A packing computational method relating fractal particle size distribution and void fraction in granular media

The study of granular systems is of great interest to many fields of science and technology. The packing of particles affects to the physical properties of the granular system. In particular, the crucial influence of particle size distribution (PSD) on the random packing structure increase the interest in relating both, either theoretically or by computational methods. A packing computational method is developed in order to estimate the void fraction corresponding to a fractal-like particle size distribution.

Parallel sets and morphological measurements of CT images of soil pore structure in a vineyard

Important physical and biological processes in soil-plant-microbial systems are dominated by the geometry of soil pore space, and a correct model of this geometry is critical for understanding them. We analyze the geometry of soil pore space with the X-ray computed tomography (CT) of intact soil columns. We present here some preliminary results of our investigation on Minkowski functionals of parallel sets to characterize soil structure. We also show how the evolution of Minkowski morphological measurements of parallel sets may help to characterize the influence of conventional tillage and permanent cover crop of resident vegetation on soil structure in a Spanish Mediterranean vineyard.

Multi-argument fuzzy measures on lattices of fuzzy sets

In this paper, we axiomatically introduce fuzzy multi-measures on bounded lattices. In particular, we make a distinction between four different types of fuzzy set multi-measures on a universe X, considering both the usual or inverse real number ordering of this lattice and increasing or decreasing monotonicity with respect to the number of arguments. We provide results from which we can derive families of measures that hold for the applicable conditions in each case.

Computer simulation of the interplay between fractal structures and surrounding heterogeneous multifractal distributions. Applications

In a large number of physical, biological and environmental processes interfaces with high irregular geometry appear separating media (phases) in which the heterogeneity of constituents is present. In this work the quantification of the interplay between irregular structures and surrounding heterogeneous distributions in the plane is made For a geometric set image and a mass distribution (measure) image supported in image, being image, the mass image gives account of the interplay between the geometric structure and the surrounding distribution. A computation method is developed for the estimation and corresponding scaling analysis of image, being image a fractal plane set of Minkowski dimension image and image a multifractal measure produced by random multiplicative cascades. The method is applied to natural and mathematical fractal structures in order to study the influence of both, the irregularity of the geometric structure and the heterogeneity of the distribution, in the scaling of image. Applications to the analysis and modeling of interplay of phases in environmental scenarios are given.

An introduction to flow and transport in fractal models of porous media: Part I

This special issue gathers together a number of recent papers on fractal geometry and its applications to the modeling of flow and transport in porous media. The aim is to provide a systematic approach for analyzing the statics and dynamics of fluids in fractal porous media by means of theory, modeling and experimentation. The topics covered include lacunarity analyses of multifractal and natural grayscale patterns, random packing's of self-similar pore/particle size distributions, Darcian and non-Darcian hydraulic flows, diffusion within fractals, models for the permeability and thermal conductivity of fractal porous media and hydrophobicity and surface erosion properties of fractal structures.

Fractal parameters of pore space from CT images of soils under contrasting management practices

Soil structure plays an important role in flow and transport phenomena, and a quantitative characterization of the spatial heterogeneity of the pore space geometry is beneficial for prediction of soil physical properties. Morphological features such as pore-size distribution, pore space volume or pore?solid surface can be altered by different soil management practices. Irregularity of these features and their changes can be described using fractal geometry. In this study, we focus primarily on the characterization of soil pore space as a 3D geometrical shape by fractal analysis and on the ability of fractal dimensions to differentiate between two a priori different soil structures. We analyze X-ray computed tomography (CT) images of soils samples from two nearby areas with contrasting management practices. Within these two different soil systems, samples were collected from three depths. Fractal dimensions of the pore-size distributions were different depending on soil use and averaged values also differed at each depth. Fractal dimensions of the volume and surface of the pore space were lower in the tilled soil than in the natural soil but their standard deviations were higher in the former as compared to the latter. Also, it was observed that soil use was a factor that had a statistically significant effect on fractal parameters. Fractal parameters provide useful complementary information about changes in soil structure due to changes in soil management. Read More: http://www.worldscientific.com/doi/abs/10.1142/S0218348X14400118?queryID=%24%7BresultBean.queryID%7D&

Computer simulation of random parckings for self-similar particle size distributions in soil and granular materials: porosity and pore size distribution

A 2D computer simulation method of random packings is applied to sets of particles generated by a self-similar uniparametric model for particle size distributions (PSDs) in granular media. The parameter p which controls the model is the proportion of mass of particles corresponding to the left half of the normalized size interval [0,1]. First the influence on the total porosity of the parameter p is analyzed and interpreted. It is shown that such parameter, and the fractal exponent of the associated power scaling, are efficient packing parameters, but this last one is not in the way predicted in a former published work addressing an analogous research in artificial granular materials. The total porosity reaches the minimum value for p = 0.6. Limited information on the pore size distribution is obtained from the packing simulations and by means of morphological analysis methods. Results show that the range of pore sizes increases for decreasing values of p showing also different shape in the volume pore size distribution. Further research including simulations with a greater number of particles and image resolution are required to obtain finer results on the hierarchical structure of pore space.

Morphological Functions with Parallel Sets for the Pore Space of X-ray CT Images of Soil Columns

During the last few decades, new imaging techniques like X-ray computed tomography have made available rich and detailed information of the spatial arrangement of soil constituents, usually referred to as soil structure. Mathematical morphology provides a plethora of mathematical techniques to analyze and parameterize the geometry of soil structure. They provide a guide to design the process from image analysis to the generation of synthetic models of soil structure in order to investigate key features of flow and transport phenomena in soil. In this work, we explore the ability of morphological functions built over Minkowski functionals with parallel sets of the pore space to characterize and quantify pore space geometry of columns of intact soil. These morphological functions seem to discriminate the effects on soil pore space geometry of contrasting management practices in a Mediterranean vineyard, and they provide the first step toward identifying the statistical significance of the observed differences.

A Packing Computational Method Relating Fractal Particle Size Distribution and Void Fraction in Granular Media

The study of granular systems is of great interest to many fields of science and technology. The packing of particles affects to the physical properties of the granular system. In particular, the crucial influence of particle size distribution (PSD) on the random packing structure increase the interest in relating both, either theoretically or by computational methods. A packing computational method is developed in order to estimate the void fraction corresponding to a fractal-like particle size distribution.

Characterization of rock joints by fractal analysis

From a physical perspective, a joint experiences fracturing processes that affect the rock at both microscopic and macroscopic levels. The result is a behaviour that follows a fractal structure. In the first place, for saw-tooth roughness profiles, the use of the triadic Koch curve appears to be adequate and by means of known correlations the JRC parameter is obtained from the angle measured on the basis of the height and length of the roughnesses. Therefore, JRC remains related to the geometric pattern that defines roughness by fractal analysis. In the second place, to characterise the geometry of irregularities with softened profiles, consequently, is proposed a characterisation of the fractal dimension of the joints with a circumference arc generator that is dependent on an average contact angle with regard to the mid-plane. The correlation between the JRC and the fractal dimension of the model is established with a defined statistical ratio.

Coherent structures in statistically-stationary homogeneous shear turbulence

La región cerca de la pared de flujos turbulentos de pared ya está bien conocido debido a su bajo número de Reynolds local y la separación escala estrecha. La región lejos de la pared (capa externa) no es tan interesante tampoco, ya que las estadísticas allí se escalan bien por las unidades exteriores. La región intermedia (capa logarítmica), sin embargo, ha estado recibiendo cada vez más atención debido a su propiedad auto-similares. Además, de acuerdo a Flores et al. (2007) y Flores & Jiménez (2010), la capa logarítmica es más o menos independiente de otras capas, lo que implica que podría ser inspeccionado mediante el aislamiento de otras dos capas, lo que reduciría significativamente los costes computacionales para la simulación de flujos turbulentos de pared. Algunos intentos se trataron después por Mizuno & Jiménez (2013), quien simulan la capa logarítmica sin la región cerca de la pared con estadísticas obtenidas de acuerdo razonablemente bien con los de las simulaciones completas. Lo que más, la capa logarítmica podría ser imitado por otra turbulencia sencillo de cizallamiento de motor. Por ejemplo, Pumir (1996) encontró que la turbulencia de cizallamiento homogéneo estadísticamente estacionario (SS-HST) también irrumpe, de una manera muy similar al proceso de auto-sostenible en flujos turbulentos de pared. Según los consideraciones arriba, esta tesis trata de desvelar en qué medida es la capa logarítmica de canales similares a la turbulencia de cizalla más sencillo, SS-HST, mediante la comparación de ambos cinemática y la dinámica de las estructuras coherentes en los dos flujos. Resultados sobre el canal se muestran mediante Lozano-Durán et al. (2012) y Lozano-Durán & Jiménez (2014b). La hoja de ruta de esta tarea se divide en tres etapas. En primer lugar, SS-HST es investigada por medio de un código nuevo de simulación numérica directa, espectral en las dos direcciones horizontales y compacto-diferencias finitas en la dirección de la cizalla. Sin utiliza remallado para imponer la condición de borde cortante periódica. La influencia de la geometría de la caja computacional se explora. Ya que el HST no tiene ninguna longitud característica externa y tiende a llenar el dominio computacional, las simulaciopnes a largo plazo del HST son ’mínimos’ en el sentido de que contiene sólo unas pocas estructuras media a gran escala. Se ha encontrado que el límite principal es el ancho de la caja de la envergadura, Lz, que establece las escalas de longitud y velocidad de la turbulencia, y que las otras dos dimensiones de la caja debe ser suficientemente grande (Lx > 2LZ, Ly > Lz) para evitar que otras direcciones estando limitado también. También se encontró que las cajas de gran longitud, Lx > 2Ly, par con el paso del tiempo la condición de borde cortante periódica, y desarrollar fuertes ráfagas linealizadas no físicos. Dentro de estos límites, el flujo muestra similitudes y diferencias interesantes con otros flujos de cizalla, y, en particular, con la capa logarítmica de flujos turbulentos de pared. Ellos son exploradas con cierto detalle. Incluyen un proceso autosostenido de rayas a gran escala y con una explosión cuasi-periódica. La escala de tiempo de ruptura es de aproximadamente universales, ~20S~l(S es la velocidad de cizallamiento media), y la disponibilidad de dos sistemas de ruptura diferentes permite el crecimiento de las ráfagas a estar relacionado con algo de confianza a la cizalladura de turbulencia inicialmente isotrópico. Se concluye que la SS-HST, llevado a cabo dentro de los parámetros de cílculo apropiados, es un sistema muy prometedor para estudiar la turbulencia de cizallamiento en general. En segundo lugar, las mismas estructuras coherentes como en los canales estudiados por Lozano-Durán et al. (2012), es decir, grupos de vórticidad (fuerte disipación) y Qs (fuerte tensión de Reynolds tangencial, -uv) tridimensionales, se estudia mediante simulación numérica directa de SS-HST con relaciones de aspecto de cuadro aceptables y número de Reynolds hasta Rex ~ 250 (basado en Taylor-microescala). Se discute la influencia de la intermitencia de umbral independiente del tiempo. Estas estructuras tienen alargamientos similares en la dirección sentido de la corriente a las familias separadas en los canales hasta que son de tamaño comparable a la caja. Sus dimensiones fractales, longitudes interior y exterior como una función del volumen concuerdan bien con sus homólogos de canales. El estudio sobre sus organizaciones espaciales encontró que Qs del mismo tipo están alineados aproximadamente en la dirección del vector de velocidad en el cuadrante al que pertenecen, mientras Qs de diferentes tipos están restringidos por el hecho de que no debe haber ningún choque de velocidad, lo que hace Q2s (eyecciones, u < 0,v > 0) y Q4s (sweeps, u > 0,v < 0) emparejado en la dirección de la envergadura. Esto se verifica mediante la inspección de estructuras de velocidad, otros cuadrantes como la uw y vw en SS-HST y las familias separadas en el canal. La alineación sentido de la corriente de Qs ligada a la pared con el mismo tipo en los canales se debe a la modulación de la pared. El campo de flujo medio condicionado a pares Q2-Q4 encontró que los grupos de vórticidad están en el medio de los dos, pero prefieren los dos cizalla capas alojamiento en la parte superior e inferior de Q2s y Q4s respectivamente, lo que hace que la vorticidad envergadura dentro de las grupos de vórticidad hace no cancele. La pared amplifica la diferencia entre los tamaños de baja- y alta-velocidad rayas asociados con parejas de Q2-Q4 se adjuntan como los pares alcanzan cerca de la pared, el cual es verificado por la correlación de la velocidad del sentido de la corriente condicionado a Q2s adjuntos y Q4s con diferentes alturas. Grupos de vórticidad en SS-HST asociados con Q2s o Q4s también están flanqueadas por un contador de rotación de los vórtices sentido de la corriente en la dirección de la envergadura como en el canal. La larga ’despertar’ cónica se origina a partir de los altos grupos de vórticidad ligada a la pared han encontrado los del Álamo et al. (2006) y Flores et al. (2007), que desaparece en SS-HST, sólo es cierto para altos grupos de vórticidad ligada a la pared asociados con Q2s pero no para aquellos asociados con Q4s, cuyo campo de flujo promedio es en realidad muy similar a la de SS-HST. En tercer lugar, las evoluciones temporales de Qs y grupos de vórticidad se estudian mediante el uso de la método inventado por Lozano-Durán & Jiménez (2014b). Las estructuras se clasifican en las ramas, que se organizan más en los gráficos. Ambas resoluciones espaciales y temporales se eligen para ser capaz de capturar el longitud y el tiempo de Kolmogorov puntual más probable en el momento más extrema. Debido al efecto caja mínima, sólo hay un gráfico principal consiste en casi todas las ramas, con su volumen y el número de estructuras instantáneo seguien la energía cinética y enstrofía intermitente. La vida de las ramas, lo que tiene más sentido para las ramas primarias, pierde su significado en el SS-HST debido a las aportaciones de ramas primarias al total de Reynolds estrés o enstrofía son casi insignificantes. Esto también es cierto en la capa exterior de los canales. En cambio, la vida de los gráficos en los canales se compara con el tiempo de ruptura en SS-HST. Grupos de vórticidad están asociados con casi el mismo cuadrante en términos de sus velocidades medias durante su tiempo de vida, especialmente para los relacionados con las eyecciones y sweeps. Al igual que en los canales, las eyecciones de SS-HST se mueven hacia arriba con una velocidad promedio vertical uT (velocidad de fricción) mientras que lo contrario es cierto para los barridos. Grupos de vórticidad, por otra parte, son casi inmóvil en la dirección vertical. En la dirección de sentido de la corriente, que están advección por la velocidad media local y por lo tanto deforman por la diferencia de velocidad media. Sweeps y eyecciones se mueven más rápido y más lento que la velocidad media, respectivamente, tanto por 1.5uT. Grupos de vórticidad se mueven con la misma velocidad que la velocidad media. Se verifica que las estructuras incoherentes cerca de la pared se debe a la pared en vez de pequeño tamaño. Los resultados sugieren fuertemente que las estructuras coherentes en canales no son especialmente asociado con la pared, o incluso con un perfil de cizalladura dado. ABSTRACT Since the wall-bounded turbulence was first recognized more than one century ago, its near wall region (buffer layer) has been studied extensively and becomes relatively well understood due to the low local Reynolds number and narrow scale separation. The region just above the buffer layer, i.e., the logarithmic layer, is receiving increasingly more attention nowadays due to its self-similar property. Flores et al. (20076) and Flores & Jim´enez (2010) show that the statistics of logarithmic layer is kind of independent of other layers, implying that it might be possible to study it separately, which would reduce significantly the computational costs for simulations of the logarithmic layer. Some attempts were tried later by Mizuno & Jimenez (2013), who simulated the logarithmic layer without the buffer layer with obtained statistics agree reasonably well with those of full simulations. Besides, the logarithmic layer might be mimicked by other simpler sheardriven turbulence. For example, Pumir (1996) found that the statistically-stationary homogeneous shear turbulence (SS-HST) also bursts, in a manner strikingly similar to the self-sustaining process in wall-bounded turbulence. Based on these considerations, this thesis tries to reveal to what extent is the logarithmic layer of channels similar to the simplest shear-driven turbulence, SS-HST, by comparing both kinematics and dynamics of coherent structures in the two flows. Results about the channel are shown by Lozano-Dur´an et al. (2012) and Lozano-Dur´an & Jim´enez (20146). The roadmap of this task is divided into three stages. First, SS-HST is investigated by means of a new direct numerical simulation code, spectral in the two horizontal directions and compact-finite-differences in the direction of the shear. No remeshing is used to impose the shear-periodic boundary condition. The influence of the geometry of the computational box is explored. Since HST has no characteristic outer length scale and tends to fill the computational domain, longterm simulations of HST are ‘minimal’ in the sense of containing on average only a few large-scale structures. It is found that the main limit is the spanwise box width, Lz, which sets the length and velocity scales of the turbulence, and that the two other box dimensions should be sufficiently large (Lx > 2LZ, Ly > Lz) to prevent other directions to be constrained as well. It is also found that very long boxes, Lx > 2Ly, couple with the passing period of the shear-periodic boundary condition, and develop strong unphysical linearized bursts. Within those limits, the flow shows interesting similarities and differences with other shear flows, and in particular with the logarithmic layer of wallbounded turbulence. They are explored in some detail. They include a self-sustaining process for large-scale streaks and quasi-periodic bursting. The bursting time scale is approximately universal, ~ 20S~l (S is the mean shear rate), and the availability of two different bursting systems allows the growth of the bursts to be related with some confidence to the shearing of initially isotropic turbulence. It is concluded that SS-HST, conducted within the proper computational parameters, is a very promising system to study shear turbulence in general. Second, the same coherent structures as in channels studied by Lozano-Dur´an et al. (2012), namely three-dimensional vortex clusters (strong dissipation) and Qs (strong tangential Reynolds stress, -uv), are studied by direct numerical simulation of SS-HST with acceptable box aspect ratios and Reynolds number up to Rex ~ 250 (based on Taylor-microscale). The influence of the intermittency to time-independent threshold is discussed. These structures have similar elongations in the streamwise direction to detached families in channels until they are of comparable size to the box. Their fractal dimensions, inner and outer lengths as a function of volume agree well with their counterparts in channels. The study about their spatial organizations found that Qs of the same type are aligned roughly in the direction of the velocity vector in the quadrant they belong to, while Qs of different types are restricted by the fact that there should be no velocity clash, which makes Q2s (ejections, u < 0, v > 0) and Q4s (sweeps, u > 0, v < 0) paired in the spanwise direction. This is verified by inspecting velocity structures, other quadrants such as u-w and v-w in SS-HST and also detached families in the channel. The streamwise alignment of attached Qs with the same type in channels is due to the modulation of the wall. The average flow field conditioned to Q2-Q4 pairs found that vortex clusters are in the middle of the pair, but prefer to the two shear layers lodging at the top and bottom of Q2s and Q4s respectively, which makes the spanwise vorticity inside vortex clusters does not cancel. The wall amplifies the difference between the sizes of low- and high-speed streaks associated with attached Q2-Q4 pairs as the pairs reach closer to the wall, which is verified by the correlation of streamwise velocity conditioned to attached Q2s and Q4s with different heights. Vortex clusters in SS-HST associated with Q2s or Q4s are also flanked by a counter rotating streamwise vortices in the spanwise direction as in the channel. The long conical ‘wake’ originates from tall attached vortex clusters found by del A´ lamo et al. (2006) and Flores et al. (2007b), which disappears in SS-HST, is only true for tall attached vortices associated with Q2s but not for those associated with Q4s, whose averaged flow field is actually quite similar to that in SS-HST. Third, the temporal evolutions of Qs and vortex clusters are studied by using the method invented by Lozano-Dur´an & Jim´enez (2014b). Structures are sorted into branches, which are further organized into graphs. Both spatial and temporal resolutions are chosen to be able to capture the most probable pointwise Kolmogorov length and time at the most extreme moment. Due to the minimal box effect, there is only one main graph consist by almost all the branches, with its instantaneous volume and number of structures follow the intermittent kinetic energy and enstrophy. The lifetime of branches, which makes more sense for primary branches, loses its meaning in SS-HST because the contributions of primary branches to total Reynolds stress or enstrophy are almost negligible. This is also true in the outer layer of channels. Instead, the lifetime of graphs in channels are compared with the bursting time in SS-HST. Vortex clusters are associated with almost the same quadrant in terms of their mean velocities during their life time, especially for those related with ejections and sweeps. As in channels, ejections in SS-HST move upwards with an average vertical velocity uτ (friction velocity) while the opposite is true for sweeps. Vortex clusters, on the other hand, are almost still in the vertical direction. In the streamwise direction, they are advected by the local mean velocity and thus deformed by the mean velocity difference. Sweeps and ejections move faster and slower than the mean velocity respectively, both by 1.5uτ . Vortex clusters move with the same speed as the mean velocity. It is verified that the incoherent structures near the wall is due to the wall instead of small size. The results suggest that coherent structures in channels are not particularly associated with the wall, or even with a given shear profile.

Multi-component assessment of chronic obstructive pulmonary disease : an evaluation of the ADO and DOSE indices and the global obstructive lung disease categories in international primary care data sets

Funding The International Primary Care Respiratory Group (IPCRG) provided funding for this research project as an UNLOCK group study for which the funding was obtained through an unrestricted grant by Novartis AG, Basel, Switzerland. The latter funders had no role in study design, data collection and analysis, decision to publish or preparation of the manuscript. Database access for the OPCRD was provided by the Respiratory Effectiveness Group (REG) and Research in Real Life; the OPCRD statistical analysis was funded by REG. The Bocholtz Study was funded by PICASSO for COPD, an initiative of Boehringer Ingelheim, Pfizer and the Caphri Research Institute, Maastricht University, The Netherlands.

Isotropic isotopy and symplectic null sets

Capacity is an important numerical invariant of symplectic manifolds. This paper studies when a subset of a symplectic manifold is null, i.e., can be removed without affecting the ambient capacity. After examples of open null sets and codimension-2 non-null sets, geometric techniques are developed to perturb any isotopy of a loop to a hamiltonian flow; it follows that sets of dimension 0 and 1 are null. For isotropic sets of higher dimensions, obstructions to the perturbation are found in homotopy groups of the orthogonal groups.

Plastid-localized acetyl-CoA carboxylase of bread wheat is encoded by a single gene on each of the three ancestral chromosome sets

5′-End fragments of two genes encoding plastid-localized acetyl-CoA carboxylase (ACCase; EC 6.4.1.2) of wheat (Triticum aestivum) were cloned and sequenced. The sequences of the two genes, Acc-1,1 and Acc-1,2, are 89% identical. Their exon sequences are 98% identical. The amino acid sequence of the biotin carboxylase domain encoded by Acc-1,1 and Acc-1,2 is 93% identical with the maize plastid ACCase but only 80–84% identical with the cytosolic ACCases from other plants and from wheat. Four overlapping fragments of cDNA covering the entire coding region were cloned by PCR and sequenced. The wheat plastid ACCase ORF contains 2,311 amino acids with a predicted molecular mass of 255 kDa. A putative transit peptide is present at the N terminus. Comparison of the genomic and cDNA sequences revealed introns at conserved sites found in the genes of other plant multifunctional ACCases, including two introns absent from the wheat cytosolic ACCase genes. Transcription start sites of the plastid ACCase genes were estimated from the longest cDNA clones obtained by 5′-RACE (rapid amplification of cDNA ends). The untranslated leader sequence encoded by the Acc-1 genes is at least 130–170 nucleotides long and is interrupted by an intron. Southern analysis indicates the presence of only one copy of the gene in each ancestral chromosome set. The gene maps near the telomere on the short arm of chromosomes 2A, 2B, and 2D. Identification of three different cDNAs, two corresponding to genes Acc-1,1 and Acc-1,2, indicates that all three genes are transcriptionally active.

Statistical modeling of large microarray data sets to identify stimulus-response profiles

A statistical modeling approach is proposed for use in searching large microarray data sets for genes that have a transcriptional response to a stimulus. The approach is unrestricted with respect to the timing, magnitude or duration of the response, or the overall abundance of the transcript. The statistical model makes an accommodation for systematic heterogeneity in expression levels. Corresponding data analyses provide gene-specific information, and the approach provides a means for evaluating the statistical significance of such information. To illustrate this strategy we have derived a model to depict the profile expected for a periodically transcribed gene and used it to look for budding yeast transcripts that adhere to this profile. Using objective criteria, this method identifies 81% of the known periodic transcripts and 1,088 genes, which show significant periodicity in at least one of the three data sets analyzed. However, only one-quarter of these genes show significant oscillations in at least two data sets and can be classified as periodic with high confidence. The method provides estimates of the mean activation and deactivation times, induced and basal expression levels, and statistical measures of the precision of these estimates for each periodic transcript.