Gradient-domain Path Tracing

We introduce gradient-domain rendering for Monte Carlo image synthesis.While previous gradient-domain Metropolis Light Transport sought to distribute more samples in areas of high gradients, we show, in contrast, that estimating image gradients is also possible using standard (non-Metropolis) Monte Carlo algorithms, and furthermore, that even without changing the sample distribution, this often leads to significant error reduction. This broadens the applicability of gradient rendering considerably. To gain insight into the conditions under which gradient-domain sampling is beneficial, we present a frequency analysis that compares Monte Carlo sampling of gradients followed by Poisson reconstruction to traditional Monte Carlo sampling. Finally, we describe Gradient-Domain Path Tracing (G-PT), a relatively simple modification of the standard path tracing algorithm that can yield far superior results.

High-resolution stratigraphic framework for Mediterranean sapropel S5

A high-resolution stratigraphic framework is presented for sapropel S5, which represents the low-mid latitude climate optimum of the previous interglacial period (Eemian). The framework is based on three sites along a transect from west to east through the eastern Mediterranean, and is further validated using a fourth site. This method allows expression of S5-based proxy records of Eemian climate variability along a standardised depth scale that offers unprecedented possibilities for assessment of spatial gradients and signal leads and lags in an interval where highresolution (radiocarbon-style) dating cannot be performed. Our lateral comparison of S5 sapropels suggests that the onset of S5 in ODP site 967C (Eratosthenes seamount) was 1-6 centuries delayed relative to the onsets in more westerly sites.

Bedding dip data from core site CRP-3 in Victoria Land, Antarctica

Bedding dips in the CRP-3 drillhole were determined in three ways: (1) analysis of a dipmeter log, (2) identification of bed boundaries on borehole televiewer log images, and (3) identification of bed boundaries on digital images of the outer surfaces of oriented cores. All three methods determine both dip magnitude and downdip azimuth of bedding. Dipmeter results document variations in bedding dip throughout the logged interval (20-902 mbsf), whereas core and televiewer results are available at present only for selected depth intervals. Dipmeter data indicate that structural dip is remarkably constant, at 21° dip to azimuth 65°, throughout the Tertiary shelf section, except for the top 100 m where dips appear to be 5-10° shallower. This pattern, in conjunction with the systematically increasing dips throughout CRP-2A, suggests that the growth faulting active during CRP-2A deposition began during the final period of deposition at CRP-3. Normal faults at 260 and 539 mbsf in CRP-3 exhibit neither drag (localized dip steepening) nor significant changes in structural dip across them. Oriented core and televiewer analyses, covering a total of 200 m in the interval 400-900 mbsf, indicate bedding patterns that confirm the dipmeter results. The doleritic breccia at the base of the Tertiary section has steeper dips than overlying structural dips, possibly indicating a sedimentary dip to ENE in these fan sediments. Dip directions in the underlying Devonian Beacon sandstone are surprisingly similar to those in the overlying Tertiary section. Superimposed on the average Beacon dip of 22° to the ENE are localized tilts of up to 20°, probably caused by Tertiary fracturing and brecciation rather than original sedimentary dip variations.

Solar radiation over and under sea ice at ROV station PS86/081-1 during POLARSTERN cruise PS86 (AURORA) in July 2014

The observed changes in physical properties of sea ice such as decreased thickness and increased melt pond cover severely impact the energy budget of Arctic sea ice. Increased light transmission leads to increased deposition of solar energy in the upper ocean and thus plays a crucial role for amount and timing of sea-ice-melt and under-ice primary production. Recent developments in underwater technology provide new opportunities to study light transmission below the largely inaccessible underside of sea ice. We measured spectral under-ice radiance and irradiance using the new Nereid Under-Ice (NUI) underwater robotic vehicle, during a cruise of the R/V Polarstern to 83°N 6°W in the Arctic Ocean in July 2014. NUI is a next generation hybrid remotely operated vehicle (H-ROV) designed for both remotely piloted and autonomous surveys underneath land-fast and moving sea ice. Here we present results from one of the first comprehensive scientific dives of NUI employing its interdisciplinary sensor suite. We combine under-ice optical measurements with three dimensional under-ice topography (multibeam sonar) and aerial images of the surface conditions. We investigate the influence of spatially varying ice-thickness and surface properties on the spatial variability of light transmittance during summer. Our results show that surface properties such as melt ponds dominate the spatial distribution of the under-ice light field on small scales (<1000 m**2), while sea ice-thickness is the most important predictor for light transmission on larger scales. In addition, we propose the use of an algorithm to obtain histograms of light transmission from distributions of sea ice thickness and surface albedo.

Influencias de los barnices incoloros en las propiedades superficiales de las maderas de construcción

En esta Tesis se cuantifica la variación cromática que producen los barnices en el color de los diferentes tipos de maderas de construcción, obteniendo un modelo matemático de predicción de color de la madera. Se analizan las prestaciones de dieciséis barnices, supuestamente incoloros, aplicados sobre veinte tipos de maderas, angiospermas y gimnospermas, de distintas densidades y latitudes. Ambos materiales son de uso frecuente en el ámbito de la construcción y de fácil localización en las tiendas y almacenes de ambos sectores. Se utilizan técnicas de descomposición cromática, mediante el empleo de microscopio óptico de reflexión, para poder obtener un abanico gráfico de histogramas con valores numéricos de luminosidad y composición cromática, y de esta forma comprobar que los supuestos barnices que se venden como incoloros, no son totalmente incoloros sino que muestran tendencias a virar hacia alguno de los colores básicos. En el proceso experimental de la Tesis, se aplican 16 barnices sobre 20 tipos de maderas, obteniéndose los histogramas de las campañas de fotografías realizadas con cinco años de diferencia, obteniéndose no solo la variación de color que producen los barnices sobre el original de la madera, sino además la influencia de un envejecimiento a los cinco años. La Tesis relaciona el tipo de barniz idóneo para cada tipo de madera, de modo que produzca la menor variación cromática. La Tesis además obtiene un modelo matemático que permite predecir el color final de la madera tratada en función del color inicial de la madera sin barnizar. Se propone en esta Tesis una recomendación de los productos a utilizar en cada uno de los tipos de madera en base a su color inicial. This Thesis quantifies the chromatic variation caused by varnishes in the colour of different types of timbers, obtaining a mathematical model for predicting the timber’s colour. The performance of sixteen varnishes, supposedly colourless, is analysed, applied on twenty types of timber, angiosperms and gymnosperms, of different densities and latitudes. Both materials are of frequent use in the construction field and easily located in the stores and warehouses of both sectors. Chromatic decomposition techniques are used, through the utilization of a reflection optical microscope, in order to obtain a graphic range of histograms with numerical values of luminosity and chromatic composition, and this way confirm that the alleged varnishes sold as colourless are not completely colourless but are prone to shift towards one of the basic colours. During the Thesis’ experimental procedure 16 varnishes are applied on 20 types of timber, obtaining the colour histograms of the photography campaigns carried out with a five years difference, resulting in not only the colour variation caused by the varnishes on the original timber, but also the influence of its ageing five years later. The Thesis links the right type of varnish for each kind of timber, so that as little chromatic variation as possible occurs. The Thesis obtains as well a mathematical model, which makes it possible to predict the final colour of the treated timber depending on the original colour of the timber with no varnish. This Thesis proposes a recommendation of the products to use on each type of timber on the basis of its original colour.

Mealiness assessment in apples and peaches using MRI techniques

Mealiness (woolliness in peaches) is a negative attribute of sensory texture that combines the sensation of a desegregated tissue with the sensation of lack of juiciness. In this study, 24 apples cv. Top Red and 8 peaches cv. Maycrest, submitted to 3 and 2 different storage conditions respectively have been tested by mechanical and MRI techniques to assess mealiness. With this study, the results obtained on apples in a previous work have been validated using mathematical features from the histograms of the T2 maps: more skewed and the presence of a tail in mealy apples, similar to internal breakdown. In peaches, MRI techniques can also be used to identify woolly fruits. Not all the changes found in the histograms of woolly peaches are similar from those observed in mealy apples pointing to a different underlying physiological change in both disorders.

Relationship between solar radiation on watercore on apple fruit assessed with MRI

This work is a preliminary studio of the possibility of assess a relationship between solar radiation and watercore development on apple fruit, during maturation, using a non destructive method such as Magnetic Resonance Imaging (MRI). For such purpose, several low cost solar radiation sensors were designed for the trial and placed at 2 different heights (1.5 and 2.5 m) on 6 adult ?Esperiega? apple trees, in a commercial orchard in Ademuz (Valencia). Sensors were connected along 27 days, during the end of the growth period and start of the fruit maturation process, and radiation measurements of the a-Si sensors were recorded every 1 minute. At the end of this period, fruits from the upper and the lower part of the canopy of each tree were harvested. In all, 152 apples were collected and images with MRI. A Principal Component Analysis, perfomed over the histograms of the images, as well as segmentation methods were performed on the MR images in order to find a pattern involving solar radiation and watercore incidence.

Crack mechanical failure in lithium niobate crystal under ion irradiation; novel simulation by extended finite elements

Swift heavy ion irradiation (ions with mass heavier than 15 and energy exceeding MeV/amu) transfer their energy mainly to the electronic system with small momentum transfer per collision. Therefore, they produce linear regions (columnar nano-tracks) around the straight ion trajectory, with marked modifications with respect to the virgin material, e.g., phase transition, amorphization, compaction, changes in physical or chemical properties. In the case of crystalline materials the most distinctive feature of swift heavy ion irradiation is the production of amorphous tracks embedded in the crystal. Lithium niobate is a relevant optical material that presents birefringence due to its anysotropic trigonal structure. The amorphous phase is certainly isotropic. In addition, its refractive index exhibits high contrast with those of the crystalline phase. This allows one to fabricate waveguides by swift ion irradiation with important technological relevance. From the mechanical point of view, the inclusion of an amorphous nano-track (with a density 15% lower than that of the crystal) leads to the generation of important stress/strain fields around the track. Eventually these fields are the origin of crack formation with fatal consequences for the integrity of the samples and the viability of the method for nano-track formation. For certain crystal cuts (X and Y), these fields are clearly anisotropic due to the crystal anisotropy. We have used finite element methods to calculate the stress/strain fields that appear around the ion-generated amorphous nano-tracks for a variety of ion energies and doses. A very remarkable feature for X cut-samples is that the maximum shear stress appears on preferential planes that form +/-45º with respect to the crystallographic planes. This leads to the generation of oriented surface cracks when the dose increases. The growth of the cracks along the anisotropic crystal has been studied by means of novel extended finite element methods, which include cracks as discontinuities. In this way we can study how the length and depth of a crack evolves as function of the ion dose. In this work we will show how the simulations compare with experiments and their application in materials modification by ion irradiation.

Silica final lens performance in laser fusion facilities: HiPER and LIFE

Nowadays, the projects LIFE (Laser Inertial Fusion Energy) in USA and HiPER (High Power Laser Energy Research) in Europe are the most advanced ones to demonstrate laser fusion energy viability. One of the main points of concern to properly achieve ignition is the performance of the final optics (lenses) under the severe irradiation conditions that take place in fusion facilities. In this paper, we calculate the radiation fluxes and doses as well as the radiation-induced temperature enhancement and colour centre formation in final lenses assuming realistic geometrical configurations for HiPER and LIFE. On these bases, the mechanical stresses generated by the established temperature gradients are evaluated showing that from a mechanical point of view lenses only fulfil specifications if ions resulting from the imploding target are mitigated. The absorption coefficient of the lenses is calculated during reactor startup and steady-state operation. The obtained results reveal the necessity of new solutions to tackle ignition problems during the startup process for HiPER. Finally, we evaluate the effect of temperature gradients on focal length changes and lens surface deformations. In summary, we discuss the capabilities and weak points of silica lenses and propose alternatives to overcome predictable problems

NURBS-Based Geometry Parameterization for Aerodynamic Shape Optimization

La motivación de esta tesis es el desarrollo de una herramienta de optimización automática para la mejora del rendimiento de formas aerodinámicas enfocado en la industria aeronáutica. Este trabajo cubre varios aspectos esenciales, desde el empleo de Non-Uniform Rational B-Splines (NURBS), al cálculo de gradientes utilizando la metodología del adjunto continuo, el uso de b-splines volumétricas como parámetros de diseño, el tratamiento de la malla en las intersecciones, y no menos importante, la adaptación de los algoritmos de la dinámica de fluidos computacional (CFD) en arquitecturas hardware de alto paralelismo, como las tarjetas gráficas, para acelerar el proceso de optimización. La metodología adjunta ha posibilitado que los métodos de optimización basados en gradientes sean una alternativa prometedora para la mejora de la eficiencia aerodinámica de los aviones. La formulación del adjunto permite calcular los gradientes de una función de coste, como la resistencia aerodinámica o la sustentación, independientemente del número de variables de diseño, a un coste computacional equivalente a una simulación CFD. Sin embargo, existen problemas prácticos que han imposibilitado su aplicación en la industria, que se pueden resumir en: integrabilidad, rendimiento computacional y robustez de la solución adjunta. Este trabajo aborda estas contrariedades y las analiza en casos prácticos. Como resumen, las contribuciones de esta tesis son: • El uso de NURBS como variables de diseño en un bucle de automático de optimización, aplicado a la mejora del rendimiento aerodinámico de alas en régimen transónico. • El desarrollo de algoritmos de inversión de punto, para calcular las coordenadas paramétricas de las coordenadas espaciales, para ligar los vértices de malla a las NURBS. • El uso y validación de la formulación adjunta para el calculo de los gradientes, a partir de las sensibilidades de la solución adjunta, comparado con diferencias finitas. • Se ofrece una estrategia para utilizar la geometría CAD, en forma de parches NURBS, para tratar las intersecciones, como el ala-fuselaje. • No existen muchas alternativas de librerías NURBS viables. En este trabajo se ha desarrollado una librería, DOMINO NURBS, y se ofrece a la comunidad como código libre y abierto. • También se ha implementado un código CFD en tarjeta gráfica, para realizar una valoración de cómo se puede adaptar un código sobre malla no estructurada a arquitecturas paralelas. • Finalmente, se propone una metodología, basada en la función de Green, como una forma eficiente de paralelizar simulaciones numéricas. Esta tesis ha sido apoyada por las actividades realizadas por el Área de Dinámica da Fluidos del Instituto Nacional de Técnica Aeroespacial (INTA), a través de numerosos proyectos de financiación nacional: DOMINO, SIMUMAT, y CORESFMULAERO. También ha estado en consonancia con las actividades realizadas por el departamento de Métodos y Herramientas de Airbus España y con el grupo Investigación y Tecnología Aeronáutica Europeo (GARTEUR), AG/52. ABSTRACT The motivation of this work is the development of an automatic optimization strategy for large scale shape optimization problems that arise in the aeronautics industry to improve the aerodynamic performance; covering several aspects from the use of Non-Uniform Rational B-Splines (NURBS), the calculation of the gradients with the continuous adjoint formulation, the development of volumetric b-splines parameterization, mesh adaptation and intersection handling, to the adaptation of Computational Fluid Dynamics (CFD) algorithms to take advantage of highly parallel architectures in order to speed up the optimization process. With the development of the adjoint formulation, gradient-based methods for aerodynamic optimization become a promising approach to improve the aerodynamic performance of aircraft designs. The adjoint methodology allows the evaluation the gradients to all design variables of a cost function, such as drag or lift, at the equivalent cost of more or less one CFD simulation. However, some practical problems have been delaying its full implementation to the industry, which can be summarized as: integrability, computer performance, and adjoint robustness. This work tackles some of these issues and analyse them in well-known test cases. As summary, the contributions comprises: • The employment of NURBS as design variables in an automatic optimization loop for the improvement of the aerodynamic performance of aircraft wings in transonic regimen. • The development of point inversion algorithms to calculate the NURBS parametric coordinates from the space coordinates, to link with the computational grid vertex. • The use and validation of the adjoint formulation to calculate the gradients from the surface sensitivities in an automatic optimization loop and evaluate its reliability, compared with finite differences. • This work proposes some algorithms that take advantage of the underlying CAD geometry description, in the form of NURBS patches, to handle intersections and mesh adaptations. • There are not many usable libraries for NURBS available. In this work an open source library DOMINO NURBS has been developed and is offered to the community as free, open source code. • The implementation of a transonic CFD solver from scratch in a graphic card, for an assessment of the implementability of conventional CFD solvers for unstructured grids to highly parallel architectures. • Finally, this research proposes the use of the Green's function as an efficient paralellization scheme of numerical solvers. The presented work has been supported by the activities carried out at the Fluid Dynamics branch of the National Institute for Aerospace Technology (INTA) through national founding research projects: DOMINO, SIMUMAT, and CORESIMULAERO; in line with the activities carried out by the Methods and Tools and Flight Physics department at Airbus and the Group for Aeronautical Research and Technology in Europe (GARTEUR) action group AG/52.

Hydrostatic instabilities in floating zone cristal growth process

If only Fluid Mechanics aspects are considered, the configuration appearing in the floating zone technique for crystal growth can be modelled as a mass of liquid spanning between two solid rods. Besides, if now the influence of temperature gradients and heat flow are not considered, the simplest fluid model consists of an isothermal liquid mass of constant properties (density and surface tension) held by capillary forces between two solid disks placed a distance L apart: the so called liquid bridge. As it is well known, if both supporting disks were parallel, coaxial and of the same diameter, 2R, the volume of liquid, V, were equal to that of a cylinder of the same L and R (V=KR~L) and no body forces were acting on the liquid column, the fluid configuration (under these conditions of cylindrical shape) will become unstable when the distance between the disks equals the length of the circumference of the supporting disks (L=2KR, the so-called Rayleigh stability limit). One should be aware that the Rayleigh stability limit can be dramatically modified when the geometry differs from the above described cylinder (due to having non-coaxial disks, different diameter disks, liquid volume different from the cylindrical one, etc) or when other external effects like accelerations either axial or lateral are considered. In this paper the stability limits of liquid bridges considering different types of perturbations are reviewed.

On a common circle: Natural scenes and Gestalt rules

To understand how the human visual system analyzes images, it is essential to know the structure of the visual environment. In particular, natural images display consistent statistical properties that distinguish them from random luminance distributions. We have studied the geometric regularities of oriented elements (edges or line segments) present in an ensemble of visual scenes, asking how much information the presence of a segment in a particular location of the visual scene carries about the presence of a second segment at different relative positions and orientations. We observed strong long-range correlations in the distribution of oriented segments that extend over the whole visual field. We further show that a very simple geometric rule, cocircularity, predicts the arrangement of segments in natural scenes, and that different geometrical arrangements show relevant differences in their scaling properties. Our results show similarities to geometric features of previous physiological and psychophysical studies. We discuss the implications of these findings for theories of early vision.

Anatomia ecológica do lenho de espécies arbustivas e arbóreas que ocorrem naturalmente em bosques com drástico gradiente de precipitação ao Noroeste da Patagônia, Argentina

A utilização de gradientes ambientais no estudo de comunidades vegetais possibilita a eleição de sítios onde há a predominância de um fator abiótico que determina o sucesso ou o fracasso de espécies ao longo de sua extensão. Entre as inúmeras ferramentas utilizadas no estudo de gradientes climáticos, se destaca a anatomia do lenho, pois, é um ramo da ciência que permite analisar, além dos aspectos espaciais, os aspectos temporais dos sítios por meio dos anéis de crescimento. Além disso, a ampla distribuição das plantas lenhosas ao longo do globo possibilita análises em praticamente todos os tipos de biomas e ecossistemas terrestres. Dentro desse contexto estão os bosques andino-patagônicos de Araucaria araucana (Pehuén) ao norte de sua distribuição na Argentina. Esses bosques ocupam territórios caracterizados por um acentuado gradiente de precipitação, que vai de cerca de 3000 a 100 milímetros anuais, entre a cordilheira do Andes e a estepe patagônica, que os define como bosques mésicos e xéricos, com diferenças ecológicas que condicionam a formação vegetal, dinâmica, estrutura, relações com o clima e vulnerabilidade em cenários de mudanças ambientais. O objetivo do projeto foi descrever e analisar comparativamente a estrutura anatômica do lenho de 33 espécies arbóreas e arbustivas ocorrentes ao longo de um gradiente de precipitação, entre a encosta da cordilheira dos Andes e a estepe Patagônica, para verificar possíveis alterações anatômicas que permitam a determinação de tendências e elucidem os limites de distribuição das espécies. Foram coletadas amostras não destrutivas de lenho durante três expedições para a Patagônia entre 2012 e 2014, seguidas de procedimentos laboratoriais de confeccção de lâminas histológicas, preparo de amostras para análises dendrocronológicas, captura de imagens com câmeras acopladas a microscópios óptico e eletrônico de varredura, mensurações, descrições e análises comparativas com o auxílio de softwares. Foram identificados caracteres anatômicos exclusivos de sítios secos e úmidos que permitiram a caracterização, posicionamento ao longo do gradiente de precipitação e grupamento de espécies xerófitas e mesófitas; A ultra-estrutura das pontoações de traqueídeos de Araucaria araucana apresentou diferenças marcantes na frequência e porosidade de suas membranas, sendo maior e menos porosas em sítios xéricos, e menor e mais porosas nos mésicos; a chave dicotômica microscópica permitiu a identificação das 32 espécies arbustivas, as espécies Chuquiraga oppositifolia e Nothofagus antarctica apresentaram potencial dendrocronológico, e foram identificadas tendências anatômicas latitudinais influenciadas pelo clima nos extremos da América do Sul. A anatomia do lenho se mostrou uma ferramenta confiável no estudo de um gradiente de precipitação na Patagônia argentina, e os resultados apontam para riscos de embolismos e morte induzida por falha no sistema hidráulico de Araucaria araucana ao longo de todo o gradiente, em função do atual cenário climático, e suas projeções em médio e longo prazos.

Fatores abióticos condicionantes da distribuição de espécies arbóreas em quatro formações florestais do Estado de São Paulo

No estudo das comunidades florestais, estabelecer a importância relativa dos fatores que definem a composição e a distribuição das espécies é um desafio. Em termos de gradientes ambientais o estudo das respostas das espécies arbóreas são essenciais para a compreensão dos processos ecológicos e decisões de conservação. Neste sentido, para contribuir com a elucidação dos processos ecológicos nas principais formações florestais do Estado de São Paulo (Floresta Ombrófila Densa de Terras Baixas, Floresta Ombrófila Densa Submontana, Floresta Estacional Semidecidual e Savana Florestada) este trabalho objetivou responder as seguintes questões: (I) a composição florística e a abundância das espécies arbóreas, em cada unidade fitogeográfica, variam conforme o gradiente edáfico e topográfico?; (II) características do solo e topografia podem influenciar na previsibilidade de ocorrência de espécies arbóreas de ampla distribuição em diferentes tipos vegetacionais? (III) existe relação entre o padrão de distribuição espacial de espécies arbóreas e os parâmetros do solo e topografia? O trabalho foi realizado em parcelas alocadas em unidades de conservação (UC) que apresentaram trechos representativos, em termos de conservação e tamanho, das quatro principais formações florestais presentes no Estado de São Paulo. Em cada UC foram contabilizados os indivíduos arbóreos (CAP ≥ 15 cm), topografia, dados de textura e atributos químicos dos solos em uma parcela de 10,24 ha, subdividida em 256 subparcelas. Análises de correspodência canônica foram aplicadas para estabelecer a correspondência entre a abundância das espécies e o gradiente ambiental (solo e topografia). O método TWINSPAN modificado foi aplicado ao diagrama de ordenação da CCA para avaliar a influência das variáveis ambientais (solo e topografia) na composição de espécies. Árvores de regressão \"ampliadas\" (BRT) foram ajustadas para a predição da ocorrência das espécies segundo as variáveis de solo e topografia. O índice de Getis-Ord (G) foi utilizado para determinar a autocorrelação espacial das variáveis ambientais utilizadas nos modelos de predição da ocorrência das espécies. Nas unidades fitogeográficas analisadas, a correspondência entre o gradiente ambiental (solo e topografia) e a abundância das espécies foi significativa, especialmente na Savana Florestada onde observou-se a maior relação. O solo e a topografia também se relacionaram com a semelhança na composição florística das subparcelas, com exceção da Floresta Estacional Semicidual (EEC). As principais variáveis de solo e topografia relacionadas a flora em cada UC foram: (1) Na Floresta Ombrófila Densa de Terras Baixas (PEIC) - teor de alumínio na camada profunda (Al (80-100 cm)) que pode refletir os teor de Al na superfície, acidez do solo (pH(H2O) (5-25 cm)) e altitude, que delimitou as áreas alagadas; (2) Na Floresta Ombrófila Densa Submontana (PECB) - altitude, fator que, devido ao relevo acidentado, influencia a temperatura e incidência de sol no sub-bosque; (3) Na Savana Florestada (EEA) - fertilidade, tolerância ao alumínio e acidez do solo. Nos modelos de predição BRT, as variáveis químicas dos solos foram mais importantes do que a textura, devido à pequena variação deste atributo no solo nas áreas amostradas. Dentre as variáveis químicas dos solos, a capacidade de troca catiônica foi utilizada para prever a ocorrência das espécies nas quatro formações florestais, sendo particularmente importante na camada mais profunda do solo da Floresta Ombrófila Densa de Terras Baixas (PEIC). Quanto à topografia, a altitude foi inserida na maioria dos modelos e apresentou diferentes influências sobre as áreas de estudo. De modo geral, para presença das espécies de ampla distribuição observou-se uma mesma tendência quando à associação com os atributos dos solos, porém com amplitudes dos descritores edáficos que variaram de acordo com a área de estudo. A ocorrência de Guapira opposita e Syagrus romanzoffiana, cujo padrão variou conforme a escala, foi explicada por variáveis com padrões espaciais agregados que somaram entre 30% e 50% de importância relativa no modelo BRT. A presença de A. anthelmia, cujo padrão também apresentou certo nível de agregação, foi associada apenas a uma variável com padrão agregado, a altitude (21%), que pode ter exercido grande influência na distribuição da espécie ao delimitar áreas alagadas. T. guianensis se associou a variáveis ambientais preditoras com padrão espacial agregado que somaram cerca de 70% de importância relativa, o que deve ter sido suficiente para estabelecer o padrão agregado em todas as escalas. No entanto, a influência dos fatores ambientais no padrão de distribuição da espécie não depende apenas do ótimo ambiental da espécie, mas um resultado da interação espécie-ambiente. Concluiu-se que: (I) características edáficas e topográficas explicaram uma pequena parcela da composição florística, em cada unidade fitogeográfica, embora a ocorrência de algumas espécies tenha se associado ao gradiente edáfico e topográfico; (II) a partir de características dos solos e da topografia foi possível prever a presença de espécies arbóreas, que apresentaram particularidades em relação a sua associação com o solo de cada fitofisionomia; (III) a partir de associações descritivas o solo e a topografia influenciam o padrão de distribuição espacial das espécies, na proporção em que contribuem para a presença das mesmas.

Differential diffusion: Often a finite-mising length effect

Many instances of differential diffusion, i e, different species having different turbulent diffusion coefficients in the same flow, can be explained as a finite mixing length effect. That is, in a simple mixing length scenario, the turbulent diffusion coefficient has the form 1 ( m )2 m m c l K w l OL   =  +    where, wm is the mixing velocity, lm the mixing length and Lc the overall distribution scale for a particular species. The first term represents the familiar gradient diffusion while the second term becomes important when lm/Lc is finite. This second term shows that different species will have different diffusion coefficients if they have different overall distribution scales. Such different Lcs may come about due to different boundary conditions and different intrinsic properties (molecular diffusivity, settling velocity etc) for different species. For momentum transfer in turbulent oscillatory boundary layers the second term is imaginary and explains observed phase leads of shear stresses ahead of velocity gradients.