Spatial Geometric Cells — Quasipolyhedra

Tiling of three-dimensional space is a very interesting and not yet fully explored type of tiling. Tiling by convex polyhedra has been partially investigated, for example, works [1, 15, 20] are devoted to tiling by various tetrahedra, once tiling realized by Platonic, Archimedean and Catalan bodies. The use of tiling begins from ancient times, on the plane with the creation of parquet floors and ornaments, in space - with the construction of houses, but even now new and new areas of applications of tiling are opening up, for example, a recent cycle of work on the use of tiling for packaging information [17]. Until now, tiling in space has been considered almost always by faceted bodies. Bodies bounded by compartments of curved surfaces are poorly considered and by themselves, one can recall the osohedra [14], dihedra, oloids, biconuses, sphericon [21], the Steinmetz figure [22], quasipolyhedra bounded by compartments of hyperbolic paraboloids described in [3] the astroid ellipsoid and hyperbolic tetrahedra, cubes, octahedra mentioned in [6], and tiling bodies with bounded curved surfaces was practically not considered, except for the infinite three-dimensional Schwartz surfaces, but they were also considered as surfaces, not as bodies., although, of course, in each such surface, you can select an elementary cell and fill it with a body, resulting in a geometric cell. With this work, we tried to eliminate this gap and described approaches to identifying geometric cells bounded by compartments of curved surfaces. The concept of tightly packed frameworks is formulated and an approach for their identification are described. A graphical algorithm for identifying polyhedra and quasipolyhedra - geometric cells are described.

Wetting between Cassie–Baxter and Wenzel regimes: a cellular model approach

The cellular model with periodic boundary conditions was proposed for the study of liquid–solid interface properties of solid surfaces decorated by a regular pattern. The solid surface was represented by a mosaic of truncated pyramids of two different slopes of side walls equivalent to a surface covered with triangular grooves of different dihedral angles. On the basis of the computations performed for a single elementary cell, the components of the interfacial energies and the apparent contact angles have been found for different Young contact angles and different tilting angles of the pyramid walls. It was found that at certain sets of angles, the wetting takes place with the partial coverage of the pyramid sidewalls—in between the Cassie–Baxter and Wenzel regimes. The influence of the line tension on the studied surface wettability was also examined. Graphic abstract

Advanced Arc Plasma Synthesis of Biomorphic Silicon Carbide Using Charcoal and Silicon Dioxide in Air

The paper presents the results of experimental studies on the advanced synthesis method for a cubic phase of silicon carbide using charcoal and silicon dioxide as precursors. The charcoal used for the synthesis was obtained by steam pyrolysis of wood wastes (sawdust). It was found that the arc synthesis could be executed in air due to the protective CO and CO2 environment formation by charcoal oxidation. With an increase of the amount of supplied energy by direct current arc plasma synthesis, the products of two crystalline phases were formed: graphite and cubic phase of silicon carbide. The phase of silicon carbide was extracted from the synthesis product by its annealing in air at 850 °C. The resulting cubic SiC phase was characterized by an elementary cell parameter of 4.359 Å. According to the data of scanning electron microscopy, the morphology of crystals obtained is common for the biomorphic silicon carbide which was identified in the synthesis product. The ceramics synthesized by spark plasma sintering from the obtained material was characterized by a density of ~2.0 g/cm3.

Analysis of Compacting Stress in Fibrous Composites Elementary Cell by Mathematical Modeling

The article represents the possibility of determining the compaction stress in the FCM cell, taking into account the self-regulation of fiber displacement during the compaction process. The study is carried out using mathematical modeling methods.

The mapping of raster images on plane isometric grid

Drawing images on curvilinear shapes with the least distortion takes place in many design tasks. In most ways, build a grid, each elementary cell of which is painted a given color. In this problem it is necessary to solve two main problems: the first - to carry out the formation of a given curvilinear grid with elementary cells in the form of squares, which are called isometric (or isothermal); the second is to paint each cell of the curved area with the corresponding pixel color of the original raster The aim of the study is to reveal the way of displaying raster images on flat curvilinear areas represented by isometric grids, and with the help of a computer model in the Maple symbolic algebra to analyze the influence of isometric grid parameters on the position and size of displayed raster images. The mapping of images onto curvilinear forms with minimal distortion takes place in many design tasks. A method of conformal mapping of arbitrary raster images onto plane curvilinear region is proposed, which are represented by isometric (also called isothermal) grids. The essence of the proposed method is as follows. Any raster image, for example, digital photography in jpg format, is characterized by the dimensions N×M - the number of pixels in width and height. In addition, each pixel has a color and brightness, which are arranged in rows and columns. To apply a raster image to a curvilinear region, it is also necessary to divide the curvilinear domain into N×M, the number of elementary squares, each of which is assigned the corresponding color from the raster. The influence and arguments of the various isometric grids constructed on the sizes and positions of an arbitrary raster image are investigated in the article. It is shown how the isometric grid, depending on and localizes the raster image - it can be located both within the limits of the isometric grid coordinate lines and beyond it, can also be oriented in different directions with respect to the and coordinate lines. It is shown the possibility of scaling a raster image that can be performed relative to the relative dimensions of an isometric grid. Since there is a correspondence between the pixel matrix of the original raster image and the - cells of the isometric grid, the rotation of the image will affect its position in the isometric grid. For example, rotating the original bitmap image at an angle 90 degrees will change its location on a plane isometric grids – from along the coordinate lines to along the coordinate lines. Note that, the curvilinear cells of the constructed isometric grids differ somewhat from the shape of the squares because the values and of the corresponding arguments and of their coordinate lines were taken somewhat too large. Otherwise, cells would degenerate into points and the corresponding grid image would not be so clear.

CALCULATION OF VERTICAL DEFORMATIONS OF THE FOUNDATIONS ON THE SOFT SOIL IMPROVED BY GEOTEXTILE ENCASED STONE COLUMNS

The article provides information on research in the field of improving weak clay bases by installing vertical soil piles in a shell of geosynthetic materials (geotextile encased stone columns). This method has proven to be effective for strengthening the foundations of large areal objects in certain soil conditions, but has not become widespread as a method for improving the foundations of building foundations, which, among other things, is due to the lack of simple engineering methods for calculating the improvement parameters. The article presents an engineering technique for determining the settlement of shallow foundations on a weak clay base which is improved by the geotextile encased stone columns. The technique is based on considering the elementary cell of the improved foundation for which the pressure distribution in the weak soil and the improvement element is determined by the iterative enumeration process. This distribution should ensure equality of the vertical deformations of the improvement element and the soft soil, which should be the same due to the stiffness of the foundation of the building or structure. The calculation of the deformations of a geotextile encased stone columns is carried out by solving the Lamé problem and the deformations of soft soil by standard methods presented in the regulatory literature. Comparison of the calculation results by the proposed method with the data of numerical modeling in an axisymmetric setting is presented. In the numerical modeling of the soil, the Mohr-Coulomb elastic-plastic model was used. Geosynthetic reinforcement was modeled using a special element that only accepts tensile stresses. The rigidity of the foundation of the base is taken to be infinitely large. The analysis of the presented simulation results showed good convergence of the calculations with the data of experimental studies and the data of numerical simulation using the finite element method.

Dielectric and Electrical Properties of BLT Ceramics Modified by Fe Ions

The solid solution of the perovskite type structure Ba0.996La0.004Ti1−yFeyO3 (BLTF) for varying iron content (y = 0.1−0.4 mol.%) was obtained as a result of a solid state reaction using the conventional method. At room temperature (Tr < TC), the as-received ceramics reveals a single-phase, tetragonal structure and a P4mm space group. An increase in the iron content causes a slight decrease in the volume of the elementary cell. In addition, this admixture significantly reduces the maximum permittivity value (εm) and the shift of the phase transition temperature (TC) towards lower temperatures. The BLTF solid solution shows a classical phase transition and low values of dielectric loss tangent (tgδ), both at room temperature and in the phase transition area. The Curie–Weiss temperature (T0) and Curie constant (C) were also determined on the basis of the dielectric measurements results. The analysis of temperature changes in DC conductivity revealed presence of the positive temperature coefficient of resistivity (PTCR) effect in the phase transition area.

The Effect of Laser Re-Solidification on Microstructure and Photo-Electrochemical Properties of Fe-Decorated TiO2 Nanotubes

Fossil fuels became increasingly unpleasant energy source due to their negative impact on the environment; thus, attractiveness of renewable, and especially solar energy, is growing worldwide. Among others, the research is focused on smart combination of simple compounds towards formation of the photoactive materials. Following that, our work concerns the optimized manipulation of laser light coupled with the iron sputtering to transform titania that is mostly UV-active, as well as exhibiting poor oxygen evolution reaction to the material responding to solar light, and that can be further used in water splitting process. The preparation route of the material was based on anodization providing well organized system of nanotubes, while magnetron sputtering ensures formation of thin iron films. The last step covering pulsed laser treatment of 355 nm wavelength significantly changes the material morphology and structure, inducing partial melting and formation of oxygen vacancies in the elementary cell. Depending on the applied fluence, anatase, rutile, and hematite phases were recognized in the final product. The formation of a re-solidified layer on the surface of the nanotubes, in which thickness depends on the laser fluence, was shown by microstructure studies. Although a drastic decrement of light absorption was recorded especially in UV range, laser-annealed samples have shown activity under visible light even 20 times higher than bare titania. Electrochemical analysis has shown that the improvement of photoresponse originates mainly from over an order of magnitude higher charge carrier density as revealed by Mott-Schottky analysis. The results show that intense laser light can modulate the semiconductor properties significantly and can be considered as a promising tool towards activation of initially inactive material for the visible light harvesting.

SYNTHESIS AND ELECTRICAL CONDUCTIVITY OF SOLID SOLUTIONS OF THE SYSTEM PbF2–NdF3–SnF2

In the system PbF2–NdF3–SnF2 are formed solid solutions of the heterovalent substitution Pb0,86-хNdхSn1,14F4+х (0 < x ≤ 0,17) with structure of β–PbSnF4. At x > 0,17 on the X-ray diffractograms, in addition to the basic structure, additional peaks are recorded to the reflexes of the individual NdF3. For single-phase solid solutions, the calculated parameters of the crystal lattice are satisfactorily described by the Vegard rule. The introduction of ions of Nd3+ into the initial structure leads to an increase in the parameter с of the elementary cell from 51.267 Å for x = 0,03 to 51.577 Å for x = 0.17. The replacement of a part of leads ions to neodymium ions an increase in electrical conductivity compared with Pb0.86Sn1.14F4. The slight replacement (3.0 mol. %) of Pb2+ ions by Nd3+ in the structure of Pb0.86Sn1.14F4 causes an increase in the electrical conductivity at T> 530 K (6.88·10-2 S/cm compared to 2.41·10-2 S/cm for the initial sample compound Pb0.86Sn1.14F4). In the region of lower temperatures, the electrical conductivity of the samples of this composition decreases, and below that temperature, on the contrary, slightly reduces the electrical conductivity, approaching the values characteristic of β-PbSnF4. The activation energy of the conductivity thus increases over the entire temperature range. A further increase in the concentration of Nd3+ ions in the synthesized samples causes an increase in their fluoride-ion conductivity throughout the temperature range. It should be noted that samples with a content of 10-15 mol% NdF3 at T>500 K have comparable conductivity values. At lower temperatures, the higher the conductivity, the higher the concentration of the substituent. The highest conductivity and the lowest activation energy have the sample Pb0.69Nd0.17Sn1.14F4.17 (σ373=3.68·10-2 S/сm, Ea=0,1 eV). The fluorine anions in synthesized phases are in three structurally-equivalent positions. The charge transfer is provided by the highly mobile interstitial fluorine anions, whose concentration increases with increasing temperature and concentration of NdF3. The transfer numbers for fluorine anions are not less than 0.99, practically independent of the concentration of neodymium trifluoride.