Testing Isotropy and a related Random Walk problem

One comes across directions as the observations in a number of situations. The first inferential question that one should answer when dealing with such data is, “Are they isotropic or uniformly distributed?” The answer to this question goes back in history which we shall retrace a bit and provide an exact and approximate solution to this so-called “Pearson’s Random Walk” problem.

Fractal-to-Euclidean crossover of the isotropy restoration feature in a family of fractal resistor networks

Fractal with microscopic anisotropy shows a unique type of macroscopic isotropy restoration phenomenon that is absent in Euclidean space [M. T. Barlow et al., Phys. Rev. Lett. 75, 3042]. In this paper the isotropy restoration feature is considered for a family of two-dimensional Sierpinski gasket type fractal resistor networks. A parameter xi is introduced to describe this phenomenon. Our numerical results show that xi satisfies the scaling law xi similar to l(-alpha), where l is the system size and alpha is an exponent independent of the degree of microscopic anisotropy, characterizing the isotropy restoration feature of the fractal systems. By changing the underlying fractal structure towards the Euclidean triangular lattice through increasing the side length b of the gasket generators, the fractal-to-Euclidean crossover behavior of the isotropy restoration feature is discussed.

Fine root isotropy in Eucalyptus grandis plantations. Towards the prediction of root length densities from root counts on trench walls

The objectives of the study were to assess changes in fine root anisotropy and specific root lengths throughout the development of Eucalyptus grandis ( W. Hill ex Maiden) plantations and to establish a predictive model of root length density (RLD) from root intercept counts on trench walls. Fine root densities (<1 mm in diameter) were studied in 6-, 12-, 22-, 28-, 54-, 68- and 72-month-old E. grandis plantations established on deep Ferralsols in southern Brazil. Fine root intercepts were counted on 3 faces of 90-198 soil cubes (1 dm(3) in volume) in each stand and fine root lengths (L) were measured inside 576 soil cubes, sampled between the depths of 10 cm and 290 cm. The number of fine root intercepts was counted on one vertical face perpendicular to the planting row (N(t)), one vertical face parallel to the planting row (N(l)) and one horizontal face (N(h)), for each soil cube sampled. An overall isotropy of fine roots was shown by paired Student's t-tests between the numbers of fine roots intersecting each face of soil cubes at most stand ages and soil depths. Specific root lengths decreased with stand age in the upper soil layers and tended to increase in deep soil layers at the end of the rotation. A linear regression established between N(t) and L for all the soil cubes sampled accounted for 36% of the variability of L. Such a regression computed for mean Nt and L values at each sampling depth and stand age explained only 55% of the variability, as a result of large differences in the relationship between L and Nt depending on stand productivity. The equation RLD=1.89*LAI*N(t), where LAI was the stand leaf area index (m(2) m(-2)) and Nt was expressed as the number of root intercepts per cm(2), made it possible to predict accurately (R(2)=0.84) and without bias the mean RLDs (cm cm(-3)) per depth in each stand, for the whole data set of 576 soil cubes sampled between 2 years of age and the end of the rotation.

Testing gaussianity, homogeneity, and isotropy with the cosmic microwave background

We review the basic hypotheses which motivate the statistical framework used to analyze the cosmic microwave background, and how that framework can be enlarged as we relax those hypotheses. In particular, we try to separate as much as possible the questions of gaussianity, homogeneity, and isotropy from each other. We focus both on isotropic estimators of nongaussianity as well as statistically anisotropic estimators of gaussianity, giving particular emphasis on their signatures and the enhanced cosmic variances that become increasingly important as our putative Universe becomes less symmetric. After reviewing the formalism behind some simple model-independent tests, we discuss how these tests can be applied to CMBdata when searching for large-scale anomalies. Copyright © 2010 L. Raul Abramo and Thiago S. Pereira.

The discriminants associated to isotropy representations of symmetric spaces

We consider a generalized discriminant associated to a symmetric space which generalizes the discriminant of real symmetric matrices, and note that it can be written as a sum of squares of real polynomials. A method to estimate the minimum number of squares required to represent the discrimininant is developed and applied in examples.

Assessment of Transverse Isotropy in Clinical-Level CT Images of Trabecular Bone Using the Gradient Structure Tensor

The aim of this study was to develop a GST-based methodology for accurately measuring the degree of transverse isotropy in trabecular bone. Using femoral sub-regions scanned in high-resolution peripheral QCT (HR-pQCT) and clinical-level-resolution QCT, trabecular orientation was evaluated using the mean intercept length (MIL) and the gradient structure tensor (GST) on the HR-pQCT and QCT data, respectively. The influence of local degree of transverse isotropy (DTI) and bone mineral density (BMD) was incorporated into the investigation. In addition, a power based model was derived, rendering a 1:1 relationship between GST and MIL eigenvalues. A specific DTI threshold (DTI thres) was found for each investigated size of region of interest (ROI), above which the estimate of major trabecular direction of the GST deviated no more than 30° from the gold standard MIL in 95% of the remaining ROIs (mean error: 16°). An inverse relationship between ROI size and DTI thres was found for discrete ranges of BMD. A novel methodology has been developed, where transversal isotropic measures of trabecular bone can be obtained from clinical QCT images for a given ROI size, DTI thres and power coefficient. Including DTI may improve future clinical QCT finite-element predictions of bone strength and diagnoses of bone disease.

Angular-planar CMB power spectrum

Gaussianity and statistical isotropy of the Universe are modern cosmology's minimal set of hypotheses. In this work we introduce a new statistical test to detect observational deviations from this minimal set. By defining the temperature correlation function over the whole celestial sphere, we are able to independently quantify both angular and planar dependence (modulations) of the CMB temperature power spectrum over different slices of this sphere. Given that planar dependence leads to further modulations of the usual angular power spectrum C(l), this test can potentially reveal richer structures in the morphology of the primordial temperature field. We have also constructed an unbiased estimator for this angular-planar power spectrum which naturally generalizes the estimator for the usual C(l)'s. With the help of a chi-square analysis, we have used this estimator to search for observational deviations of statistical isotropy in WMAP's 5 year release data set (ILC5), where we found only slight anomalies on the angular scales l = 7 and l = 8. Since this angular-planar statistic is model-independent, it is ideal to employ in searches of statistical anisotropy (e.g., contaminations from the galactic plane) and to characterize non-Gaussianities.

Impact on HDPE and PVC plates - Experimental tests and numerical simulations

This paper presents first material tests on HDPE and PVC, and subsequently impact tests on plates made of the same materials. Finally, numerical simulations of the plate impact tests are compared with the experimental results. A rather comprehensive series of mechanical material tests were performed to disclose the behaviour of PVC and HDPE in tension and compression. Quasi-static tests were carried out at three rates in compression and two in tension. Digital image correlation. DIC, was used to measure the in-plane strains, revealing true stress-strain curves and allowing to analyze strain-rate sensitivity and isotropy of Poisson`s ratio. In addition, dynamic compression tests were carried out in a split-Hopkinson pressure bar. Quasi-static and dynamic tests were also performed on clamped plates made of the same PVC and HDPE materials, using an optical technique to measure the full-field out-of-plane deformations. These tests, together with the material data, were used for comparative purposes of a finite element analysis. A reasonable agreement between experimental and numerical results was achieved. (C) 2010 Elsevier Ltd. All rights reserved.

A study of the interaction between operator style and machine capability for a hydraulic mining excavator

This paper presents a case study that explores how operator digging style juxtaposes with mechanical capability for a class of hydraulic mining excavators. The relationships between actuator and digging forces are developed and these are used to identify the excavator's capability to apply forces in various directions. Two distinct modes of operation are examined to see how they relate to the mechanical capabilities of the linkage and to establish if one has merit over the other. It is found that one of these styles results in lower loading of the machine.

Elastic moduli of model random three-dimensional closed-cell cellular solids

Most cellular solids are random materials, while practically all theoretical structure-property results are for periodic models. To be able to generate theoretical results for random models, the finite element method (FEM) was used to study the elastic properties of solids with a closed-cell cellular structure. We have computed the density (rho) and microstructure dependence of the Young's modulus (E) and Poisson's ratio (PR) for several different isotropic random models based on Voronoi tessellations and level-cut Gaussian random fields. The effect of partially open cells is also considered. The results, which are best described by a power law E infinity rho (n) (1<n<2), show the influence of randomness and isotropy on the properties of closed-cell cellular materials, and are found to be in good agreement with experimental data. (C) 2001 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved.

Otimização da anisotropia fronto-calosa e ressonância magnética [1,5T] no idoso normal e com risco cérebro-vascular

RESUMO: Os mais recentes métodos de neuro imagem tal como a Ressonância Magnética (RM) permitiram obter imagens detalhadas do cérebro humano in vivo. Essas imagens revelam, muitas vezes, achados imprevistos face ao padrão normal, com elevada propensão para os indivíduos idosos e franca coexistência com fatores de risco vascular, como característica dum processo de envelhecimento normal. Embora na última década tenham surgido várias publicações sobre este assunto, ele continua ainda pouco explicado. Um pouco por todo o mundo têm emergido os programas de prevenção da doença e promoção da saúde desenvolvidos pela Saúde Pública suportadas sobretudo pelo avanço das tecnologias médicas que resultaram, entre outros impactos, num crescimento da população idosa. Estima-se, em 2030, uma composição demográfica com 20% de indivíduos acima dos 65 anos. Neste contexto, a doença microvascular cerebral é a causa mais frequente de comprometimento cognitivo vascular no idoso sendo as características senescentes na imagem por RM do tipo lesões isquémicas da Substância Branca (Leukoaraiosis) e enfartes lacunares (Status lacunar), atrofia cerebral, gliose e acumulação excessiva de ferro nos núcleos da base. Esta tese, considerando a linha de investigação de que deriva – Ciências da Vida - especialização em Medicina Clinica - Biotecnologia, reúne e reflete sobre três vertentes ligadas à RM e interdependentes em relação a uma problemática comum. A primeira trata da caracterização da Tecnologia por Ressonância Magnética existente em Portugal, a qual inclui uma avaliação exploratória da aplicação da técnica de Difusão Anisotrópica nos estudos cerebrais. As dimensões analíticas estudadas foram a Tecnológica, Sociodemográfica e Económica. Na recolha de dados recorreu-se a várias fontes de informação e a uma metodologia exploratória faseada, validada pela triangulação dos resultados. A sua análise obedeceu a critérios de estratificação e agrupamento segundo as mesmas dimensões analíticas. Otimização da anisotropia fronto-calosa e [RM 1,5T] no idoso normal e com risco cérebro-vascular A segunda descreve o estudo anátomo – radiológico que recaiu sobre parâmetros de quantificação assente na temática do cérebro do idoso em cadáver segundo uma metodologia experimental aplicada às métricas da difusão por RM. Na terceira, e última, é apresentado o estudo técnico - radiológico para avaliação e otimização da imagem ponderada em difusão em estudos clínicos associados ao cérebro do idoso “The Usual Brain Aging” ou Envelhecimento Cerebral Normal, com base metodológica assente nos critérios e indicadores estabelecidos pelo Estudo de Imagem de Roterdão (Rotterdam Scan Study - RSS). Como principais resultados obteve-se que não existem em Portugal estruturas para avaliação dos equipamentos pesados ou Agência de Avaliação das Tecnologias da Saúde para desenvolver o importante papel da produção de estudos comparativos entre os equipamentos disponíveis no mercado, a relação preço-qualidade e a sua afetação às necessidades clínico-epidemiológicas. Constatou-se que a implementação de equipamentos de RM está fortemente assente em critérios económicos carecendo de recomendações e diretivas para o uso racionalizado destas tecnologias. Quanto a dados quantitativos concluímos que a maioria dos equipamentos está instalada em instituições privadas (80,2%); a intensidade de campo magnético mais frequente é [1,5T] com 119 equipamentos; os equipamentos estão instalados maioritariamente nos distritos de Lisboa (55 unidades) e do Porto (39 unidades); o rácio médio de equipamentos por habitante em Portugal é de 1 para 65 195 habitantes; a amplitude de gradientes com maior expressão na amostra é 30-39mT/m; a maioria dos equipamentos foi instalada no intervalo temporal [2009-2012] com 59 equipamentos; apenas 6 instituições desenvolvem investigação clinica e a maioria das bobinas para estudos de crânio são do tipo Array. O estudo de otimização da técnica da difusão revelou, quanto à avaliação dos valoresb, que os mais baixos (b=500 s/mm2 e b=1000 s/mm2), apresentam maior IS e SNR sendo esta uma boa medida referente à qualidade de imagem, no entanto, os valores-b mais elevados (b=2000 s/mm2) apresentam maior CNR e CR, face aos anteriores, o Otimização da anisotropia fronto-calosa e [RM 1,5T] no idoso normal e com risco cérebro-vascular que apesar de proporcionar inferior detalhe anatómico e consequentemente inferior qualidade de imagem, num encéfalo normal, pode auxiliar na interpretação e apresentar vantagens na identificação de lesões microvasculares sempre que persistirem dúvidas em relação ao diagnóstico diferencial de doença microvascular do tipo status lacunar ou Hiperintensidades da Substância Branca. As alterações deste parâmetro são particularmente refletidas nas diferenças da avaliação da qualidade de imagem na região fronto-calos Concluímos da avaliação quantitativa da concentração média de ferro (26Fe) em todas as faixas etárias que os núcleos da base que apresentam maior concentração são, por ordem decrescente: Substância Nigra, Globus Pallidus, Putamen, Tálamo, Núcleo Rubro e Núcleo Caudado; que existe uma predominância na concentração de ferro (26Fe) no hemisfério esquerdo e que os indivíduos do género masculino apresentam mais ferro (26Fe) que os do género feminino nas faixas etárias [30-40[, [40-50[ e [50-60[. Como principal conclusão do estudo da concentração média de ferro em relação à idade destacamos que a concentração média de ferro (26Fe) é superior nos grupos etários superiores, logo aumenta com a idade, sobretudo na Substância Nigra e no Núcleo Lenticular. No estudo técnico-radiológico encontrámos evidências do aumento da difusibilidade da água na substância branca subcortical dos sujeitos idosos comparativamente aos mais jovens. Uma relação idêntica foi avaliada nos tálamos. O aumento relacionado com a idade parece ser predominantemente observado em doentes com mais de 65 anos de idade o que pode refletir alterações estruturais ligeiras associados ao envelhecimento normal. Os resultados indicam que a análise quantitativa das imagens ponderadas em difusão fornece informações, sobre a estrutura do cérebro, as quai s não estão disponíveis apenas por inspeção visual, tanto nas imagens ponderadas em difusão como em outras sequências de aplicação clínica de rotina. Para fazer face às desvantagens dos sistemas de quantificação das HSB os quais são dispendiosos, complexos, requererem tecnologia e formação específicas, recomendamos que a aplicação automatizada GUIAL, desenvolvida ao longo do nosso trabalho é de utilização elementar e prática para que seja introduzida nos sistemas de aquisição de imagem por RM com o fim de integrar o processamento de imagem nos indivíduos portadores de fatores de risco vascular. A avaliação do ADC, nesta amostra, permitiu concluir que a variação desta variável é explicada estatisticamente pela existência da condição clínica de status lacunar em ambos os hemisférios ou por outras palavras, o status lacunar influencia o valor de ADC. Embora uma pequena percentagem da variação do ADC seja explicada pelo género, o ADC nos homens foi superior ao das mulheres o que não nos surpreende, pois são também os homens onde a frequência de doença microvascular se revelou mais expressiva. Os valores do ADC, globalmente, entre os hemisférios cerebrais não mostraram alterações exceto na SB entre os idosos e não idosos. A SB da região frontal mostrou valores diminuídos na anisotropia e isotropia face às restantes áreas anatómicas. Os estudos indicam que na idade avançada existe uma maior predisposição para suscetibilidades de estrutura com status de desconexão. A classificação das HSB foi superior em indivíduos mais velhos e com status lacunar, e em menor quantidade (inferior rating de classificação) nos indivíduos idosos sem status lacunar. As alterações volumétricas foram mais frequentes no homem do que na mulher, presumivelmente devido à associação com a elevada classificação de status lacunar. Um aumento do índice de Evan correspondeu, neste estudo, ao aumento das HSB, à diminuição do volume cerebral total, à expansão ventrículo-sulcal frontal e ao aumento da medida do ângulo caloso. Estes resultados foram agravados pela classificação elevada de status lacunar nos indivíduos que apresentaram indícios de doença de pequenos vasos, com manifesto aumento dos espaços de Virchow-Robin,enfartes lacunares ou HSB. Esses resultados foram mais expressivos no género masculino do que no feminino revelando uma maior vulnerabilidade sobretudo na atrofia frontal nos homens. Por sua vez as dimensões do Corpo Caloso tornaram-se reduzidas devido à compressão dos ventrículos laterais e terceiro ventrículo. Estes indicadores tiveram expressão particularmente nos indivíduos com mais de 65 anos. ---------------------------------------------------------------------------------------------ABSTRACT: The latest neuroimaging methods, such as Magnetic Resonance Imaging (MRI), have enabled detailed images of in vivo human brain. These images reveal often unexpected findings related to the normal pattern, with high predisposition for the elderly people with forthright coexistence with vascular risk factors such as characteristics of a normal aging process. Although it has been, in the last decade, several publications on this subject, it is still little explained. All over the world have emerged disease prevention programs and health promotion developed by the Public Health sector, supported mainly by the advancement of medical technologies that have resulted, among other impacts, in a growing of the elderly population. It is estimated, in 2030, a demographic composition with 20% o people over 65 years. In this context, microvascular disease is the most common cause of cognitive vascular impairment in the elderly and senescent characteristics in the MRI trough ischemic lesions of the white matter (Leukoaraiosis) and lacunar infarcts (lacunar status), cerebral atrophy, gliosis and iron accumulation in the basal ganglia in excess.This thesis, considering the research line that stems - Life Sciences - specialization in Clinical Medicine, Biotechnology, gathers and reflects on three aspects linked to MR, interdependent and related to a common problem. The first deals with the Magnetic Resonance Technology characterization in Portugal, which includes an exploratory evaluation of the implementation of Anisotropic Diffusion technique in brain studies. The analytical dimensions studied were the Technologic, Socio-demographic and Economics. Collecting data was supported by different sources of information and was applied an exploratory methodology whose results were validated by triangulation. The research method was grouped and stratified criteria under the same analytical dimensions. The second describes the anatomical study - which was focused on radiological measurement parameters, based on the brain’s specimen under an experimental methodology applied to MRI diffusion metrics. Radiological evaluation and optimization of the weighted image diffusion in clinical studies were associated with the brain of the elderly "The Usual Brain Aging" with methodological basis based on established criteria and indicators by Rotterdam Scan Study (RSS). The main results obtained reveal the inexistence frameworks in Portugal for evaluation of equipments or Agency of Health Technology to produce studies comparing the equipment available on the market, the value for money and its allocation to clinical and epidemiological needs. It was found that the implementation of MRI equipment is strongly based on economic criteria lacking recommendations and guidelines for the rationalized use of these technologies. As the quantitative data we conclude that most of the scanners are located in private clinical institutions (80,2%); the most frequent magnetic field intensity is [1.5T] with 119 scanners; the scanners are mainly installed in Lisbon (55 units) and Porto (39 units) districts; the average ratio of equipment per capita in Portugal is 1 to 65 195 people; the gradient power with higher expression in the sample is 30-39mT / m;most of the scanners were installed in the years range [2009-2012 years] with 59 equipment; only 6 clinical placements develop clinical research and the most coils for brain studies are of Array type. The optimization study of diffusion technique revealed, as the assessment of the bvalues, the lower (b = 500 s / mm2 and b = 1000 s / mm 2), promotes an increase in the SI and SNR being this measure related to a higher image quality, however the highest b values (b = 2000 s / mm 2) have a higher CNR (Contrast to Noise-Ratio) and CR (Contrast Ratio), compared to the previous ones. This may provide less anatomical details and, thus, ower image quality, of a normal brain, however can help the interpretation and have advantages in identifying microvascular injuries when doubts persist regarding the differential diagnosis of microvascular disease of lacunar or WMH (White Matter Hyperintensities) status type. Changes on this parameter are Otimização da anisotropia fronto-calosa e [RM 1,5T] no idoso normal e com risco cérebro-vascular particularly reflected in the differences of image quality evaluation in the frontocallosum anatomical area. We conclude from the quantitative assessment of the average concentration of iron (26Fe), in all age groups to the basal ganglia, that the higher concentrations are, in descending order: Nigral Substantia, Globus pallidus, Putamen, Thalamus, Rubio nucleus and Caudate nucleus; that there is a predominance in the concentration of iron (26Fe) in the left hemisphere and that male gender show higher iron (26Fe) level tha females, in the age groups [30-40 [[40-50 [and [50- 60 [. Regarding a main conclusion of the mean concentration study of iron, in terms of age we point out that the average concentration of iron (26Fe) is higher among older groups and increases with age, especially in Nigral Substantia and Lenticular Nucleus. On the technical and radiological study we found evidence of an increased in water /diffusivity in the ubcortical white matter of the elderly compared with younger subjects. A similar relationship was assessed in the Thalamus. The increase agerelated seems to be predominantly observed in patients over 65 years which may reflect minor structural changes associated with normal aging. The results indicate that quantitative analysis of diffusion weighted imaging can provide information about the structure of the brain which is not reached only by visual inspection or standard sequences applied in clinical routine. To address the disadvantages the systems of quantification of WMH which the authors state that are costly, complex, require specific technology and training, we recommend that the automated application GUIAL, developed over our work is basic and practical to use and to be introduced in MR image systems acquisition in order to integrate image processing in patients with vascular risk factors. The evaluation of the ADC showed that its variation is statistically explained by the existence of the medical condition of lacunar status, in both hemispheres, or in other words, the lacunar status influences the ADC value. Although a small percentage of the ADC variation is explained by gender, the ADC in men was higher than women which Otimização da anisotropia fronto-calosa e [RM 1,5T] no idoso normal e com risco cérebro-vascular do not surprise us, since they are also men where the frequency of microvasculardisease has proved more significant. The values of ADC, overall, between the cerebral hemispheres showed no changes but were different in WM among the elderly and non-elderly subjects.The WM's forehead showed decreased values in anisotropy and isotropy face the other anatomical areas. The studies indicate that in old age there is a greater tendency to higher susceptibility to disconnection- status framework. The classification of WMH was higher in elderly people and lacunar status, and fewer (lower classification rating) in the elderly without lacunar status. volumetric changes were more frequent in men than in women, most probably because of its association with high lacunar status rating. An increase of Evan index corresponded, in this study, to an increase in WMH, to a decreased of total brain volume, to a ventricle sulcal frontal and callous angle expansion. These results were wound up by high ranking of lacunar status in subjects who had small vessel disease, clear increase in spaces of Virchow-Robin, lacunar infarctions or WMH. These results were more significant in males than in females revealing vulnerability particularly in the frontal atrophy in men. In turn the size of Corpus Callosum because reduced due to the compression of the lateral and third ventricles. These indicators had expression particularly in individuals over 65 years.

Efecto de la microestructura en el comportamiento mecánico de aceros de herramienta para trabajo en frío

El estudio desarrollado en la tesis doctoral profundiza en las relaciones existentes entre la microestructura y el comportamiento a rotura y fatiga de tres tipos de Aceros de Herramienta para trabajo en Frío, dos obtenidos por colada y un tercero mediante pulvimetalúrgia. En primer lugar se evaluaron los aspectos microestructurales relacionados con las dos vias de procesamiento empleadas, además del efecto del cambio en la composición química. Asimismo se documentó la influencia del trabajado en caliente sobre la isotropía microestructural. Considerando las caracteristicas microestructurales se evaluó el comportamiento a rotura en tres orientaciones referidas al sentido de la deformación en caliente. Para ello , se empleó la Mecánica de la Fractura Elástica Lineal como marco analítico. Los resultados fueron tratados siguiendo la estadística de Weibull. Para el caso de los aceros colados se implementa un analisis de curva-R para explicar el crecimiento subcrítico de grietas observado experimentalmente. El estudio del comportamiento a fatiga incluyó la determinación del limite a fatiga para todas la orientaciones microestructurales escogidas y el estudio de la cinetica de propagación de fisuras físicamente pequeñas para la orientación con mejor respuesta mecánica.

The mapping of the local contributions of Fermi and Coulomb correlation into intracule and extracule density distributions

The contributions of the correlated and uncorrelated components of the electron-pair density to atomic and molecular intracule I(r) and extracule E(R) densities and its Laplacian functions ∇2I(r) and ∇2E(R) are analyzed at the Hartree-Fock (HF) and configuration interaction (CI) levels of theory. The topologies of the uncorrelated components of these functions can be rationalized in terms of the corresponding one-electron densities. In contrast, by analyzing the correlated components of I(r) and E(R), namely, IC(r) and EC(R), the effect of electron Fermi and Coulomb correlation can be assessed at the HF and CI levels of theory. Moreover, the contribution of Coulomb correlation can be isolated by means of difference maps between IC(r) and EC(R) distributions calculated at the two levels of theory. As application examples, the He, Ne, and Ar atomic series, the C2-2, N2, O2+2 molecular series, and the C2H4 molecule have been investigated. For these atoms and molecules, it is found that Fermi correlation accounts for the main characteristics of IC(r) and EC(R), with Coulomb correlation increasing slightly the locality of these functions at the CI level of theory. Furthermore, IC(r), EC(R), and the associated Laplacian functions, reveal the short-ranged nature and high isotropy of Fermi and Coulomb correlation in atoms and molecules

The Fry method applied to an augen orthogneiss: Problems and results

The application of the Fry method to measure strain in deformed porphyritic granites is discussed. This method requires that the distribution of markers has to satisfy at least two conditions. It has to be homogeneous and isotropic. Statistics on point distribution with the help of a Morishita diagram can easily test homogeneity. Isotropy can be checked with a cumulative histogram of angles between points. Application of these tests to undeformed (Mte Capanne granite, Elba) and to deformed (Randa orthogneiss, Alps of Switzerland) porphyritic granite reveals that their K-feldspars phenocrysts both satisfy these conditions and can be used as strain markers with the Fry method. Other problems are also examined. One is the possible distribution of deformation on discrete shear-bands. Providing several tests are met, we conclude that the Fry method can be used to estimate strain in deformed porphyritic granites. (c) 2006 Elsevier Ltd. All rights reserved.

EFFECTS OF COMPACTION DUE TO MACHINERY TRAFFIC ON SOIL PORE CONFIGURATION

Soil compaction has been recognized as a severe problem in mechanized agriculture and has an influence on many soil properties and processes. Yet, there are few studies on the long-term effects of soil compaction, and the development of soil compaction has been shown through a limited number of soil parameters. The objectives of this study were to evaluate the persistence of soil compaction effects (three traffic treatments: T0, without traffic; T3, three tractor passes; and T5, five tractor passes) on pore system configuration, through static and dynamic determinations; and to determine changes in soil pore orientation due to soil compaction through measurement of hydraulic conductivity of saturated soil in samples taken vertically and horizontally. Traffic led to persistent changes in all the dynamic indicators studied (saturated hydraulic conductivity, K0; effective macro- and mesoporosity, εma and εme), with significantly lower values of K0, εma, and εme in the T5 treatment. The static indicators of bulk density (BD), derived total porosity (TP), and total macroporosity (θma) did not vary significantly among the treatments. This means that machine traffic did not produce persistent changes on these variables after two years. However, the orientation of the soil pore system was modified by traffic. Even in T0, there were greater changes in K0 measured in the samples taken vertically than horizontally, which was more related to the presence of vertical biopores, and to isotropy of K0 in the treatments with machine traffic. Overall, the results showed that dynamic indicators are more sensitive to the effects of compaction and that, in the future, static indicators should not be used as compaction indicators without being complemented by dynamic indicators.