37 resultados para auxiliary
em Universidad Politécnica de Madrid
Resumo:
This work is related to the output impedance improvement of a Multiphase Buck converter with Peak Current Mode Control (PCMC) by means of introducing an additional power path that virtually increases the output capacitance during transients. Various solutions that can be employed to improve the dynamic behavior of the converter system exist, but nearly all solutions are developed for a Single Phase Buck converter with Voltage Mode Control (VMC), while in the VRM applications, due to the high currents, the system is usually implemented as a Multiphase Buck Converter with Current Mode Control. The additional energy path, as presented here, is introduced with the Output Impedance Correction Circuit (OICC) based on the Controlled Current Source (CCS). The OICC is used to inject or extract a current n-1 times larger than the output capacitor current, thus virtually increasing n times the value of the output capacitance during the transients. Furthermore, this work extends the OICC concept to a Multiphase Buck Converter system while comparing proposed solution with the system that has n times bigger output capacitor. In addition, the OICC is implemented as a Synchronous Buck Converter with PCMC, thus reducing its influence on the system efficiency.
Resumo:
In this paper, a mathematical programming model and a heuristically derived solution is described to assist with the efficient planning of services for a set of auxiliary bus lines (a bus-bridging system) during disruptions of metro and rapid transit lines. The model can be considered static and takes into account the average flows of passengers over a given period of time (i.e., the peak morning traffic hour) Auxiliary bus services must accommodate very high demand levels, and the model presented is able to take into account the operation of a bus-bridging system under congested conditions. A general analysis of the congestion in public transportation lines is presented, and the results are applied to the design of a bus-bridging system. A nonlinear integer mathematical programming model and a suitable approximation of this model are then formulated. This approximated model can be solved by a heuristic procedure that has been shown to be computationally viable. The output of the model is as follows: (a) the number of bus units to assign to each of the candidate lines of the bus-bridging system; (b) the routes to be followed by users passengers of each of the origin–destination pairs; (c) the operational conditions of the components of the bus-bridging system, including the passenger load of each of the line segments, the degree of saturation of the bus stops relative to their bus input flows, the bus service times at bus stops and the passenger waiting times at bus stops. The model is able to take into account bounds with regard to the maximum number of passengers waiting at bus stops and the space available at bus stops for the queueing of bus units. This paper demonstrates the applicability of the model with two realistic test cases: a railway corridor in Madrid and a metro line in Barcelona Planificación de los servicios de lineas auxiliares de autobuses durante las incidencias de las redes de metro y cercanías. El modelo estudia el problema bajo condiciones de alta demanda y condiciones de congestión. El modelo no lineal resultante es resuelto mediante heurísticas que demuestran su utilidad. Se demuestran los resultados en dos corredores de las ciudades de Barcelona y Madrid.
Resumo:
The stability analysis of open cavity flows is a problem of great interest in the aeronautical industry. This type of flow can appear, for example, in landing gears or auxiliary power unit configurations. Open cavity flows is very sensitive to any change in the configuration, either physical (incoming boundary layer, Reynolds or Mach numbers) or geometrical (length to depth and length to width ratio). In this work, we have focused on the effect of geometry and of the Reynolds number on the stability properties of a threedimensional spanwise periodic cavity flow in the incompressible limit. To that end, BiGlobal analysis is used to investigate the instabilities in this configuration. The basic flow is obtained by the numerical integration of the Navier-Stokes equations with laminar boundary layers imposed upstream. The 3D perturbation, assumed to be periodic in the spanwise direction, is obtained as the solution of the global eigenvalue problem. A parametric study has been performed, analyzing the stability of the flow under variation of the Reynolds number, the L/D ratio of the cavity, and the spanwise wavenumber β. For consistency, multidomain high order numerical schemes have been used in all the computations, either basic flow or eigenvalue problems. The results allow to define the neutral curves in the range of L/D = 1 to L/D = 3. A scaling relating the frequency of the eigenmodes and the length to depth ratio is provided, based on the analysis results.
Resumo:
La Guadua (Guadua angustifolia Kunth) es una de las especies forestales más características de Colombia. Perteneciente a la familia del bambú, ésta planta nativa de Colombia usada en la construcción permite una reducción de costos, garantizados, entre otras ventajas, por sus propiedades físico-mecánicas de flexibilidad, resistencia, dureza, efecto climatizado y sismo resistencia. En el proyecto se plantea inicialmente un estudio de la Guadua como material estructural. Se estudiará su anatomía, sus propiedades físicas y mecánicas así como la normativa existente que rige su uso en construcción y por último se darán algunos ejemplos en los que se puede comprobar su uso en la actualidad. Posteriormente se procederá al desarrollo del proyecto cuya finalidad es el diseño de una estructura modular multifuncional que se necesita para llevarla a cabo en un proyecto de cooperación localizado en Neiva (Colombia). El proyecto incluirá todos los documentos necesarios para un trabajo de estas características: memoria, pliego de condiciones técnicas, presupuesto, planos, así como el Estudio de Seguridad y Salud Laboral. Como solución a las necesidades planteadas en el proyecto de cooperación, se realizará el diseño de dos estructuras modulares cuya finalidad sea las de uso como oficina y como almacén. Se aplicará para su cálculo el CTE cómo normativa de construcción, pero apoyándose en algunos parámetros en la NSR-10, estableciendo una comparativa posterior entre ambas normativas. Debido a la importancia de la acción sísmica en Colombia se comprobará la resistencia sísmica del módulo diseñado según el “Manual de Construcción, evaluación y rehabilitación sismo resistente de viviendas de mampostería” creado por la Asociación Colombiana de Ingeniería Sísmica. Basándose en este manual se definirán los tipos de uniones más favorables sísmicamente de los módulos con el diseño de una cercha auxiliar necesaria según el tipo de unión. ABSTRACT PROJECT: Structural applications of the guadua (Guadua angustifolia Kunth). Project of modular multifunctional structure in Colombia Guadua (Guadua angustifolia Kunth) is one of the forest species more characteristics of Colombia. Pertaining to the family of the bamboo, this one native plant of Colombia used in the construction allows a reduction of costs, guaranteed, among others advantages, by its physic mechanical properties of flexibility, resistance, hardness, climatic effect and earthquake resistance. The project initially considers a study of the Guadua as structural material. We will study its anatomy, its physical and mechanical properties as well as the existing norm that governs its use in construction and finally some examples will be provided in which its actual use can be verified. Later on, we will proceed with the development of the project which purpose is the design of a multifunctional modular structure required to in a project of cooperation located in Neiva (Colombia). The project will include all the necessary documents for a work of these characteristics: memory, technical specifications, budget, drawings, as well as the Security and Labor Health Study. In order to satisfy the needs raised in the cooperation project, we will undertake the design of two modular structures with the purpose to be used as office and warehouse. The construction normative CTE will be applied for its calculation, but some parameters will be based in the NSR-10, establishing a comparison between both norms. Due to the importance of the seismic action in Colombia, the seismic resistance of the module will be verified according to the “Manual of Construction, evaluation and rehabilitation resistant earthquake of rubblework houses” created by the Colombian Association of Seismic Engineering,. We will also use this Manual to define the types of unions more favorable from seismic point of view, designing the required auxiliary segments according to the type of union.
Resumo:
Esta Tesis Doctoral se encuadra en el ámbito de la medida de emisiones contaminantes y de consumo de combustible en motores de combustión interna alternativos cuando se utilizan como plantas de potencia para propulsión de vehículos ligeros de carretera, y más concretamente en las medidas dinámicas con el vehículo circulando en tráfico real. En este ámbito, el objetivo principal de la Tesis es estudiar los problemas asociados a la medición en tiempo real con equipos embarcados de variables medioambientales, energéticas y de actividad, de vehículos ligeros propulsados por motores térmicos en tráfico real. Y como consecuencia, desarrollar un equipo y una metodología apropiada para este objetivo, con el fin de realizar consiguientemente un estudio sobre los diferentes factores que influyen sobre las emisiones y el consumo de combustible de vehículos turismo en tráfico real. La Tesis se comienza realizando un estudio prospectivo sobre los trabajos de otros autores relativos al desarrollo de equipos portátiles de medida de emisiones (Portable Emission Measurement Systems – PEMS), problemas asociados a la medición dinámica de emisiones y estudios de aplicación en tráfico real utilizando este tipo de equipos. Como resultado de este estudio se plantea la necesidad de disponer de un equipo específicamente diseñado para ser embarcado en un vehículo que sea capaz de medir en tiempo real las concentraciones de emisiones y el caudal de gases de escape, al mismo tiempo que se registran variables del motor, del vehículo y del entorno como son la pendiente y los datos meteorológicos. De esta forma se establecen las especificaciones y condiciones de diseño del equipo PEMS. Aunque al inicio de esta Tesis ya existían en el mercado algunos sistemas portátiles de medida de emisiones (PEMS: Portable Emissions Measurement Systems), en esta Tesis se investiga, diseña y construye un nuevo sistema propio, denominado MIVECO – PEMS. Se exponen, discuten y justifican todas las soluciones técnicas incorporadas en el sistema que incluyen los subsistema de análisis de gases, subsistemas de toma de muestra incluyendo caudalímetro de gases de escape, el subsistema de medida de variables del entorno y actividad del vehículo y el conjunto de sistemas auxiliares. El diseño final responde a las hipótesis y necesidades planteadas y se valida en uso real, en banco de rodillos y en comparación con otro equipos de medida de emisiones estacionarios y portátiles. En esta Tesis se presenta también toda la investigación que ha conducido a establecer la metodología de tratamiento de las señales registradas en tiempo real que incluye la sincronización, cálculos y propagación de errores. La metodología de selección y caracterización de los recorridos y circuitos y de las pautas de conducción, preparación del vehículo y calibración de los equipos forma también parte del legado de esta Tesis. Para demostrar la capacidad de medida del equipo y el tipo de resultados que pueden obtenerse y que son útiles para la comunidad científica, y las autoridades medioambientales en la parte final de esta Tesis se plantean y se presentan los resultados de varios estudios de variables endógenas y exógenas que afectan a las emisiones instantáneas y a los factores de emisión y consumo (g/km) como: el estilo de conducción, la infraestructura vial, el nivel de congestión del tráfico, tráfico urbano o extraurbano, el contenido de biocarburante, tipo de motor (diesel y encendido provocado), etc. Las principales conclusiones de esta Tesis son que es posible medir emisiones másicas y consumo de motores de vehículos en uso real y que los resultados permiten establecer políticas de reducción de impacto medio ambiental y de eficiencia energética, pero, se deben establecer unas metodologías precisas y se debe tener mucho cuidado en todo el proceso de calibración, medida y postratamientos de los datos. Abstract This doctoral thesis is in the field of emissions and fuel consumption measurement of reciprocating internal combustion engines when are used as power-trains for light-duty road vehicles, and especially in the real-time dynamic measurements procedures when the vehicle is being driven in real traffic. In this context, the main objective of this thesis is to study the problems associated with on-board real-time measuring systems of environmental, energy and activity variables of light vehicles powered by internal combustion engines in real traffic, and as a result, to develop an instrument and an appropriate methodology for this purpose, and consequently to make a study of the different factors which influence the emissions and the fuel consumption of passenger cars in real traffic. The thesis begins developing a prospective study on other authors’ works about development of Portable Emission Measurement Systems (PEMS), problems associated with dynamic emission measurements and application studies on actual traffic using PEMS. As a result of this study, it was shown that a measuring system specifically designed for being on-board on a vehicle, which can measure in real time emission concentrations and exhaust flow, and at the same time to record motor vehicle and environment variables as the slope and atmospheric data, is needed; and the specifications and design parameters of the equipment are proposed. Although at the beginning of this research work there were already on the market some PEMS, in this Thesis a new system is researched, designed and built, called MIVECO – PEMS, in order to meet such measurements needs. Following that, there are presented, discussed and justify all technical solutions incorporated in the system, including the gas analysis subsystem, sampling and exhaust gas flowmeter subsystem, the subsystem for measurement of environment variables and of the vehicle activity and the set of auxiliary subsystems. The final design meets the needs and hypotheses proposed, and is validated in real-life use and chassis dynamometer testing and is also compared with other stationary and on-board systems. This thesis also presents all the research that has led to the methodology of processing the set of signals recorded in real time including signal timing, calculations and error propagation. The methodology to select and characterize of the routes and circuits, the driving patterns, and the vehicle preparation and calibration of the instruments and sensors are part of the legacy of this thesis. To demonstrate the measurement capabilities of the system and the type of results that can be obtained and that are useful for the scientific community and the environmental authorities, at the end of this Thesis is presented the results of several studies of endogenous and exogenous variables that affect the instantaneous and averaged emissions and consumption factors (g/km), as: driving style, road infrastructure, the level of traffic congestion, urban and extra-urban traffic, biofuels content, type of engine (diesel or spark ignition) etc. The main conclusions of this thesis are that it is possible to measure mass emissions and consumption of vehicle engines in actual use and that the results allow us to establish policies to reduce environmental impact and improve energy efficiency, but, to establish precise methodologies and to be very careful in the entire process of calibration, measurement and data post-treatment is necessary.
Resumo:
El proyecto tiene por objeto describir los trabajos de estabilización del talud que se desean realizar en la estación de servicio sita en la Carretera Nacional 525, p.k. 534,600 en San Cibrao das Viñas, provincia de Orense. Y en base al proyecto solicitar la licencia de obras y todos los permisos necesarios para realizarlos, tales como ocupación de vía pública, retirada de escombros y residuos resultantes y existentes, etc. El motivo por el cual se desea realizar las obras de estabilización del talud es como consecuencia de los desprendimientos que se producen desde el macizo rocoso que está ubicado encima de la estación de servicio, debido al estado de meteorización en el que se encuentra la parte superficial de la roca que forma dicho macizo. Se pretende evitar posibles accidentes ya que se trata de una estación de servicio y se almacena combustible para suministro de vehículos, con las posibles consecuencias que se pueden derivar de los desprendimientos que puedan producirse sobre las descargas de combustible y el edificio auxiliar de la tienda y la integridad física de los trabajadores y clientes. Abstract The project describe the slope stabilization works to be done in the service station located on National Road 525, pk 534.600 in San Cibrao das Viñas, province of Orense . And based on the project, apply for the works permits and all permits necessary to perform them, such as occupation of public roads, removal of debris and waste arising and existing. The reason to make the slope stabilization work is as a result of landslides that occur from the rock mass which is located above the station, due to the state of weathering of the surface of the rock mass. This is to avoid accidents, because it is a service station with fuel stored for the supply of vehicles, with the consequences that may result from landslides that may occur on the discharge of fuel and the auxiliary building of the store, and the physical integrity of workers and customers.
Resumo:
El proyecto consiste en el diseño del sistema de climatización de un edificio ubicado en la ciudad de Madrid que utilice la energía solar como fuente de calor y electricidad. El objetivo es que el edificio tenga un consumo energético lo más bajo posible y que utilice energías de origen renovable para su explotación. Se incluye el cálculo de cargas térmicas, el dimensionamiento del sistema de climatización y de los sistemas de captación de energía solar (térmica y fotovoltaica). Adicionalmente, se definen las principales características de un sistema de control centralizado que permita optimizar el rendimiento y monitorizar el funcionamiento de la instalación de forma continua. Se incluye el diseño de las instalaciones auxiliares con un grado de detalle suficiente que permita su valoración, tanto desde el punto de vista energético como económico. Como parte fundamental del proyecto, se extraen conclusiones acerca del ahorro energético de las instalaciones y se analiza la viabilidad económica de las inversiones. ABSTRACT The project covers the design of a Heating and Climatization System for a building located in the city of Madrid (Spain). The facilities will use solar energy as the main source for both heat and electricity. The main goals are to achieve the lowest possible energy consumption and to use renewable sources of energy to cover it. Calculation of thermal charges is included, together with the sizing of both the Climatization System and the Solar Energy (Thermal and PV) facilities. In addition, the main characteristics of a Centralized Control System are defined. This will help both to optimize the performance of the different systems involved and to monitor the operation. Design of all auxiliary systems is included with enough level of detail as to be able to evaluate them from both energetic and economic points of view. Paramount in this project is to be able to draw conclusions about the energy savings and the profitability (or not) of the main investments to be carried out
Resumo:
Mesh adaptation based on error estimation has become a key technique to improve th eaccuracy o fcomputational-fluid-dynamics computations. The adjoint-based approach for error estimation is one of the most promising techniques for computational-fluid-dynamics applications. Nevertheless, the level of implementation of this technique in the aeronautical industrial environment is still low because it is a computationally expensive method. In the present investigation, a new mesh refinement method based on estimation of truncation error is presented in the context of finite-volume discretization. The estimation method uses auxiliary coarser meshes to estimate the local truncation error, which can be used for driving an adaptation algorithm. The method is demonstrated in the context of two-dimensional NACA0012 and three-dimensional ONERA M6 wing inviscid flows, and the results are compared against the adjoint-based approach and physical sensors based on features of the flow field.
Resumo:
In recent years, there has been continuing interest in the participation of university research groups in space technology studies by means of their own microsatellites. The involvement in such projects has some inherent challenges, such as limited budget and facilities. Also, due to the fact that the main objective of these projects is for educational purposes, usually there are uncertainties regarding their in orbit mission and scientific payloads at the early phases of the project. On the other hand, there are predetermined limitations for their mass and volume budgets owing to the fact that most of them are launched as an auxiliary payload in which the launch cost is reduced considerably. The satellite structure subsystem is the one which is most affected by the launcher constraints. This can affect different aspects, including dimensions, strength and frequency requirements. In this paper, the main focus is on developing a structural design sizing tool containing not only the primary structures properties as variables but also the system level variables such as payload mass budget and satellite total mass and dimensions. This approach enables the design team to obtain better insight into the design in an extended design envelope. The structural design sizing tool is based on analytical structural design formulas and appropriate assumptions including both static and dynamic models of the satellite. Finally, a Genetic Algorithm (GA) multiobjective optimization is applied to the design space. The result is a Pareto-optimal based on two objectives, minimum satellite total mass and maximum payload mass budget, which gives a useful insight to the design team at the early phases of the design.
Resumo:
Background: [NiFe] hydrogenases are enzymes that catalyze the oxidation of hydrogen into protons and electrons, to use H2 as energy source, or the production of hydrogen through proton reduction, as an escape valve for the excess of reduction equivalents in anaerobic metabolism. Biosynthesis of [NiFe] hydrogenases is a complex process that occurs in the cytoplasm, where a number of auxiliary proteins are required to synthesize and insert the metal cofactors into the enzyme structural units. The endosymbiotic bacterium Rhizobium leguminosarum requires the products of eighteen genes (hupSLCDEFGHIJKhypABFCDEX) to synthesize an active hydrogenase. hupF and hupK genes are found only in hydrogenase clusters from bacteria expressing hydrogenase in the presence of oxygen. Results: HupF is a HypC paralogue with a similar predicted structure, except for the C-terminal domain present only in HupF. Deletion of hupF results in the inability to process the hydrogenase large subunit HupL, and also in reduced stability of this subunit when cells are exposed to high oxygen tensions. A ?hupF mutant was fully complemented for hydrogenase activity by a C-terminal deletion derivative under symbiotic, ultra low-oxygen tensions, but only partial complementation was observed in free living cells under higher oxygen tensions (1% or 3%). Co-purification experiments using StrepTag-labelled HupF derivatives and mass spectrometry analysis indicate the existence of a major complex involving HupL and HupF, and a less abundant HupF-HupK complex. Conclusions: The results indicate that HupF has a dual role during hydrogenase biosynthesis: it is required for hydrogenase large subunit processing and it also acts as a chaperone to stabilize HupL when hydrogenase is synthesized in the presence of oxygen.
Resumo:
This paper presents an adaptive control for the auxiliary circuit, called ARCN (Auxiliary Resonant Commutating Network), used to achieve ZVS in full active bridge converters under a wide load range. Depending on the load conditions, the proposed control adapts the timing of the ARCN to minimize the losses. The principle of operation and implementation considerations are presented for a three phase full active bridge converter, proposing different methods to implement the control according to the specifications. The experimental results shown verify the proposed methodology.
Resumo:
This paper analyzed the building techniques based in the use of rammed earth in the Late Medieval fortifications in the province of Soria, Spain. The manorial castles of Serón de Nágima and Yanguas were built completely with rammed earth. However, these techinques are different. Through the study of the constructive signals, we can reconstruct the constructive process and made an hypothesis of the auxiliary scaffolding necessary for the construction. After, other four cases in which there is presence of rammed earth are described: Ágreda, Arcos de Jalón, Caracena and the tower of Martín González or castle of La Raya (the Border). Rammed earth is used in some secondary architectural elements and also as a filling of the masonry walls, but somtimes there are ancient rammed earth walls overlaid with stone masonry.
Resumo:
Este trabajo propone una serie de algoritmos con el objetivo de extraer información de conjuntos de datos con redes de neuronas. Se estudian dichos algoritmos con redes de neuronas Enhenced Neural Networks (ENN), debido a que esta arquitectura tiene algunas ventajas cuando se aproximan funciones mediante redes neuronales. En la red ENN los pesos de la matriz principal varián con cada patrón, por lo que se comete un error menor en la aproximación. Las redes de neuronas ENN reúnen la información en los pesos de su red auxiliar, se propone un método para obtener información de la red a través de dichos pesos en formas de reglas y asignando un factor de certeza de dichas reglas. La red ENN obtiene un error cuadrático medio menor que el error teórico de una aproximación matemática por ejemplo mediante polinomios de Taylor. Se muestra como una red ENN, entrenada a partir un conjunto de patrones obtenido de una función de variables reales, sus pesos asociados tienen unas relaciones similares a las que se veri_can con las variables independientes con dicha función de variables reales. Las redes de neuronas ENN aproximan polinomios, se extrae conocimiento de un conjunto de datos de forma similar a la regresión estadística, resolviendo de forma más adecuada el problema de multicolionalidad en caso de existir. Las relaciones a partir de los pesos asociados de la matriz de la red auxiliar se obtienen similares a los coeficientes de una regresión para el mismo conjunto numérico. Una red ENN entrenada a partir de un conjunto de datos de una función boolena extrae el conocimiento a partir de los pesos asociados, y la influencia de las variables de la regla lógica de la función booleana, queda reejada en esos pesos asociados a la red auxiliar de la red ENN. Se plantea una red de base radial (RBF) para la clasificación y predicción en problemas forestales y agrícolas, obteniendo mejores resultados que con el modelo de regresión y otros métodos. Los resultados con una red RBF mejoran al método de regresión si existe colinealidad entre los datos que se dispone y no son muy numerosos. También se detecta que variables tienen más importancia en virtud de la variable pronóstico. Obteniendo el error cuadrático medio con redes RBF menor que con otros métodos, en particular que con el modelo de regresión. Abstract A series of algorithms is proposed in this study aiming at the goal of producing information about data groups with a neural network. These algorithms are studied with Enheced Neural Networks (ENN), owing to the fact that this structure shows sever advantages when the functions are approximated by neural networks. Main matrix weights in th ENN vary on each pattern; so, a smaller error is produced when approximating. The neural network ENN joins the weight information contained in their auxiliary network. Thus, a method to obtain information on the network through those weights is proposed by means of rules adding a certainty factor. The net ENN obtains a mean squared error smaller than the theorical one emerging from a mathematical aproximation such as, for example, by means of Taylor's polynomials. This study also shows how in a neural network ENN trained from a set of patterns obtained through a function of real variables, its associated weights have relationships similar to those ones tested by means of the independent variables connected with such functions of real variables. The neural network ENN approximates polynomials through it information about a set of data may be obtained in a similar way than through statistical regression, solving in this way possible problems of multicollinearity in a more suitable way. Relationships emerging from the associated weights in the auxiliary network matrix obtained are similar to the coeficients corresponding to a regression for the same numerical set. A net ENN trained from a boolean function data set obtains its information from its associated weights. The inuence of the variables of the boolean function logical rule are reected on those weights associated to the net auxiliar of the ENN. A radial basis neural networks (RBF) for the classification and prediction of forest and agricultural problems is proposed. This scheme obtains better results than the ones obtained by means of regression and other methods. The outputs with a net RBF better the regression method if the collineality with the available data and their amount is not very large. Detection of which variables are more important basing on the forecast variable can also be achieved, obtaining a mean squared error smaller that the ones obtained through other methods, in special the one produced by the regression pattern.
Resumo:
Aims Dehesas are agroforestry systems characterized by scattered trees among pastures, crops and/or fallows. A study at a Spanish dehesa has been carried out to estimate the spatial distribution of the soil organic carbon stock and to assess the influence of the tree cover. Methods The soil organic carbon stock was estimated from the five uppermost cm of themineral soil with high spatial resolution at two plots with different grazing intensities. The Universal Kriging technique was used to assess the spatial distribution of the soil organic carbon stocks, using tree coverage within a buffering area as an auxiliary variable. Results A significant positive correlation between tree presence and soil organic carbon stocks up to distances of around 8 m from the trees was found. The tree crown cover within a buffer up to a distance similar to the crown radius around the point absorbed 30 % of the variance in the model for both grazing intensities, but residual variance showed stronger spatial autocorrelation under regular grazing conditions. Conclusions Tree cover increases soil organic carbon stocks, and can be satisfactorily estimated by means of crown parameters. However, other factors are involved in the spatial pattern of the soil organic carbon distribution. Livestock plays an interactive role together with tree presence in soil organic carbon distribution.
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In solid mechanics the weak formulation produces an integral equation ready for a discretization and with less restrictive requiremets than the standard field equations. Fundamentally the weak formulation is a expresion of a green formula. An alternative is to choose another green formula materializing a reciprocity relationship between the basis unknowns and an auxiliary family of functions. The degree of smoothness requiered to practice the discretization is then translated to the auxiliar functions. The subsequent discretization (constant, linear etc.)produces a set of equations on the boundary of the domain. For linear 3-D problems the BIEM appears then as a powerful alternative to FEM, because of the reduction to 2-D thanks to the features previously described.