Computation of the linear elastic properties of random porous materials with a wide variety of microstructure

A finite-element method is used to study the elastic properties of random three-dimensional porous materials with highly interconnected pores. We show that Young's modulus, E, is practically independent of Poisson's ratio of the solid phase, nu(s), over the entire solid fraction range, and Poisson's ratio, nu, becomes independent of nu(s) as the percolation threshold is approached. We represent this behaviour of nu in a flow diagram. This interesting but approximate behaviour is very similar to the exactly known behaviour in two-dimensional porous materials. In addition, the behaviour of nu versus nu(s) appears to imply that information in the dilute porosity limit can affect behaviour in the percolation threshold limit. We summarize the finite-element results in terms of simple structure-property relations, instead of tables of data, to make it easier to apply the computational results. Without using accurate numerical computations, one is limited to various effective medium theories and rigorous approximations like bounds and expansions. The accuracy of these equations is unknown for general porous media. To verify a particular theory it is important to check that it predicts both isotropic elastic moduli, i.e. prediction of Young's modulus alone is necessary but not sufficient. The subtleties of Poisson's ratio behaviour actually provide a very effective method for showing differences between the theories and demonstrating their ranges of validity. We find that for moderate- to high-porosity materials, none of the analytical theories is accurate and, at present, numerical techniques must be relied upon.

Prediction of absolute rate coefficients and product branching ratios for the C(P-3) plus allene reaction system

Complex chemical reactions in the gas phase can be decomposed into a network of elementary (e.g., unimolecular and bimolecular) steps which may involve multiple reactant channels, multiple intermediates, and multiple products. The modeling of such reactions involves describing the molecular species and their transformation by reaction at a detailed level. Here we focus on a detailed modeling of the C(P-3)+allene (C3H4) reaction, for which molecular beam experiments and theoretical calculations have previously been performed. In our previous calculations, product branching ratios for a nonrotating isomerizing unimolecular system were predicted. We extend the previous calculations to predict absolute unimolecular rate coefficients and branching ratios using microcanonical variational transition state theory (mu-VTST) with full energy and angular momentum resolution. Our calculation of the initial capture rate is facilitated by systematic ab initio potential energy surface calculations that describe the interaction potential between carbon and allene as a function of the angle of attack. Furthermore, the chemical kinetic scheme is enhanced to explicitly treat the entrance channels in terms of a predicted overall input flux and also to allow for the possibility of redissociation via the entrance channels. Thus, the computation of total bimolecular reaction rates and partial capture rates is now possible. (C) 2002 American Institute of Physics.

Branching processes and computational collapse of discretized unimodal mappings

In computer simulations of smooth dynamical systems, the original phase space is replaced by machine arithmetic, which is a finite set. The resulting spatially discretized dynamical systems do not inherit all functional properties of the original systems, such as surjectivity and existence of absolutely continuous invariant measures. This can lead to computational collapse to fixed points or short cycles. The paper studies loss of such properties in spatial discretizations of dynamical systems induced by unimodal mappings of the unit interval. The problem reduces to studying set-valued negative semitrajectories of the discretized system. As the grid is refined, the asymptotic behavior of the cardinality structure of the semitrajectories follows probabilistic laws corresponding to a branching process. The transition probabilities of this process are explicitly calculated. These results are illustrated by the example of the discretized logistic mapping.

Conditional simulation of random fields by successive residuals

This paper presents a new approach to the LU decomposition method for the simulation of stationary and ergodic random fields. The approach overcomes the size limitations of LU and is suitable for any size simulation. The proposed approach can facilitate fast updating of generated realizations with new data, when appropriate, without repeating the full simulation process. Based on a novel column partitioning of the L matrix, expressed in terms of successive conditional covariance matrices, the approach presented here demonstrates that LU simulation is equivalent to the successive solution of kriging residual estimates plus random terms. Consequently, it can be used for the LU decomposition of matrices of any size. The simulation approach is termed conditional simulation by successive residuals as at each step, a small set (group) of random variables is simulated with a LU decomposition of a matrix of updated conditional covariance of residuals. The simulated group is then used to estimate residuals without the need to solve large systems of equations.

Exogenous Slit2 does not affect ureteric branching or nephron formation during kidney development

In an attempt to elucidate the role of Slit2 invertebrate kidney development, the effect of adding exogenous human Slit2 protein (hSlit2) to developing murine metanephric kidney explants was examined. To confirm the activity of the recombinant Slit2 protein, neurons from 8 day old chick sympathetic nerve chain dorsal root ganglia were cultured with hSlit2 protein, which induced significant neurite branching and outgrowth. Using kidney explants as a model system, metanephric development in the presence of hSlit2 protein was examined. Addition of hSlit2 up to a final concentration of 1 mug/ml had no detectable effect on the formation of nephrons or on branching morphogenesis of the ureteric tree after 2 or 4 days in culture, as assessed via immunofluorescence for the markers WT1 and calbindin 28K respectively. Similarly, maturation of the nephrogenic mesenchyme occurred in a phenotypically normal fashion. In situ analysis of the Slit receptors, Robot and Robot, the vasculogenic markers VEGFA and Flk-1, and the stromal cell marker BF2 displayed no difference in comparison to controls.

MAX4 and RMS1 are orthologous dioxygenase-like genes that regulate shoot branching in Arabidopsis and pea

Shoot branching is inhibited by auxin transported down the stem from the shoot apex. Auxin does not accumulate in inhibited buds and so must act indirectly. We show that mutations in the MAX4 gene of Arabidopsis result in increased and auxin-resistant bud growth. Increased branching in max4 shoots is restored to wild type by grafting to wild-type rootstocks, suggesting that MAX4 is required to produce a mobile branch-inhibiting signal, acting downstream of auxin. A similar role has been proposed for the pea gene, RMS1. Accordingly, MAX4 and RMS1 were found to encode orthologous, auxin-inducible members of the polyene dioxygenase family.

Mean anisotropy of homogeneous Gaussian random fields and anisotropic norms of linear translation-invariant operators on multidimensional integer lattices

Sensitivity of output of a linear operator to its input can be quantified in various ways. In Control Theory, the input is usually interpreted as disturbance and the output is to be minimized in some sense. In stochastic worst-case design settings, the disturbance is considered random with imprecisely known probability distribution. The prior set of probability measures can be chosen so as to quantify how far the disturbance deviates from the white-noise hypothesis of Linear Quadratic Gaussian control. Such deviation can be measured by the minimal Kullback-Leibler informational divergence from the Gaussian distributions with zero mean and scalar covariance matrices. The resulting anisotropy functional is defined for finite power random vectors. Originally, anisotropy was introduced for directionally generic random vectors as the relative entropy of the normalized vector with respect to the uniform distribution on the unit sphere. The associated a-anisotropic norm of a matrix is then its maximum root mean square or average energy gain with respect to finite power or directionally generic inputs whose anisotropy is bounded above by a≥0. We give a systematic comparison of the anisotropy functionals and the associated norms. These are considered for unboundedly growing fragments of homogeneous Gaussian random fields on multidimensional integer lattice to yield mean anisotropy. Correspondingly, the anisotropic norms of finite matrices are extended to bounded linear translation invariant operators over such fields.

Dendritic branching of pyramidal cells in the visual cortex of the nocturnal owl monkey: A fractal analysis

The branching structure of neurones is thought to influence patterns of connectivity and how inputs are integrated within the arbor. Recent studies have revealed a remarkable degree of variation in the branching structure of pyramidal cells in the cerebral cortex of diurnal primates, suggesting regional specialization in neuronal function. Such specialization in pyramidal cell structure may be important for various aspects of visual function, such as object recognition and color processing. To better understand the functional role of regional variation in the pyramidal cell phenotype in visual processing, we determined the complexity of the dendritic branching pattern of pyramidal cells in visual cortex of the nocturnal New World owl monkey. We used the fractal dilation method to quantify the branching structure of pyramidal cells in the primary visual area (V1), the second visual area (V2) and the caudal and rostral subdivisions of inferotemporal cortex (ITc and ITr, respectively), which are often associated with color processing. We found that, as in diurnal monkeys, there was a trend for cells of increasing fractal dimension with progression through these cortical areas. The increasing complexity paralleled a trend for increasing symmetry. That we found a similar trend in both diurnal and nocturnal monkeys suggests that it was a feature of a common anthropoid ancestor.

Application to quantify fetal lung branching on rat explants

Recently, regulating mechanisms of branching morphogenesis of fetal lung rat explants have been an essential tool for molecular research. The development of accurate and reliable segmentation techniques may be essential to improve research outcomes. This work presents an image processing method to measure the perimeter and area of lung branches on fetal rat explants. The algorithm starts by reducing the noise corrupting the image with a pre-processing stage. The outcome is input to a watershed operation that automatically segments the image into primitive regions. Then, an image pixel is selected within the lung explant epithelial, allowing a region growing between neighbouring watershed regions. This growing process is controlled by a statistical distribution of each region. When compared with manual segmentation, the results show the same tendency for lung development. High similarities were harder to obtain in the last two days of culture, due to the increased number of peripheral airway buds and complexity of lung architecture. However, using semiautomatic measurements, the standard deviation was lower and the results between independent researchers were more coherent

Automated image analysis of lung branching morphogenesis from microscopic images of fetal rat explants

Background: Regulating mechanisms of branching morphogenesis of fetal lung rat explants have been an essential tool for molecular research. This work presents a new methodology to accurately quantify the epithelial, outer contour and peripheral airway buds of lung explants during cellular development from microscopic images. Methods: The outer contour was defined using an adaptive and multi-scale threshold algorithm whose level was automatically calculated based on an entropy maximization criterion. The inner lung epithelial was defined by a clustering procedure that groups small image regions according to the minimum description length principle and local statistical properties. Finally, the number of peripheral buds were counted as the skeleton branched ends from a skeletonized image of the lung inner epithelial. Results: The time for lung branching morphometric analysis was reduced in 98% in contrast to the manual method. Best results were obtained in the first two days of cellular development, with lesser standard deviations. Non-significant differences were found between the automatic and manual results in all culture days. Conclusions: The proposed method introduces a series of advantages related to its intuitive use and accuracy, making the technique suitable to images with different lightning characteristics and allowing a reliable comparison between different researchers.

Automated image analysis of lung branching morphogenesis

Regulating mechanisms of branchingmorphogenesis of fetal lung rat explants have been an essential tool formolecular research.This work presents a new methodology to accurately quantify the epithelial, outer contour, and peripheral airway buds of lung explants during cellular development frommicroscopic images. Methods.Theouter contour was defined using an adaptive and multiscale threshold algorithm whose level was automatically calculated based on an entropy maximization criterion. The inner lung epithelium was defined by a clustering procedure that groups small image regions according to the minimum description length principle and local statistical properties. Finally, the number of peripheral buds was counted as the skeleton branched ends from a skeletonized image of the lung inner epithelia. Results. The time for lung branching morphometric analysis was reduced in 98% in contrast to themanualmethod. Best results were obtained in the first two days of cellular development, with lesser standard deviations. Nonsignificant differences were found between the automatic and manual results in all culture days. Conclusions. The proposed method introduces a series of advantages related to its intuitive use and accuracy, making the technique suitable to images with different lighting characteristics and allowing a reliable comparison between different researchers.

Application to quantify fetal lung branching on rat explant

Recently, regulating mechanisms of branching morphogenesis of fetal lung rat explants have been an essential tool for molecular research. The development of accurate and reliable segmentation techniques may be essential to improve research outcomes. This work presents an image processing method to measure the perimeter and area of lung branches on fetal rat explants. The algorithm starts by reducing the noise corrupting the image with a pre-processing stage. The outcome is input to a watershed operation that automatically segments the image into primitive regions. Then, an image pixel is selected within the lung explant epithelial, allowing a region growing between neighbouring watershed regions. This growing process is controlled by a statistical distribution of each region. When compared with manual segmentation, the results show the same tendency for lung development. High similarities were harder to obtain in the last two days of culture, due to the increased number of peripheral airway buds and complexity of lung architecture. However, using semiautomatic measurements, the standard deviation was lower and the results between independent researchers were more coherent.

GA topology optimization using random keys for tree encoding of structures

Topology optimization consists in finding the spatial distribution of a given total volume of material for the resulting structure to have some optimal property, for instance, maximization of structural stiffness or maximization of the fundamental eigenfrequency. In this paper a Genetic Algorithm (GA) employing a representation method based on trees is developed to generate initial feasible individuals that remain feasible upon crossover and mutation and as such do not require any repairing operator to ensure feasibility. Several application examples are studied involving the topology optimization of structures where the objective functions is the maximization of the stiffness and the maximization of the first and the second eigenfrequencies of a plate, all cases having a prescribed material volume constraint.