Asymmetric MRI magnet design using a hybrid numerical method

This paper describes a hybrid numerical method for the design of asymmetric magnetic resonance imaging magnet systems. The problem is formulated as a field synthesis and the desired current density on the surface of a cylinder is first calculated by solving a Fredholm equation of the first kind. Nonlinear optimization methods are then invoked to fit practical magnet coils to the desired current density. The field calculations are performed using a semi-analytical method. A new type of asymmetric magnet is proposed in this work. The asymmetric MRI magnet allows the diameter spherical imaging volume to be positioned close to one end of the magnet. The main advantages of making the magnet asymmetric include the potential to reduce the perception of claustrophobia for the patient, better access to the patient by attending physicians, and the potential for reduced peripheral nerve stimulation due to the gradient coil configuration. The results highlight that the method can be used to obtain an asymmetric MRI magnet structure and a very homogeneous magnetic field over the central imaging volume in clinical systems of approximately 1.2 m in length. Unshielded designs are the focus of this work. This method is flexible and may be applied to magnets of other geometries. (C) 1999 Academic Press.

Method of numerical correction of errors occasioned by delay of records during the monitoring of environmental variables of interest for animal production

Thermal and air conditions inside animal facilities change during the day due to the influence of the external environment. For statistical and geostatistical analyses to be representative, a large number of points spatially distributed in the facility area must be monitored. This work suggests that the time variation of environmental variables of interest for animal production, monitored within animal facility, can be modeled accurately from discrete-time records. The aim of this study was to develop a numerical method to correct the temporal variations of these environmental variables, transforming the data so that such observations are independent of the time spent during the measurement. The proposed method approached values recorded with time delays to those expected at the exact moment of interest, if the data were measured simultaneously at the moment at all points distributed spatially. The correction model for numerical environmental variables was validated for environmental air temperature parameter, and the values corrected by the method did not differ by Tukey's test at 5% significance of real values recorded by data loggers.

Method of numerical correction of errors occasioned by delay of records during the monitoring of environmental variables of interest for animal production

As condições de ambiente térmico e aéreo, no interior de instalações para animais, alteram-se durante o dia, devido à influência do ambiente externo. Para que análises estatísticas e geoestatísticas sejam representativas, uma grande quantidade de pontos distribuídos espacialmente na área da instalação deve ser monitorada. Este trabalho propõe que a variação no tempo das variáveis ambientais de interesse para a produção animal, monitoradas no interior de instalações para animais, pode ser modelada com precisão a partir de registros discretos no tempo. O objetivo deste trabalho foi desenvolver um método numérico para corrigir as variações temporais dessas variáveis ambientais, transformando os dados para que tais observações independam do tempo gasto durante a aferição. O método proposto aproximou os valores registrados com retardos de tempo aos esperados no exato momento de interesse, caso os dados fossem medidos simultaneamente neste momento em todos os pontos distribuídos espacialmente. O modelo de correção numérica para variáveis ambientais foi validado para o parâmetro ambiental temperatura do ar, sendo que os valores corrigidos pelo método não diferiram pelo teste Tukey, a 5% de probabilidade dos valores reais registrados por meio de dataloggers.

A study of a numerical solution of the steady two dimensions Navier-Stokes equations in a constricted channel problem by a compact fourth order method

We present a numerical solution for the steady 2D Navier-Stokes equations using a fourth order compact-type method. The geometry of the problem is a constricted symmetric channel, where the boundary can be varied, via a parameter, from a smooth constriction to one possessing a very sharp but smooth corner allowing us to analyse the behaviour of the errors when the solution is smooth or near singular. The set of non-linear equations is solved by the Newton method. Results have been obtained for Reynolds number up to 500. Estimates of the errors incurred have shown that the results are accurate and better than those of the corresponding second order method. (C) 2002 Elsevier B.V. All rights reserved.

Electroosmotic pumping in rectangular microchannels: A numerical treatment by the finite element method

In this work, the analysis of electroosmotic pumping mechanisms in microchannels is performed through the solution of Poisson-Boltzmann and Navier Stokes equations by the Finite Element Method. This approach is combined with a Newton-Raphson iterative scheme, allowing a full treatment of the non-linear Poisson-Boltzmann source term which is normally approximated by linearizations in other methods.

An efficient nonlinear transformation for the numerical computation of the singular integrals appearing in the 2-D Boundary Element Method

We discuss several methods, based on coordinate transformations, for the evaluation of singular and quasisingular integrals in the direct Boundary Element Method. An intrinsec error of some of these methods is detected. Two new transformations are suggested which improve on those currently available.

Application of X-ray microtomography to numerical simulations of agglomerate breakage by distinct element method

Computer-aided tomography has been used for many years to provide significant information about the internal properties of an object, particularly in the medical fraternity. By reconstructing one-dimensional (ID) X-ray images, 2D cross-sections and 3D renders can provide a wealth of information about an object's internal structure. An extension of the methodology is reported here to enable the characterization of a model agglomerate structure. It is demonstrated that methods based on X-ray microtomography offer considerable potential in the validation and utilization of distinct element method simulations also examined.

Monte Carlo Method for Reconstruction of Densities

2000 Mathematics Subject Classification: 65C05

Symmetric Interior Penalty DG Methods for the Compressible Navier-Stokes Equations I: Method Formulation

In this article we consider the development of discontinuous Galerkin finite element methods for the numerical approximation of the compressible Navier-Stokes equations. For the discretization of the leading order terms, we propose employing the generalization of the symmetric version of the interior penalty method, originally developed for the numerical approximation of linear self-adjoint second-order elliptic partial differential equations. In order to solve the resulting system of nonlinear equations, we exploit a (damped) Newton-GMRES algorithm. Numerical experiments demonstrating the practical performance of the proposed discontinuous Galerkin method with higher-order polynomials are presented.

Method of numerical correction of errors occasioned by delay of records during the monitoring of environmental variables of interest for animal production

As condições de ambiente térmico e aéreo, no interior de instalações para animais, alteram-se durante o dia, devido à influência do ambiente externo. Para que análises estatísticas e geoestatísticas sejam representativas, uma grande quantidade de pontos distribuídos espacialmente na área da instalação deve ser monitorada. Este trabalho propõe que a variação no tempo das variáveis ambientais de interesse para a produção animal, monitoradas no interior de instalações para animais, pode ser modelada com precisão a partir de registros discretos no tempo. O objetivo deste trabalho foi desenvolver um método numérico para corrigir as variações temporais dessas variáveis ambientais, transformando os dados para que tais observações independam do tempo gasto durante a aferição. O método proposto aproximou os valores registrados com retardos de tempo aos esperados no exato momento de interesse, caso os dados fossem medidos simultaneamente neste momento em todos os pontos distribuídos espacialmente. O modelo de correção numérica para variáveis ambientais foi validado para o parâmetro ambiental temperatura do ar, sendo que os valores corrigidos pelo método não diferiram pelo teste Tukey, a 5% de probabilidade dos valores reais registrados por meio de dataloggers.

Wavelets And Adaptive Grids For The Discontinuous Galerkin Method

In this paper, space adaptivity is introduced to control the error in the numerical solution of hyperbolic systems of conservation laws. The reference numerical scheme is a new version of the discontinuous Galerkin method, which uses an implicit diffusive term in the direction of the streamlines, for stability purposes. The decision whether to refine or to unrefine the grid in a certain location is taken according to the magnitude of wavelet coefficients, which are indicators of local smoothness of the numerical solution. Numerical solutions of the nonlinear Euler equations illustrate the efficiency of the method. © Springer 2005.

Bending of stochastic Kirchhoff plates on Winkler foundations via the Galerkin method and the Askey-Wiener scheme

In this paper, the method of Galerkin and the Askey-Wiener scheme are used to obtain approximate solutions to the stochastic displacement response of Kirchhoff plates with uncertain parameters. Theoretical and numerical results are presented. The Lax-Milgram lemma is used to express the conditions for existence and uniqueness of the solution. Uncertainties in plate and foundation stiffness are modeled by respecting these conditions, hence using Legendre polynomials indexed in uniform random variables. The space of approximate solutions is built using results of density between the space of continuous functions and Sobolev spaces. Approximate Galerkin solutions are compared with results of Monte Carlo simulation, in terms of first and second order moments and in terms of histograms of the displacement response. Numerical results for two example problems show very fast convergence to the exact solution, at excellent accuracies. The Askey-Wiener Galerkin scheme developed herein is able to reproduce the histogram of the displacement response. The scheme is shown to be a theoretically sound and efficient method for the solution of stochastic problems in engineering. (C) 2009 Elsevier Ltd. All rights reserved.

GENERALIZED FINITE ELEMENT METHOD FOR NONLINEAR THREE-DIMENSIONAL ANALYSIS OF SOLIDS

The Generalized Finite Element Method (GFEM) is employed in this paper for the numerical analysis of three-dimensional solids tinder nonlinear behavior. A brief summary of the GFEM as well as a description of the formulation of the hexahedral element based oil the proposed enrichment strategy are initially presented. Next, in order to introduce the nonlinear analysis of solids, two constitutive models are briefly reviewed: Lemaitre`s model, in which damage and plasticity are coupled, and Mazars`s damage model suitable for concrete tinder increased loading. Both models are employed in the framework of a nonlocal approach to ensure solution objectivity. In the numerical analyses carried out, a selective enrichment of approximation at regions of concern in the domain (mainly those with high strain and damage gradients) is exploited. Such a possibility makes the three-dimensional analysis less expensive and practicable since re-meshing resources, characteristic of h-adaptivity, can be minimized. Moreover, a combination of three-dimensional analysis and the selective enrichment presents a valuable good tool for a better description of both damage and plastic strain scatterings.

Consolidation of elastic-plastic saturated porous media by the boundary element method

This paper presents a domain boundary element formulation for inelastic saturated porous media with rate-independent behavior for the solid skeleton. The formulation is then applied to elastic-plastic behavior for the solid. Biot`s consolidation theory, extended to include irreversible phenomena is considered and the direct boundary element technique is used for the numerical solution after time discretization by the implicit Euler backward algorithm. The associated nonlinear algebraic problem is solved by the Newton-Raphson procedure whereby the loading/unloading conditions are fully taken into account and the consistent tangent operator defined. Only domain nodes (nodes defined inside the domain) are used to represent all domain values and the corresponding integrals are computed by using an accurate sub-elementation scheme. The developments are illustrated through the Drucker-Prager elastic-plastic model for the solid skeleton and various examples are analyzed with the proposed algorithms. (c) 2008 Elsevier B.V. All rights reserved.