923 resultados para Mean Value Theorem


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Changes in the Southeast Asia monsoon winds and surface circulation patterns since the last glaciation are inferred using multiple paleoceanographic indicators including planktic foraminifer faunal abundances, fauna and alkenones sea-surface temperature (SST) estimates, oxygen and carbon isotopes of planktic and benthic foraminifers, and sedimentary fluxes of carbonates and organic carbon obtained from deep-sea core SCS90-36 from the South China Sea (SCS) (17°59.70'N, 111°29.64'E at water depth 2050 m). All these paleoceanographic evidences indicate marked changes in the SCS ocean system over the last glacial toward the Holocene. Planktic foraminiferal faunal SST estimates show stable warm-season SST of 28.6°C, close to the modern value, throughout the glacial-interglacial cycle. In contrast, cold-season SST increases gradually from 23.6°C in the last glacial to a mean value of 26.4°C in the Holocene with a fluctuation of about 3°C during 13-16 ka. SST estimates by UK'37 method reveal less variability and are in average 1-3°C lower than the fauna-derived winter-season SST. These patterns reveal that the seasonality of the SST is not only higher by about 3-4°C in the glacial, but also a function of the winter season SST. Sedimentation rates decrease from the last glacial-deglacial stage to the Holocene due to a reduction in supply of terrigenous components, which led to an increase of carbonate contents. Total organic carbon (TOC) contents of primarily marine sources decrease from the last glacial-deglacial to the Holocene. The last deglaciation is also characterized by high surface productivity as indicated by increased ketones abundances and high mass accumulation rates (MAR) of the TOC and carbonates. The gradient of planktic foraminifer ocygen and carbon isotopes of between surface dwellers and deep dwellers increases significantly toward Termination I and Holocene, and is indiscernibly small in the carbon isotope gradient of between 14 and 24 ka, revealing a deep-mixing condition in surface layers prior to 10 ka. The glacial-interglacial fluctuation of the carbon isotope value of a benthic foraminifer is 0.61%. which is significantly larger than a global mean value. The large carbon isotope fluctuation indicates an amplification of marginal-sea effects which is most likely resulted from an increase in surface productivity in the northern SCS during the last glacial-deglacial stage. The multiple proxies consistently indicate that the last glacial-deglacial stage winter monsoon in the Southeast Asia was probably strengthened in the northern SCS, leading to a development of deep-mixing surface layer conditions and a more efficient nutrient cycling which supports more marine organic carbon production.

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An improved procedure for lithium isotope analysis using Li3PO4 as the ion source has been investigated for application to geological samples. The 7Li/6Li ratio is measured using double rhenium filament thermal ionization mass spectrometry in which isotopic fractionation is minimized at high temperatures. The method produces a stable, high intensity Li+ ion beam that allows measurement of nanogram quantities of lithium. This results in a reduction in sample size of up to 1000 times relative to that required for the established Li2BO2+ method while maintaining a comparable precision of better than 1? (1 sigma). Replicate analyses of the NBS L-SVEC Li2CO3 standard yielded a mean value of 12.1047+/-0.0043 (n=21), which is close to the reported absolute value of 12.02+/-0.03. Intercalibration with a wide range of geological samples shows excellent agreement between the Li3PO4 and Li2BO2+ techniques. Replicate analyses of seawater and a fresh submarine basalt display high precision results that agree with previous measurements. Taking advantage of the high ionization efficiency of the phosphate ion source, we have made the first measurements of the lithium concentration (by isotope dilution) and isotopic composition of calcareous foraminiferal tests and other marine carbonates. Preliminary results indicate that substantial lithium exchange occurs between carbonate sediments and their interstitial waters. In addition, a possible link between lithium paleoceanography and paleoclimate during the last 1000 ky may be derived from planktonic foraminiferal tests. This highly sensitive technique can be applied in the examination of low lithium reservoirs and thereby provide insight into some fundamental aspects of lithium geochemistry.

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The Mauritanian coastal area is one of the most biologically productive upwelling regions in the world ocean. Shipboard observations carried out during maximum upwelling season and short-term moored observations are used to investigate diapycnal mixing processes and to quantify diapycnal fluxes of nutrients. The observations indicate strong tide-topography interactions that are favored by near-critical angles occurring on large parts of the continental slope. Moored velocity observations reveal the existence of highly nonlinear internal waves and bores and levels of internal wave spectra are strongly elevated near the buoyancy frequency. Dissipation rates of turbulent kinetic energy at the slope and shelf determined from microstructure measurements in the upper 200 m averages to ? = 5 × 10-8 W kg-1. Particularly elevated dissipation rates were found at the continental slope close to the shelf break, being enhanced by a factor of 100 to 1000 compared to dissipation rates farther offshore. Vertically integrated dissipation rates per unit volume are strongest at the upper continental slope reaching values of up to 30 mW m-2. A comparison of fine-scale parameterizations of turbulent dissipation rates for shelf regions and the open ocean to the measured dissipation rates indicates deficiencies in reproducing the observations. Diapycnal nitrate fluxes above the continental slope at the base of the mixed layer yielding a mean value of 12 × 10-2 µmol m-2 s-1 are amongst the largest published to date. However, they seem to only represent a minor contribution (10% to 25%) to the net community production in the upwelling region.

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Fifty samples of Roman time soil preserved under the thick ash layer of the A.D.79 eruption of Mt Vesuvius were studied by pollen analysis: 33 samples from a former vineyard surrounding a Villa Rustica at Boscoreale (excavation site 40 x 50 m), 13 samples taken along the 60 m long swimming pool in the sculpture garden of the Villa of Poppaea at Oplontis, and four samples from the formal garden (12.4 x 17.5 m) of the House of the Gold Bracelet in Pompeii. To avoid contamination with modern pollen all samples were taken immediately after uncovering a new portion of the A.D. 79 soil. For comparison also samples of modern Italian soils were studied. Using standard methods for pollen preparation the pollen content of 15 of the archaeological samples proved to be too little to reach a pollen sum of more than 100 grains. The pollen spectra of these samples are not shown in the pollen tables. (Flotation with a sodium tungstate solution, Na2WO4, D = 2.05, following treatment with HCl and NaOH would probably have given a somewhat better result. This method was, however, not available as too expensive at that time.) Although the archaeological samples were taken a few meters apart their pollen values differ very much from one sample to the other. E.g., at Boscoreale (SW quarter). the pollen values of Pinus range from 1.5 to 54.5% resp. from 1 to 244 pine pollen grains per 1 gram of soil, the extremes even found under pine trees. Vitis pollen was present in 7 of the 11 vineyard samples from Boscoreale (NE quarter) only. Although a maximum of 21.7% is reached, the values of Vitis are mostly below 1.5%. Even the values of common weeds differ very much, not only at Boscoreale, but also at the other two sites. The pollen concentration values show similar variations: 3 to 3053 grains and spores were found in 1 g of soil. The mean value (290) is much less than the number of pollen grains, which would fall on 1 cm2 of soil surface during one year. In contrast, the pollen and spore concentrations of the recent soil samples, treated in exactly the same manner, range from 9313 to almost 80000 grains per 1 g of soil. Evidently most of the Roman time pollen has disappeared since its deposition, the reasons not being clear. Not even species which are known to have been cultivated in the garden of Oplontis, like Citrus and Nerium, plant species with easily distinguishable pollen grains, could be traced by pollen analysis. The loss of most of the pollen grains originally contained in the soil prohibits any detailed interpretation of the Pompeian pollen data. The pollen counts merely name plant species which grew in the region, but not necessarily on the excavated plots.

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The aim of the present study was to evaluate the influence of different light quality, especially ultraviolet radiation (UVR), on the dynamics of volatile halogenated organic compounds (VHOCs) at the sea surface. Short term experiments were conducted with floating gas-tight mesocosms of different optical qualities. Six halocarbons (CH3I, CHCl3, CH2Br2, CH2ClI, CHBr3 and CH2I2), known to be produced by phytoplankton, together with a variety of biological and environmental variables were measured in the coastal southern Baltic Sea and in the Raunefjord (North Sea). These experiments showed that ambient levels of UVR have no significant influence on VHOC dynamics in the natural systems. We attribute it to the low radiation doses that phytoplankton cells receive in a normal turbulent surface mixed layer. The VHOC concentrations were influenced by their production and removal processes, but they were not correlated with biological or environmental parameters investigated. Diatoms were most likely the dominant biogenic source of VHOCs in the Baltic Sea experiment, whereas in the Raunefjord experiment macroalgae probably contributed strongly to the production of VHOCs. The variable stable carbon isotope signatures (d13C values) of bromoform (CHBr3) also indicate that different autotrophic organisms were responsible for CHBr3 production in the two coastal environments. In the Raunefjord, despite strong daily variations in CHBr3 concentration, the carbon isotopic ratio was fairly stable with a mean value of -26 per mil. During the declining spring phytoplankton bloom in the Baltic Sea, the d13C values of CHBr3 were enriched in 13C and showed noticeable diurnal changes (-12 per mil ± 4). These results show that isotope signature analysis is a useful tool to study both the origin and dynamics of VHOCs in natural systems.

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The traditional teaching methods used for training civil engineers are currently being called into question as a result of the new knowledge and skills now required by the labor market. In addition, the European Higher Education Area is requesting that students be given a greater say in their learning. In the subject called Construction and Building Materials at the Civil Engineering School of the Universidad Politécnica de Madrid, a path was set three academic years ago to lead to an improvement in traditional teaching by introducing active methodologies. The innovations are based on cooperative learning, new technologies, and continuous assessment. The writers’ proposal is to offer their experience as a contribution to the debate on how students can be encouraged to acquire the skills currently demanded from a civil engineer, though not overlooking solid, top-quality training. From the outcomes obtained, it can be concluded that using new teaching techniques to supplement a traditional approach provides more opportunities for students to learn while boosting their motivation. In our case, the introduction of these changes has resulted in an increased pass rate of 29% on average, when such a figure is considered in the light of the mean value of passes during the last decade.

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Se han clasificado visualmente, según la norma española UNE 56544; 150 piezas de madera aserrada de pino radiata procedentes de Cataluña (España) con una sección de 80x150 mm y una longitud de 2.500 mm. Esta norma establece dos calidades visuales (ME-1 y ME-2) para piezas con grueso menor o igual que 70 mm y una única calidad visual (MEG) para gruesos mayores de 70 mm. Con el fin de conocer el efecto frontera entre la pequeña y la gran escuadría se clasificaron las piezas según ambas categorías. Se determinó la tensión de rotura en flexión, el módulo de elasticidad en flexión y la densidad de cada pieza mediante el ensayo de acuerdo con la norma UNE-EN 408 siguiendo los ajustes definidos en la norma UNE-EN 384. Un 53 % de las piezas se clasificaron como MEG con una resistencia característica a flexión de 28 N/mm2 y un valor medio del módulo de elasticidad de 9.900 N/mm2. Por otra, un 42 % de las piezas se clasificaron como ME-2 y sólo un 3 % como ME-1; en este caso las propiedades mecánicas de la calidad ME-2 no se alejan mucho de las de la calidad MEG. El elevado porcentaje de piezas rechazadas (47 % frente a la MEG) se debe principalmente al defecto de alabeo responsable de un 39 % de rechazo. Si no se considera el alabeo en la clasificación el porcentaje de rechazo desciende al 17 % y las propiedades mecánicas de la calidad MEG presentan un valor característico de resistencia a flexión de 21 N/mm2 y un módulo de elasticidad de 9.100 N/mm2. A sample of 150 pieces of radiata pine sawn timber with 180x120 mm in cross-section and 2.500 mm in length sourcing from Catalonia (Spain) were visually graded according to Spanish standard UNE 56544. This standard establish two visual grades (ME-1 and ME-2) for timber pieces with thickness equal or less than 70 mm, and one grade (MEG) for thickness bigger than 70 mm. In order to know the border effect between small and larger cross-section the pieces were graded in both categories. The modulus of rupture, modulus of elasticity and density were obtained by test according to EN 408 standard and the adjustments of EN 384. A 53 % of pieces were classified as MEG with a characteristic bending strength of 28 N/mm2 and a mean value of MOE of 9.900 N/mm2. On the other hand, a 42 % of pieces were classified as ME-2 and only a 3 % as ME-1; in this case the mechanical properties of ME-2 are not far from MEG properties. The high percentage of rejected pieces (47 % vs MEG) is mainly due to the twist defect with a 39 % of rejected pieces. If twist is not considered in the grading process the reject percentage decreases to 17 % and the mechanical properties of MEG grade present a characteristic value of bending strength of 21 N/mm2 and a MOE of 9.100 N/mm2.

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RESUMEN La dispersión del amoniaco (NH3) emitido por fuentes agrícolas en medias distancias, y su posterior deposición en el suelo y la vegetación, pueden llevar a la degradación de ecosistemas vulnerables y a la acidificación de los suelos. La deposición de NH3 suele ser mayor junto a la fuente emisora, por lo que los impactos negativos de dichas emisiones son generalmente mayores en esas zonas. Bajo la legislación comunitaria, varios estados miembros emplean modelos de dispersión inversa para estimar los impactos de las emisiones en las proximidades de las zonas naturales de especial conservación. Una revisión reciente de métodos para evaluar impactos de NH3 en distancias medias recomendaba la comparación de diferentes modelos para identificar diferencias importantes entre los métodos empleados por los distintos países de la UE. En base a esta recomendación, esta tesis doctoral compara y evalúa las predicciones de las concentraciones atmosféricas de NH3 de varios modelos bajo condiciones, tanto reales como hipotéticas, que plantean un potencial impacto sobre ecosistemas (incluidos aquellos bajo condiciones de clima Mediterráneo). En este sentido, se procedió además a la comparación y evaluación de varias técnicas de modelización inversa para inferir emisiones de NH3. Finalmente, se ha desarrollado un modelo matemático simple para calcular las concentraciones de NH3 y la velocidad de deposición de NH3 en ecosistemas vulnerables cercanos a una fuente emisora. La comparativa de modelos supuso la evaluación de cuatro modelos de dispersión (ADMS 4.1; AERMOD v07026; OPS-st v3.0.3 y LADD v2010) en un amplio rango de casos hipotéticos (dispersión de NH3 procedente de distintos tipos de fuentes agrícolas de emisión). La menor diferencia entre las concentraciones medias estimadas por los distintos modelos se obtuvo para escenarios simples. La convergencia entre las predicciones de los modelos fue mínima para el escenario relativo a la dispersión de NH3 procedente de un establo ventilado mecánicamente. En este caso, el modelo ADMS predijo concentraciones significativamente menores que los otros modelos. Una explicación de estas diferencias podríamos encontrarla en la interacción de diferentes “penachos” y “capas límite” durante el proceso de parametrización. Los cuatro modelos de dispersión fueron empleados para dos casos reales de dispersión de NH3: una granja de cerdos en Falster (Dinamarca) y otra en Carolina del Norte (EEUU). Las concentraciones medias anuales estimadas por los modelos fueron similares para el caso americano (emisión de granjas ventiladas de forma natural y balsa de purines). La comparación de las predicciones de los modelos con concentraciones medias anuales medidas in situ, así como la aplicación de los criterios establecidos para la aceptación estadística de los modelos, permitió concluir que los cuatro modelos se comportaron aceptablemente para este escenario. No ocurrió lo mismo en el caso danés (nave ventilada mecánicamente), en donde el modelo LADD no dio buenos resultados debido a la ausencia de procesos de “sobreelevacion de penacho” (plume-rise). Los modelos de dispersión dan a menudo pobres resultados en condiciones de baja velocidad de viento debido a que la teoría de dispersión en la que se basan no es aplicable en estas condiciones. En situaciones de frecuente descenso en la velocidad del viento, la actual guía de modelización propone usar un modelo que sea eficaz bajo dichas condiciones, máxime cuando se realice una valoración que tenga como objeto establecer una política de regularización. Esto puede no ser siempre posible debido a datos meteorológicos insuficientes, en cuyo caso la única opción sería utilizar un modelo más común, como la versión avanzada de los modelos Gausianos ADMS o AERMOD. Con el objetivo de evaluar la idoneidad de estos modelos para condiciones de bajas velocidades de viento, ambos modelos fueron utilizados en un caso con condiciones Mediterráneas. Lo que supone sucesivos periodos de baja velocidad del viento. El estudio se centró en la dispersión de NH3 procedente de una granja de cerdos en Segovia (España central). Para ello la concentración de NH3 media mensual fue medida en 21 localizaciones en torno a la granja. Se realizaron también medidas de concentración de alta resolución en una única localización durante una campaña de una semana. En este caso, se evaluaron dos estrategias para mejorar la respuesta del modelo ante bajas velocidades del viento. La primera se basó en “no zero wind” (NZW), que sustituyó periodos de calma con el mínimo límite de velocidad del viento y “accumulated calm emissions” (ACE), que forzaban al modelo a calcular las emisiones totales en un periodo de calma y la siguiente hora de no-calma. Debido a las importantes incertidumbres en los datos de entrada del modelo (inputs) (tasa de emisión de NH3, velocidad de salida de la fuente, parámetros de la capa límite, etc.), se utilizó el mismo caso para evaluar la incertidumbre en la predicción del modelo y valorar como dicha incertidumbre puede ser considerada en evaluaciones del modelo. Un modelo dinámico de emisión, modificado para el caso de clima Mediterráneo, fue empleado para estimar la variabilidad temporal en las emisiones de NH3. Así mismo, se realizó una comparativa utilizando las emisiones dinámicas y la tasa constante de emisión. La incertidumbre predicha asociada a la incertidumbre de los inputs fue de 67-98% del valor medio para el modelo ADMS y entre 53-83% del valor medio para AERMOD. La mayoría de esta incertidumbre se debió a la incertidumbre del ratio de emisión en la fuente (50%), seguida por la de las condiciones meteorológicas (10-20%) y aquella asociada a las velocidades de salida (5-10%). El modelo AERMOD predijo mayores concentraciones que ADMS y existieron más simulaciones que alcanzaron los criterios de aceptabilidad cuando se compararon las predicciones con las concentraciones medias anuales medidas. Sin embargo, las predicciones del modelo ADMS se correlacionaron espacialmente mejor con las mediciones. El uso de valores dinámicos de emisión estimados mejoró el comportamiento de ADMS, haciendo empeorar el de AERMOD. La aplicación de estrategias destinadas a mejorar el comportamiento de este último tuvo efectos contradictorios similares. Con el objeto de comparar distintas técnicas de modelización inversa, varios modelos (ADMS, LADD y WindTrax) fueron empleados para un caso no agrícola, una colonia de pingüinos en la Antártida. Este caso fue empleado para el estudio debido a que suponía la oportunidad de obtener el primer factor de emisión experimental para una colonia de pingüinos antárticos. Además las condiciones eran propicias desde el punto de vista de la casi total ausencia de concentraciones ambiente (background). Tras el trabajo de modelización existió una concordancia suficiente entre las estimaciones obtenidas por los tres modelos. De este modo se pudo definir un factor de emisión de para la colonia de 1.23 g NH3 por pareja criadora por día (con un rango de incertidumbre de 0.8-2.54 g NH3 por pareja criadora por día). Posteriores aplicaciones de técnicas de modelización inversa para casos agrícolas mostraron también un buen compromiso estadístico entre las emisiones estimadas por los distintos modelos. Con todo ello, es posible concluir que la modelización inversa es una técnica robusta para estimar tasas de emisión de NH3. Modelos de selección (screening) permiten obtener una rápida y aproximada estimación de los impactos medioambientales, siendo una herramienta útil para evaluaciones de impactos en tanto que permite eliminar casos que presentan un riesgo potencial de daño bajo. De esta forma, lo recursos del modelo pueden Resumen (Castellano) destinarse a casos en donde la posibilidad de daño es mayor. El modelo de Cálculo Simple de los Límites de Impacto de Amoniaco (SCAIL) se desarrolló para obtener una estimación de la concentración media de NH3 y de la tasa de deposición seca asociadas a una fuente agrícola. Está técnica de selección, basada en el modelo LADD, fue evaluada y calibrada con diferentes bases de datos y, finalmente, validada utilizando medidas independientes de concentraciones realizadas cerca de las fuentes. En general SCAIL dio buenos resultados de acuerdo a los criterios estadísticos establecidos. Este trabajo ha permitido definir situaciones en las que las concentraciones predichas por modelos de dispersión son similares, frente a otras en las que las predicciones difieren notablemente entre modelos. Algunos modelos nos están diseñados para simular determinados escenarios en tanto que no incluyen procesos relevantes o están más allá de los límites de su aplicabilidad. Un ejemplo es el modelo LADD que no es aplicable en fuentes con velocidad de salida significativa debido a que no incluye una parametrización de sobreelevacion del penacho. La evaluación de un esquema simple combinando la sobreelevacion del penacho y una turbulencia aumentada en la fuente mejoró el comportamiento del modelo. Sin embargo más pruebas son necesarias para avanzar en este sentido. Incluso modelos que son aplicables y que incluyen los procesos relevantes no siempre dan similares predicciones. Siendo las razones de esto aún desconocidas. Por ejemplo, AERMOD predice mayores concentraciones que ADMS para dispersión de NH3 procedente de naves de ganado ventiladas mecánicamente. Existe evidencia que sugiere que el modelo ADMS infraestima concentraciones en estas situaciones debido a un elevado límite de velocidad de viento. Por el contrario, existen evidencias de que AERMOD sobreestima concentraciones debido a sobreestimaciones a bajas Resumen (Castellano) velocidades de viento. Sin embrago, una modificación simple del pre-procesador meteorológico parece mejorar notablemente el comportamiento del modelo. Es de gran importancia que estas diferencias entre las predicciones de los modelos sean consideradas en los procesos de evaluación regulada por los organismos competentes. Esto puede ser realizado mediante la aplicación del modelo más útil para cada caso o, mejor aún, mediante modelos múltiples o híbridos. ABSTRACT Short-range atmospheric dispersion of ammonia (NH3) emitted by agricultural sources and its subsequent deposition to soil and vegetation can lead to the degradation of sensitive ecosystems and acidification of the soil. Atmospheric concentrations and dry deposition rates of NH3 are generally highest near the emission source and so environmental impacts to sensitive ecosystems are often largest at these locations. Under European legislation, several member states use short-range atmospheric dispersion models to estimate the impact of ammonia emissions on nearby designated nature conservation sites. A recent review of assessment methods for short-range impacts of NH3 recommended an intercomparison of the different models to identify whether there are notable differences to the assessment approaches used in different European countries. Based on this recommendation, this thesis compares and evaluates the atmospheric concentration predictions of several models used in these impact assessments for various real and hypothetical scenarios, including Mediterranean meteorological conditions. In addition, various inverse dispersion modelling techniques for the estimation of NH3 emissions rates are also compared and evaluated and a simple screening model to calculate the NH3 concentration and dry deposition rate at a sensitive ecosystem located close to an NH3 source was developed. The model intercomparison evaluated four atmospheric dispersion models (ADMS 4.1; AERMOD v07026; OPS-st v3.0.3 and LADD v2010) for a range of hypothetical case studies representing the atmospheric dispersion from several agricultural NH3 source types. The best agreement between the mean annual concentration predictions of the models was found for simple scenarios with area and volume sources. The agreement between the predictions of the models was worst for the scenario representing the dispersion from a mechanically ventilated livestock house, for which ADMS predicted significantly smaller concentrations than the other models. The reason for these differences appears to be due to the interaction of different plume-rise and boundary layer parameterisations. All four dispersion models were applied to two real case studies of dispersion of NH3 from pig farms in Falster (Denmark) and North Carolina (USA). The mean annual concentration predictions of the models were similar for the USA case study (emissions from naturally ventilated pig houses and a slurry lagoon). The comparison of model predictions with mean annual measured concentrations and the application of established statistical model acceptability criteria concluded that all four models performed acceptably for this case study. This was not the case for the Danish case study (mechanically ventilated pig house) for which the LADD model did not perform acceptably due to the lack of plume-rise processes in the model. Regulatory dispersion models often perform poorly in low wind speed conditions due to the model dispersion theory being inapplicable at low wind speeds. For situations with frequent low wind speed periods, current modelling guidance for regulatory assessments is to use a model that can handle these conditions in an acceptable way. This may not always be possible due to insufficient meteorological data and so the only option may be to carry out the assessment using a more common regulatory model, such as the advanced Gaussian models ADMS or AERMOD. In order to assess the suitability of these models for low wind conditions, they were applied to a Mediterranean case study that included many periods of low wind speed. The case study was the dispersion of NH3 emitted by a pig farm in Segovia, Central Spain, for which mean monthly atmospheric NH3 concentration measurements were made at 21 locations surrounding the farm as well as high-temporal-resolution concentration measurements at one location during a one-week campaign. Two strategies to improve the model performance for low wind speed conditions were tested. These were ‘no zero wind’ (NZW), which replaced calm periods with the minimum threshold wind speed of the model and ‘accumulated calm emissions’ (ACE), which forced the model to emit the total emissions during a calm period during the first subsequent non-calm hour. Due to large uncertainties in the model input data (NH3 emission rates, source exit velocities, boundary layer parameters), the case study was also used to assess model prediction uncertainty and assess how this uncertainty can be taken into account in model evaluations. A dynamic emission model modified for the Mediterranean climate was used to estimate the temporal variability in NH3 emission rates and a comparison was made between the simulations using the dynamic emissions and a constant emission rate. Prediction uncertainty due to model input uncertainty was 67-98% of the mean value for ADMS and between 53-83% of the mean value for AERMOD. Most of this uncertainty was due to source emission rate uncertainty (~50%), followed by uncertainty in the meteorological conditions (~10-20%) and uncertainty in exit velocities (~5-10%). AERMOD predicted higher concentrations than ADMS and more of the simulations met the model acceptability criteria when compared with the annual mean measured concentrations. However, the ADMS predictions were better correlated spatially with the measurements. The use of dynamic emission estimates improved the performance of ADMS but worsened the performance of AERMOD and the application of strategies to improved model performance had similar contradictory effects. In order to compare different inverse modelling techniques, several models (ADMS, LADD and WindTrax) were applied to a non-agricultural case study of a penguin colony in Antarctica. This case study was used since it gave the opportunity to provide the first experimentally-derived emission factor for an Antarctic penguin colony and also had the advantage of negligible background concentrations. There was sufficient agreement between the emission estimates obtained from the three models to define an emission factor for the penguin colony (1.23 g NH3 per breeding pair per day with an uncertainty range of 0.8-2.54 g NH3 per breeding pair per day). This emission estimate compared favourably to the value obtained using a simple micrometeorological technique (aerodynamic gradient) of 0.98 g ammonia per breeding pair per day (95% confidence interval: 0.2-2.4 g ammonia per breeding pair per day). Further application of the inverse modelling techniques for a range of agricultural case studies also demonstrated good agreement between the emission estimates. It is concluded, therefore, that inverse dispersion modelling is a robust technique for estimating NH3 emission rates. Screening models that can provide a quick and approximate estimate of environmental impacts are a useful tool for impact assessments because they can be used to filter out cases that potentially have a minimal environmental impact allowing resources to be focussed on more potentially damaging cases. The Simple Calculation of Ammonia Impact Limits (SCAIL) model was developed as a screening model to provide an estimate of the mean NH3 concentration and dry deposition rate downwind of an agricultural source. This screening tool, based on the LADD model, was evaluated and calibrated with several experimental datasets and then validated using independent concentration measurements made near sources. Overall SCAIL performed acceptably according to established statistical criteria. This work has identified situations where the concentration predictions of dispersion models are similar and other situations where the predictions are significantly different. Some models are simply not designed to simulate certain scenarios since they do not include the relevant processes or are beyond the limits of their applicability. An example is the LADD model that is not applicable to sources with significant exit velocity since the model does not include a plume-rise parameterisation. The testing of a simple scheme combining a momentum-driven plume rise and increased turbulence at the source improved model performance, but more testing is required. Even models that are applicable and include the relevant process do not always give similar predictions and the reasons for this need to be investigated. AERMOD for example predicts higher concentrations than ADMS for dispersion from mechanically ventilated livestock housing. There is evidence to suggest that ADMS underestimates concentrations in these situations due to a high wind speed threshold. Conversely, there is also evidence that AERMOD overestimates concentrations in these situations due to overestimation at low wind speeds. However, a simple modification to the meteorological pre-processor appears to improve the performance of the model. It is important that these differences between the predictions of these models are taken into account in regulatory assessments. This can be done by applying the most suitable model for the assessment in question or, better still, using multiple or hybrid models.

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The aim of this paper is to evaluate the performance of mobile WiMAX technology for users in a highly mobility scenario for an operating frequency of 3.5 GHz. By utilizing a modified version of the extended Erceg’s propagation model, based on the introduction of Rayleigh fading due to multipath, we have calculated the received desired power and the interference power to obtain the statistical signal-to-interference-plusnoise rate (as a function of mean value and variance of cochannel interference) and the user throughput. A rural scenario composed of a transmitting base station and users in moving vehicles along a cell sector is proposed. The obtained results about coverage and throughput have been simulated by a tool built in MATLAB

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Surface tension induced convection in a liquid bridge held between two parallel, coaxial, solid disks is considered. The surface tension gradient is produced by a small temperature gradient parallel Co the undisturbed surface. The study is performed by using a mathematical regular perturbation approach based on a small parameter, e, which measures the deviation of the imposed temperature field from its mean value. The first order velocity field is given by a Stokes-type problem (viscous terms are dominant) with relatively simple boundary conditions. The first order temperature field is that imposed from the end disks on a liquid bridge immersed in a non-conductive fluid. Radiative effects are supposed to be negligible. The second order temperature field, which accounts for convective effects, is split into three components, one due to the bulk motion, and the other two to the distortion of the free surface. The relative importance of these components in terms of the heat transfer to or from the end disks is assessed

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Purpose: Accurate delineation of the rectum is of high importance in off-line adaptive radiation therapy since it is a major dose-limiting organ in prostate cancer radiotherapy. The intensity-based deformable image registration (DIR) methods cannot create a correct spatial transformation if there is no correspondence between the template and the target images. The variation of rectal filling, gas, or feces, creates a noncorrespondence in image intensities that becomes a great obstacle for intensity-based DIR. Methods: In this study the authors have designed and implemented a semiautomatic method to create a rectum mask in pelvic computed tomography (CT) images. The method, that includes a DIR based on the demons algorithm, has been tested in 13 prostate cancer cases, each comprising of two CT scans, for a total of 26 CT scans. Results: The use of the manual segmentation in the planning image and the proposed rectum mask method (RMM) method in the daily image leads to an improvement in the DIR performance in pelvic CT images, obtaining a mean value of overlap volume index = 0.89, close to the values obtained using the manual segmentations in both images. Conclusions: The application of the RMM method in the daily image and the manual segmentations in the planning image during prostate cancer treatments increases the performance of the registration in presence of rectal fillings, obtaining very good agreement with a physician's manual contours.

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Purpose: Accurate delineation of the rectum is of high importance in off-line adaptive radiation therapy since it is a major dose-limiting organ in prostate cancer radiotherapy. The intensity-based deformable image registration (DIR) methods cannot create a correct spatial transformation if there is no correspondence between the template and the target images. The variation of rectal filling, gas, or feces, creates a noncorrespondence in image intensities that becomes a great obstacle for intensity-based DIR. Methods: In this study the authors have designed and implemented a semiautomatic method to create a rectum mask in pelvic computed tomography (CT) images. The method, that includes a DIR based on the demons algorithm, has been tested in 13 prostate cancer cases, each comprising of two CT scans, for a total of 26 CT scans. Results: The use of the manual segmentation in the planning image and the proposed rectum mask method (RMM) method in the daily image leads to an improvement in the DIR performance in pelvic CT images, obtaining a mean value of overlap volume index = 0.89, close to the values obtained using the manual segmentations in both images. Conclusions: The application of the RMM method in the daily image and the manual segmentations in the planning image during prostate cancer treatments increases the performance of the registration in presence of rectal fillings, obtaining very good agreement with a physician's manual contours.

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One of the more aspects that have shaped the landscape is the human impact. The human impact has the clearest indicator of the density of settlements in a particular geographic region. In this paper we study all settlements shown on the map of the Kingdom of Valencia, Spain Geographic Atlas (AGE) of Tomas Lopez (1788), and their correspondence with the current ones. To meet this goal we have developed a specific methodology, the systematic study of all existing settlements in historical cartography. This will determine which have disappeared and which have been renamed. The material used has been the historical cartography of Tomas Lopez, part of the AGE (1789), the Kingdom of Valencia (1789), sheets numbers (78, 79, 80 and 81); Current mapping of the provinces of Alicante, Valencia, Castellon, Teruel, Tattagona and Cuenca; As main software ArcGis V.9.3. The steps followed in the methodology are as follows: 1. Check the scale of the maps. Analyze the possible use of a spherical earth model. 2. Geo-reference of maps with latitude and longitude framework. Move the historical longitude origin to the origin longitude of modern cartography. 3 Digitize of all population settlements or cities. 4 Identify historic settlements or cities corresponding with current ones. 5. If the maps have the same orientation and scale, replace the coordinate transformation of historical settlements with a new one, by a translation in latitude and longitude equal to the calculated mean value of all ancient map points corresponding to the new. 6. Calculation of absolute accuracy of the two maps, i.e. the linear distance between the points of both maps. 7 draw in the GIS, the settlements without correspondence, in the current coordinates, and with a circle of mean error of the sheet, in order to locate their current location. If there are actual settlements exist within this circle, they are candidates to be the searched settlements. We analyzed more than 2000 settlements represented in the Atlas of Tomas Lopez of the Kingdom of Valencia (1789), of which almost 14.5% have no correspondence with the existing settlements. The rural landscape evolution of the Valencia, oldest kingdom of Valencia, one can say that can be severely affected by the anthropization suffered in the period from 1789 to the present, since 70% of existing settlements actually have appeared after Tomas Lopez¿s cartography, dated on 1789

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Purpose: In this paper we study all settlements shown on the map of the Province of Madrid, sheet number 1 of AGE (Atlas Geográfico de España of Tomas Lopez 1804) and their correspondence with the current ones. This map is divided in to zones: Madrid and Almonacid de Zorita. Method: The steps followed in the methodology are as follow: 1. Geo-reference of maps with latitude and longitude framework. Move the historical longitude origin to the origin longitude of modern cartography. 2 Digitize of all population settlements or cities (97 on Madrid and 42 on Almonacid de Zorita), 3 Identify historic settlements or cities corresponding with current ones. 4. If the maps have the same orientation and scale, replace the coordinate transformation of historical settlements with a new one, by a translation in latitude and longitude equal to the calculated mean value of all ancient map points corresponding to the new. 5. Calculation of absolute accuracy of the two maps. 6 draw in the GIS, the settlements accuracy. Result: It was found that all AGE settlements have good correspondence with current, ie only 27 settlements lost in Madrid and 2 in Almonacid. The average accuracy is 2.3 and 5.7 km to Madrid and Almonacid de Zorita respectively. Discussion & Conclusion: The final accuracy map obtained shows that there is less error in the middle of the map. This study highlights the great work done by Tomas Lopez in performing this mapping without fieldwork. This demonstrates the great value that has been the work of Tomas Lopez in the history of cartography.

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La presente tesis es un estudio analítico y numérico del electrospray. En la configuración más sencilla, un caudal constante del líquido a atomizar, que debe tener una cierta conductividad eléctrica, se inyecta en un medio dieléctrico (un gas u otro líquido inmiscible con el primero) a través de un tubo capilar metálico. Entre este tubo y un electrodo lejano se aplica un voltaje continuo que origina un campo eléctrico en el líquido conductor y en el espacio que lo rodea. El campo eléctrico induce una corriente eléctrica en el líquido, que acumula carga en su superficie, y da lugar a un esfuerzo eléctrico sobre la superficie, que tiende a alargarla en la dirección del campo eléctrico. El líquido forma un menisco en el extremo del tubo capilar cuando el campo eléctrico es suficientemente intenso y el caudal suficientemente pequeño. Las variaciones de presión y los esfuerzos viscosos asociados al movimiento del líquido son despreciables en la mayor parte de este menisco, siendo dominantes los esfuerzos eléctrico y de tensión superficial que actúan sobre la superficie del líquido. En el modo de funcionamiento llamado de conochorro, el balance de estos esfuerzos hace que el menisco adopte una forma cónica (el cono de Taylor) en una región intermedia entre el extremo del tubo y la punta del menisco. La velocidad del líquido aumenta al acercarse al vértice del cono, lo cual propicia que las variaciones de la presión en el líquido generadas por la inercia o por la viscosidad entren en juego, desequilibrando el balance de esfuerzos mencionado antes. Como consecuencia, del vértice del cono sale un delgado chorro de líquido, que transporta la carga eléctrica que se acumula en la superficie. La acción del campo eléctrico tangente a la superficie sobre esta carga origina una tracción eléctrica que tiende a alargar el chorro. Esta tracción no es relevante en el menisco, donde el campo eléctrico tangente a la superficie es muy pequeño, pero se hace importante en el chorro, donde es la causa del movimiento del líquido. Lejos del cono, el chorro puede o bien desarrollar una inestabilidad asimétrica que lo transforma en una espiral (whipping) o bien romperse en un spray de gotas prácticamente monodispersas cargadas eléctricamente. La corriente eléctrica transportada por el líquido es la suma de la corriente de conducción en el interior del líquido y la corriente debida a la convección de la carga acumulada en su superficie. La primera domina en el menisco y la segunda en el chorro lejano, mientras que las dos son comparables en una región intermedia de transferencia de corriente situada al comienzo del chorro aunque aguas abajo de la región de transición cono-chorro, en la que el menisco deja de ser un cono de Taylor. Para un campo exterior dado, la acumulación de carga eléctrica en la superficie del líquido reduce el campo eléctrico en el interior del mismo, que llega a anularse cuando la carga alcanza un estado final de equilibrio. El tiempo característico de este proceso es el tiempo de relajación dieléctrica, que es una propiedad del líquido. Cuando el tiempo de residencia del líquido en la región de transición cono-chorro (o en otra región del campo fluido) es grande frente al tiempo de relajación dieléctrica, la carga superficial sigue una sucesión de estados de equilibrio y apantalla al líquido del campo exterior. Cuando esta condición deja de cumplirse, aparecen efectos de relajación de carga, que se traducen en que el campo exterior penetra en el líquido, a no ser que su constante dieléctrica sea muy alta, en cuyo caso el campo inducido por la carga de polarización evita la entrada del campo exterior en el menisco y en una cierta región del chorro. La carga eléctrica en equilibrio en la superficie de un menisco cónico intensifica el campo eléctrico y determina su variación espacial hasta distancias aguas abajo del menisco del orden de su tamaño. Este campo, calculado por Taylor, es independiente del voltaje aplicado, por lo que las condiciones locales del flujo y el valor de la corriente eléctrica son también independientes del voltaje en tanto los tamaños de las regiones que determinan estas propiedades sean pequeños frente al tamaño del menisco. Los resultados experimentales publicados en la literatura muestran que existe un caudal mínimo para el que el modo cono-chorro que acabamos de describir deja de existir. El valor medio y la desviación típica de la distribución de tamaños de las gotas generadas por un electrospray son mínimos cuando se opera cerca del caudal mínimo. A pesar de que los mecanismos responsables del caudal mínimo han sido muy estudiados, no hay aún una teoría completa del mismo, si bien su existencia parece estar ligada a la aparición de efectos de relajación de carga en la región de transición cono-chorro. En esta tesis, se presentan estimaciones de orden de magnitud, algunas existentes y otras nuevas, que muestran los balances dominantes responsables de las distintas regiones de la estructura asintótica de la solución en varios casos de interés. Cuando la inercia del líquido juega un papel en la transición cono-chorro, los resultados muestran que la región de transferencia de corriente, donde la mayor parte de la corriente pasa a la superficie, está en el chorro aguas abajo de la región de transición cono-chorro. Los efectos de relajación de carga aparecen de forma simultánea en el chorro y la región de transición cuando el caudal se disminuye hasta valores de un cierto orden. Para caudales aún menores, los efectos de relajación de carga se notan en el menisco, en una región grande comparada con la de transición cono-chorro. Cuando el efecto de las fuerzas de viscosidad es dominante en la región de transición, la región de transferencia de corriente está en el chorro pero muy próxima a la región de transición cono-chorro. Al ir disminuyendo el caudal, los efectos de relajación de carga aparecen progresivamente en el chorro, en la región de transición y por último en el menisco. Cuando el caudal es mucho mayor que el mínimo del modo cono-chorro, el menisco deja de ser cónico. El campo eléctrico debido al voltaje aplicado domina en la región de transferencia de corriente, y tanto la corriente eléctrica como el tamaño de las diferentes regiones del problema pasan a depender del voltaje aplicado. Como resultado de esta dependencia, el plano caudal-voltaje se divide en diferentes regiones que se analizan separadamente. Para caudales suficientemente grandes, la inercia del líquido termina dominando frente a las fuerzas de la viscosidad. Estos resultados teóricos se han validado con simulaciones numéricas. Para ello se ha formulado un modelo simplificado del flujo, el campo eléctrico y el transporte de carga en el menisco y el chorro del electrospray. El movimiento del líquido se supone casi unidireccional y se describe usando la aproximación de Cosserat para un chorro esbelto. Esta aproximación, ampliamente usada en la literatura, permite simular con relativa facilidad múltiples casos y cubrir amplios rangos de valores de los parámetros reteniendo los efectos de la viscosidad y la inercia del líquido. Los campos eléctricos dentro y fuera del liquido están acoplados y se calculan sin simplificación alguna usando un método de elementos de contorno. La solución estacionaria del problema se calcula mediante un método iterativo. Para explorar el espacio de los parámetros, se comienza calculando una solución para valores fijos de las propiedades del líquido, el voltaje aplicado y el caudal. A continuación, se usa un método de continuación que permite delinear la frontera del dominio de existencia del modo cono-chorro, donde el método iterativo deja de converger. Cuando el efecto de la inercia del líquido domina en la región de transición cono-chorro, el caudal mínimo para el cual el método iterativo deja de converger es del orden del valor estimado del caudal para el que comienza a haber efectos de relajación de carga en el chorro y el cono. Aunque las simulaciones no convergen por debajo de dicho caudal, el valor de la corriente eléctrica para valores del caudal ligeramente mayores parece ajustarse a las estimaciones para caudales menores, reflejando un posible cambio en los balances aplicables. Por el contrario, cuando las fuerzas viscosas dominan en la región de transición, se pueden obtener soluciones estacionarias para caudales bastante menores que aquel para el que aparecen efectos de relajación de carga en la región de transición cono-chorro. Los resultados numéricos obtenidos para estos pequeños caudales se ajustan perfectamente a las estimaciones de orden de magnitud que se describen en la memoria. Por último, se incluyen como anexos dos estudios teóricos que han surgido de forma natural durante el desarrollo de la tesis. El primero hace referencia a la singularidad en el campo eléctrico que aparece en la línea de contacto entre el líquido y el tubo capilar en la mayoría de las simulaciones. Primero se estudia en qué situaciones el campo eléctrico tiende a infinito en la línea de contacto. Después, se comprueba que dicha singularidad no supone un fallo en la descripción del problema y que además no afecta a la solución lejos de la línea de contacto. También se analiza si los esfuerzos eléctricos infinitamente grandes a los que da lugar dicha singularidad pueden ser compensados por el resto de esfuerzos que actúan en la superficie del líquido. El segundo estudio busca determinar el tamaño de la región de apantallamiento en un chorro de líquido dieléctrico sin carga superficial. En esta región, el campo exterior es compensado parcialmente por el campo que induce la carga de polarización en la superficie del líquido, de forma que en el interior del líquido el campo eléctrico es mucho menor que en el exterior. Una región como ésta aparece en las estimaciones cuando los efectos de relajación de carga son importantes en la región de transferencia de corriente en el chorro. ABSTRACT This aim of this dissertation is a theoretical and numerical analysis of an electrospray. In its most simple configuration, a constant flow rate of the liquid to be atomized, which has to be an electrical conductor, is injected into a dielectric medium (a gas or another inmiscible fluid) through a metallic capillary tube. A constant voltage is applied between this tube and a distant electrode that produces an electric field in the liquid and the surrounding medium. This electric field induces an electric current in the liquid that accumulates charge at its surface and leads to electric stresses that stretch the surface in the direction of the electric field. A meniscus appears on the end of the capillary tube when the electric field is sufficiently high and the flow rate is small. Pressure variations and viscous stresses due to the motion of the liquid are negligible in most of the meniscus, where normal electric and surface tension stresses acting on the surface are dominant. In the so-called cone-jet mode, the balance of these stresses forces the surface to adopt a conical shape -Taylor cone- in a intermediate region between the end of the tube and the tip of the meniscus. When approaching the cone apex, the velocity of the liquid increases and leads to pressure variations that eventually disturb the balance of surfaces tension and electric stresses. A thin jet emerges then from the tip of the meniscus that transports the charge accumulated at its surface. The electric field tangent to the surface of the jet acts on this charge and continuously stretches the jet. This electric force is negligible in the meniscus, where the component of the electric field tangent to the surface is small, but becomes very important in the jet. Far from the cone, the jet can either develop an asymmetrical instability named “whipping”, whereby the jet winds into a spiral, or break into a spray of small, nearly monodisperse, charged droplets. The electric current transported by the liquid has two components, the conduction current in the bulk of the liquid and the convection current due to the transport of the surface charge by the flow. The first component dominates in the meniscus, the second one in the far jet, and both are comparable in a current transfer region located in the jet downstream of the cone-jet transition region where the meniscus ceases to be a Taylor cone. Given an external electric field, the charge that accumulates at the surface of the liquid reduces the electric field inside the liquid, until an equilibrium is reached in which the electric field induced by the surface charge counters the external electric field and shields the liquid from this field. The characteristic time of this process is the electric relaxation time, which is a property of the liquid. When the residence time of the liquid in the cone-jet transition region (or in other region of the flow) is greater than the electric relaxation time, the surface charge follows a succession of equilibrium states and continuously shield the liquid from the external field. When this condition is not satisfied, charge relaxation effects appear and the external field penetrates into the liquid unless the liquid permittivity is large. For very polar liquids, the field due to the polarization charge at the surface prevents the external field from entering the liquid in the cone and in certain region of the jet. The charge at the surface of a conical meniscus intensifies the electric field around the cone, determining its spatial variation up to distances downstream of the apex of the order of the size of the meniscus. This electric field, first computed by Taylor, is independent of the applied voltage. Therefore local flow characteristics and the electric current carried by the jet are also independent of the applied voltage provided the size of the regions that determine these magnitudes are small compared with the size of the meniscus. Many experiments in the literature show the existence of a minimum flow rate below which the cone-jet mode cannot be established. The mean value and the standard deviation of the electrospray droplet size distribution are minimum when the device is operated near the minimum flow rate. There is no complete explanation of the minimum flow rate, even though possible mechanisms have been extensively studied. The existence of a minimum flow rate seems to be connected with the appearance of charge relaxation effects in the transition region. In this dissertation, order of magnitude estimations are worked out that show the dominant balances in the different regions of the asymptotic structure of the solution for different conditions of interest. When the inertia of the liquid plays a role in the cone-jet transition region, the region where most of the electric current is transfered to the surface lies in the jet downstream the cone-jet transition region. When the flow rate decreases to a certain value, charge relaxation effects appear simultaneously in the jet and in the transition region. For smaller values of the flow rate, charge relaxation effects are important in a region of the meniscus larger than the transition region. When viscous forces dominate in the flow in the cone-jet transition region, the current transfer region is located in the jet immediately after the transition region. When flow rate is decreased, charge relaxation effects appears gradually, first in the jet, then in the transition region, and finally in the meniscus. When flow rate is much larger than the cone-jet mode minimum, the meniscus ceases to be a cone. The electric current and the structure of the solution begin to depend on the applied voltage. The flow rate-voltage plane splits into different regions that are analyzed separately. For sufficiently large flow rates, the effect of the inertia of the liquid always becomes greater than the effect of the viscous forces. A set of numerical simulations have been carried out in order to validate the theoretical results. A simplified model of the problem has been devised to compute the flow, the electric field and the surface charge in the meniscus and the jet of an electrospray. The motion of the liquid is assumed to be quasi-unidirectional and described by Cosserat’s approximation for a slender jet. This widely used approximation allows to easily compute multiple configurations and to explore wide ranges of values of the governing parameters, retaining the effects of the viscosity and the inertia of the liquid. Electric fields inside and outside the liquid are coupled and are computed without any simplification using a boundary elements method. The stationary solution of the problem is obtained by means of an iterative method. To explore the parameter space, a solution is first computed for a set of values of the liquid properties, the flow rate and the applied voltage, an then a continuation method is used to find the boundaries of the cone-jet mode domain of existence, where the iterative method ceases to converge. When the inertia of the liquid dominates in the cone-jet transition region, the iterative method ceases to converge for values of the flow rate for which order-of-magnitude estimates first predict charge relaxation effects to be important in the cone and the jet. The electric current computed for values of the flow rate slightly above the minimum for which convergence is obtained seems to agree with estimates worked out for lower flow rates. When viscous forces dominate in the transition region, stationary solutions can be obtained for flow rates significantly smaller than the one for which charge relaxation effects first appear in the transition region. Numerical results obtained for those small values of the flow rate agree with our order of magnitude estimates. Theoretical analyses of two issues that have arisen naturally during the thesis are summarized in two appendices. The first appendix contains a study of the singularity of the electric field that most of the simulations show at the contact line between the liquid and the capillary tube. The electric field near the contact line is analyzed to determine the ranges of geometrical configurations and liquid permittivity where a singularity appears. Further estimates show that this singularity does not entail a failure in the description of the problem and does not affect the solution far from the contact line. The infinite electric stresses that appear at the contact line can be effectively balanced by surface tension. The second appendix contains an analysis of the size and slenderness of the shielded region of a dielectric liquid in the absence of free surface charge. In this region, the external electric field is partially offset by the polarization charge so that the inner electric field is much lower than the outer one. A similar region appears in the estimates when charge relaxation effects are important in the current transfer region.