The design of advanced nanostructured materials with predetermined physical properties requires knowledge of the relationship between these properties and the internal structure of the material at the nanoscale, as well as the dependence of the internal structure on the production (synthesis) parameters. This work is the first report of computer-aided analysis of high pressure consolidation (cold sintering) of bimetallic nanoparticles of two immiscible (Fe and Cu) metals using the embedded atom method (EAM). A detailed study of the effect of cold sintering parameters on the internal structure and properties of bulk Fe–Cu nanocomposites was conducted within the limitations of the numerical model. The variation of estimated density and bulk porosity as a function of Fe-to-Cu ratio and consolidation pressure was found in good agreement with the experimental data. For the first time, topological analysis using Minkowski functionals was applied to characterize the internal structure of a bimetallic nanocomposite. The dependence of topological invariants on input processing parameters was described for various components and structural phases. The model presented allows formalizing the relationship between the internal structure and properties of the studied nanocomposites. Based on the obtained topological invariants and Hadwiger’s theorem we propose a new tool for computer-aided design of bimetallic Fe–Cu nanocomposites.

We present a methodology for a numerical analysis of three-dimensional tomographic images in this paper. The methodology is based on integral geometry, topology, and morphological analysis methods. It involves calculating cumulative and non-cumulative pore size distributions of Minkowski functionals and Betti numbers. We investigated 13 samples in dry and wet (saturated beyond the field capacity) conditions within different horizons of the Phaeozem albic. For samples of the arable horizon, an increase in the Euler characteristic was observed in the process of wetting. For samples from the A2, AB and B2 horizons, the Euler-Poincare characteristic decreased during wetting. It has been proven that both Betti numbers (number of isolated pores and number of “tunnels”) decrease with swelling of the AB and B2 horizons at a depth of 20–90 cm. For samples from the arable horizon, another dependence was observed: A Betti number of zero increased first but decreased during wetting. Based on the change in topological characteristics, two methods of changing the topology of the void space of the soil were demonstrated. The above-described quantitative changes of proposed parameters of pore space tomographic images prove the possibility and progressiveness of their usage for the pore space transformation estimate.

The technique of numerical analysis of three-dimensional tomographic images of the pore space of soil objects has been used in this paper. It applies methods of integral geometry, topology and morphological analysis. To characterize quantitatively the transformation of the pore space structure, tomographic images of four undisturbed soils were analyzed, i.e., heavy loamy agro-gray soil (Retic Phaeozem), agromineral (Sapric Rheic Mineralic Histosols), and hypnum (brown moss Sapric Rheic Histosols) peat soils in dry and wet conditions. For samples of the subplow horizon in agro-gray soil, a decrease in both Betty numbers was observed on wetting, where the zero number (b0) stands for the amount of topologically simple closed pores, and the first number (b1) indicates a decrease in pore connectivity, which varies in a narrower range of pore sizes as compared to b0. When a sample of agromineral peat soil is moistened, the Euler–Poincaré characteristic is negative ​in the pore range of 0.1–0.16 mm, which points to the predominating complicated branched structure of the pore space and high pore connectivity. When hypnum moss is saturated, a lot of tunnel pores get narrower (“collapse”), and the connectivity decreases due to the structural specifics of long-stemmed plant residues. The number of pores and connections between them in peat soils is an order of magnitude higher than those in the subplow horizon A of the agro-gray soil. The provided quantitative changes in the considered parameters of tomographic images of the soil pore space confirm the possibility of applying them for estimating the transformation of the pore space in soils.

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Nowadays material science involves powerful 3D imaging techniques such as X-ray computed tomography that generates high-resolution images of different structures. These methods are widely used to reveal information about the internal structure of geological cores; therefore, there is a need to develop modern approaches for quantitative analysis of the obtained images, their comparison, and classification. Topological persistence is a useful technique for characterizing the internal structure of 3D images. We show how persistent data analysis provides a useful tool for the classification of porous media structure from 3D images of hydrocarbon reservoirs obtained using computed tomography. We propose a methodology of 3D structure classification based on geometry-topology analysis via persistent homology.