simple, con el objetivo de validar la eficiencia y la usabilidad en el hormigón de las FMR de dos diferentes tipos, y su comportamiento con respecto a fibras de acero comerciales. Se describe a continuación la campaña principal, consistente en ensayos sobre ocho vigas en flexión simple a escala 1:1 (variando contenido en FRM, Ø/s,eff y recubrimiento) y doce columnas a flexión compuesta (variando contenido en FMR, Ø/s,eff y nivel de fuerza axil). Los resultados obtenidos en la campaña principal son presentados y comentados, resaltando las mejoras obtenidas en el comportamiento a fisuración de las vigas y columnas, y la rigidez estructural de las columnas. Estos resultados se comparan con las predicciones del modelo propuesto. Los principales parámetros estudiados para describir la fisuración y el comportamiento seccional de las vigas son: la separación entre fisuras, el alargamiento medio de las armaduras y la abertura de fisura, mientras que en los ensayos de las columnas se ha contrastado las leyes momento/curvatura, la tensión en las barras de armadura y la abertura de fisura en el empotramiento en la base. La comparación muestra un buen acuerdo entre las predicciones y los resultados experimentales. Asimismo, se nota la mejora en el comportamiento a fisuración debido a la incorporación de FMR en aquellos elementos con cuantías de armadura bajas en flexión simple, en elementos con axiles bajos y para el control de la fisuración en elementos con grandes recubrimientos, siendo por tanto resultados de inmediato impacto en la práctica ingenieril (diseño de losas, tanques, estructuras integrales, etc.). VIIIComo punto final, se presentan aplicaciones de las FMR en estructuras reales. Se discuten dos casos de elementos sometidos a flexión pura, en particular una viga simplemente apoyada y un tanque para el tratamiento de agua. En ambos casos la adicción de FMR al hormigón lleva a mejoras en el comportamiento a fisuración. Luego, utilizando el método simplificado para el análisis en servicio de columnas de estructuras sin juntas, se calcula la máxima longitud admisible en casos típicos de puentes y edificación. En particular, se demuestra que las limitaciones de la práctica ingenieril actual (sobre todo en edificación) pueden ser aumentadas considerando el comportamiento real de las columnas en HA. Finalmente, los mismos casos son modificados para considerar el uso de MFR, y se presentan las mejoras tanto en la máxima longitud admisible como en la abertura de fisura para una longitud y deformación impuesta. This work deals with elements reinforced with both rebars and Recycled Steel Fibres (RSFs). Its main objective is to improve cracking behaviour of elements subjected to pure bending and bending and axial force, resulting in better serviceability conditions for these structures demanding keen crack width control. Among these structures a particularly interesting type are the so-called integral structures, i.e. long jointless structures (bridges and buildings) subjected to gravitational loads and imposed deformations due to shrinkage, creep and temperature. RSFs are obtained from End of Life Tyres, and due to the recycling process that is focused on the rubber rather than on the steel they come out crooked and with variable length. Although the effectiveness of RSFs had already been proven by previous research, the innovation of this work consists in the proposing the combined action of conventional rebars and RSFs to improve cracking behaviour. Therefore, the objective is to improve the sustainability of RC structures by, on the one hand, using recycled materials, and on the other improving their durability. A state of the art on cracking in RC elements is firstly drawn. It is then expanded to elements reinforced with both rebars and fibres (R/FRC elements). Finally, the simplified method for analysis of columns of long jointless structures already proposed by Pérez et al. is resumed, with a special focus on the points that conflict when taking into account the action of fibres. Afterwards, a model to describe sectional deformability and cracking of R/FRC elements is presented, taking also into account the effect of shrinkage (negative tension stiffening). The model is then used to implement the simplified method for columns. The novelty represented by this is that a comprehensive methodology to analyse this type of elements is presented. A preliminary experimental campaign consisting in small beams subjected to pure bending is described, with the objective of validating the effectiveness and usability in concrete of RSFs of two different types, and their behaviour when compared with commercial steel fibres. With the results and lessons learnt from this campaign in mind, the main experimental campaign is then described, consisting in cracking tests of eight unscaled beams in pure bending (varying RSF content, Ø/s,eff and concrete cover) and twelve columns subjected to imposed displacement and axial force (varying RSF content, Ø/s,eff and squashing load ratio). The results obtained from the main campaign are presented and discussed, with particular focus on the improvement in cracking behaviour for the beams and columns, and structural stiffness for the columns. They are then compared with the proposed model. The main parameters studied to describe cracking and sectional behaviours of the beam tests are crack spacing, mean steel strain and crack width, while for the column tests these were moment/curvature, stress in rebars and crack with at column embedment. The comparison showed satisfactory agreement between experimental results and model predictions. Moreover, it is pointed out the improvement in cracking behaviour due to the addition of RSF for elements with low reinforcement ratios, elements with low squashing load ratios and for crack width control of elements with large concrete covers, thus representing results with a immediate impact in engineering practice (slab design, tanks, integral structures, etc.). Applications of RSF to actual structures are finally presented. Two cases of elements in pure bending are presented, namely a simple supported beam and a water treatment tank. In both cases the addition of RSF to concrete leads to improvements in cracking behaviour. Then, using the simplified model for the serviceability analysis of columns of jointless structures, the maximum achievable jointless length of typical cases of a bridge and building is obtained. In XIIparticular, it is shown how the limitations of current engineering practice (this is especially the case of buildings) can be increased by considering the actual behaviour of RC supports. Then, the same cases are modified considering the use of RSF, and the improvements both in maximum achievable length and in crack width for a given length and imposed strain at the deck/first floor are shown.

Large-scale assessment of language proficiency: theoretical and pedagogical reflections on the use of multiple-choice tests

The new requirement placed on students in tertiary settings in Spain to demonstrate a B1 or a B2 proficiency level of English, in accordance with the Common European Framework of Reference for Languages (CEFRL), has led most Spanish universities to develop a program of certification or accreditation of the required level. The first part of this paper aims to provide a rationale for the type of test that has been developed at the Universidad Politécnica de Madrid for the accreditation of a B2 level, a multiple choice version, and to describe how it was constructed and validated. Then, in the second part of the paper, the results from its application to 924 students enrolled in different degree courses at a variety of schools and faculties at the university are analyzed based on a final test version item analysis. To conclude, some theoretical as well as practical conclusions about testing grammar that affect the teaching and learning process are drawn. RESUMEN. Las nuevas exigencias sobre niveles de competencia B1 y B2 en inglés según el Marco Común Europeo de Referencia para las Lenguas (MCERL) que se imponen sobre los estudiantes de grado y posgrado han llevado a la mayoría de las universidades españolas a desarrollar programas de acreditación o de certificación de estos niveles. La primera parte de este trabajo trata sobre las razones que fundamentan la elección de un tipo concreto de examen para la acreditación del nivel B2 de lengua inglesa en la Universidad Politécnica de Madrid. Se trata de un test de opción múltiple y en esta parte del trabajo se describe cómo fue diseñado y validado. En la segunda parte, se analizan los resultados de la aplicación del test a gran escala a un total de 924 estudiantes matriculados en varias escuelas y Facultades de la Universidad. Para terminar, se apuntan una serie de conclusiones teóricas y prácticas sobre la evaluación de la gramática y de qué modo influye en los procesos de enseñanza y aprendizaje.

Physical characterization of laser interaction and shock generation in laser shock processing: coupled theoretical-experimental analysis

Laser Shock Processing is developing as a key technology for the improvement of surface mechanical and corrosion resistance properties of metals due to its ability to introduce intense compressive residual stresses fields into high elastic limit materials by means of an intense laser driven shock wave generated by laser with intensities exceeding the 109 W/cm2 threshold, pulse energies in the range of 1 Joule and interaction times in the range of several ns. However, because of the relatively difficult-to-describe physics of shock wave formation in plasma following laser-matter interaction in solid state, only limited knowledge is available in the way of full comprehension and predictive assessment of the characteristic physical processes and material transformations with a specific consideration of real material properties. In the present paper, an account of the physical issues dominating the development of LSP processes from a moderately high intensity laser-matter interaction point of view is presented along with the theoretical and computational methods developed by the authors for their predictive assessment and new experimental contrast results obtained at laboratory scale.