The purpose of this study was to obtain information on the influence of the size factor on the climatic aging of circular fiber plastics produced by pultrusion. The kinetics of moisture transfer was obtained in humidification and drying modes at 60 °C in samples of epoxy basalt fiber reinforcement bars: after 28 months of exposure in the extremely cold climate of Yakutsk and 30 months of exposure in the moderately warm climate of Gelendzhik. It was shown that the 2D Langmuir model adequately describes the kinetics. The diffusion coefficients in the reinforcement direction for bars with diameters of 6, 8, 10, 16 and 20 mm turned out to be significantly higher than in the radial direction. To clarify the aging mechanism of the bars and the tensile, compressive and bending strength, the coefficient of linear thermal expansion and the glass transition temperature of the epoxy matrix of the bars with a diameter of 6, 8 and 10 mm after 51 months of exposure in Yakutsk and 54 months of exposure in Gelendzhik were measured. It was shown that after climatic exposure, the deformability of the bars decreased with increasing diameter of the bar; the glass transition temperature increased more significantly in the bar with a smaller diameter. In 6 mm diameter bars, the compressive and bending strength limits decreased by 10–25 % due to the plasticizing effect of moisture. With the same depth of moisture penetration into the volume of the samples, its effect on the strength of thin bars was significant, and for thick bars, it was insignificant. An increase in the glass transition temperature by 6 °C, associated with the additional curing of the polymer matrix, occurred in the surface layer of the epoxy basalt fiber reinforcement bars and was revealed in bars with a smaller diameter.

The durability of basalt fiber-reinforced polymer (BFRP) and glass fiber-reinforced polymer (GFRP) composites was evaluated under extreme cold conditions in Yakutsk ($-54$ to $+36$ °C. Laminates (18 layers, epoxy CYD-128) were exposed outdoors for three years. Mechanical testing showed tensile strength and modulus reductions of 22–32% for GFRP, compared with only 6–12% for BFRP. Dynamic mechanical analysis indicated that the glass transition temperature decreased by 11–14 °C in GFRP and 4–6 °C in BFRP. Mass loss kinetics were studied on specimens of different sizes (10 × 10, 20 × 20, and 40 × 40 mm) over 405 days. Seasonal sorption ranged between 0.01–0.19%, while long-term degradation followed a Fickian law with diffusion coefficients of degradation products from $1\times {10}^{-4}$ to $0.29{\mathrm{mm}}^2/\mathrm{day}$. A diffusion-based model was proposed, where total mass change is represented as the superposition of reversible sorption and irreversible degradation. The model accurately reproduced experimental trends, highlighting the higher resistance of BFRP. Surface morphology analysis revealed matrix erosion and microcracking on exposed surfaces, with average roughness increasing from 1.61–5.61 µm to 5.86–11.73 µm. Thermomechanical analysis confirmed that BFRP maintained more stable coefficients of linear thermal expansion ($-60$ to $100$ °C) than GFRP, reducing thermally induced stresses during seasonal cycles. These findings demonstrate the superior stability of BFRP compared with GFRP under cold-climate exposure. Comparison of experimental results with mathematical modeling demonstrated that the primary cause of polymer matrix degradation is the action of abrupt internal stresses arising during thermal cycling under extreme cold climate conditions.

Detailed analyses of the reasons for changes in the mechanical parameters of fiberglass exposed to different climatic zones have been made available in the literature; however, such detailed studies of basalt plastic do not yet exist. It is possible to make reasonable conclusions on the climatic resistance of reinforced plastics by monitoring the deformation–strength characteristics in combination with fractographic and DMA analyses of the solar- and shadow-exposed parts of the plastics; additionally, one can conduct analyses of the IR spectrum and the moisture sorbtion kinetics. As a starting point for the climatic aging of polymer composite materials, it is necessary to accept the time of exposure in which the maximum values of the elastic strength properties of polymeric materials are achieved. Based on the results of the DMA analysis, it was found that, unlike basalt-reinforced plastics (where the material is post-cured exclusively at the initial stage of the exposure), in glass-reinforced plastic, a process of destruction occurs. The formation of internal stresses in the material and their growth were determined through observing the duration of climatic exposure. The formation of closed porosity, depending on the duration of exposure, can be assessed using the values of the increase in the average moisture content. A set of experimental studies has established that glass-reinforced plastics are subject to greater destruction under the influence of a very cold climate than the basalt-reinforced plastic.

The direct Lyapunov method is used to prove the absolute linear instability of steadystate plane-parallel shear flows of an inviscid stratified incompressible fluid in the gravity field with respect to plane perturbations both in the Boussinesq and non-Boussinesq approximations. A strict description is given for the applicability of the known necessary condition for linear instability of steady-state plane-parallel shear flows of an ideal nonuniform (by density) incompressible fluid in the gravity field both in the Boussinesq and non-Boussinesq approximations (the Miles theorem). Analytical examples of illustrative character are constructed.

A quite simple method is proposed for the assessment of extremely cold subarctic climate environment destruction of the basalt fiber reinforced epoxy (BFRE) rebar. The method involves the comparison of experimentally obtained long-term moisture uptake kinetic curves of unexposed and exposed BFRP rebars. A moisture uptake test was carried out at the temperature of 60 °C and relative humidity of 98 ± 2% for 306 days. The plasticization can be neglected because of low-level moisture saturation (<0.41% wt.); the swelling and structural relaxation of the polymer network can be neglected due to the high fiber content of BFRP rebar; moisture diffusion into the basalt fibers can be neglected since it is a much lesser amount than in the epoxy binder. These assumptions made it possible to build a three-stage diffusion model. It is observed that an increase in the density of defects with an increase in the diameter of the BFRP rebar is the result of the technology of manufacturing a periodic profile. The diffusion coefficient of the BFRP rebar with a 6, 10, or 18 mm diameter increased at an average of 82.7%, 56.7%, and 30%, respectively, after exposure to the climate of Yakutsk during 28 months, whereas it was known that the strength indicators had been increased.