On the spatial distribution of woody plant species in a tropical montane cloud forest

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.

Spatial distribution of the soil carbon pool in a Holm oak dehesa in Spain

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.

Calculation of the spatial distribution of photovoltaic field by arbitrary 2D ilumination patterns en LiNbO3; application to photovoltaic particle trapping.

Patterns of evanescent photovoltaic field induced by illumination on a surface of lithium niobate (LN) have been calculated and compared with the experimental patterns of nano- and microparticles trapped by dielectrophoretic forces. A tool for this calculation has been developed. Calculo de distribución espacial de campo por efecto fotovoltaico con patrones arbitrarios de iluminación, en LiNbO3

Three-dimensional spatial distribution of synapses in the neocortex: A dual-beam electron microscopy study

In the cerebral cortex, most synapses are found in the neuropil, but relatively little is known about their 3-dimensional organization. Using an automated dual-beam electron microscope that combines focused ion beam milling and scanning electron microscopy, we have been able to obtain 10 three-dimensional samples with an average volume of 180 µm(3) from the neuropil of layer III of the young rat somatosensory cortex (hindlimb representation). We have used specific software tools to fully reconstruct 1695 synaptic junctions present in these samples and to accurately quantify the number of synapses per unit volume. These tools also allowed us to determine synapse position and to analyze their spatial distribution using spatial statistical methods. Our results indicate that the distribution of synaptic junctions in the neuropil is nearly random, only constrained by the fact that synapses cannot overlap in space. A theoretical model based on random sequential absorption, which closely reproduces the actual distribution of synapses, is also presented.

Origin and patterns of distribution of trace elements in street dust. Unleaded petrol and urban lead

The elemental composition, patterns of distribution and possible sources of street dust are not common to all urban environments, but vary according to the peculiarities of each city. The common features and dissimilarities in the origin and nature of street dust were investigated through a series of studies in two widely different cities, Madrid (Spain) and Oslo (Norway), between 1990 and 1994. The most comprehensive sampling campaign was carried out in the Norwegian capital during the summer of 1994. An area of 14 km2, covering most of downtown Oslo and some residential districts to the north of the city, was divided into 1 km2 mapping units, and 16 sampling increments of approximately 150 g were collected from streets and roads in each of them. The fraction below 100 μm was acid-digested and analysed by ICP-MS. Statistical analyses of the results suggest that chemical elements in street dust can be classified into three groups: “urban” elements (Ba, Cd, Co, Cu, Mg, Pb, Sb, Ti, Zn), “natural” elements (Al, Ga, La, Mn, Na, Sr, Th, Y) and elements of a mixed origin or which have undergone geochemical changes from their original sources (Ca, Cs, Fe, Mo, Ni, Rb, Sr, U). Soil resuspension and/or mobilisation appears to be the most important source of “natural” elements, while “urban” elements originate primarily from traffic and from the weathering and corrosion of building materials. The data for Pb seem to prove that the gradual shift from leaded to unleaded petrol as fuel for automobiles has resulted in an almost proportional reduction in the concentration of Pb in dust particles under 100 μm. This fact and the spatial distribution of Pb in the city strongly suggest that lead sources other than traffic (i.e. lead accumulated in urban soil over the years) may contribute as much lead, if not more, to urban street dust.

Three-dimensional distribution of cortical synapses: a replicated point pattern-based analysis

The biggest problem when analyzing the brain is that its synaptic connections are extremely complex. Generally, the billions of neurons making up the brain exchange information through two types of highly specialized structures: chemical synapses (the vast majority) and so-called gap junctions (a substrate of one class of electrical synapse). Here we are interested in exploring the three-dimensional spatial distribution of chemical synapses in the cerebral cortex. Recent research has showed that the three-dimensional spatial distribution of synapses in layer III of the neocortex can be modeled by a random sequential adsorption (RSA) point process, i.e., synapses are distributed in space almost randomly, with the only constraint that they cannot overlap. In this study we hypothesize that RSA processes can also explain the distribution of synapses in all cortical layers. We also investigate whether there are differences in both the synaptic density and spatial distribution of synapses between layers. Using combined focused ion beam milling and scanning electron microscopy (FIB/SEM), we obtained three-dimensional samples from the six layers of the rat somatosensory cortex and identified and reconstructed the synaptic junctions. A total volume of tissue of approximately 4500μm3 and around 4000 synapses from three different animals were analyzed. Different samples, layers and/or animals were aggregated and compared using RSA replicated spatial point processes. The results showed no significant differences in the synaptic distribution across the different rats used in the study. We found that RSA processes described the spatial distribution of synapses in all samples of each layer. We also found that the synaptic distribution in layers II to VI conforms to a common underlying RSA process with different densities per layer. Interestingly, the results showed that synapses in layer I had a slightly different spatial distribution from the other layers.

A partial study of vertical distribution of conventional no-till seeders and spatial variability of seed depth placement of maize in the Alentejo region, Portugal

The requirements for a good stand in a no-till field are the same as those for conventional planting as well as added field and machinery management. Among the various factors that contribute towards producing a successful maize crop, seed depth placement is a key determinant. Although most no-till planters on the market work well under good soil and residue conditions, adjustments and even modifications are frequently needed when working with compacted or wet soils or with heavy residues. The main objective of this study, carried out in 2010, 2011 and 2012, was to evaluate the vertical distribution and spatial variability of seed depth placement in a maize crop under no-till conditions, using precision farming technologies and conventional no-till seeders. The results obtained indicate that the seed depth placement was affected by soil moisture content and forward speed. The seed depth placement was negatively correlated with soil resistance and seeding depth had a significant impact on mean emergence time and the percentage of emerged plants. Shallow average depth values and high coefficients of variation suggest a need for improvements in controlling the seeders’ sowing depth mechanism or more accurate calibration by operators in the field.

Contribute to the Study of Vertical Distribution of Conventional No-Till Seeders and Spatial Variability of Seed Depth Placement of Maize in Alentejo, Portugal

Entre os vários fatores que contribuem para a produção de uma cultura de milho, a distribuição vertical dos semeadores avaliada através da localização da semente em profundidade é um fator-chave, especialmente na técnica de sementeira direta. Simultaneamente, dada a complexidade dos ecossistemas naturais e agrícolas em sistemas de agricultura de conservação, a gestão diferenciada e localizada das parcelas assume um importante papel na análise e gestão da variabilidade das propriedades do solo e estabelecimento das culturas, nomeadamente utilizando informação geo referenciada e tecnologia expedita. Assim, o principal objetivo desta Tese foi a avaliação em culturas de milho da variabilidade espacial da localização de semente em profundidade e estabelecimento da cultura em sementeira direta usando sistemas convencionais de controlo de profundidade, tendo-se comparado com diferentes sistemas de mobilização e recorrendo a tecnologias de agricultura de precisão. Os ensaios decorreram na região Mediterrânea do Alentejo, em propriedades agrícolas no decorrer das campanhas de 2010, 2011, 2012 e 2015 em 6 diferentes campos experimentais. O trabalho experimental consistiu em ensaios com avaliações in loco do solo e cultura, consumo de combustível das operações e deteção remota. Os resultados obtidos indicam que não só o sistema de mobilização afetou a localização da semente em profundidade, como em sementeira direta a profundidade de sementeira foi afetada pelo teor de humidade do solo, resistência do solo à profundidade e velocidade da operação de sementeira. Adicionalmente observaram-se condições heterogéneas de emergência e estabelecimento da cultura afetadas por condições físicas de compactação do solo. Comparando os diferentes sistemas de mobilização, obteve-se uma significativa redução de combustível para a técnica de sementeira direta, apesar de se terem observado diferenças estatísticas significativas considerando diferentes calibrações de profundidade de sementeira Do trabalho realizado nesta Tese ressalva-se a importância que as tecnologias de agricultura de precisão podem ter no acompanhamento e avaliação de culturas em sementeira direta, bem como a necessidade de melhores procedimentos no controlo de profundidade dos semeadores pelo respetivos operadores ou ao invés, a adoção de semeadores com mecanismos ativos de controlo de profundidade. ABSTRACT Among the various factors that contribute towards producing a successful maize crop, seeders vertical distribution evaluated through seed depth placement is a key determinant, especially under a no-tillage technique. At the same time in conservation agriculture systems due to the complexity of natural and agricultural ecosystems site specific management became an important approach to understand and manage the variability of soil properties and crop establishment, especially when using geo spatial information and affording readily technology Thus, the main objective of this Thesis was to evaluate the spatial variability of seed depth placement and crop establishment in maize crops under no-tillage conditions compared to different tillage systems, using conventional seed depth control no till seeders and precision farming technologies. Trials were carried out in the Mediterranean region of Alentejo, in private farms along the sowing operations season over the years 2010, 2011, 2012 and 2015 in 6 different experimental fields. Experimental work covered field tests with in loco soil and crop evaluations, fuel operation evaluations and aerial sensing. The results obtained indicate that not only tillage system affected seed depth placement but under no till conditions seed depth was affected by soil moisture content, soil resistance to penetration and seeders forward speed. In addition uneven crop seedling and establishment depended on seed depth placement and could be affected by physical problems of compaction layers. Significant reduction in fuel consumption was observed for no till operations although significant differences observed according to different setting calibrations of seed depth control. According to the results, precision agriculture is an important tool to evaluate crops under no till conditions and seed depth mechanisms should be more accurate by the operators or is determinant the adoption of new active depth control technology to improve seeders performance.

Competition may explain the fine-scale spatial patterns and genetic structure of two co-occurring plant congeners

1. The spatial distribution of individual plants within a population and the population’s genetic structure are determined by several factors, like dispersal, reproduction mode or biotic interactions. The role of interspecific interactions in shaping the spatial genetic structure of plant populations remains largely unknown. 2. Species with a common evolutionary history are known to interact more closely with each other than unrelated species due to the greater number of traits they share. We hypothesize that plant interactions may shape the fine genetic structure of closely related congeners. 3. We used spatial statistics (georeferenced design) and molecular techniques (ISSR markers) to understand how two closely related congeners, Thymus vulgaris (widespread species) and T. loscosii (narrow endemic) interact at the local scale. Specific cover, number of individuals of both study species and several community attributes were measured in a 10 × 10 m plot. 4. Both species showed similar levels of genetic variation, but differed in their spatial genetic structure. Thymus vulgaris showed spatial aggregation but no spatial genetic structure, while T. loscosii showed spatial genetic structure (positive genetic autocorrelation) at short distances. The spatial pattern of T. vulgaris’ cover showed significant dissociation with that of T. loscosii. The same was true between the spatial patterns of the cover of T. vulgaris and the abundance of T. loscosii and between the abundance of each species. Most importantly, we found a correlation between the genetic structure of T. loscosii and the abundance of T. vulgaris: T. loscosii plants were genetically more similar when they were surrounded by a similar number of T. vulgaris plants. 5. Synthesis. Our results reveal spatially complex genetic structures of both congeners at small spatial scales. The negative association among the spatial patterns of the two species and the genetic structure found for T. loscosii in relation to the abundance of T. vulgaris indicate that competition between the two species may account for the presence of adapted ecotypes of T. loscosii to the abundance of a competing congeneric species. This suggests that the presence and abundance of close congeners can influence the genetic spatial structure of plant species at fine scales.

Fine spatial pattern of an epiphytic lichen species is affected by habitat conditions in two forest types in the Iberian Mediterranean region

Persistence and abundance of species is determined by habitat availability and the ability to disperse and colonize habitats at contrasting spatial scales. Favourable habitat fragments are also heterogeneous in quality, providing differing opportunities for establishment and affecting the population dynamics of a species. Based on these principles, we suggest that the presence and abundance of epiphytes may reflect their dispersal ability, which is primarily determined by the spatial structure of host trees, but also by host quality. To our knowledge there has been no explicit test of the importance of host tree spatial pattern for epiphytes in Mediterranean forests. We hypothesized that performance and host occupancy in a favourable habitat depend on the spatial pattern of host trees, because this pattern affects the dispersal ability of each epiphyte and it also determines the availability of suitable sites for establishment. We tested this hypothesis using new point pattern analysis tools and generalized linear mixed models to investigate the spatial distribution and performance of the epiphytic lichen Lobaria pulmonaria, which inhabits two types of host trees (beeches and Iberian oaks). We tested the effects on L. pulmonaria distribution of tree size, spatial configuration, and host tree identity. We built a model including tree size, stand structure, and several neighbourhood predictors to understand the effect of host tree on L. pulmonaria. We also investigated the relative importance of spatial patterning on the presence and abundance of the species, independently of the host tree configuration. L. pulmonaria distribution was highly dependent on habitat quality for successful establishment, i.e., tree species identity, tree diameter, and several forest stand structure surrogates. For beech trees, tree diameter was the main factor influencing presence and cover of the lichen, although larger lichen-colonized trees were located close to focal trees, i.e., young trees. However, oak diameter was not an important factor, suggesting that bark roughness at all diameters favoured lichen establishment. Our results indicate that L. pulmonaria dispersal is not spatially restricted, but it is dependent on habitat quality. Furthermore, new spatial analysis tools suggested that L. pulmonaria cover exhibits a distinct pattern, although the spatial pattern of tree position and size was random.

Fine spatial pattern of an epiphytic lichen species is affected by habitat conditions in two forest types in the Iberian Mediterranean region

Persistence and abundance of species is determined by habitat availability and the ability to disperse and colonize habitats at contrasting spatial scales. Favourable habitat fragments are also heterogeneous in quality, providing differing opportunities for establishment and affecting the population dynamics of a species. Based on these principles, we suggest that the presence and abundance of epiphytes may reflect their dispersal ability, which is primarily determined by the spatial structure of host trees, but also by host quality. To our knowledge there has been no explicit test of the importance of host tree spatial pattern for epiphytes in Mediterranean forests. We hypothesized that performance and host occupancy in a favourable habitat depend on the spatial pattern of host trees, because this pattern affects the dispersal ability of each epiphyte and it also determines the availability of suitable sites for establishment. We tested this hypothesis using new point pattern analysis tools and generalized linear mixed models to investigate the spatial distribution and performance of the epiphytic lichen Lobaria pulmonaria, which inhabits two types of host trees (beeches and Iberian oaks). We tested the effects on L. pulmonaria distribution of tree size, spatial configuration, and host tree identity. We built a model including tree size, stand structure, and several neighbourhood predictors to understand the effect of host tree on L. pulmonaria. We also investigated the relative importance of spatial patterning on the presence and abundance of the species, independently of the host tree configuration. L. pulmonaria distribution was highly dependent on habitat quality for successful establishment, i.e., tree species identity, tree diameter, and several forest stand structure surrogates. For beech trees, tree diameter was the main factor influencing presence and cover of the lichen, although larger lichen-colonized trees were located close to focal trees, i.e., young trees. However, oak diameter was not an important factor, suggesting that bark roughness at all diameters favoured lichen establishment. Our results indicate that L. pulmonaria dispersal is not spatially restricted, but it is dependent on habitat quality. Furthermore, new spatial analysis tools suggested that L. pulmonaria cover exhibits a distinct pattern, although the spatial pattern of tree position and size was random.

Topological invariance and spatial scaling of surface roughness in two highly eroded zones of Mexico: a comparative study

The Fractal Image Informatics toolbox (Oleschko et al., 2008 a; Torres-Argüelles et al., 2010) was applied to extract, classify and model the topological structure and dynamics of surface roughness in two highly eroded catchments of Mexico. Both areas are affected by gully erosion (Sidorchuk, 2005) and characterized by avalanche-like matter transport. Five contrasting morphological patterns were distinguished across the slope of the bare eroded surface of Faeozem (Queretaro State) while only one (apparently independent on the slope) roughness pattern was documented for Andosol (Michoacan State). We called these patterns ?the roughness clusters? and compared them in terms of metrizability, continuity, compactness, topological connectedness (global and local) and invariance, separability, and degree of ramification (Weyl, 1937). All mentioned topological measurands were correlated with the variance, skewness and kurtosis of the gray-level distribution of digital images. The morphology0 spatial dynamics of roughness clusters was measured and mapped with high precision in terms of fractal descriptors. The Hurst exponent was especially suitable to distinguish between the structure of ?turtle shell? and ?ramification? patterns (sediment producing zone A of the slope); as well as ?honeycomb? (sediment transport zone B) and ?dinosaur steps? and ?corals? (sediment deposition zone C) roughness clusters. Some other structural attributes of studied patterns were also statistically different and correlated with the variance, skewness and kurtosis of gray distribution of multiscale digital images. The scale invariance of classified roughness patterns was documented inside the range of five image resolutions. We conjectured that the geometrization of erosion patterns in terms of roughness clustering might benefit the most semi-quantitative models developed for erosion and sediment yield assessments (de Vente and Poesen, 2005).

Distribution of indole-3-acetic acid in Petunia hybrida shoot tip cuttings and relationship between auxin transport, carbohydrate metabolism and adventitious root formation.

To determine the contribution of polar auxin transport (PAT) to auxin accumulation and to adventitious root (AR) formation in the stem base of Petunia hybrida shoot tip cuttings, the level of indole-3-acetic acid (IAA) was monitored in non-treated cuttings and cuttings treated with the auxin transport blocker naphthylphthalamic acid (NPA) and was complemented with precise anatomical studies. The temporal course of carbohydrates, amino acids and activities of controlling enzymes was also investigated. Analysis of initial spatial IAA distribution in the cuttings revealed that approximately 40 and 10% of the total IAA pool was present in the leaves and the stem base as rooting zone, respectively. A negative correlation existed between leaf size and IAA concentration. After excision of cuttings, IAA showed an early increase in the stem base with two peaks at 2 and 24h post excision and, thereafter, a decline to low levels. This was mirrored by the expression pattern of the auxin-responsive GH3 gene. NPA treatment completely suppressed the 24-h peak of IAA and severely inhibited root formation. It also reduced activities of cell wall and vacuolar invertases in the early phase of AR formation and inhibited the rise of activities of glucose-6-phosphate dehydrogenase and phosphofructokinase during later stages. We propose a model in which spontaneous AR formation in Petunia cuttings is dependent on PAT and on the resulting 24-h peak of IAA in the rooting zone, where it induces early cellular events and also stimulates sink establishment. Subsequent root development stimulates glycolysis and the pentosephosphate pathway

Lacunarity of the Spatial Distributions of Soil Types in Europe.

Lacunarity as a means of quantifying textural properties of spatial distributions suggests a classification into three main classes of the most abundant soils that cover 92% of Europe. Soils with a well-defined self-similar structure of the linear class are related to widespread spatial patterns that are nondominant but ubiquitous at continental scale. Fractal techniques have been increasingly and successfully applied to identify and describe spatial patterns in natural sciences. However, objects with the same fractal dimension can show very different optical properties because of their spatial arrangement. This work focuses primary attention on the geometrical structure of the geographical patterns of soils in Europe. We made use of the European Soil Database to estimate lacunarity indexes of the most abundant soils that cover 92% of the surface of Europe and investigated textural properties of their spatial distribution. We observed three main classes corresponding to three different patterns that displayed the graphs of lacunarity functions, that is, linear, convex, and mixed. They correspond respectively to homogeneous or self-similar, heterogeneous or clustered and those in which behavior can change at different ranges of scales. Finally, we discuss the pedological implications of that classification.

Spatial linear global instability analysis of the HIFiRE-5 elliptic cone model flow

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