Geometric diagnostics of complex patterns: Spiral defect chaos

Motivated by the observation of spiral patterns in a wide range of physical, chemical, and biological systems, we present an automated approach that aims at characterizing quantitatively spiral-like elements in complex stripelike patterns. The approach provides the location of the spiral tip and the size of the spiral arms in terms of their arc length and their winding number. In addition, it yields the number of pattern components (Betti number of order 1), as well as their size and certain aspects of their shape. We apply the method to spiral defect chaos in thermally driven Rayleigh- Bénard convection and find that the arc length of spirals decreases monotonically with decreasing Prandtl number of the fluid and increasing heating. By contrast, the winding number of the spirals is nonmonotonic in the heating. The distribution function for the number of spirals is significantly narrower than a Poisson distribution. The distribution function for the winding number shows approximately an exponential decay. It depends only weakly on the heating, but strongly on the Prandtl number. Large spirals arise only for larger Prandtl numbers. In this regime the joint distribution for the spiral length and the winding number exhibits a three-peak structure, indicating the dominance of Archimedean spirals of opposite sign and relatively straight sections. For small Prandtl numbers the distribution function reveals a large number of small compact pattern components.

Optimización de la Exactitud Geométrica al Integrar Diversas Fuentes de Datos en Proyectos de Inventario Forestal Basados en Escaneo Laser Aerotransportado=Optimizing Geometric Accuracy in Data Source Integration for Airborne Laser Scanning-based Forest Inventory Projects

La mayoría de las aplicaciones forestales del escaneo laser aerotransportado (ALS, del inglés airborne laser scanning) requieren la integración y uso simultaneo de diversas fuentes de datos, con el propósito de conseguir diversos objetivos. Los proyectos basados en sensores remotos normalmente consisten en aumentar la escala de estudio progresivamente a lo largo de varias fases de fusión de datos: desde la información más detallada obtenida sobre un área limitada (la parcela de campo), hasta una respuesta general de la cubierta forestal detectada a distancia de forma más incierta pero cubriendo un área mucho más amplia (la extensión cubierta por el vuelo o el satélite). Todas las fuentes de datos necesitan en ultimo termino basarse en las tecnologías de sistemas de navegación global por satélite (GNSS, del inglés global navigation satellite systems), las cuales son especialmente erróneas al operar por debajo del dosel forestal. Otras etapas adicionales de procesamiento, como la ortorectificación, también pueden verse afectadas por la presencia de vegetación, deteriorando la exactitud de las coordenadas de referencia de las imágenes ópticas. Todos estos errores introducen ruido en los modelos, ya que los predictores se desplazan de la posición real donde se sitúa su variable respuesta. El grado por el que las estimaciones forestales se ven afectadas depende de la dispersión espacial de las variables involucradas, y también de la escala utilizada en cada caso. Esta tesis revisa las fuentes de error posicional que pueden afectar a los diversos datos de entrada involucrados en un proyecto de inventario forestal basado en teledetección ALS, y como las propiedades del dosel forestal en sí afecta a su magnitud, aconsejando en consecuencia métodos para su reducción. También se incluye una discusión sobre las formas más apropiadas de medir exactitud y precisión en cada caso, y como los errores de posicionamiento de hecho afectan a la calidad de las estimaciones, con vistas a una planificación eficiente de la adquisición de los datos. La optimización final en el posicionamiento GNSS y de la radiometría del sensor óptico permitió detectar la importancia de este ultimo en la predicción de la desidad relativa de un bosque monoespecífico de Pinus sylvestris L. ABSTRACT Most forestry applications of airborne laser scanning (ALS) require the integration and simultaneous use of various data sources, pursuing a variety of different objectives. Projects based on remotely-sensed data generally consist in upscaling data fusion stages: from the most detailed information obtained for a limited area (field plot) to a more uncertain forest response sensed over a larger extent (airborne and satellite swath). All data sources ultimately rely on global navigation satellite systems (GNSS), which are especially error-prone when operating under forest canopies. Other additional processing stages, such as orthorectification, may as well be affected by vegetation, hence deteriorating the accuracy of optical imagery’s reference coordinates. These errors introduce noise to the models, as predictors displace from their corresponding response. The degree to which forest estimations are affected depends on the spatial dispersion of the variables involved and the scale used. This thesis reviews the sources of positioning errors which may affect the different inputs involved in an ALS-assisted forest inventory project, and how the properties of the forest canopy itself affects their magnitude, advising on methods for diminishing them. It is also discussed how accuracy should be assessed, and how positioning errors actually affect forest estimation, toward a cost-efficient planning for data acquisition. The final optimization in positioning the GNSS and optical image allowed to detect the importance of the latter in predicting relative density in a monospecific Pinus sylvestris L. forest.

Parametrization of the average ionization and radiative cooling rates of carbon plasmas in a wide range of density and temperature

In this work we present an analysis of the influence of the thermodynamic regime on the monochromatic emissivity, the radiative power loss and the radiative cooling rate for optically thin carbon plasmas over a wide range of electron temperature and density assuming steady state situations. Furthermore, we propose analytical expressions depending on the electron density and temperature for the average ionization and cooling rate based on polynomial fittings which are valid for the whole range of plasma conditions considered in this work.

Geometric documentation of the flour factory "El Puente Colgante" in Aranjuez (Madrid).

The goal of this communication is to offer, through computer-aided design tools, a methodology to recover and virtually reconstruct disappeared buildings of our industrial historical heritage. It will be applied to the case of the flour factory "El Puente Colgante" (The Suspended Bridge) in Aranjuez, which was demolished in 2001. The process is as follows: After a historical analysis of the evolution in time of the flour factory, a field work provides data allowing an info graphic reconstruction of the factory. Once this information has been processed, a lifting of the current state is made with AutoCAD, and a three-dimensional model is built with the Rhinoceros application. Then images of the ensemble are obtained with the applications Rhinoceros and V-Ray, ending with a postproduction with Photoshop. The proposed methodology has permitted to obtain a three-dimensional model of the flour factory ?El Puente Colgante? in Aranjuez, with an accurate virtual reconstruction of its original state prior to demolition. The procedure exposed is susceptible to be generalized for any other example of industrial architecture.

Looking beyond the average agricultural impacts in defining adaptation needs in Europe.

The effects of climate change on agriculture are often characterised by changes in the average productivity of crops; however, these indicators provide limited information regarding the risks associated with fluctuations in productivity resulting from future changes in climate variability that may also affect agriculture. In this context, this study evaluates the combined effects of the risks associated with anomalies reflected by changes in the mean crop yield and the variability of productivity in European agroclimatic regions under future climate change scenarios. The objective of this study is to evaluate adaptation needs and to identify regional effects that should be addressed with greater urgency in the light of the risks and opportunities that are identified. The results show differential effects on regional agriculture and highlight the importance of considering both regional average impacts and the variability in crop productivity in setting priorities for the adaptation and maintenance of rural incomes and agricultural insurance programmes

Analysis of pixel-mapping rounding on geometric distortion as a prediction for view synthesis distortion

We analyze the performance of the geometric distortion, incurred when coding depth maps in 3D Video, as an estimator of the distortion of synthesized views. Our analysis is motivated by the need of reducing the computational complexity required for the computation of synthesis distortion in 3D video encoders. We propose several geometric distortion models that capture (i) the geometric distortion caused by the depth coding error, and (ii) the pixel-mapping precision in view synthesis. Our analysis starts with the evaluation of the correlation of geometric distortion values obtained with these models and the actual distortion on synthesized views. Then, the different geometric distortion models are employed in the rate-distortion optimization cycle of depth map coding, in order to assess the results obtained by the correlation analysis. Results show that one of the geometric distortion models is performing consistently better than the other models in all tests. Therefore, it can be used as a reasonable estimator of the synthesis distortion in low complexity depth encoders.

Einstein-like geometric structures on surfaces

An AH (affine hypersurface) structure is a pair comprising a projective equivalence class of torsion-free connections and a conformal structure satisfying a compatibility condition which is automatic in two dimensions. They generalize Weyl structures, and a pair of AH structures is induced on a co-oriented non-degenerate immersed hypersurface in flat affine space. The author has defined for AH structures Einstein equations, which specialize on the one hand to the usual Einstein Weyl equations and, on the other hand, to the equations for affine hyperspheres. Here these equations are solved for Riemannian signature AH structures on compact orientable surfaces, the deformation spaces of solutions are described, and some aspects of the geometry of these structures are related. Every such structure is either Einstein Weyl (in the sense defined for surfaces by Calderbank) or is determined by a pair comprising a conformal structure and a cubic holomorphic differential, and so by a convex flat real projective structure. In the latter case it can be identified with a solution of the Abelian vortex equations on an appropriate power of the canonical bundle. On the cone over a surface of genus at least two carrying an Einstein AH structure there are Monge-Amp`ere metrics of Lorentzian and Riemannian signature and a Riemannian Einstein K"ahler affine metric. A mean curvature zero spacelike immersed Lagrangian submanifold of a para-K"ahler four-manifold with constant para-holomorphic sectional curvature inherits an Einstein AH structure, and this is used to deduce some restrictions on such immersions.

Geometric Study of the Weak Equilibrium in a Weighted Case for a Two-Dimensional Competition Game

In this work, an improvement of the results presented by [1] Abellanas et al. (Weak Equilibrium in a Spatial Model. International Journal of Game Theory, 40(3), 449-459) is discussed. Concretely, this paper investigates an abstract game of competition between two players that want to earn the maximum number of points from a finite set of points in the plane. It is assumed that the distribution of these points is not uniform, so an appropriate weight to each position is assigned. A definition of equilibrium which is weaker than the classical one is included in order to avoid the uniqueness of the equilibrium position typical of the Nash equilibrium in these kinds of games. The existence of this approximated equilibrium in the game is analyzed by means of computational geometry techniques.

Analysis of the geometric altimetry to support aircraft optimal trajectories within the future 4d trajectory management

Over the past few years, the common practice within air traffic management has been that commercial aircraft fly by following a set of predefined routes to reach their destination. Currently, aircraft operators are requesting more flexibility to fly according to their prefer- ences, in order to achieve their business objectives. Due to this reason, much research effort is being invested in developing different techniques which evaluate aircraft optimal trajectory and traffic synchronisation. Also, the inefficient use of the airspace using barometric altitude overall in the landing and takeoff phases or in Continuous Descent Approach (CDA) trajectories where currently it is necessary introduce the necessary reference setting (QNH or QFE). To solve this problem and to permit a better airspace management born the interest of this research. Where the main goals will be to evaluate the impact, weakness and strength of the use of geometrical altitude instead of the use of barometric altitude. Moreover, this dissertation propose the design a simplified trajectory simulator which is able to predict aircraft trajectories. The model is based on a three degrees of freedom aircraft point mass model that can adapt aircraft performance data from Base of Aircraft Data, and meteorological information. A feature of this trajectory simulator is to support the improvement of the strategic and pre-tactical trajectory planning in the future Air Traffic Management. To this end, the error of the tool (aircraft Trajectory Simulator) is measured by comparing its performance variables with actual flown trajectories obtained from Flight Data Recorder information. The trajectory simulator is validated by analysing the performance of different type of aircraft and considering different routes. A fuel consumption estimation error was identified and a correction is proposed for each type of aircraft model. In the future Air Traffic Management (ATM) system, the trajectory becomes the fundamental element of a new set of operating procedures collectively referred to as Trajectory-Based Operations (TBO). Thus, governmental institutions, academia, and industry have shown a renewed interest for the application of trajectory optimisation techniques in com- mercial aviation. The trajectory optimisation problem can be solved using optimal control methods. In this research we present and discuss the existing methods for solving optimal control problems focusing on direct collocation, which has received recent attention by the scientific community. In particular, two families of collocation methods are analysed, i.e., Hermite-Legendre-Gauss-Lobatto collocation and the pseudospectral collocation. They are first compared based on a benchmark case study: the minimum fuel trajectory problem with fixed arrival time. For the sake of scalability to more realistic problems, the different meth- ods are also tested based on a real Airbus 319 El Cairo-Madrid flight. Results show that pseudospectral collocation, which has shown to be numerically more accurate and computa- tionally much faster, is suitable for the type of problems arising in trajectory optimisation with application to ATM. Fast and accurate optimal trajectory can contribute properly to achieve the new challenges of the future ATM. As atmosphere uncertainties are one of the most important issues in the trajectory plan- ning, the final objective of this dissertation is to have a magnitude order of how different is the fuel consumption under different atmosphere condition. Is important to note that in the strategic phase planning the optimal trajectories are determined by meteorological predictions which differ from the moment of the flight. The optimal trajectories have shown savings of at least 500 [kg] in the majority of the atmosphere condition (different pressure, and temperature at Mean Sea Level, and different lapse rate temperature) with respect to the conventional procedure simulated at the same atmosphere condition.This results show that the implementation of optimal profiles are beneficial under the current Air traffic Management (ATM).

Time-resolved evolution of coherent structures in turbulent channels

El objetivo de esta tesis es estudiar la dinámica de la capa logarítmica de flujos turbulentos de pared. En concreto, proponemos un nuevo modelo estructural utilizando diferentes tipos de estructuras coherentes: sweeps, eyecciones, grupos de vorticidad y streaks. La herramienta utilizada es la simulación numérica directa de canales turbulentos. Desde los primeros trabajos de Theodorsen (1952), las estructuras coherentes han jugado un papel fundamental para entender la organización y dinámica de los flujos turbulentos. A día de hoy, datos procedentes de simulaciones numéricas directas obtenidas en instantes no contiguos permiten estudiar las propiedades fundamentales de las estructuras coherentes tridimensionales desde un punto de vista estadístico. Sin embargo, la dinámica no puede ser entendida en detalle utilizando sólo instantes aislados en el tiempo, sino que es necesario seguir de forma continua las estructuras. Aunque existen algunos estudios sobre la evolución temporal de las estructuras más pequeñas a números de Reynolds moderados, por ejemplo Robinson (1991), todavía no se ha realizado un estudio completo a altos números de Reynolds y para todas las escalas presentes de la capa logarítmica. El objetivo de esta tesis es llevar a cabo dicho análisis. Los problemas más interesantes los encontramos en la región logarítmica, donde residen las cascadas de vorticidad, energía y momento. Existen varios modelos que intentan explicar la organización de los flujos turbulentos en dicha región. Uno de los más extendidos fue propuesto por Adrian et al. (2000) a través de observaciones experimentales y considerando como elemento fundamental paquetes de vórtices con forma de horquilla que actúan de forma cooperativa para generar rampas de bajo momento. Un modelo alternativo fué ideado por del Álamo & Jiménez (2006) utilizando datos numéricos. Basado también en grupos de vorticidad, planteaba un escenario mucho más desorganizado y con estructuras sin forma de horquilla. Aunque los dos modelos son cinemáticamente similares, no lo son desde el punto de vista dinámico, en concreto en lo que se refiere a la importancia que juega la pared en la creación y vida de las estructuras. Otro punto importante aún sin resolver se refiere al modelo de cascada turbulenta propuesto por Kolmogorov (1941b), y su relación con estructuras coherentes medibles en el flujo. Para dar respuesta a las preguntas anteriores, hemos desarrollado un nuevo método que permite seguir estructuras coherentes en el tiempo y lo hemos aplicado a simulaciones numéricas de canales turbulentos con números de Reynolds lo suficientemente altos como para tener un rango de escalas no trivial y con dominios computacionales lo suficientemente grandes como para representar de forma correcta la dinámica de la capa logarítmica. Nuestros esfuerzos se han desarrollado en cuatro pasos. En primer lugar, hemos realizado una campaña de simulaciones numéricas directas a diferentes números de Reynolds y tamaños de cajas para evaluar el efecto del dominio computacional en las estadísticas de primer orden y el espectro. A partir de los resultados obtenidos, hemos concluido que simulaciones con cajas de longitud 2vr y ancho vr veces la semi-altura del canal son lo suficientemente grandes para reproducir correctamente las interacciones entre estructuras coherentes de la capa logarítmica y el resto de escalas. Estas simulaciones son utilizadas como punto de partida en los siguientes análisis. En segundo lugar, las estructuras coherentes correspondientes a regiones con esfuerzos de Reynolds tangenciales intensos (Qs) en un canal turbulento han sido estudiadas extendiendo a tres dimensiones el análisis de cuadrantes, con especial énfasis en la capa logarítmica y la región exterior. Las estructuras coherentes han sido identificadas como regiones contiguas del espacio donde los esfuerzos de Reynolds tangenciales son más intensos que un cierto nivel. Los resultados muestran que los Qs separados de la pared están orientados de forma isótropa y su contribución neta al esfuerzo de Reynolds medio es nula. La mayor contribución la realiza una familia de estructuras de mayor tamaño y autosemejantes cuya parte inferior está muy cerca de la pared (ligada a la pared), con una geometría compleja y dimensión fractal « 2. Estas estructuras tienen una forma similar a una ‘esponja de placas’, en comparación con los grupos de vorticidad que tienen forma de ‘esponja de cuerdas’. Aunque el número de objetos decae al alejarnos de la pared, la fracción de esfuerzos de Reynolds que contienen es independiente de su altura, y gran parte reside en unas pocas estructuras que se extienden más allá del centro del canal, como en las grandes estructuras propuestas por otros autores. Las estructuras dominantes en la capa logarítmica son parejas de sweeps y eyecciones uno al lado del otro y con grupos de vorticidad asociados que comparten las dimensiones y esfuerzos con los remolinos ligados a la pared propuestos por Townsend. En tercer lugar, hemos estudiado la evolución temporal de Qs y grupos de vorticidad usando las simulaciones numéricas directas presentadas anteriormente hasta números de Reynolds ReT = 4200 (Reynolds de fricción). Las estructuras fueron identificadas siguiendo el proceso descrito en el párrafo anterior y después seguidas en el tiempo. A través de la interseción geométrica de estructuras pertenecientes a instantes de tiempo contiguos, hemos creado gratos de conexiones temporales entre todos los objetos y, a partir de ahí, definido ramas primarias y secundarias, de tal forma que cada rama representa la evolución temporal de una estructura coherente. Una vez que las evoluciones están adecuadamente organizadas, proporcionan toda la información necesaria para caracterizar la historia de las estructuras desde su nacimiento hasta su muerte. Los resultados muestran que las estructuras nacen a todas las distancias de la pared, pero con mayor probabilidad cerca de ella, donde la cortadura es más intensa. La mayoría mantienen tamaños pequeños y no viven mucho tiempo, sin embargo, existe una familia de estructuras que crecen lo suficiente como para ligarse a la pared y extenderse a lo largo de la capa logarítmica convirtiéndose en las estructuras observas anteriormente y descritas por Townsend. Estas estructuras son geométricamente autosemejantes con tiempos de vida proporcionales a su tamaño. La mayoría alcanzan tamaños por encima de la escala de Corrsin, y por ello, su dinámica está controlada por la cortadura media. Los resultados también muestran que las eyecciones se alejan de la pared con velocidad media uT (velocidad de fricción) y su base se liga a la pared muy rápidamente al inicio de sus vidas. Por el contrario, los sweeps se mueven hacia la pared con velocidad -uT y se ligan a ella más tarde. En ambos casos, los objetos permanecen ligados a la pared durante 2/3 de sus vidas. En la dirección de la corriente, las estructuras se desplazan a velocidades cercanas a la convección media del flujo y son deformadas por la cortadura. Finalmente, hemos interpretado la cascada turbulenta, no sólo como una forma conceptual de organizar el flujo, sino como un proceso físico en el cual las estructuras coherentes se unen y se rompen. El volumen de una estructura cambia de forma suave, cuando no se une ni rompe, o lo hace de forma repentina en caso contrario. Los procesos de unión y rotura pueden entenderse como una cascada directa (roturas) o inversa (uniones), siguiendo el concepto de cascada de remolinos ideado por Richardson (1920) y Obukhov (1941). El análisis de los datos muestra que las estructuras con tamaños menores a 30η (unidades de Kolmogorov) nunca se unen ni rompen, es decir, no experimentan el proceso de cascada. Por el contrario, aquellas mayores a 100η siempre se rompen o unen al menos una vez en su vida. En estos casos, el volumen total ganado y perdido es una fracción importante del volumen medio de la estructura implicada, con una tendencia ligeramente mayor a romperse (cascada directa) que a unirse (cascade inversa). La mayor parte de interacciones entre ramas se debe a roturas o uniones de fragmentos muy pequeños en la escala de Kolmogorov con estructuras más grandes, aunque el efecto de fragmentos de mayor tamaño no es despreciable. También hemos encontrado que las roturas tienen a ocurrir al final de la vida de la estructura y las uniones al principio. Aunque los resultados para la cascada directa e inversa no son idénticos, son muy simétricos, lo que sugiere un alto grado de reversibilidad en el proceso de cascada. ABSTRACT The purpose of the present thesis is to study the dynamics of the logarithmic layer of wall-bounded turbulent flows. Specifically, to propose a new structural model based on four different coherent structures: sweeps, ejections, clusters of vortices and velocity streaks. The tool used is the direct numerical simulation of time-resolved turbulent channels. Since the first work by Theodorsen (1952), coherent structures have played an important role in the understanding of turbulence organization and its dynamics. Nowadays, data from individual snapshots of direct numerical simulations allow to study the threedimensional statistical properties of those objects, but their dynamics can only be fully understood by tracking them in time. Although the temporal evolution has already been studied for small structures at moderate Reynolds numbers, e.g., Robinson (1991), a temporal analysis of three-dimensional structures spanning from the smallest to the largest scales across the logarithmic layer has yet to be performed and is the goal of the present thesis. The most interesting problems lie in the logarithmic region, which is the seat of cascades of vorticity, energy, and momentum. Different models involving coherent structures have been proposed to represent the organization of wall-bounded turbulent flows in the logarithmic layer. One of the most extended ones was conceived by Adrian et al. (2000) and built on packets of hairpins that grow from the wall and work cooperatively to gen- ´ erate low-momentum ramps. A different view was presented by del Alamo & Jim´enez (2006), who extracted coherent vortical structures from DNSs and proposed a less organized scenario. Although the two models are kinematically fairly similar, they have important dynamical differences, mostly regarding the relevance of the wall. Another open question is whether such a model can be used to explain the cascade process proposed by Kolmogorov (1941b) in terms of coherent structures. The challenge would be to identify coherent structures undergoing a turbulent cascade that can be quantified. To gain a better insight into the previous questions, we have developed a novel method to track coherent structures in time, and used it to characterize the temporal evolutions of eddies in turbulent channels with Reynolds numbers high enough to include a non-trivial range of length scales, and computational domains sufficiently long and wide to reproduce correctly the dynamics of the logarithmic layer. Our efforts have followed four steps. First, we have conducted a campaign of direct numerical simulations of turbulent channels at different Reynolds numbers and box sizes, and assessed the effect of the computational domain in the one-point statistics and spectra. From the results, we have concluded that computational domains with streamwise and spanwise sizes 2vr and vr times the half-height of the channel, respectively, are large enough to accurately capture the dynamical interactions between structures in the logarithmic layer and the rest of the scales. These simulations are used in the subsequent chapters. Second, the three-dimensional structures of intense tangential Reynolds stress in plane turbulent channels (Qs) have been studied by extending the classical quadrant analysis to three dimensions, with emphasis on the logarithmic and outer layers. The eddies are identified as connected regions of intense tangential Reynolds stress. Qs are then classified according to their streamwise and wall-normal fluctuating velocities as inward interactions, outward interactions, sweeps and ejections. It is found that wall-detached Qs are isotropically oriented background stress fluctuations, common to most turbulent flows, and do not contribute to the mean stress. Most of the stress is carried by a selfsimilar family of larger wall-attached Qs, increasingly complex away from the wall, with fractal dimensions « 2. They have shapes similar to ‘sponges of flakes’, while vortex clusters resemble ‘sponges of strings’. Although their number decays away from the wall, the fraction of the stress that they carry is independent of their heights, and a substantial part resides in a few objects extending beyond the centerline, reminiscent of the very large scale motions of several authors. The predominant logarithmic-layer structures are sideby- side pairs of sweeps and ejections, with an associated vortex cluster, and dimensions and stresses similar to Townsend’s conjectured wall-attached eddies. Third, the temporal evolution of Qs and vortex clusters are studied using time-resolved DNS data up to ReT = 4200 (friction Reynolds number). The eddies are identified following the procedure presented above, and then tracked in time. From the geometric intersection of structures in consecutive fields, we have built temporal connection graphs of all the objects, and defined main and secondary branches in a way that each branch represents the temporal evolution of one coherent structure. Once these evolutions are properly organized, they provide the necessary information to characterize eddies from birth to death. The results show that the eddies are born at all distances from the wall, although with higher probability near it, where the shear is strongest. Most of them stay small and do not last for long times. However, there is a family of eddies that become large enough to attach to the wall while they reach into the logarithmic layer, and become the wall-attached structures previously observed in instantaneous flow fields. They are geometrically self-similar, with sizes and lifetimes proportional to their distance from the wall. Most of them achieve lengths well above the Corrsin’ scale, and hence, their dynamics are controlled by the mean shear. Eddies associated with ejections move away from the wall with an average velocity uT (friction velocity), and their base attaches very fast at the beginning of their lives. Conversely, sweeps move towards the wall at -uT, and attach later. In both cases, they remain attached for 2/3 of their lives. In the streamwise direction, eddies are advected and deformed by the local mean velocity. Finally, we interpret the turbulent cascade not only as a way to conceptualize the flow, but as an actual physical process in which coherent structures merge and split. The volume of an eddy can change either smoothly, when they are not merging or splitting, or through sudden changes. The processes of merging and splitting can be thought of as a direct (when splitting) or an inverse (when merging) cascade, following the ideas envisioned by Richardson (1920) and Obukhov (1941). It is observed that there is a minimum length of 30η (Kolmogorov units) above which mergers and splits begin to be important. Moreover, all eddies above 100η split and merge at least once in their lives. In those cases, the total volume gained and lost is a substantial fraction of the average volume of the structure involved, with slightly more splits (direct cascade) than mergers. Most branch interactions are found to be the shedding or absorption of Kolmogorov-scale fragments by larger structures, but more balanced splits or mergers spanning a wide range of scales are also found to be important. The results show that splits are more probable at the end of the life of the eddy, while mergers take place at the beginning of the life. Although the results for the direct and the inverse cascades are not identical, they are found to be very symmetric, which suggests a high degree of reversibility of the cascade process.

Characterization of rock joints by fractal analysis

From a physical perspective, a joint experiences fracturing processes that affect the rock at both microscopic and macroscopic levels. The result is a behaviour that follows a fractal structure. In the first place, for saw-tooth roughness profiles, the use of the triadic Koch curve appears to be adequate and by means of known correlations the JRC parameter is obtained from the angle measured on the basis of the height and length of the roughnesses. Therefore, JRC remains related to the geometric pattern that defines roughness by fractal analysis. In the second place, to characterise the geometry of irregularities with softened profiles, consequently, is proposed a characterisation of the fractal dimension of the joints with a circumference arc generator that is dependent on an average contact angle with regard to the mid-plane. The correlation between the JRC and the fractal dimension of the model is established with a defined statistical ratio.

Spatial analysis of geometric design consistency and road sight distance

Because of the high number of crashes occurring on highways, it is necessary to intensify the search for new tools that help in understanding their causes. This research explores the use of a geographic information system (GIS) for an integrated analysis, taking into account two accident-related factors: design consistency (DC) (based on vehicle speed) and available sight distance (ASD) (based on visibility). Both factors require specific GIS software add-ins, which are explained. Digital terrain models (DTMs), vehicle paths, road centerlines, a speed prediction model, and crash data are integrated in the GIS. The usefulness of this approach has been assessed through a study of more than 500 crashes. From a regularly spaced grid, the terrain (bare ground) has been modeled through a triangulated irregular network (TIN). The length of the roads analyzed is greater than 100 km. Results have shown that DC and ASD could be related to crashes in approximately 4% of cases. In order to illustrate the potential of GIS, two crashes are fully analyzed: a car rollover after running off road on the right side and a rear-end collision of two moving vehicles. Although this procedure uses two software add-ins that are available only for ArcGIS, the study gives a practical demonstration of the suitability of GIS for conducting integrated studies of road safety.

Diseño de un modelo para la identificación y análisis de tramos de carreteras sin accidentes : una nueva visión de la seguridad vial

El planteamiento tradicional de análisis de la accidentalidad en carretera pasa por la consideración de herramientas paliativas, como son la identificación y gestión de los puntos negros o tramos de concentración de accidentes, o preventivas, como las auditorías e inspecciones de seguridad vial. En esta tesis doctoral se presenta un planteamiento complementario a estas herramientas, desde una perspectiva novedosa: la consideración de los tramos donde no se producen accidentes; son los denominados Tramos Blancos. La tesis persigue demostrar que existen determinados parámetros del diseño de las carreteras y del tráfico que, bajo características generales similares de las vías, tienen influencia en el hecho de que se produzcan o no accidentes, adicionalmente a la exposición al riesgo, como factor principal, y a otros factores. La propia definición de los Tramos Blancos, entendidos como tramos de carreteras de longitud representativa donde no se han producido accidentes con víctimas mortales o heridos graves durante un periodo largo de tiempo, garantiza que esta situación no se produzca como consecuencia de la aleatoriedad de los accidentes, sino que pudiera deberse a una confluencia específica de determinados parámetros de la geometría de la vía y del tráfico total y de vehículos pesados. Para el desarrollo de esta investigación se han considerado la red de autopistas de peaje y las carreteras convencionales de la Red del Estado de España, que supone un total de 17.000 kilómetros, y los datos de accidentes con víctimas mortales y heridos graves en el periodo 2006-2010, ambos incluidos, en estas redes (un total de 10.000 accidentes). La red viaria objeto de análisis supone el 65% de la longitud de la Red de Carreteras del Estado, por la que circula el 33% de su tráfico; en ella se produjeron en el año 2013 el 47% de los accidentes con víctimas y el 60% de las víctimas mortales de la Red de Carreteras del Estado. Durante la investigación se ha desarrollado una base de datos de 250.130 registros y más de 3.5 millones de datos en el caso de las autopistas de peaje de la Red de Carreteras del Estado y de 935.402 registros y más de 14 millones de datos en el caso de la red convencional del Estado analizada. Tanto las autopistas de peaje como las carreteras convencionales han sido clasificadas según sus características de tráfico, de manera que se valoren vías con nivel de exposición al riesgo similar. Para cada tipología de vía, se ha definido como longitud de referencia para que un tramo se considere Tramo Blanco la longitud igual al percentil 95 de las longitudes de tramos sin accidentes con heridos graves o víctimas mortales durante el periodo 2006-2010. En el caso de las autopistas de peaje, en la tipología que ha sido considerada para la definición del modelo, esta longitud de referencia se estableció en 14.5 kilómetros, mientras que en el caso de las carreteras convencionales, se estableció en 7.75 kilómetros. Para cada uno de los tipos de vía considerados se han construido una base de datos en la que se han incluido las variables de existencia o no de Tramo Blanco, así como las variables de tráfico (intensidad media diaria total, intensidad de vehículos pesados y porcentaje de vehículos pesados ), la velocidad media y las variables de geometría (número de carriles, ancho de carril, ancho de arcén derecho e izquierdo, ancho de calzada y plataforma, radio, peralte, pendiente y visibilidad directa e inversa en los casos disponibles); como variables adicionales, se han incluido el número de accidentes con víctimas, los fallecidos y heridos graves, índices de peligrosidad, índices de mortalidad y exposición al riesgo. Los trabajos desarrollados para explicar la presencia de Tramos Blancos en la red de autopistas de peaje han permitido establecer las diferencias entre los valores medios de las variables de tráfico y diseño geométrico en Tramos Blancos respecto a tramos no blancos y comprobar que estas diferencias son significativas. Así mismo, se ha podido calibrar un modelo de regresión logística que explica parcialmente la existencia de Tramos Blancos, para rangos de tráfico inferiores a 10.000 vehículos diarios y para tráficos entre 10.000 y 15.000 vehículos diarios. Para el primer grupo (menos de 10.000 vehículos al día), las variables que han demostrado tener una mayor influencia en la existencia de Tramo Blanco son la velocidad media de circulación, el ancho de carril, el ancho de arcén izquierdo y el porcentaje de vehículos pesados. Para el segundo grupo (entre 10.000 y 15.000 vehículos al día), las variables independientes más influyentes en la existencia de Tramo Blanco han sido la velocidad de circulación, el ancho de calzada y el porcentaje de vehículos pesados. En el caso de las carreteras convencionales, los diferentes análisis realizados no han permitido identificar un modelo que consiga una buena clasificación de los Tramos Blancos. Aun así, se puede afirmar que los valores medios de las variables de intensidad de tráfico, radio, visibilidad, peralte y pendiente presentan diferencias significativas en los Tramos Blancos respecto a los no blancos, que varían en función de la intensidad de tráfico. Los resultados obtenidos deben considerarse como la conclusión de un análisis preliminar, dado que existen otros parámetros, tanto de diseño de la vía como de la circulación, el entorno, el factor humano o el vehículo que podrían tener una influencia en el hecho que se analiza, y no se han considerado por no disponer de esta información. En esta misma línea, el análisis de las circunstancias que rodean al viaje que el usuario de la vía realiza, su tipología y motivación es una fuente de información de interés de la que no se tienen datos y que permitiría mejorar el análisis de accidentalidad en general, y en particular el de esta investigación. Adicionalmente, se reconocen limitaciones en el desarrollo de esta investigación, en las que sería preciso profundizar en el futuro, reconociendo así nuevas líneas de investigación de interés. The traditional approach to road accidents analysis has been based in the use of palliative tools, such as black spot (or road sections) identification and management, or preventive tools, such as road safety audits and inspections. This thesis shows a complementary approach to the existing tools, from a new perspective: the consideration of road sections where no accidents have occurred; these are the so-called White Road Sections. The aim of this thesis is to show that there are certain design parameters and traffic characteristics which, under similar circumstances for roads, have influence in the fact that accidents occur, in addition to the main factor, which is the risk exposure, and others. White Road Sections, defined as road sections of a representative length, where no fatal accidents or accidents involving serious injured have happened during a long period of time, should not be a product of randomness of accidents; on the contrary, they might be the consequence of a confluence of specific parameters of road geometry, traffic volumes and heavy vehicles traffic volumes. For this research, the toll motorway network and single-carriageway network of the Spanish National Road Network have been considered, which is a total of 17.000 kilometers; fatal accidents and those involving serious injured from the period 2006-2010 have been considered (a total number of 10.000 accidents). The road network covered means 65% of the total length of the National Road Network, which allocates 33% of traffic volume; 47% of accidents with victims and 60% of fatalities happened in these road networks during 2013. During the research, a database of 250.130 registers and more than 3.5 million data for toll motorways and 935.042 registers and more than 14 million data for single carriageways of the National Road Network was developed. Both toll motorways and single-carriageways have been classified according to their traffic characteristics, so that the analysis is performed over roads with similar risk exposure. For each road type, a reference length for White Road Section has been defined, as the 95 percentile of all road sections lengths without accidents (with fatalities or serious injured) for 2006-2010. For toll motorways, this reference length concluded to be 14.5 kilometers, while for single-carriageways, it was defined as 7.75 kilometers. A detailed database was developed for each type of road, including the variable “existence of White Road Section”, as well as variables of traffic (average daily traffic volume, heavy vehicles average daily traffic and percentage of heavy vehicles from the total traffic volume), average speed and geometry variables (number of lanes, width of lane, width of shoulders, carriageway width, platform width, radius, superelevation, slope and visibility); additional variables, such as number of accidents with victims, number of fatalities or serious injured, risk and fatality rates and risk exposure, have also been included. Research conducted for the explanation of the presence of White Road Sections in the toll motorway network have shown statistically significant differences in the average values of variables of traffic and geometric design in White Road Sections compared with other road sections. In addition, a binary logistic model for the partial explanation of the presence of White Road Sections was developed, for traffic volumes lower than 10.000 daily vehicles and for those running from 10.000 to 15.000 daily vehicles. For the first group, the most influent variables for the presence of White Road Sections were the average speed, width of lane, width of left shoulder and percentage of heavy vehicles. For the second group, the most influent variables were found to be average speed, carriageway width and percentage of heavy vehicles. For single-carriageways, the different analysis developed did not reach a proper model for the explanation of White Road Sections. However, it can be assumed that the average values of the variables of traffic volume, radius, visibility, superelevation and slope show significant differences in White Road Sections if compared with others, which also vary with traffic volumes. Results obtained should be considered as a conclusion of a preliminary analysis, as there are other parameters, not only design-related, but also regarding traffic, environment, human factor and vehicle which could have an influence in the fact under research, but this information has not been considered in the analysis, as it was not available. In parallel, the analysis of the circumstances around the trip, including its typology and motivation is an interesting source of information, from which data are not available; the availability of this information would be useful for the improvement of accident analysis, in general, and for this research work, in particular. In addition, there are some limitations in the development of the research work; it would be necessary to develop an in-depth analysis in the future, thus assuming new research lines of interest.

Methodology for instantaneous average exhaust gas mass flow rate measurement

This paper presents a new methodology for measurement of the instantaneous average exhaust mass flow rate in reciprocating internal combustion engines to be used to determinate real driving emissions on light duty vehicles, as part of a Portable Emission Measurement System (PEMS). Firstly a flow meter, named MIVECO flow meter, was designed based on a Pitot tube adapted to exhaust gases which are characterized by moisture and particle content, rapid changes in flow rate and chemical composition, pulsating and reverse flow at very low engine speed. Then, an off-line methodology was developed to calculate the instantaneous average flow, considering the ?square root error? phenomenon. The paper includes the theoretical fundamentals, the developed flow meter specifications, the calibration tests, the description of the proposed off-line methodology and the results of the validation test carried out in a chassis dynamometer, where the validity of the mass flow meter and the methodology developed are demonstrated.