Force chains, friction, and flow: Behavior of granular media across length scales

We study the behavior of granular materials at three length scales. At the smallest length scale, the grain-scale, we study inter-particle forces and "force chains". Inter-particle forces are the natural building blocks of constitutive laws for granular materials. Force chains are a key signature of the heterogeneity of granular systems. Despite their fundamental importance for calibrating grain-scale numerical models and elucidating constitutive laws, inter-particle forces have not been fully quantified in natural granular materials. We present a numerical force inference technique for determining inter-particle forces from experimental data and apply the technique to two-dimensional and three-dimensional systems under quasi-static and dynamic load. These experiments validate the technique and provide insight into the quasi-static and dynamic behavior of granular materials.

At a larger length scale, the mesoscale, we study the emergent frictional behavior of a collection of grains. Properties of granular materials at this intermediate scale are crucial inputs for macro-scale continuum models. We derive friction laws for granular materials at the mesoscale by applying averaging techniques to grain-scale quantities. These laws portray the nature of steady-state frictional strength as a competition between steady-state dilation and grain-scale dissipation rates. The laws also directly link the rate of dilation to the non-steady-state frictional strength.

At the macro-scale, we investigate continuum modeling techniques capable of simulating the distinct solid-like, liquid-like, and gas-like behaviors exhibited by granular materials in a single computational domain. We propose a Smoothed Particle Hydrodynamics (SPH) approach for granular materials with a viscoplastic constitutive law. The constitutive law uses a rate-dependent and dilation-dependent friction law. We provide a theoretical basis for a dilation-dependent friction law using similar analysis to that performed at the mesoscale. We provide several qualitative and quantitative validations of the technique and discuss ongoing work aiming to couple the granular flow with gas and fluid flows.

Pulse shaping properties of volume holographic gratings in anisotropic media

Based on a modified coupled wave theory, the pulse shaping properties of volume holographic gratings (VHGs) in anisotropic media VHGs are studied systematically. Taking photorefractive LiNbO3 crystals as an example, the combined effect that the grating parameters, the dispersion and optical anisotropy of the crystal, the pulse width, and the polarization state of the input ultrashort pulsed beam (UPB) have on the pulse shaping properties are considered when the input UPB with arbitrary polarization state propagates through the VHG. Under the combined effect, the diffraction bandwidth, pulse profiles of the diffracted and transmitted pulsed beams, and the total diffraction efficiency are shown. The studies indicate that the properties of the shaping of the o and e components of the input UPB in the crystal are greatly different; this difference can be used for pulse shaping applications. (c) 2006 Optical Society of America.

Pulsed neutron measurements in two adjacent finite media

The pulsed neutron technique has been used to investigate the decay of thermal neutrons in two adjacent water-borated water finite media. Experiments were performed with a 6x6x6 inches cubic assembly divided in two halves by a thin membrane and filled with pure distilled water on one side and borated water on the other side.

The fundamental decay constant was measured versus the boric acid concentration in the poisoned medium. The experimental results showed good agreement with the predictions of the time dependent diffusion model. It was assumed that the addition of boric acid increases the absorption cross section of the poisoned medium without affecting its diffusion properties: In these conditions, space-energy separability and the concept of an “effective” buckling as derived from diffusion theory were introduced. Their validity was supported by the experimental results.

Measurements were performed with the absorption cross section of the poisoned medium increasing gradually up to 16 times its initial value. Extensive use of the IBM 7090-7094 Computing facility was made to analyze properly the decay data (Frantic Code). Attention was given to the count loss correction scheme and the handling of the statistics involved. Fitting of the experimental results into the analytical form predicted by the diffusion model led to

Ʃ_av = 4721 sec^-1 (±150)

D_o = 35972 cm²sec^-1 (±800) for water at 21˚C

C (given) = 3420 cm⁴sec^-1

These values, when compared with published data, show that the diffusion model is adequate in describing the experiment.

Comparación de la rugosidad media y máxima obtenida mediante diferentes instrumentos: análisis del filtro y Lc empleados

[ES]Este trabajo pretende analizar la influencia que tiene la longitud de corte elegida y el filtro empleado en la medida de la rugosidad. Se realizan medidas de rugosidad en tres probetas que han sido sometidas a diferentes procesos de fabricación (fresado, rectificado y electroerosión). Además, se utilizan tres instrumentos diferentes para la medición. Tras realizar las medidas, se comparan los resultados y se extraen las conclusiones

Time-dependent monoenergetic neutron transport in two adjacent semi-infinite media

An exact solution to the monoenergetic Boltzmann equation is obtained for the case of a plane isotropic burst of neutrons introduced at the interface separating two adjacent, dissimilar, semi-infinite media. The method of solution used is to remove the time dependence by a Laplace transformation, solve the transformed equation by the normal mode expansion method, and then invert to recover the time dependence.

The general result is expressed as a sum of definite, multiple integrals, one of which contains the uncollided wave of neutrons originating at the source plane. It is possible to obtain a simplified form for the solution at the interface, and certain numerical calculations are made there.

The interface flux in two adjacent moderators is calculated and plotted as a function of time for several moderator materials. For each case it is found that the flux decay curve has an asymptotic slope given accurately by diffusion theory. Furthermore, the interface current is observed to change directions when the scattering and absorption cross sections of the two moderator materials are related in a certain manner. More specifically, the reflection process in two adjacent moderators appears to depend initially on the scattering properties and for long times on the absorption properties of the media.

This analysis contains both the single infinite and semi-infinite medium problems as special cases. The results in these two special cases provide a check on the accuracy of the general solution since they agree with solutions of these problems obtained by separate analyses.

Anisotropic diffraction of stratified volume holographic grating in photorefractive media

We have studied the anisotropic diffraction properties of the stratified volume holographic gratings recorded in photorefractive media using the anisotropic coupled wave theory. It is shown that the diffraction efficiency of such system exhibit the uniform periodic Bragg selectivity properties. In addition the dependence of the stratified volume holographic optical elements (SVHOEs) diffraction properties on the buffer-layer thickness, grating-layer thickness, number of modulation layers, and total thickness of system are discussed in detail. (c) 2005 Elsevier GrnbH. All rights reserved.

The resolution of the thermodynamic paradox and the theory of guided wave propagation in anisotropic media

The resolution of the so-called thermodynamic paradox is presented in this paper. It is shown, in direct contradiction to the results of several previously published papers, that the cutoff modes (evanescent modes having complex propagation constants) can carry power in a waveguide containing ferrite. The errors in all previous “proofs” which purport to show that the cutoff modes cannot carry power are uncovered. The boundary value problem underlying the paradox is studied in detail; it is shown that, although the solution is somewhat complicated, there is nothing paradoxical about it.

The general problem of electromagnetic wave propagation through rectangular guides filled inhomogeneously in cross-section with transversely magnetized ferrite is also studied. Application of the standard waveguide techniques reduces the TM part to the well-known self-adjoint Sturm Liouville eigenvalue equation. The TE part, however, leads in general to a non-self-adjoint eigenvalue equation. This equation and the associated expansion problem are studied in detail. Expansion coefficients and actual fields are determined for a particular problem.

Electromagnetic scattering from cylindrically and spherically stratified bodies

A method is developed for calculating the electromagnetic field scattered by certain types of bodies. The bodies consist of inhomogeneous media whose constitutive parameters vary only with the distance from some axis or point of symmetry. The method consists in an extension of the invariant imbedding method for treating wave problems. This method, which is familiar in the case of a one-dimensional inhomogeneity, is extended to handle special types of two and three-dimensional inhomogeneities. Comparisons are made with other methods which have been proposed for treating these kinds of problems. Examples of applications of the method are given, some of which are of interest in themselves.

Microscopic Origin of Macroscopic Strength in Granular Media: A Numerical and Analytical Approach

Constitutive modeling in granular materials has historically been based on macroscopic experimental observations that, while being usually effective at predicting the bulk behavior of these type of materials, suffer important limitations when it comes to understanding the physics behind grain-to-grain interactions that induce the material to macroscopically behave in a given way when subjected to certain boundary conditions.

The advent of the discrete element method (DEM) in the late 1970s helped scientists and engineers to gain a deeper insight into some of the most fundamental mechanisms furnishing the grain scale. However, one of the most critical limitations of classical DEM schemes has been their inability to account for complex grain morphologies. Instead, simplified geometries such as discs, spheres, and polyhedra have typically been used. Fortunately, in the last fifteen years, there has been an increasing development of new computational as well as experimental techniques, such as non-uniform rational basis splines (NURBS) and 3D X-ray Computed Tomography (3DXRCT), which are contributing to create new tools that enable the inclusion of complex grain morphologies into DEM schemes.

Yet, as the scientific community is still developing these new tools, there is still a gap in thoroughly understanding the physical relations connecting grain and continuum scales as well as in the development of discrete techniques that can predict the emergent behavior of granular materials without resorting to phenomenology, but rather can directly unravel the micro-mechanical origin of macroscopic behavior.

In order to contribute towards closing the aforementioned gap, we have developed a micro-mechanical analysis of macroscopic peak strength, critical state, and residual strength in two-dimensional non-cohesive granular media, where typical continuum constitutive quantities such as frictional strength and dilation angle are explicitly related to their corresponding grain-scale counterparts (e.g., inter-particle contact forces, fabric, particle displacements, and velocities), providing an across-the-scale basis for better understanding and modeling granular media.

In the same way, we utilize a new DEM scheme (LS-DEM) that takes advantage of a mathematical technique called level set (LS) to enable the inclusion of real grain shapes into a classical discrete element method. After calibrating LS-DEM with respect to real experimental results, we exploit part of its potential to study the dependency of critical state (CS) parameters such as the critical state line (CSL) slope, CSL intercept, and CS friction angle on the grain's morphology, i.e., sphericity, roundness, and regularity.

Finally, we introduce a first computational algorithm to ``clone'' the grain morphologies of a sample of real digital grains. This cloning algorithm allows us to generate an arbitrary number of cloned grains that satisfy the same morphological features (e.g., roundness and aspect ratio) displayed by their real parents and can be included into a DEM simulation of a given mechanical phenomenon. In turn, this will help with the development of discrete techniques that can directly predict the engineering scale behavior of granular media without resorting to phenomenology.

Melhor idade? A responsabilidade civil em relação ao idoso no contexto familiar

Busca-se no presente estudo tecer alguns comentários sobre tema muito controvertido: a possibilidade, ou não, de condenação à reparação de danos morais nas relações de família envolvendo idosos. Primeiramente, o objetivo será traçar notas sobre a evolução do direito de família e a importância da Constituição de 1988 nesse contexto. Também será dado destaque para os elementos da responsabilidade civil, a noção de dano moral e os direitos garantidos pelo Estatuto do Idoso. Apontado como paradigma para uma melhor análise do tema principal, será analisada a obrigação de reparar danos morais em razão de abandono afetivo de filho menor. O terceiro ponto, por sua vez, pretende trazer à baila a discussão acerca da responsabilidade civil nas relações com idosos no seio da família. Serão enfrentadas questões importantes, introduzidas por uma análise psicanalítica do processo de envelhecimento. Serão estudados qual o conceito de família e de idoso para os fins da responsabilidade civil, os seus elementos aplicados à hipótese, bem como a possibilidade de reparação pecuniária nestes casos.

Corrections to the paraxial approximation solutions in transversely nonuniform refractive-index media

The coupled differential recurrence equations for the corrections to the paraxial approximation solutions in transversely nonuniform refractive-index media are established in terms of the perturbation method. All the corrections (including the longitudinal field corrections) to the paraxial approximation solutions are presented in the weak-guidance approximation. As a concrete application, the first-order longitudinal field correction and the second-order transverse field correction to the paraxial approximation of a Gaussian beam propagating in a transversely quadratic refractive index medium are analytically investigated. (C) 1999 Optical Society of America [S0740-3232(99)00310-5].

Spatiotemporal instabilities in nonlinear Kerr media in the presence of arbitrary higher-order dispersions

Spatiotemporal instabilities in nonlinear Kerr media with arbitrary higher-order dispersions are studied by use of standard linear-stability analysis. A generic expression for instability growth rate that unifies and expands on previous results for temporal, spatial, and spatiotemporal instabilities is obtained. It is shown that all odd-order dispersions contribute nothing to instability, whereas all even-order dispersions not only affect the conventional instability regions but may also lead to the appearance of new instability regions. The role of fourth-order dispersion in spatiotemporal instabilities is studied exemplificatively to demonstrate the generic results. Numerical simulations confirm the obtained analytic results. (C) 2002 Optical Society of America.

Los linajes de Bizkaia en la Baja Edad Media: poder, parentesco y conflicto

Este libro se ocupa del principal protagonista de la historia medieval de Bizkaia: el hidalgo. Como en el resto de Europa Occidental, la nobleza del Señorío, organizada social y políticamente en linajes, acapara las fuentes de renta y traza sus estrategias sobre la alianza y la violencia. Sin embargo, en Bizkaia, la violencia feudal alcanzará cotas extremas en lo que se conoce como "luchas de bandos". La competencia entre los hidalgos se fundamenta en un argumento tan sólido como simple: el "más valer". "Más valer" en rentas y atreguados, "más valer" en descendencia bastarda o legítima, "más valer" que mueve a matar al vecino como forma extrema de sometimiento. En este contexto el linaje destaca como una referencia existencial paralela a tan extrema ideología de la competencia. En él se desarrolla la vida, se revelan los signos del poder y se conforma la imagen propia sobre la de los antepasados. Al filo del 1500, esta manifestación local de la honra tendrá tal éxito que contagiará al resto de los vizcaínos de la época forzando la implantación de la "hidalguía universal"

Violência familiar e estado nutricional de adolescentes numa unidade de saúde

O presente trabalho teve como objetivos verificar a possível associação entre violência intrafamiliar sofrida por adolescentes e estado nutricional. Foram investigadas as prevalências de agressão verbal, violências física, abuso psicológico e de estado nutricional inadequado dos adolescentes. Para tanto, foi realizado um estudo observacional de corte transversal numa amostra de 201 adolescentes de 10 a 19 anos cadastrados no Programa Bolsa Família e monitorados pelo Serviço de Nutrição de uma unidade de saúde do município do Rio de Janeiro. Junto aos adolescentes foi realizada avaliação antropométrica, e para a determinação do estado nutricional foi analisado o Índice de Massa Corporal (IMC) pelo parâmetro adotado pela OMS a partir de 2007. A violência familiar foi investigada por meio de dois instrumentos. O Conflict Tactics Scales Form R (CTS1) foi utilizado para avaliar os conflitos intrafamiliares no relacionamento entre pais e filhos e a escala de violência psicológica contra adolescentes para identificar a presença de violência psicológica contra os adolescentes. Além disso, foram avaliadas outras co-variáveis que pudessem influenciar a associação entre violência e situação nutricional da população estudada como informações sobre maturação sexual, sócio-demográficas e percepção corporal. No que diz respeito ao IMC, foram identificados 4,5% de baixo peso, 13,4% de sobrepeso e 5% de obesidade. No que se refere à violência familiar, foram observados 83,1% de agressão verbal, 50,2% de violência psicológica, 32,8% de agressão física grave e 48,3% de abuso físico menor. Através da regressão linear múltipla foi observada um associação entre violência familiar e o IMC em adolescentes do sexo feminino. A presença de agressão verbal perpetrada tanto pelo pai como pela mãe está relacionado ao IMC de forma estatisticamente significativa para as meninas. Já para os adolescentes masculinos não foi encontrada nenhuma associação significativa entre os diferentes tipos de violência familiar e o IMC, mas aponta para a redução do IMC. Outras estratégias de pesquisa de natureza qualitativa devem ser realizadas para esclarecer sobre os efeitos desfavoráveis do abuso verbal sobre o IMC junto aos pais e a sociedade já que a agressão verbal é um tipo de abuso normalmente utilizado no ambiente familiar e considerado como algo natural e aceitável