Marco Vilhena

In this work, we present a review of the GILTT (Generalized Integral Laplace Transform Technique) solutions for the one and two-dimensional, time-dependent, advection-diffusion equations focusing the application to pollutant dispersion simulation in atmosphere, assuming both Fickian and counter-gradient models for a wide class of problems. For sake of completeness, we also report numerical simulations and statistical comparisons with experimental data and results of literature.

An analytical method to solve the advection-diffusion equation is described in this paper. The model is based on a discretization of the planetary boundary layer in N sub-layers. In each sub-layer the advection-diffusion equation is solved by the Laplace transform technique, considering averaged values for the eddy diffusivity and the wind speed. As a consequence, the present approach allows us to employ realistic semi-empirical profiles for the eddy diffusivity and wind speed, in such a way that the inhomogeneous turbulence can be handled. By using the Prairie Grass data set the model performance is evaluated against experimental ground-level concentrations.

In this work an algebraic formulation to evaluate the eddy diffusivities in the Convective Boundary Layer (CBL) is derived. The expression depends on the turbulence properties (z height dependence) and the distance from the source. It is based on the turbulent kinetic energy spectra and Taylor's statistical diffusion theory. It has been tested and compared through an experimental dataset, with another complex integral formulation taken from the literature. The agreement between the complex integral formulation and simple algebraic expression points out that this new parameterization is valid and can be used as a surrogate for eddy diffusivities in the inhomogeneous convective turbulence present in the CBL. The validation shows that the proposed algebraic vertical eddy diffusivity is suitable for application in advanced air quality regulatory models.

Firstly, an analytical solution for the one-dimensional discrete ordinates equation (Sn equations - an approximation of the one-dimensional linear Boltzmann transport equation) in cylindrical geometry and isotropic scattering is computed by the integral transform technique, namely the Hankel transform technique, dubbed as HTSN solution. The main idea relies on the application of the Hankel transform to the set of ordinary differential equations (Sn equations). Secondly, an outline for anisotropic problem in cylindrical geometry is addressed by means of a decomposition method.

Simultaneous estimation of bioluminescence source term and boundary conditions from in situ irradiance data is presented. Inverse analysis is performed by solving a nonlinear optimization problem, where the objective function is given by the square difference between experimental and computed data plus a regularization term. The forward problem is tackled with the LTSn method that numerically solves the radiative transfer equation. The experimental data are simulated with synthetic data corrupted with noise.

The present article is an attempt to provide a parametrization for particle acceleration probabilities in the very high energy range combining a discrete fractal scheme for interaction probabilities and the observational fact of a power law energy spectrum for cosmic ray particles.

RESUMO. O fluxo turbulento de concentração pode ser assumido como proporcional à magnitude do gradiente de concentração média. Esta hipótese, juntamente com a equação da continuidade, conduz à equação de difusão-advecção e uma parametrização da camada limite planetária. Neste trabalho, as performances de alguns coeficientes de difusão sugeridos na literatura são avaliadas usando uma recente solução analítica bidimensional estacionária da equação de difusão-advecção aplicada ao experimento de Copenhagen. ABSTRACT. 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 and a parameterisation of planetary boundary layer. In this work, the performances of some eddy diffusivities schemes suggested in literature have been evaluated using a recent steady-state two-dimensional analytical solution of advection-diffusion equation applied t...

ABSTRACT In the last decade Vilhena and coworkers reported an analytical solution to the two-dimensional nodal discrete-ordinates approximations of the neutron transport equation in a convex domain. The key feature of these works was the application of the combined collocation method of the angular variable and nodal approach in the spatial variables. By nodal approach we mean the transverse integration of the SN equations. This procedure leads to a set of one-dimensional S{sub N} equations for the average angular fluxes in the variables x and y. These equations were solved by the old version of the LTS{sub N} method, which consists in the application of the Laplace transform to the set of nodal S{sub N} equations and solution of the resulting linear system by symbolic computation. It is important to recall that this procedure allow us to increase N the order of S{sub N} up to 16. To overcome this drawback we step forward performing a spectral painstaking analysis of the nodal S{sub N} equations for N up to 16 and we begin the convergence of the S{sub N} nodal equations defining an error for the angular flux and estimating the error in terms of the truncation error of the quadrature approximations of the integral term. Furthermore, we compare numerical results of this approach with those of other techniques used to solve the two-dimensional discrete approximations of the neutron transport equation. (authors)

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Controlled nuclear reactions in a nuclear reactor are one of the energy resources that may contribute to attend the increasing energy demand while minimizing impact on the environment. Because of its efficient energy release per nuclear reaction in comparison to processes that involve chemical reactions for instance (which differ by more than eight orders in magnitude) reactor control and safety is a crucial issue. Evidently, while designing new reactor conceptions or operating existing reactors the microscopic as well as macroscopic response of the nuclear process must be understood in detail and described adequately in terms of mathematical models together with experimental data such as the nuclear reaction cross sections (Sekimoto 2007). The physics of the nuclear reactions taking place in a power reactor and its influence on the neutron flux by perturbations from inside or outside the system are known reasonably well. Nevertheless, as the present contribution will show there is ...

The structure of the stratified atmospheric boundary layer (ABL) over a flat uniform terrain is fairly well understood, but many known results remain mathematically unjustified. A number of factors contribute to this situation, the diversity of physical processes acting on the flow probably being the most important one. Much has been accomplished in the past in the fields of meteorology and fluid mechanics by the use of perturbation techniques. In this way, the atmospheric flow over small topographic features was addressed by (Towsend, 1972). The authors of (Knight, 1977) studied the turbulent flow over wavy surfaces and in (Jackson and Hunt, 1975) a two-layer structure for the ABL over a gentle hill was proposed. Another work (Sykes, 1980) used the asymptotic expansion method to study the influence of small terrain elevations on the main flow and on turbulence. The same idea was improved in (Hunt et al., in Quart. J. Roy. Meteor. Soc., 114:1435 1988), (Hunt et al., in Quart. J. Roy...

1.1 Introduction Fundamental Solutions play an essential role in numerical methods as the Boundary Elements Method (BEM) and Fundamental Solutions Method (FSM). Important properties and their eciency come from these solutions, which can be the response of an innite or semi-innite domain subjected to a point load and submitted to radiation boundary conditions (Sommerfeld Type). Material's inuence on mechanical and thermal responses of structures has been studied for decades. The generalized Hooke's Law describes a stress-strain linear relationship in elastic solids, in which several crystals and metals can be included. Due to the internal symmetries and to the crystalline lattice's form, all the elastic materials can be arranged into eight dierent symmetries ([CoMe95], [ChVi01]). The Hooke's Law counterpart in heat conduction in solids is known as Fourier's Law, which describes a relationship between the heat ux and the temperature's distribution. It is expres...

ABSTRACT In this work we present a variational approach to some methods to solve transport problems of neutral particles. We consider a convex domain X (for example the geometry of slab, or a convex set in the plane, or a convex bounded set in the space) and we use discrete ordinates quadrature to get a system of differential equations derived from the neutron transport equation. The boundary conditions are vacuum for a subset of the boundary, and of specular reflection for the complementary subset of the boundary. Recently some different approximation methods have been presented to solve these transport problems. We introduce in this work the adjoint equations and the conjugate functions obtained by means of the variational approach. First we consider the general formulation, and then some numerical methods such as spherical harmonics and spectral collocation method.

ABSTRACT Generalized discrete ordinates (SN) methods for steady-state monoenergetic neutral particle transport problems in slab geometry are developed for arbitrary order L of scattering anisotropy including odd-order N of Gauss–Legendre quadrature sets, provided L≤N−1. The Laplace transform (LTSN) method is applied to solve analytically the SN problems in homogeneous slabs. Numerical results are given to analyze the accuracy of the odd-order Gauss–Legendre SN formulations.

ABSTRACT In the present contribution the equation of radiative-conductive transfer in a plane parallel heterogeneous medium is solved without linearization or a reduction to a diffusion equation. The approach used in this study maintains the nonlinearity that represents the crucial ingredient in the problem. The solution of the discretized problem in the angular variable can be given in closed analytical form, which permits to calculate numerical results in principle to any desired accuracy. Moreover, the influence of the nonlinearity can be analyzed in an analytical fashion directly from the formal solution.

The spectral method is used to develop a solution for multidimensional transport problems for neutral particles in cartesian geometry. The procedure is based on the expansion of the angular flux in a truncated series of orthogonal polynomials that results in the transformation of the multidimensional problem into a set of one-dimensional problems, whose solutions are well established. The convergence of

An analytical solution of the point kinetics equations to calculate time-dependent reactivity by the decomposition method has recently appeared in the literature. In this paper, we consider the neutron point kinetics equations together with temperature feedback effects. To this end, point kinetics is perturbed by a temperature equation that depends on the neutron density, obtaining a second-order non-linear ordinary differential equation. This equation is then solved by the decomposition method by expanding the neutron density in a series and expressing the non-linear terms by Adomian polynomials. Upon substituting these expansions into the non-linear ordinary equation, we construct a recursive set of linear problems that can be solved and resulting in an exact analytical representation for the solution. We also report numerical simulations and comparison against literature results.

ABSTRACT Country-Specific Mortality and Growth Failure in Infancy and Yound Children and Association With Material Stature Use interactive graphics and maps to view and sort country-specific infant and early dhildhood mortality and growth failure data and their association with maternal