956 resultados para Spatial Point Pattern analysis
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The study was carried out on the main plots (Main Experiment) of a large grassland biodiversity experiment, the Jena Experiment. In the main experiment, 82 grassland plots of 20 x 20 m were established from a pool of 60 species belonging to four functional groups (grasses, legumes, tall and small herbs). In May 2002, varying numbers of plant species from this species pool were sown into the plots to create a gradient of plant species richness (1, 2, 4, 8, 16 and 60 species) and functional richness (1, 2, 3, 4 functional groups). Plots were maintained by bi-annual weeding and mowing. This data set consists of standard deviation (SD), mean and stability (stab) of soil microbial basal respiration (µl O2/h/g dry soil) and microbial biomass carbon (µg C/g dry soil). Data were derived by taking soil samples and measuring basal and substrate-induced microbial respiration with an oxygen-consumption apparatus. Samples for calculating the spatial stability of soil microbial properties were taken on the 20th of September in 2010. Oxygen consumption of soil microorganisms in fresh soil equivalent to 3.5 g dry weight was measured at 22°C over a period of 24 h. Basal respiration (µlO2/g dry soil/h) was calculated as mean of the oxygen consumption rates of hours 14 to 24 after the start of measurements. Substrate- induced respiration was determined by adding D-glucose to saturate catabolic enzymes of microorganisms according to preliminary studies (4 mg g-1 dry soil solved in 400 µl deionized water). Maximum initial respiratory response (µl O2/g dry soil/ h) was calculated as mean of the lowest three oxygen consumption values within the first 10 h after glucose addition. Microbial biomass carbon (µg C/g dry soil) was calculated as 38 × Maximum initial respiratory response according to prelimiray studies.
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The Asia-Pacific Region has enjoyed remarkable economic growth in the last three decades. This rapid economic growth can be partially attributed to the global spread of production networks, which has brought about major changes in spatial interdependence among economies within the region. By applying an Input-Output based spatial decomposition technique to the Asian International Input-Output Tables for 1985 and 2000, this paper not only analyzes the intrinsic mechanism of spatial economic interdependence, but also shows how value added, employment and CO2 emissions induced are distributed within the international production networks.
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The present contribution discusses the development of a PSE-3D instability analysis algorithm, in which a matrix forming and storing approach is followed. Alternatively to the typically used in stability calculations spectral methods, new stable high-order finitedifference-based numerical schemes for spatial discretization 1 are employed. Attention is paid to the issue of efficiency, which is critical for the success of the overall algorithm. To this end, use is made of a parallelizable sparse matrix linear algebra package which takes advantage of the sparsity offered by the finite-difference scheme and, as expected, is shown to perform substantially more efficiently than when spectral collocation methods are used. The building blocks of the algorithm have been implemented and extensively validated, focusing on classic PSE analysis of instability on the flow-plate boundary layer, temporal and spatial BiGlobal EVP solutions (the latter necessary for the initialization of the PSE-3D), as well as standard PSE in a cylindrical coordinates using the nonparallel Batchelor vortex basic flow model, such that comparisons between PSE and PSE-3D be possible; excellent agreement is shown in all aforementioned comparisons. Finally, the linear PSE-3D instability analysis is applied to a fully three-dimensional flow composed of a counter-rotating pair of nonparallel Batchelor vortices.
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There is no unanimous consensus yet on the propagation mechanism before the break point inside tunnels. Some deem that the propagation mechanism follows the free space model, others argue that it should be described by the multimode waveguide model. Firstly, this paper analyzes the propagation loss in two mechanisms. Then, by conjunctively using the propagation theory and the three-dimensional solid geometry, a generic analytical model for the boundary between the free space mechanism and the multi-mode waveguide mechanism inside tunnels has been presented. Three measurement campaigns validate the model in different tunnels at different frequencies. Furthermore, the condition of the validity of the free space model used in tunnel environment has been discussed in some specific situations. Finally, through mathematical derivation, the seemingly conflicting viewpoints on the free space mechanism and the multi-mode waveguide mechanism have been unified in some specific situations by the presented generic model. The results in this paper can be helpful to gain deeper insight and better understanding of the propagation mechanism inside tunnels
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This paper proposes a method for the identification of different partial discharges (PDs) sources through the analysis of a collection of PD signals acquired with a PD measurement system. This method, robust and sensitive enough to cope with noisy data and external interferences, combines the characterization of each signal from the collection, with a clustering procedure, the CLARA algorithm. Several features are proposed for the characterization of the signals, being the wavelet variances, the frequency estimated with the Prony method, and the energy, the most relevant for the performance of the clustering procedure. The result of the unsupervised classification is a set of clusters each containing those signals which are more similar to each other than to those in other clusters. The analysis of the classification results permits both the identification of different PD sources and the discrimination between original PD signals, reflections, noise and external interferences. The methods and graphical tools detailed in this paper have been coded and published as a contributed package of the R environment under a GNU/GPL license.
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As a result of advances in mobile technology, new services which benefit from the ubiquity of these devices are appearing. Some of these services require the identification of the subject since they may access private user information. In this paper, we propose to identify each user by drawing his/her handwritten signature in the air (in-airsignature). In order to assess the feasibility of an in-airsignature as a biometric feature, we have analysed the performance of several well-known patternrecognitiontechniques—Hidden Markov Models, Bayes classifiers and dynamic time warping—to cope with this problem. Each technique has been tested in the identification of the signatures of 96 individuals. Furthermore, the robustness of each method against spoofing attacks has also been analysed using six impostors who attempted to emulate every signature. The best results in both experiments have been reached by using a technique based on dynamic time warping which carries out the recognition by calculating distances to an average template extracted from several training instances. Finally, a permanence analysis has been carried out in order to assess the stability of in-airsignature over time.
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Abstract The cloud forest is a special type of forest ecosystem that depends on suitable conditions of humidity and temperature to exist; hence, it is a very fragile ecosystem. The cloud forest is also one of the richest ecosystems in terms of species diversity and rate of endemism. However, today, it is one of the most threatened ecosystems in the world. Little is known about tree species distribution and coexistence among cloud forest trees. Trees are essential to understanding ecosystem functioning and maintenance because they support the ecosystem in important ways. For this dissertation, an analysis of woody plant species distribution at a small scale in a north-Peruvian Andean cloud forest was performed, and some of the factors implicated in the observed patterns were identified. Towards that end, different natural factors acting on species distribution within the forest were investigated: (i) intra-specific arrangements, (ii) heterospecific spatial relationships and (iii) relationships with external environmental factors. These analyses were conducted first on standing woody plants and then on seedlings. The woody plants were found to be clumped in the forest, either considering all the species together or each species separately. However, each species presented a specific pattern and specific spatial relationship among different-age individuals. Dispersal mode, growth form and shade tolerance played roles in the final distribution of the species. Furthermore, spatial associations among species, either positive or negative, were observed. These associations were more numerous when considering individuals of the interacting species at different developmental stages, i.e., younger individuals from one species and older individuals from another. Accordingly, competition and facilitation are asymmetric processes and vary throughout the life of an individual. Moreover, some species appear to prefer certain habitat conditions and avoid other habitats. The habitat definition that best explains species distribution is that which includes both environmental and stand characteristics; thus, a combination of these factors is necessary to understanding species' niche preferences. Seedling distribution was also associated with habitat conditions, but these conditions explained less than the 30% of the spatial variation. The position of conspecific adult individuals also affected seedling distribution; although the seedlings of many tree species avoid the vicinity of conspecifics, a few species appeared to prefer the formation of cohorts around their parent trees. The importance of habitat conditions and distance dependence with conspecifics varied among regions within the forest as well as on the developmental stage of the stand. The results from this thesis suggest that different species can coexist within a given space, forming a “puzzle” of species as a result of the intra- and interspecific spatial relationships along with niche preferences and adaptations that operate at different scales. These factors not only affect each species in a different way, but specific preferences also vary throughout species' lifespans. Resumen Resumen El bosque de niebla es uno de los ecosistemas más amenazados del mundo además de ser uno de los más frágiles. Son formaciones azonales que dependen de la existencia de unas condiciones de humedad y temperatura que permitan la formación de nubes que cubran el bosque; lo que dificulta en gran medida su conservación. También es uno de los ecosistemas con mayor riqueza de especies además de tener uno de los mayores porcentajes de endemismos. Uno de los aspectos más importantes para entender el ecosistema, es identificar y entender los elementos que lo componen y los mecanismos que regulan las relaciones entre ellos. Los árboles son el soporte del ecosistema. Sin embargo, apenas hay información sobre la distribución y coexistencia de los árboles en los bosques de niebla. Esta tesis presenta un análisis de la distribución a pequeña escala de las plantas leñosas en un bosque de niebla situado en la cordillera andina del norte de Perú; así como el análisis de algunos de los factores que pueden estar implicados en que se origine la distribución observada. Para este propósito se estudia cómo influyen factores de diferente naturaleza en la distribución de las especies (i) organización intra-específica (ii) relaciones espaciales heterospecíficas y (iii) relación con factores ambientales externos. En estos análisis se estudiaron primero las plantas jóvenes y las adultas, y después las plántulas. Los árboles aparecieron agregados en el bosque, tanto considerando todos a la vez como cuando se estudió cada especie por separado. Sin embargo, cada especie mostró un patrón distinto así como una particular relación espacial entre individuos jóvenes y adultos. El modo de dispersión, la forma de vida y la tolerancia de la especies estuvieron relacionados con el patrón general observado. Se vio también que ciertas especies aparecían relacionadas con otras, tanto de forma positiva (compartiendo zonas) como negativa (apareciendo en áreas distintas). Las asociaciones fueron mucho más numerosas cuando se consideraron los pares de especies en diferente estado de desarrollo, es decir, individuos jóvenes de una especie e individuos mayores de la otra. Eso indicaría que los procesos de competencia y facilitación son asimétricos y además varían durante la vida de la planta. Por otro lado, algunas especies aparecen preferentemente bajo ciertas condiciones de hábitat y evitan otras. La definición de hábitat a la que mejor responden las especies es cuando se incluyen tanto variables ambientales como de masa; así que ambos tipos de variables son necesarias para entender la preferencia de las especies por ciertos nichos. La distribución de las plántulas también estuvo relacionada con condiciones de hábitat, pero eso sólo llegaba a explicar hasta un 30% de la variabilidad espacial. La posición de los adultos de la misma especie también afectó a la distribución de las plántulas. En bastantes especies las plántulas evitan la cercanía de adultos de su misma especie, padres potenciales, aunque algunas especies aisladas mostraron el patrón contrario y aparecieron preferentemente en las mismas áreas que sus padres. La importancia de las condiciones de hábitat y posición de los adultos en la disposición de las plántulas varía de una zona a otra del bosque y además también varía según el estado de desarrollo de la masa.
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One important task in the design of an antenna is to carry out an analysis to find out the characteristics of the antenna that best fulfills the specifications fixed by the application. After that, a prototype is manufactured and the next stage in design process is to check if the radiation pattern differs from the designed one. Besides the radiation pattern, other radiation parameters like directivity, gain, impedance, beamwidth, efficiency, polarization, etc. must be also evaluated. For this purpose, accurate antenna measurement techniques are needed in order to know exactly the actual electromagnetic behavior of the antenna under test. Due to this fact, most of the measurements are performed in anechoic chambers, which are closed areas, normally shielded, covered by electromagnetic absorbing material, that simulate free space propagation conditions, due to the absorption of the radiation absorbing material. Moreover, these facilities can be employed independently of the weather conditions and allow measurements free from interferences. Despite all the advantages of the anechoic chambers, the results obtained both from far-field measurements and near-field measurements are inevitably affected by errors. Thus, the main objective of this Thesis is to propose algorithms to improve the quality of the results obtained in antenna measurements by using post-processing techniques and without requiring additional measurements. First, a deep revision work of the state of the art has been made in order to give a general vision of the possibilities to characterize or to reduce the effects of errors in antenna measurements. Later, new methods to reduce the unwanted effects of four of the most commons errors in antenna measurements are described and theoretical and numerically validated. The basis of all them is the same, to perform a transformation from the measurement surface to another domain where there is enough information to easily remove the contribution of the errors. The four errors analyzed are noise, reflections, truncation errors and leakage and the tools used to suppress them are mainly source reconstruction techniques, spatial and modal filtering and iterative algorithms to extrapolate functions. Therefore, the main idea of all the methods is to modify the classical near-field-to-far-field transformations by including additional steps with which errors can be greatly suppressed. Moreover, the proposed methods are not computationally complex and, because they are applied in post-processing, additional measurements are not required. The noise is the most widely studied error in this Thesis, proposing a total of three alternatives to filter out an important noise contribution before obtaining the far-field pattern. The first one is based on a modal filtering. The second alternative uses a source reconstruction technique to obtain the extreme near-field where it is possible to apply a spatial filtering. The last one is to back-propagate the measured field to a surface with the same geometry than the measurement surface but closer to the AUT and then to apply also a spatial filtering. All the alternatives are analyzed in the three most common near-field systems, including comprehensive noise statistical analyses in order to deduce the signal-to-noise ratio improvement achieved in each case. The method to suppress reflections in antenna measurements is also based on a source reconstruction technique and the main idea is to reconstruct the field over a surface larger than the antenna aperture in order to be able to identify and later suppress the virtual sources related to the reflective waves. The truncation error presents in the results obtained from planar, cylindrical and partial spherical near-field measurements is the third error analyzed in this Thesis. The method to reduce this error is based on an iterative algorithm to extrapolate the reliable region of the far-field pattern from the knowledge of the field distribution on the AUT plane. The proper termination point of this iterative algorithm as well as other critical aspects of the method are also studied. The last part of this work is dedicated to the detection and suppression of the two most common leakage sources in antenna measurements. A first method tries to estimate the leakage bias constant added by the receiver’s quadrature detector to every near-field data and then suppress its effect on the far-field pattern. The second method can be divided into two parts; the first one to find the position of the faulty component that radiates or receives unwanted radiation, making easier its identification within the measurement environment and its later substitution; and the second part of this method is able to computationally remove the leakage effect without requiring the substitution of the faulty component. Resumen Una tarea importante en el diseño de una antena es llevar a cabo un análisis para averiguar las características de la antena que mejor cumple las especificaciones fijadas por la aplicación. Después de esto, se fabrica un prototipo de la antena y el siguiente paso en el proceso de diseño es comprobar si el patrón de radiación difiere del diseñado. Además del patrón de radiación, otros parámetros de radiación como la directividad, la ganancia, impedancia, ancho de haz, eficiencia, polarización, etc. deben ser también evaluados. Para lograr este propósito, se necesitan técnicas de medida de antenas muy precisas con el fin de saber exactamente el comportamiento electromagnético real de la antena bajo prueba. Debido a esto, la mayoría de las medidas se realizan en cámaras anecoicas, que son áreas cerradas, normalmente revestidas, cubiertas con material absorbente electromagnético. Además, estas instalaciones se pueden emplear independientemente de las condiciones climatológicas y permiten realizar medidas libres de interferencias. A pesar de todas las ventajas de las cámaras anecoicas, los resultados obtenidos tanto en medidas en campo lejano como en medidas en campo próximo están inevitablemente afectados por errores. Así, el principal objetivo de esta Tesis es proponer algoritmos para mejorar la calidad de los resultados obtenidos en medida de antenas mediante el uso de técnicas de post-procesado. Primeramente, se ha realizado un profundo trabajo de revisión del estado del arte con el fin de dar una visión general de las posibilidades para caracterizar o reducir los efectos de errores en medida de antenas. Después, se han descrito y validado tanto teórica como numéricamente nuevos métodos para reducir el efecto indeseado de cuatro de los errores más comunes en medida de antenas. La base de todos ellos es la misma, realizar una transformación de la superficie de medida a otro dominio donde hay suficiente información para eliminar fácilmente la contribución de los errores. Los cuatro errores analizados son ruido, reflexiones, errores de truncamiento y leakage y las herramientas usadas para suprimirlos son principalmente técnicas de reconstrucción de fuentes, filtrado espacial y modal y algoritmos iterativos para extrapolar funciones. Por lo tanto, la principal idea de todos los métodos es modificar las transformaciones clásicas de campo cercano a campo lejano incluyendo pasos adicionales con los que los errores pueden ser enormemente suprimidos. Además, los métodos propuestos no son computacionalmente complejos y dado que se aplican en post-procesado, no se necesitan medidas adicionales. El ruido es el error más ampliamente estudiado en esta Tesis, proponiéndose un total de tres alternativas para filtrar una importante contribución de ruido antes de obtener el patrón de campo lejano. La primera está basada en un filtrado modal. La segunda alternativa usa una técnica de reconstrucción de fuentes para obtener el campo sobre el plano de la antena donde es posible aplicar un filtrado espacial. La última es propagar el campo medido a una superficie con la misma geometría que la superficie de medida pero más próxima a la antena y luego aplicar también un filtrado espacial. Todas las alternativas han sido analizadas en los sistemas de campo próximos más comunes, incluyendo detallados análisis estadísticos del ruido con el fin de deducir la mejora de la relación señal a ruido lograda en cada caso. El método para suprimir reflexiones en medida de antenas está también basado en una técnica de reconstrucción de fuentes y la principal idea es reconstruir el campo sobre una superficie mayor que la apertura de la antena con el fin de ser capaces de identificar y después suprimir fuentes virtuales relacionadas con las ondas reflejadas. El error de truncamiento que aparece en los resultados obtenidos a partir de medidas en un plano, cilindro o en la porción de una esfera es el tercer error analizado en esta Tesis. El método para reducir este error está basado en un algoritmo iterativo para extrapolar la región fiable del patrón de campo lejano a partir de información de la distribución del campo sobre el plano de la antena. Además, se ha estudiado el punto apropiado de terminación de este algoritmo iterativo así como otros aspectos críticos del método. La última parte de este trabajo está dedicado a la detección y supresión de dos de las fuentes de leakage más comunes en medida de antenas. El primer método intenta realizar una estimación de la constante de fuga del leakage añadido por el detector en cuadratura del receptor a todos los datos en campo próximo y después suprimir su efecto en el patrón de campo lejano. El segundo método se puede dividir en dos partes; la primera de ellas para encontrar la posición de elementos defectuosos que radian o reciben radiación indeseada, haciendo más fácil su identificación dentro del entorno de medida y su posterior substitución. La segunda parte del método es capaz de eliminar computacionalmente el efector del leakage sin necesidad de la substitución del elemento defectuoso.
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A unified solution framework is presented for one-, two- or three-dimensional complex non-symmetric eigenvalue problems, respectively governing linear modal instability of incompressible fluid flows in rectangular domains having two, one or no homogeneous spatial directions. The solution algorithm is based on subspace iteration in which the spatial discretization matrix is formed, stored and inverted serially. Results delivered by spectral collocation based on the Chebyshev-Gauss-Lobatto (CGL) points and a suite of high-order finite-difference methods comprising the previously employed for this type of work Dispersion-Relation-Preserving (DRP) and Padé finite-difference schemes, as well as the Summationby- parts (SBP) and the new high-order finite-difference scheme of order q (FD-q) have been compared from the point of view of accuracy and efficiency in standard validation cases of temporal local and BiGlobal linear instability. The FD-q method has been found to significantly outperform all other finite difference schemes in solving classic linear local, BiGlobal, and TriGlobal eigenvalue problems, as regards both memory and CPU time requirements. Results shown in the present study disprove the paradigm that spectral methods are superior to finite difference methods in terms of computational cost, at equal accuracy, FD-q spatial discretization delivering a speedup of ð (10 4). Consequently, accurate solutions of the three-dimensional (TriGlobal) eigenvalue problems may be solved on typical desktop computers with modest computational effort.
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Iniciación a las herramientas de Spatial Analysis de ArcGIS 10.
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For the past 20 years, dynamic analysis of shells has been one of the most fascinating fields for research. Using the new light materials the building engineer soon discovered that the subsequent reduction of gravity forces produced not only the desired shape freedom but the appearance of ecologic loads as the first factor of design; loads which present strong random properties and marked dynamic influence. On the other hand, the technological advance in the aeronautical and astronautical field placed the engineers in front of shell structures of nonconventional shape and able to sustain substantialy dynamic loads. The response to the increasingly challenger problems of the last two decades has been very bright; new forms, new materials and new methods of analysis have arosen in the design of off-shore platforms, nuclear vessels, space crafts, etc. Thanks to the intensity of the lived years we have at our disposition a coherent and homogeneous amount of knowledge which enable us to face problems of inconceivable complexity when IASS was founded. The open minded approach to classical problems and the impact of the computer are, probably, important factors in the Renaissance we have enjoyed these years, and a good proof of this are the papers presented to the previous IASS meetings as well as that we are going to consider in this one. Particularly striking is the great number of papers based on a mathematical modeling in front of the meagerness of those treating laboratory experiments on physical models. The universal entering of the computer into almost every phase of our lifes, and the cost of physical models, are –may be- reasons for this lack of experimental methods. Nevertheless they continue offering useful results as are those obtained with the shaking-table in which the computer plays an essential role in the application of loads as well as in the instantaneous treatment of control data. Plates 1 and 2 record the papers presented under dynamic heading, 40% of them are from Japan in good correlation with the relevance that Japanese research has traditionally showed in this area. Also interesting is to find old friends as profesors Tanaka, Nishimura and Kostem who presented valuable papers in previous IASS conferences. As we see there are papers representative of all tendencies, even purely analytical! Better than discuss them in detail, which can be done after the authors presentation, I think we can comment in the general pattern of the dynamical approach are summarized in plate 3.
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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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According to UN provisions in the period from 2007 to 2050 world population will grow up to 9200 million people. In fact, for the first time in history, in the year 2008 world urban population became higher than rural population. The increase of urban areas and their transport infrastructures has influenced agricultural land use due to their irreversible change, especially when they remain as periurban vacant land, losing their character and identity. In the Europe of the nineties, the traditional urban-rural gradient, characterized by a neat contact between both land types, has become so complex that it has change to a gradient in which it is difficult to separate urban and rural land uses. [Antrop 2004]. A literature review has been made on methodologies used for the urban-rural gradient analysis. One of these methodologies was selected that integrates ecological characterization based on the use of spatial metrics and geographical characterization based on spatial components. Cartographical sources used were Corine Land Cover at 1: 100000 scale and the Spanish Land Use Information System at 1:25000 scale. Urban-rural gradient paradigm is an analysis methodology, coming from landscape ecology, which enables to investigate how urbanization provokes changes in ecological patterns and processes into landscape. [Hahs and McDonnell 2006].The present research adapt this methodology to study the urban-rural gradient in the outskirts of Madrid, Toledo and Guadalajara. Both scales (1:25000 and 1:100000) were simultaneously used to reach the next objectives: 1) Analysis of landscape pattern dynamics in relation to distance to the town centre and major infrastructures. 2) Analysis of landscape pattern dynamics in the fringe of protected areas. The paper presents a new approach to the urban-rural relationship which allows better planning and management of urban áreas.
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To better understand destruction mechanisms of wake-vortices behind aircraft, the point vortex method for stability (inviscid) used by Crow is here compared with viscous modal global stability analysis of the linearized Navier-Stokes equations acting on a two-dimensional basic flow, i.e. BiGlobal stability analysis. The fact that the BiGlobal method is viscous, and uses a flnite área vortex model, gives rise to results somewhat different from the point vortex model. It adds more parameters to the problem, but is more realistic.
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The linear instability of the three-dimensional boundary-layer over the HIFiRE-5 flight test geometry, i.e. a rounded-tip 2:1 elliptic cone, at Mach 7, has been analyzed through spatial BiGlobal analysis, in a effort to understand transition and accurately predict local heat loads on next-generation ight vehicles. The results at an intermediate axial section of the cone, Re x = 8x10 5, show three different families of spatially amplied linear global modes, the attachment-line and cross- ow modes known from earlier analyses, and a new global mode, peaking in the vicinity of the minor axis of the cone, termed \center-line mode". We discover that a sequence of symmetric and anti-symmetric centerline modes exist and, for the basic ow at hand, are maximally amplied around F* = 130kHz. The wavenumbers and spatial distribution of amplitude functions of the centerline modes are documented