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.

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.

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.

Computer Simulation of Packing of Particles with Size Distributions Produced by Fragmentation Processes

Fragmentation schemes inspired by theoretical results and conjectures of Kolmogorov are applied to produce particle size distributions of different natures, depending on fragmentation parameters. A two-dimensional computer simulation method of packing is applied to the resulting distributions and the void fraction is evaluated. The relationship between the void fraction and characteristic parameters of the fragmentation process is studied.

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.

Packing of atermal polymers in the bulk and under confinement

Polymers constitute a distinct class of anisotropic particles with unique dynamical, rheological and mechanical properties.

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.

Tridimensional simulation of the speed, pressure and turbulence fields of the air flow on the geometry of a freight truck inside a wind tunnel

This study shows the air flow behavior through the geometry of a freight truck inside a AF6109 wind tunnel with the purpose to predict the speed, pressure and turbulence fields made by the air flow, to decrease the aerodynamic resistance, to calculate the dragging coefficient, to evaluate the aerodynamics of the geometry of the prototype using the CFD technique and to compare the results of the simulation with the results obtained experimentally with the “PETER 739 HAULER” scaled freight truck model located on the floor of the test chamber. The Geometry went through a numerical simulation process using the CFX 5,7. The obtained results showed the behavior of the air flow through the test chamber, and also it showed the variations of speed and pressure at the exit of the chamber and the calculations of the coefficient and the dragging force on the geometry of the freight truck. The evaluation of the aerodynamics showed that the aerodynamic deflector is a device that helped the reduction the dragging produced in a significant way by the air. Furthermore, the dragging coefficient and force on the prototype freight truck could be estimated establishing an incomplete similarity.

Soil aggregate geometry: Measurements and morphology

Aggregates provide physical microenvironments for microorganisms, the vital actors of soil systems, and thus play a major role as both, an arena and a product of soil carbon stabilization and dynamics. The surface of an aggregate is what enables exchange of the materials and air and water fluxes between aggregate exterior and interior regions. We made use of 3D images from X-ray CT of aggregates and mathematical morphology to provide an exhaustive quantitative description of soil aggregate morphology that includes both intra-aggregate pore space structure and aggregate surface features. First, the evolution of Minkowski functionals (i.e. volume, boundary surface, curvature and connectivity) for successive dilations of the solid part of aggregates was investigated to quantify its 3D geometrical features. Second, the inner pore space was considered as the object of interest. We devised procedures (a) to define the ends of the accessible pores that are connected to the aggregate surface and (b) to separate accessible and inaccessible porosity. Geometrical Minkowski functionals of the intra-aggregate pore space provide the exhaustive characterization of the inner structure of the aggregates. Aggregates collected from two different soil treatments were analyzed to explore the utility of these morphological tools in capturing the impact on their morphology of two different soil managements, i.e. conventional tillage management, and native succession vegetation treatment. The quantitative tools of mathematical morphology distinguished differences in patterns of aggregate structure associated to the different soil managements.

Computer simulation of packing of particles with size distributions produced by fragmentation processes

Fragmentation schemes inspired by theoretical results and conjectures of Kolmogorov are applied to produce particle size distributions of different natures, depending on fragmentation parameters. A two-dimensional computer simulation method of packing is applied to the resulting distributions and the void fraction is evaluated. The relationship between the void fraction and characteristic parameters of the fragmentation process is studied.

The interspecific mass–density relationship and plant geometry

We present an a priori theoretical framework for the interspecific allometric relationship between stand mass and plant population density. Our model predicts a slope of −\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}\frac{1}{3}\end{equation*}\end{document} between the logarithm of stand mass and the logarithm of stand density, thus conflicting with a previously assumed slope of −½. Our model rests on a heuristic separation of resource-limited living mass and structural mass in the plant body. We point out that because of similar resource requirements among plants of different sizes, a nonzero plant mass–density slope is primarily defined by structural mass. Specifically, the slope is a result of (i) the physical size-dependent relationship between stem width and height, (ii) foliage-dependent demands of conductance, and (iii) the cumulative nature of structural mass. The data support our model, both when the potential sampling bias of taxonomic relatedness is accounted for and when it is not. Independent contrasts analyses show that observed relationships among variables are not significantly different from the assumptions made to build the model or from its a priori predictions. We note that the dependence of the plant mass–density slope on the functions of structural mass provides a cause for the difference from the zero slope found in the animal population mass–density relationship; for the most part, animals do not have a comparable cumulative tissue type.

The making of the architecture of the plant cell wall: How cells exploit geometry

Cell wall deposition is a key process in the formation, growth, and differentiation of plant cells. The most important structural components of the wall are long cellulose microfibrils, which are synthesized by synthases embedded in the plasma membrane. A fundamental question is how the microfibrils become oriented during deposition at the plasma membrane. The current textbook explanation for the orientation mechanism is a guidance system mediated by cortical microtubules. However, too many contraindications are known in secondary cell walls for this to be a universal mechanism, particularly in the case of helicoidal arrangements, which occur in many situations. An additional construction mechanism involves liquid crystalline self-assembly [A. C. Neville (1993) Biology of Fibrous Composites: Development Beyond the Cell Membrane (Cambridge Univ. Press, Cambridge, U.K.)], but the required amount of bulk material that is able to equilibrate thermally is not normally present at any stage of the wall deposition process. Therefore, we have asked whether the complex ordered texture of helicoidal cell walls can be formed in the absence of direct cellular guidance mechanisms. We propose that they can be formed by a mechanism that is based on geometrical considerations. It explains the genesis of the complicated helicoidal texture and shows that the cell has intrinsic, versatile tools for creating a variety of textures. A compelling feature of the model is that local rules generate global order, a typical phenomenon of life.

DNA packing in stable lipid complexes designed for gene transfer imitates DNA compaction in bacteriophage

The structure of complexes made from DNA and suitable lipids (lipoplex, Lx) was examined by cryo-electron microscopy (cryoEM). We observed a distinct concentric ring-like pattern with striated shells when using plasmid DNA. These spherical multilamellar particles have a mean diameter of 254 nm with repetitive spacing of 7.5 nm with striation of 5.3 nm width. Small angle x-ray scattering revealed repetitive ordering of 6.9 nm, suggesting a lamellar structure containing at least 12 layers. This concentric and lamellar structure with different packing regimes also was observed by cryoEM when using linear double-stranded DNA, single-stranded DNA, and oligodeoxynucleotides. DNA chains could be visualized in DNA/lipid complexes. Such specific supramolecular organization is the result of thermodynamic forces, which cause compaction to occur through concentric winding of DNA in a liquid crystalline phase. CryoEM examination of T4 phage DNA packed either in T4 capsides or in lipidic particles showed similar patterns. Small angle x-ray scattering suggested an hexagonal phase in Lx-T4 DNA. Our results indicate that both lamellar and hexagonal phases may coexist in the same Lx preparation or particle and that transition between both phases may depend on equilibrium influenced by type and length of the DNA used.

Kinematic geometry of mass-triangles and reduction of Schrödinger’s equation of three-body systems to partial differential equations solely defined on triangular parameters

Schrödinger’s equation of a three-body system is a linear partial differential equation (PDE) defined on the 9-dimensional configuration space, ℝ9, naturally equipped with Jacobi’s kinematic metric and with translational and rotational symmetries. The natural invariance of Schrödinger’s equation with respect to the translational symmetry enables us to reduce the configuration space to that of a 6-dimensional one, while that of the rotational symmetry provides the quantum mechanical version of angular momentum conservation. However, the problem of maximizing the use of rotational invariance so as to enable us to reduce Schrödinger’s equation to corresponding PDEs solely defined on triangular parameters—i.e., at the level of ℝ6/SO(3)—has never been adequately treated. This article describes the results on the orbital geometry and the harmonic analysis of (SO(3),ℝ6) which enable us to obtain such a reduction of Schrödinger’s equation of three-body systems to PDEs solely defined on triangular parameters.

Specific atomic groups and RNA helix geometry in acceptor stem recognition by a tRNA synthetase

Oligonucleotides that recapitulate the acceptor stems of tRNAs are substrates for aminoacylation by many tRNA synthetases in vitro, even though these substrates are missing the anticodon trinucleotides of the genetic code. In the case of tRNAAla a single acceptor stem G⋅U base pair at position 3·70 is essential, based on experiments where the wobble pair has been replaced by alternatives such as I⋅U, G⋅C, and A⋅U, among others. These experiments led to the conclusion that the minor-groove free 2-amino group (of guanosine) of the G⋅U wobble pair is essential for charging. Moreover, alanine-inserting tRNAs (amber suppressors) that replace G⋅U with mismatches such as G⋅A and C⋅A are partially active in vivo and can support growth of an Escherichia coli tRNAAla knockout strain, leading to the hypothesis that a helix irregularity and nucleotide functionalities are important for recognition. Herein we investigate the charging in vitro of oligonucleotide and full-length tRNA substrates that contain mismatches at the position of the G⋅U pair. Although most of these substrates have undetectable activity, G⋅A and C⋅A variants retain some activity, which is, nevertheless, reduced by at least 100-fold. Thus, the in vivo assays are much less sensitive to large changes in aminoacylation kinetic efficiency of 3·70 variants than is the in vitro assay system. Although these functional data do not clarify all of the details, it is now clear that specific atomic groups are substantially more important in determining kinetic efficiency than is a helical distortion. By implication, the activity of mutant tRNAs measured in the in vivo assays appears to be more dependent on factors other than aminoacylation kinetic efficiency.