The approaches for discretizing the direction variable in particle transport calculations are the discrete-ordinates method and function-expansion methods. Both approaches are limited if the transport solution is not smooth. Angular discretization errors in the discrete-ordinates method arise from the inability of a given quadrature set to accurately perform the needed integrals over the direction ("angular") domain. We propose that an adaptive discrete-ordinate algorithm will be useful in many problems of practical interest. We start with a "base quadrature set" and add quadrature points as needed in order to resolve the angular flux function. We compare an interpolated angular-flux value against a calculated value. If the values are within a user specified tolerance, the point is not added; otherwise it is. Upon the addition of a point we must recalculate weights. Our interpolatory functions map angular-flux values at the quadrature directions to a continuous function that can be evaluated at any direction. We force our quadrature weights to be consistent with these functions in the sense that the quadrature integral of the angular flux is the exact integral of the interpolatory function (a finite-element methodology that determines coefficients by collocation instead of the usual weightedresidual procedure). We demonstrate our approach in two-dimensional Cartesian geometry, focusing on the azimuthal direction The interpolative methods we test are simple linear, linear in sine and cosine, an Abu-Shumays “base” quadrature with a simple linear adaptive and an Abu-Shumays “base” quadrature with a linear in sine and cosine adaptive. In the latter two methods the local refinement does not reduce the ability of the base set to integrate high-order spherical harmonics (important in problems with highly anisotropic scattering). We utilize a variety of one-group test problems to demonstrate that in all cases, angular discretization errors (including "ray effects") can be eliminated to whatever tolerance the user requests. We further demonstrate through detailed quantitative analysis that local refinement does indeed produce a more efficient placement of unknowns. We conclude that this work introduces a very promising approach to a long-standing problem in deterministic transport, and we believe it will lead to fruitful avenues of further investigation.

The source and nature, as well as the history of ray-effects, is described. A benchmark code, using piecewise constant functions in angle and diamond differencing in space, is derived in order to analyze four sample problems. The results of this analysis are presented showing the ray effects and how increasing the resolution (number of angles) eliminates them. The theory of wavelets is introduced and the use of wavelets in multiresolution analysis is discussed. This multiresolution analysis is applied to the transport equation, and equations that can be solved to calculate the coefficients in the wavelet expansion for the angular flux are derived. The use of thresholding to eliminate wavelet coefficients that are not required to adequately solve a problem is then discussed. An iterative sweeping algorithm, called the SN-WN method, is derived to solve the wavelet-based equations. The convergence of the SN-WN method is discussed. An algorithm for solving the equations is derived, by solving a matrix within each cell directly for the expansion coefficients. This algorithm is called the CWWN method. The results of applying the CW-WN method to the benchmark problems are presented. These results show that more research is needed to improve the convergence of the SN-WN method, and that the CW-WN method is computationally too costly to be seriously considered.

The approaches for discretizing the direction variable in particle transport calculations are the discrete-ordinates method and function-expansion methods. Both approaches are limited if the transport solution is not smooth. Angular discretization errors in the discrete-ordinates method arise from the inability of a given quadrature set to accurately perform the needed integrals over the direction ("angular") domain. We propose that an adaptive discrete-ordinate algorithm will be useful in many problems of practical interest. We start with a "base quadrature set" and add quadrature points as needed in order to resolve the angular flux function. We compare an interpolated angular-flux value against a calculated value. If the values are within a user specified tolerance, the point is not added; otherwise it is. Upon the addition of a point we must recalculate weights. Our interpolatory functions map angular-flux values at the quadrature directions to a continuous function that can be evaluated at any direction. We force our quadrature weights to be consistent with these functions in the sense that the quadrature integral of the angular flux is the exact integral of the interpolatory function (a finite-element methodology that determines coefficients by collocation instead of the usual weightedresidual procedure). We demonstrate our approach in two-dimensional Cartesian geometry, focusing on the azimuthal direction The interpolative methods we test are simple linear, linear in sine and cosine, an Abu-Shumays â baseâ quadrature with a simple linear adaptive and an Abu-Shumays â baseâ quadrature with a linear in sine and cosine adaptive. In the latter two methods the local refinement does not reduce the ability of the base set to integrate high-order spherical harmonics (important in problems with highly anisotropic scattering). We utilize a variety of one-group test problems to demonstrate that in all cases, angular discretization errors (including "ray effects") can be eliminated to whatever tolerance the user requests. We further demonstrate through detailed quantitative analysis that local refinement does indeed produce a more efficient placement of unknowns. We conclude that this work introduces a very promising approach to a long-standing problem in deterministic transport, and we believe it will lead to fruitful avenues of further investigation.

A fotosensibilidade à radiação dos vidros fosfatos é uma propriedade que tem despertado grande interesse nas últimas décadas12. No presente trabalho, foi realizado um estudo sistemático e comparativo dos fenômenos fotoinduzidos por meio da caracterização de filmes do sistema (Sb(PO3)3)n - Sb2O3 quando dopados com óxido de cobre (CuO). Neste estudo, foram observadas as mudanças fotoestruturais e os efeitos causados por ação dos Raios-X. Os danos causados pela radiação sobre as amostras foram investigados através de medidas de perfilometria, Difração de Raio-X, EPR (Electron Paramagnetic Resonance) e SFG (Sum Frequency Generation) para a análise morfológica dos filmes, usadas para a compreensão das mudanças estruturais ocorridas. Além disso, foram realizadas medidas de absorção UV-Vis para a determinação de suas propriedades ópticas. Estudos recentes mostraram que o sistema vítreo (Sb(PO3)3)n - Sb2O3 sofre efeito de fotoclareamento e fotocontração, devido a irradiação com laser UV16. Nossos resultados mostraram que filmes do mesmo sistema vítreo dopados com 3%CuO, quando irradiados com Raio-X, apresentam efeito de fotoescurecimento, que foi observado visivelmente, e fotoexpansão, que foi confirmado por medidas de perfilometria. Ambos os efeitos, fotoescurecimento e fotoexpansão, ocorrem simultaneamente nos filmes irradiados e tem uma evidente dependência com a variação de parâmetros como espessura do filme e tempo de exposição à radiação / The photosensibility to radiation of phosphate glasses is a property that has attracted great interest in the last decades12. In this work, we realized a systematic and comparative study of the photoinduced phenomena through characterization of the doped copper oxide (CuO) (Sb(PO3)3)n-Sb2O3 system films. In this study, we observed the photostructural changes and the effects caused by X-ray. The radiation damage on the samples was investigated by measurements of profilometry, X-ray diffraction, EPR (Electron Paramagnetic Resonance) and SFG (Sum Frequency Generation) for morphological analysis, used for the understanding of the structural changes occurred. Besides that, we realized UV-Vis absorption measurements for the determination of its optical properties. Recents studies have shown the (Sb(PO3)3)n-Sb2O3 glassy system has photobleaching and photocontraction effects, when irradiated with UV laser16. Our results have shown that films of the same glassy system doped with 3%CuO, when irradiated with X-ray, show the photodarkening effect, which was visually observed, and photoexpansion, which was confirmed by profilometry measurements. Both effects, photodarkening and photoexpansion, occur simultaneously in the irradiated films and have a evident dependence with the parameters changes, as film thickness and radiation exposure time.

No description available.

A fotosensibilidade à radiação dos vidros fosfatos é uma propriedade que tem despertado grande interesse nas últimas décadas12. No presente trabalho, foi realizado um estudo sistemático e comparativo dos fenômenos fotoinduzidos por meio da caracterização de filmes do sistema (Sb(PO3)3)n - Sb2O3 quando dopados com óxido de cobre (CuO). Neste estudo, foram observadas as mudanças fotoestruturais e os efeitos causados por ação dos Raios-X. Os danos causados pela radiação sobre as amostras foram investigados através de medidas de perfilometria, Difração de Raio-X, EPR (Electron Paramagnetic Resonance) e SFG (Sum Frequency Generation) para a análise morfológica dos filmes, usadas para a compreensão das mudanças estruturais ocorridas. Além disso, foram realizadas medidas de absorção UV-Vis para a determinação de suas propriedades ópticas. Estudos recentes mostraram que o sistema vítreo (Sb(PO3)3)n - Sb2O3 sofre efeito de fotoclareamento e fotocontração, devido a irradiação com laser UV16. Nossos resultados mostraram que filmes do mesmo sistema vítreo dopados com 3%CuO, quando irradiados com Raio-X, apresentam efeito de fotoescurecimento, que foi observado visivelmente, e fotoexpansão, que foi confirmado por medidas de perfilometria. Ambos os efeitos, fotoescurecimento e fotoexpansão, ocorrem simultaneamente nos filmes irradiados e tem uma evidente dependência com a variação de parâmetros como espessura do filme e tempo de exposição à radiação / The photosensibility to radiation of phosphate glasses is a property that has attracted great interest in the last decades12. In this work, we realized a systematic and comparative study of the photoinduced phenomena through characterization of the doped copper oxide (CuO) (Sb(PO3)3)n-Sb2O3 system films. In this study, we observed the photostructural changes and the effects caused by X-ray. The radiation damage on the samples was investigated by measurements of profilometry, X-ray diffraction, EPR (Electron Paramagnetic Resonance) and SFG (Sum Frequency Generation) for morphological analysis, used for the understanding of the structural changes occurred. Besides that, we realized UV-Vis absorption measurements for the determination of its optical properties. Recents studies have shown the (Sb(PO3)3)n-Sb2O3 glassy system has photobleaching and photocontraction effects, when irradiated with UV laser16. Our results have shown that films of the same glassy system doped with 3%CuO, when irradiated with X-ray, show the photodarkening effect, which was visually observed, and photoexpansion, which was confirmed by profilometry measurements. Both effects, photodarkening and photoexpansion, occur simultaneously in the irradiated films and have a evident dependence with the parameters changes, as film thickness and radiation exposure time.