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In this paper we present an algorithm that is able to generate locally regular node layouts with spatially variable nodal density for interiors of arbitrary domains in two, three and higher dimensions. It is demonstrated that the generated node distributions are suitable to use in the RBF-FD method, which is demonstrated by solving thermo-fluid problem in 2D and 3D. Additionally, local minimal spacing guarantees are proven for both uniform and variable nodal densities. The presented algorithm has time complexity O(N ) to generate N nodes with constant nodal spacing and O(N log N ) to generate variably spaced nodes. Comparison with existing algorithms is performed in terms of node quality, time complexity, execution time and PDE solution accuracy.

The dependence of the water self-diffusion coefficients as well as of the proton spin-lattice and spin-spin relaxation rates on the concentration have been studied in the gelatin-water system and in hydrated native collagen. The bound and free water fractions and the corresponding spinspin and spin-lattice relaxation rates have been determined within the multi-phase water proton exchange model. Various theoretical models for the water proton cross-relaxation to the biopolymer have been studied and the results compared with the observed Larmor frequency dependence of the water proton spin-lattice relaxation rate.

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