Statistical mechanics approaches to granular media: between micromechanics and macromechanics

The mechanical behavior of granular materials has been traditionally approached through two theoretical and computational frameworks: macromechanics and micromechanics. Macromechanics focuses on continuum based models. In consequence it is assumed that the matter in the granular material is homogeneous and continuously distributed over its volume so that the smallest element cut from the body possesses the same physical properties as the body. In particular, it has some equivalent mechanical properties, represented by complex and non-linear constitutive relationships. Engineering problems are usually solved using computational methods such as FEM or FDM. On the other hand, micromechanics is the analysis of heterogeneous materials on the level of their individual constituents. In granular materials, if the properties of particles are known, a micromechanical approach can lead to a predictive response of the whole heterogeneous material. Two classes of numerical techniques can be differentiated: computational micromechanics, which consists on applying continuum mechanics on each of the phases of a representative volume element and then solving numerically the equations, and atomistic methods (DEM), which consist on applying rigid body dynamics together with interaction potentials to the particles. Statistical mechanics approaches arise between micro and macromechanics. It tries to state which the expected macroscopic properties of a granular system are, by starting from a micromechanical analysis of the features of the particles and the interactions. The main objective of this paper is to introduce this approach.

Representing microstates of static granular matter in a stress phase space

A stress phase space is proposed to compare the static packings of a granular system (microstates) that are compatible to a macrostate described by external stresses. The equivalent stress of each particle of a static packing can be obtained from the mechanical interaction forces, and the associated volume is given by the respective Voronoi cell. Therefore, particles can be located at different stress levels and grouped into categories or configurations, which are defined in base of the geometrical features of the local arrangement (in particular, of the number of forces that keep them force-balanced). They can be represented as points in a stress phase space. The nature of this space is analyzed in detail. The integration limits of the stress variables that avoid or limit tensile states and the capability of each configuration to represent specific stress states establish its main features. Furthermore, if some stress variables are used, instead of the usual components of the Cauchy stress tensor, then some symmetries can be found. Results obtained from molecular dynamics simulations are used to check this nature. Finally, some statistical ensembles are written in terms of the coordinates of this phase space. These require some assumptions that are made in base on continuum mechanics principles.

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.

Thermodynamic aproach to particle size distribution in granular media

The study of particulate systems is of great interest in many fields of science and technology. Soil, sediments, powders, granular materials, colloidal and particulate suspensions are examples of systems involving many size particles. For those systems, the statistical description of the particle size distribution (PSD), that is, the mathematical distribution that defines the relative amounts of particles present, sorted according to size, is a crutial issue. The PSD can be important in understanding soil hydraulic properties, the geological origin or sediments or the physical and chemical properties of granular materials and ceramics, among others.

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.

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.

Permanent deformation estimates of dynamic equipment foundations: Application to a gas turbine in granular soils

Permanent displacements of a gas turbine founded on a fine, poorly graded, and medium density sand are studied. The amplitudes and modes of vibration are computed using Barkan´s formulation, and the “High-Cycle Accumulation” (HCA) model is employed to account for accumulated deformations due to the high number of cycles. The methodology is simple: it can be easily incorporated into standard mathematical software, and HCA model parameters can be estimated based on granulometry and index properties. Special attention is devoted to ‘transient’ situations at equipment´s start-up, during which a range of frequencies – including frequencies that could be similar to the natural frequencies of the ground – is traversed. Results show that such transient situations could be more restrictive than stationary situations corresponding to normal operation. Therefore, checking the stationary situation only might not be enough, and studying the influence of transient situations on computed permanent displacements is needed to produce a proper foundation design

Especificaciones eMathTeacher, creación del Modelo Granular Lingüístico de la evaluación del aprendizaje humano, y diseño de sistemas que implementan estos conceptos

El concepto de algoritmo es básico en informática, por lo que es crucial que los alumnos profundicen en él desde el inicio de su formación. Por tanto, contar con una herramienta que guíe a los estudiantes en su aprendizaje puede suponer una gran ayuda en su formación. La mayoría de los autores coinciden en que, para determinar la eficacia de una herramienta de visualización de algoritmos, es esencial cómo se utiliza. Así, los estudiantes que participan activamente en la visualización superan claramente a los que la contemplan de forma pasiva. Por ello, pensamos que uno de los mejores ejercicios para un alumno consiste en simular la ejecución del algoritmo que desea aprender mediante el uso de una herramienta de visualización, i. e. consiste en realizar una simulación visual de dicho algoritmo. La primera parte de esta tesis presenta los resultados de una profunda investigación sobre las características que debe reunir una herramienta de ayuda al aprendizaje de algoritmos y conceptos matemáticos para optimizar su efectividad: el conjunto de especificaciones eMathTeacher, además de un entorno de aprendizaje que integra herramientas que las cumplen: GRAPHs. Hemos estudiado cuáles son las cualidades esenciales para potenciar la eficacia de un sistema e-learning de este tipo. Esto nos ha llevado a la definición del concepto eMathTeacher, que se ha materializado en el conjunto de especificaciones eMathTeacher. Una herramienta e-learning cumple las especificaciones eMathTeacher si actúa como un profesor virtual de matemáticas, i. e. si es una herramienta de autoevaluación que ayuda a los alumnos a aprender de forma activa y autónoma conceptos o algoritmos matemáticos, corrigiendo sus errores y proporcionando pistas para encontrar la respuesta correcta, pero sin dársela explícitamente. En estas herramientas, la simulación del algoritmo no continúa hasta que el usuario introduce la respuesta correcta. Para poder reunir en un único entorno una colección de herramientas que cumplan las especificaciones eMathTeacher hemos creado GRAPHs, un entorno ampliable, basado en simulación visual, diseñado para el aprendizaje activo e independiente de los algoritmos de grafos y creado para que en él se integren simuladores de diferentes algoritmos. Además de las opciones de creación y edición del grafo y la visualización de los cambios producidos en él durante la simulación, el entorno incluye corrección paso a paso, animación del pseudocódigo del algoritmo, preguntas emergentes, manejo de las estructuras de datos del algoritmo y creación de un log de interacción en XML. Otro problema que nos planteamos en este trabajo, por su importancia en el proceso de aprendizaje, es el de la evaluación formativa. El uso de ciertos entornos e-learning genera gran cantidad de datos que deben ser interpretados para llegar a una evaluación que no se limite a un recuento de errores. Esto incluye el establecimiento de relaciones entre los datos disponibles y la generación de descripciones lingüísticas que informen al alumno sobre la evolución de su aprendizaje. Hasta ahora sólo un experto humano era capaz de hacer este tipo de evaluación. Nuestro objetivo ha sido crear un modelo computacional que simule el razonamiento del profesor y genere un informe sobre la evolución del aprendizaje que especifique el nivel de logro de cada uno de los objetivos definidos por el profesor. Como resultado del trabajo realizado, la segunda parte de esta tesis presenta el modelo granular lingüístico de la evaluación del aprendizaje, capaz de modelizar la evaluación y generar automáticamente informes de evaluación formativa. Este modelo es una particularización del modelo granular lingüístico de un fenómeno (GLMP), en cuyo desarrollo y formalización colaboramos, basado en la lógica borrosa y en la teoría computacional de las percepciones. Esta técnica, que utiliza sistemas de inferencia basados en reglas lingüísticas y es capaz de implementar criterios de evaluación complejos, se ha aplicado a dos casos: la evaluación, basada en criterios, de logs de interacción generados por GRAPHs y de cuestionarios de Moodle. Como consecuencia, se han implementado, probado y utilizado en el aula sistemas expertos que evalúan ambos tipos de ejercicios. Además de la calificación numérica, los sistemas generan informes de evaluación, en lenguaje natural, sobre los niveles de competencia alcanzados, usando sólo datos objetivos de respuestas correctas e incorrectas. Además, se han desarrollado dos aplicaciones capaces de ser configuradas para implementar los sistemas expertos mencionados. Una procesa los archivos producidos por GRAPHs y la otra, integrable en Moodle, evalúa basándose en los resultados de los cuestionarios. ABSTRACT The concept of algorithm is one of the core subjects in computer science. It is extremely important, then, for students to get a good grasp of this concept from the very start of their training. In this respect, having a tool that helps and shepherds students through the process of learning this concept can make a huge difference to their instruction. Much has been written about how helpful algorithm visualization tools can be. Most authors agree that the most important part of the learning process is how students use the visualization tool. Learners who are actively involved in visualization consistently outperform other learners who view the algorithms passively. Therefore we think that one of the best exercises to learn an algorithm is for the user to simulate the algorithm execution while using a visualization tool, thus performing a visual algorithm simulation. The first part of this thesis presents the eMathTeacher set of requirements together with an eMathTeacher-compliant tool called GRAPHs. For some years, we have been developing a theory about what the key features of an effective e-learning system for teaching mathematical concepts and algorithms are. This led to the definition of eMathTeacher concept, which has materialized in the eMathTeacher set of requirements. An e-learning tool is eMathTeacher compliant if it works as a virtual math trainer. In other words, it has to be an on-line self-assessment tool that helps students to actively and autonomously learn math concepts or algorithms, correcting their mistakes and providing them with clues to find the right answer. In an eMathTeacher-compliant tool, algorithm simulation does not continue until the user enters the correct answer. GRAPHs is an extendible environment designed for active and independent visual simulation-based learning of graph algorithms, set up to integrate tools to help the user simulate the execution of different algorithms. Apart from the options of creating and editing the graph, and visualizing the changes made to the graph during simulation, the environment also includes step-by-step correction, algorithm pseudo-code animation, pop-up questions, data structure handling and XML-based interaction log creation features. On the other hand, assessment is a key part of any learning process. Through the use of e-learning environments huge amounts of data can be output about this process. Nevertheless, this information has to be interpreted and represented in a practical way to arrive at a sound assessment that is not confined to merely counting mistakes. This includes establishing relationships between the available data and also providing instructive linguistic descriptions about learning evolution. Additionally, formative assessment should specify the level of attainment of the learning goals defined by the instructor. Till now, only human experts were capable of making such assessments. While facing this problem, our goal has been to create a computational model that simulates the instructor’s reasoning and generates an enlightening learning evolution report in natural language. The second part of this thesis presents the granular linguistic model of learning assessment to model the assessment of the learning process and implement the automated generation of a formative assessment report. The model is a particularization of the granular linguistic model of a phenomenon (GLMP) paradigm, based on fuzzy logic and the computational theory of perceptions, to the assessment phenomenon. This technique, useful for implementing complex assessment criteria using inference systems based on linguistic rules, has been applied to two particular cases: the assessment of the interaction logs generated by GRAPHs and the criterion-based assessment of Moodle quizzes. As a consequence, several expert systems to assess different algorithm simulations and Moodle quizzes have been implemented, tested and used in the classroom. Apart from the grade, the designed expert systems also generate natural language progress reports on the achieved proficiency level, based exclusively on the objective data gathered from correct and incorrect responses. In addition, two applications, capable of being configured to implement the expert systems, have been developed. One is geared up to process the files output by GRAPHs and the other one is a Moodle plug-in set up to perform the assessment based on the quizzes results.

Na,K-ATPase transport from endoplasmic reticulum to Golgi requires the Golgi spectrin–ankyrin G119 skeleton in Madin Darby canine kidney cells

Spectrin (βIΣ∗) and ankyrin (AnkG119) associate with Golgi membranes and the dynactin complex, but their role in vesicle trafficking remains uncertain. We find that the actin-binding domain and membrane-association domain 1 (MAD1) of βI spectrin together form a constitutive Golgi targeting signal in transfected MDCK cells. Expression of this signal in transfected cells disrupts the endogenous Golgi spectrin skeleton and blocks transport of α- and β-Na,K-ATPase and vesicular stomatitis virus-G protein from the endoplasmic reticulum (ER) but does not disrupt the formation of Golgi stacks, the distribution of β-COP, or the transport and surface display of E-cadherin. The Golgi spectrin skeleton is thus required for the transport of a subset of membrane proteins from the ER to the Golgi. We postulate that together with polyfunctional adapter proteins such as AnkG119, Golgi spectrin forms a docking complex that acts prior to the cis-Golgi, presumably with vesicular–tubular clusters (VTCs or ERGIC), to sequester specific membrane proteins into vesicles transiting between the ER and Golgi, and subsequently (probably involving other isoforms of spectrin and ankyrin) to mediate cargo transport within the Golgi and to other membrane compartments. We hypothesize that this vesicular spectrin–ankyrin adapter-protein trafficking (or tethering) system (SAATS) mediates the capture and transport of many membrane proteins and acts in conjunction with vesicle-targeting molecules to effect the efficient transport of cargo proteins.

Segregation of Two Spectrin Isoforms: Polarized Membrane-binding Sites Direct Polarized Membrane Skeleton Assembly

Spectrin isoforms are often segregated within specialized plasma membrane subdomains where they are thought to contribute to the development of cell surface polarity. It was previously shown that ankyrin and β spectrin are recruited to sites of cell–cell contact in Drosophila S2 cells expressing the homophilic adhesion molecule neuroglian. Here, we show that neuroglian has no apparent effect on a second spectrin isoform (αβH), which is constitutively associated with the plasma membrane in S2 cells. Another membrane marker, the Na,K-ATPase, codistributes with ankyrin and αβ spectrin at sites of neuroglian-mediated contact. The distributions of these markers in epithelial cells in vivo are consistent with the order of events observed in S2 cells. Neuroglian, ankyrin, αβ spectrin, and the Na,K-ATPase colocalize at the lateral domain of salivary gland cells. In contrast, αβH spectrin is sorted to the apical domain of salivary gland and somatic follicle cells. Thus, the two spectrin isoforms respond independently to positional cues at the cell surface: in one case an apically sorted receptor and in the other case a locally activated cell–cell adhesion molecule. The results support a model in which the membrane skeleton behaves as a transducer of positional information within cells.

Calcium-dependent enzyme activation and vacuole formation in the apical granular region of pancreatic acinar cells

The pancreatic acinar cell produces powerful digestive enzymes packaged in zymogen granules in the apical pole. Ca2+ signals elicited by acetylcholine or cholecystokinin (CCK) initiate enzyme secretion by exocytosis through the apical membrane. Intracellular enzyme activation is normally kept to a minimum, but in the often-fatal human disease acute pancreatitis, autodigestion occurs. How the enzymes become inappropriately activated is unknown. We monitored the cytosolic Ca2+ concentration ([Ca2+]i), intracellular trypsin activation, and its localization in isolated living cells with specific fluorescent probes and studied intracellular vacuole formation by electron microscopy as well as quantitative image analysis (light microscopy). A physiological CCK level (10 pM) eliciting regular Ca2+ spiking did not evoke intracellular trypsin activation or vacuole formation. However, stimulation with 10 nM CCK, evoking a sustained rise in [Ca2+]i, induced pronounced trypsin activation and extensive vacuole formation, both localized in the apical pole. Both processes were abolished by preventing abnormal [Ca2+]i elevation, either by preincubation with the specific Ca2+ chelator 1,2-bis(O-aminophenoxy)ethane-N,N-N′,N′-tetraacetic acid (BAPTA) or by removal of external Ca2+. CCK hyperstimulation evokes intracellular trypsin activation and vacuole formation in the apical granular pole. Both of these processes are mediated by an abnormal sustained rise in [Ca2+]i.

Does the granular matter?

Granular materials, such as sand, gravel, powders, and pharmaceutical pills, are large aggregates of macroscopic, individually solid particles, or “grains.” Far from being simple materials with simple properties, they display an astounding range of complex behavior that defies their categorization as solid, liquid, or gas. Just consider how sand can stream through the orifice of an hourglass yet support one's weight on the beach; how it can form patterns strikingly similar to a liquid when vibrated, yet respond to stirring by “unmixing” of large and small grains. Despite much effort, there still is no comprehensive understanding of other forms of matter, like ordinary fluids or solids. In what way, therefore, is granular matter special, and what makes it so difficult to understand? An emerging interdisciplinary approach to answering these questions focuses directly on the material's discontinuous granular nature.

Endogenous Msx1 antisense transcript: In vivo and in vitro evidences, structure, and potential involvement in skeleton development in mammals

Msx1 is a key factor for the development of tooth and craniofacial skeleton and has been proposed to play a pivotal role in terminal cell differentiation. In this paper, we demonstrated the presence of an endogenous Msx1 antisense RNA (Msx1-AS RNA) in mice, rats, and humans. In situ analysis revealed that this RNA is expressed only in differentiated dental and bone cells with an inverse correlation with Msx1 protein. These in vivo data and overexpression of Msx1 sense and AS RNA in an odontoblastic cell line (MO6-G3) showed that the balance between the levels of the two Msx1 RNAs is related to the expression of Msx1 protein. To analyze the impact of this balance in the Msx-Dlx homeoprotein pathway, we analyzed the effect of Msx1, Msx2, and Dlx5 overexpression on proteins involved in skeletal differentiation. We showed that the Msx1-AS RNA is involved in crosstalk between the Msx-Dlx pathways because its expression was abolished by Dlx5. Msx1 was shown to down-regulate a master gene of skeletal cells differentiation, Cbfa1. All these data strongly suggest that the ratio between Msx1 sense and antisense RNAs is a very important factor in the control of skeletal terminal differentiation. Finally, the initiation site for Msx1-AS RNA transcription was located by primer extension in both mouse and human in an identical region, including a consensus TATA box, suggesting an evolutionary conservation of the AS RNA-mediated regulation of Msx1 gene expression.

Studies on the biosynthesis of taxol: the taxane carbon skeleton is not of mevalonoid origin.

A cell culture of Taxus chinensis was established to produce the diterpene 2alpha,5alpha,10beta,14beta-tetra-acetoxy4 ++ +(20),11-taxadiene (taxuyunnanine C) in 2.6% (dry weight) yield. The incorporation of [U-13C6]glucose, [1-13C]glucose, and [1,2-13C2]acetate into this diterpene was analyzed by NMR spectroscopy. Label from [1,2-13C2]acetate was diverted to the four acetyl groups of taxuyunnanine C, but not to the taxane ring system. Label from [1-13C]glucose and [U-13C6]glucose was efficiently incorporated into both the taxane ring system and the acetyl groups. The four isoprenoid moieties of the diterpene showed identical labeling patterns. The analysis of long-range 13C13C couplings in taxuyunnanine C obtained from an experiment with [U-13C6]glucose documents the involvement of an intramolecular rearrangement in the biosynthesis of the isoprenoid precursor. The labeling patterns are inconsistent with the mevalonate pathway. The taxoid data share important features with the alternative pathway of isoprenoid biosynthesis operating in certain eubacteria Rohmer, M., Knani, M., Simonin, P., Sutter, B. & Sahm, H. (1993) Biochem. J. 295, 517-524].