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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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This paper considers a numerical solution of a linear elasticity problem, namely the Cauchy-Navier equation, using a strong form method based on a local Weighted Least Squares (WLS) approximation. The main advantage of the employed numerical approach, also referred to as a Meshless Local Strong Form method, is its generality in terms of approximation setup and positions of computational nodes. In this paper, flexibility regarding the nodal position is demonstrated through two numerical examples, i.e. a drilled cantilever beam, where an irregular domain is treated with a relatively simple nodal positioning algorithm, and a Hertzian contact problem, where again, a relatively simple h-refinement algorithm is used to extensively refine discretization under the contact area. The results are presented in terms of accuracy and convergence rates, using different approximations and refinement setups, namely Gaussian and monomial based approximations, and a comparison of execution time for each block of the solution procedure.

Summary This paper proposes an original adaptive refinement framework using radial basis function–generated finite differences method. Node distributions are generated with a Poisson disc sampling–based algorithm from a given continuous density function, which is altered during the refinement process based on the error indicator. All elements of the proposed adaptive strategy rely only on meshless concepts, which leads to great flexibility and generality of the solution procedure. The proposed framework is tested on four gradually more complex contact problems. First, a disc under pressure is considered and the computed stress field is compared to the closed‐form solution of the problem to assess the behaviour of the algorithm and the influence of free parameters. Second, a Hertzian contact problem is studied to analyse the proposed algorithm with an ad hoc error indicator and to test both refinement and derefinement. A contact problem, typical for fretting fatigue, with no known closed‐form solution is considered and solved next. It is demonstrated that the proposed methodology produces results comparable with finite element method without the need for manual refinement or any human intervention. In the last case, generality of the proposed approach is demonstrated by solving a three‐dimensional Boussinesq's problem.

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The temperature dependences of the second moments M2 of the proton magnetic resonance absorption spectra and of the proton spin–lattice relaxation times T1 of perovskite layer compounds (CnH2n+1NH3)2CdCl4 with n=1–3 and (NH3– (CH2)n–NH3) CdCl4 with n=2−5 have been studied together with the frequency dispersion of T1. The structural phase transitions in these compounds were found to be connected with a change in the state of motion of the alkyl or alkylene groups, i.e., by an interplay of transitions between different N–H−−−Cl hydrogen bonding schemes and the excitation of hindered rotations of the hydrocarbon chains.