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Often, detailed simulations of heat conduction in complicated, porous media have large runtimes. Then homogenization is a powerful tool to speed up the calculations by preserving accurate solutions at the same time. Unfortunately real structures are generally non-periodic, which requires unpractical, complicated homogenization techniques. We demonstrate in this paper, that the application of simple, periodic techniques to realistic media, that are just close to periodic, gives accurate, approximative solutions. In order to obtain effective parameters for the homogenized heat equation, we have to solve a so called “cell problem”. In contrast to periodic structures it is not trivial to determine a suitable unit cell, which represents a non-periodic media. To overcome this problem, we give a rule of thumb on how to choose a good cell. Finally we demonstrate the efficiency of our method for virtually generated foams as well as real foams and compare these results to periodic structures.
We present a concise mini overview on the approaches to the disposal of nuclear waste currently used or deployed. The disposal of nuclear waste is the end point of nuclear waste management (NWM) activities and is the emplacement of waste in an appropriate facility without the intention to retrieve it. The IAEA has developed an internationally accepted classification scheme based on the end points of NWM, which is used as guidance. Retention times needed for safe isolation of waste radionuclides are estimated based on the radiotoxicity of nuclear waste. Disposal facilities usually rely on a multi-barrier defence system to isolate the waste from the biosphere, which comprises the natural geological barrier and the engineered barrier system. Disposal facilities could be of a trench type, vaults, tunnels, shafts, boreholes, or mined repositories. A graded approach relates the depth of the disposal facilities’ location with the level of hazard. Disposal practices demonstrate the reliability of nuclear waste disposal with minimal expected impacts on the environment and humans.