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A Closed-Form Formulation for the Build-Up Factor and Absorbed Energy for Photons and Electrons in the Compton Energy Range in Cartesian Geometry

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World Journal of Nuclear Science and Technology 2012年第1期2卷 23-28页

作者： Volnei Borges Julio Cesar Fernandes bardo ernest bodmann Marco Túllio Vilhena Bárbara Rodriguez 不详

In this work, we report on a closed-form formulation for the build-up factor and absorbed energy, in one and two di- mensional Cartesian geometry for photons and electrons, in the Compton energy range. For the one-dimensional case we use the LTSN method, assuming the Klein-Nishina scattering kernel for the determination of the angular radiation intensity for photons. We apply the two-dimensional LTSN nodal solution for the averaged angular radiation evaluation for the two-dimensional case, using the Klein-Nishina kernel for photons and the Compton kernel for electrons. From the angular radiation intensity we construct a closed-form solution for the build-up factor and evaluate the absorbed energy. We present numerical simulations and comparisons against results from the literature.

关键词： Build-Up Factor Compton Energy Cartesian Geometry Fokker-Plank Equation

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Air Pollution Steady-State Advection-Diffusion Equation: The General Three-Dimensional Solution

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Journal of Environmental Protection 2012年第9期3卷 1124-1134页

作者： Daniela Buske Marco Túllio Vilhena Tiziano Tirabassi bardo bodmann Department of Mathematics and Statistics (IFM/DME) Federal University of Pelotas (UFPel) Pelotas Brazil Graduate Program in Mechanical Engineering Federal University of Rio Grande do Sul (UFRGS) Porto Alegre Brazil Institute of Atmospheric Sciences and Climate (ISAC) National Research Council (CNR) Bologna Italy

Atmospheric air pollution turbulent fluxes can be assumed to be proportional to the mean concentration gradient. This assumption, along with the equation of continuity, leads to the advection-diffusion equation. Many models simulating air pollution dispersion are based upon the solution (numerical or analytical) of the advection-diffusion equation as- suming turbulence parameterization for realistic physical scenarios. We present the general steady three-dimensional solution of the advection-diffusion equation considering a vertically inhomogeneous atmospheric boundary layer for arbitrary vertical profiles of wind and eddy-diffusion coefficients. Numerical results and comparison with experimental data are shown.

关键词： Advection-Diffusion Equation Analytical Solution Laplace Transform Air Pollution Modeling Atmospheric Boundary Layer Eulerian Models

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On the Build-Up Factor from the Multi-Group Neutron Diffusion Equation with Cylindrical Symmetry

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World Journal of Nuclear Science and Technology 2013年第1期3卷 1-5页

作者： Julio Cesar Lombaldo Fernandes Marco Túllio Vilhena bardo Ernst bodmann Volnei Borges DepartmentofAppliedMath Universidade Federal do Rio Grande do Sul Porto Alegre Brazil

We consider the time dependent neutron diffusion equation for one energy group in cylinder coordinates, assuming translational symmetry along the cylinder axis. This problem for a specific energy group is solved analytically applying the Hankel transform in the radial coordinate r. Our special interest rests in the build-up factor for a time dependent linear neutron source aligned with the cylinder axis, which in the limit of zero decay constant reproduces also the static case. The new approach to solve the diffusion equation by integral transform technique is presented and results for several parameter sets and truncation in the solution for the flux and build-up factor are shown and found to be compatible to those of literature [1,2].

关键词： Build-Up Factor Cylindrical Geometry Hankel Transform

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