A novel two-dimensional finite element method for modelling the diffusion which occurs in Fricke or ferrous sulphate type radiation dosimetry gels is presented. In most of the previous work, the diffusion coefficient has been estimated using simple one-dimensional models. This work presents a two-dimensional model which enables the diffusion coefficient to be determined in a much wider range of experimental situations. The model includes the provision for the determination of a drift parameter. To demonstrate the technique comparative diffusion measurements between ferrous sulphate radiation dosimetry gels, with and without xylenol orange chelating agent and carbohydrate additives have been undertaken. Diffusion coefficients of 9.7 +/- 0.4, 13.3 +/- 0.6 and 9.5 +/- 0.8 10(-3) cm2h-1 were determined for ferrous sulphate radiation dosimetry gels with and without xylenol orange and with xylenol orange and sucrose additives respectively.
Transient acoustic radiation from a closed axisymmetric three-dimensional object is modeled using the time domain boundary element method. The widely reported instability problems are overcome by reformulating the integral equation to obtain a Burton and Miller type equation in the time domain. The stability of such an approach is mathematically justified and supported by subsequent numerical results. The hypersingular integrals which arise are evaluated using a method valid for any surface discretization. Numerical results for the radiation of a spherical wave are presented and compared with an exact solution. The accuracy and stability of the results are verified for several geometrically different radiating objects.
Magnetic resonance imaging (MRI) may be used to image three-dimensional dose distributions of ionizing radiation in tissue equivalent gels infused with ferrous sulphate solutions, commonly known as Fricke gels. In this technique, ferrous (Fe2+) ions are oxidized to ferric (Fe3+) ions by free radicals produced by ionizing radiation. A limitation on this technique is the diffusion of ferric (Fe3+) ions in the gel. A method is presented for evaluating the diffusion coefficient in Fricke gels. Finite elements are used to model variations of the concentration in space, coupled with an analytical scheme to integrate the resulting system of equations through time. This method may be used for problems with one, two or three space dimensions and with arbitrary initial and boundary conditions. Results are presented for one- and two-dimensional data.
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