A novel three-dimensional imaging array recording and computational method by means of coded cameras reconstruction

In this paper, we propose a novel three-dimensional imaging method by which the object is captured by a coded cameras array (CCA) and computationally reconstructed as a series of longitudinal layered surface images of the object. The distribution of cameras in array, named code pattern, is crucial for reconstructed images fidelity when the correlation decoding is used. We use DIRECT global optimization algorithm to design the code patterns that possess proper imaging property. We have conducted primary experiments to verify and test the performance of the proposed method with a simple discontinuous object and a small-scale CCA including nine cameras. After certain procedures such as capturing, photograph integrating, computational reconstructing and filtering, etc., we obtain reconstructed longitudinal layered surface images of the object with higher signal-to-noise ratio. The results of experiments show that the proposed method is feasible. It is a promising method to be used in fields such as remote sensing, machine vision, etc. (c) 2006 Elsevier GmbH. All rights reserved.

Anisotropic Bragg diffraction of finite-sized volume holographic grating in photorefractive crystals

Anisotropic diffraction of uniform plane wave by finite-sized volume holographic grating in photorefractive crystals is considered. It is found that the anisotropic diffraction can take place when some special conditions are satisfied. The diffracted image is obtained in experiment for the anisotropic Bragg diffraction in Fe:LiNbO3 crystals. A coupled wave analysis is presented to study the properties of anisotropic diffraction. An analytical integral solution for the amplitudes of the diffracted beams is submitted. A trade off between high diffraction efficiency and the deterioration of reconstruction fidelity is analyzed. Numerical evaluations also show that the finite-sized anisotropic volume grating exhibits strong angular and wavelength selectivity. All the results are useful for the optimizing design of VHOE based on finite-sized volume grating structures. (c) 2006 Elsevier GmbH. All rights reserved.

Numerical simulation of wavefronts diffracted by apertures with circular symmetry

The numerical simulation of the wavefronts diffracted by apertures with circular symmetry is realized by a numerical method. It is based on the angular spectrum of plane waves, which ignored the vector nature of light. The on-axial irradiance distributions of plane wavefront and Gauss wavefront diffracted by the circular aperture have been calculated along the propagation direction. Comparisons of the simulation results with the analytical results and the experimental results tell us that it is a feasible method to calculate the diffraction of apertures. (c) 2006 Published by Elsevier GmbH.

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.

Um método sintético de difusão para aceleração do esquema de fonte de espalhamento em cálculos SN unidimensionais de fonte fixa

O esquema iterativo de fonte de espalhamento (SI) é tradicionalmente aplicado para a convergência da solução numérica de malha fina para problemas de transporte de nêutrons monoenergéticos na formulação de ordenadas discretas com fonte fixa. O esquema SI é muito simples de se implementar sob o ponto de vista computacional; porém, o esquema SI pode apresentar taxa de convergência muito lenta, principalmente para meios difusivos (baixa absorção) com vários livres caminhos médios de extensão. Nesta dissertação descrevemos uma técnica de aceleração baseada na melhoria da estimativa inicial para a distribuição da fonte de espalhamento no interior do domínio de solução. Em outras palavras, usamos como estimativa inicial para o fluxo escalar médio na grade de discretização de malha fina, presentes nos termos da fonte de espalhamento das equações discretizadas SN usadas nas varreduras de transporte, a solução numérica da equação da difusão de nêutrons em grade espacial de malha grossa com condições de contorno especiais, que aproximam as condições de contorno prescritas que são clássicas em cálculos SN, incluindo condições de contorno do tipo vácuo. Para aplicarmos esta solução gerada pela equação da difusão em grade de discretização de malha grossa nas equações discretizadas SN de transporte na grade de discretização de malha fina, primeiro implementamos uma reconstrução espacial dentro de cada nodo de discretização, e então determinamos o fluxo escalar médio em grade de discretização de malha fina para usá-lo nos termos da fonte de espalhamento. Consideramos um número de experimentos numéricos para ilustrar a eficiência oferecida pela presente técnica (DSA) de aceleração sintética de difusão.

Um método de matriz resposta com esquema iterativo de inversão parcial por região para problemas unidimensionais de transporte de nêutrons monoenergéticos na formulação de ordenadas discretas

Um método de matriz resposta (RM) é descrito para gerar soluções numéricas livres de erros de truncamento espacial para problemas de transporte de nêutrons monoenergéticos e com fonte fixa, em geometria unidimensional na formulação de ordenadas discretas (SN). O método RM com esquema iterativo de inversão parcial por região (RBI) converge valores numéricos para os fluxos angulares nas fronteiras das regiões que coincidem com os valores da solução analítica das equações SN, afora os erros de arredondamento da aritmética finita computacional. Desenvolvemos um esquema numérico de reconstrução espacial, que fornece a saída para os fluxos escalares de nêutrons em qualquer ponto do domínio definido pelo usuário, com um passo de avanço também escolhido pelo usuário. Resultados numéricos são apresentados para ilustrar a precisão do presente método em cálculos de malha grossa.