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This report satisfies the U.S. Department of Energy, National Nuclear Security Administration Nevada Field Office (NNSA/NFO) commitment to prepare a quarterly summary of waste shipments to the Nevada National Security Site (NNSS) Radioactive Waste Management Complex (RWMC) in Area 5.
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Consider the class of zero-mean functions with fixed L ∞ and L 1 norms and exactly N ϵ N nodal points. Which functions f minimize W p (f + ,f – ), the Wasserstein distance between the measures whose densities are the positive and negative parts? We provide a complete solution to this minimization problem on the line and the circle, which provides sharp constants for previously proven “uncertainty principle”-type inequalities, i.e., lower bounds on N • W p (f + ,f – ). We further show that, while such inequalities hold in many metric measure spaces, they are no longer sharp when the non-branching assumption is violated; indeed, for metric star-graphs, the optimal lower bound on W p (f + ,f – ) is not inversely proportional to the size of the nodal set, N. Here, based on similar reductions, we make connections between the analogous problem of minimizing W p (f + ,f – ) for f defined on Ω C R d with an equivalent optimal domain partition problem.
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Cement-based materials are more and more recognized as fractal materials. From a practical point of view, fractality means that the pore size distribution can be described using fractal scaling law (i.e. power functions). Here, the simplest scaling law making use of a single fractal dimension was used to generate simple and virtual fractal porous media (based on bundles of parallel cylindrical pores). The capillary curve and permeability (relative and intrinsic) of the virtual porous media were then estimated through theoretical and numerical approaches. The results show that: (1) although bereft of any physical basis, van Genuchten equation bears some fractal information; (2) although highly flexible, van Genuchten equation fails to perfectly fit the capillary curves and can thus generate error in inverse analysis (for intrinsic permeability evaluation) and (3) there seems to be a relation between the intrinsic permeability and van Genuchten pressure parameter.
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