Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences

This issue of the journal commemorates the 95$^\mathrm{th}$ anniversary of the Moscow Aviation Institute (MAI) and the 55$^\mathrm{th}$ anniversary of its Institute of Computer Science and Applied Mathematics, featuring scientific contributions from the Institute's staff. The focus lies on presenting the Institute as a leading center that combines fundamental mathematical training with project-based learning in cutting-edge IT technologies.

The annotation highlights the Institute's achievements in education, including its participation in a pilot project to reform higher education and its success in a competition to establish a Center for training top-level IT specialists. The key research priorities of the Institute are outlined, encompassing numerical modeling, fluid and gas mechanics, and optimization, with their results being implemented at enterprises of the United Aircraft Corporation, the United Engine Corporation, and Roscosmos. The Institute's role as a scientific and methodological center is underscored by the operation of two doctoral dissertation councils.

This study develops an analytical framework for mathematical modeling of locally nonequilibrium heat transfer in the context of boundary value problems for hyperbolic-type equations with generalized boundary conditions. Nonstandard operational relations based on the Laplace transform and their corresponding originals, which are absent from known handbooks on operational calculus, are presented. The obtained image–original relations are characteristic of operational solutions to a broad class of generalized boundary value problems arising in various branches of mathematical physics (heat conduction, diffusion, hydrodynamics, oscillation theory, electrodynamics, thermomechanics). The lack of a developed mathematical apparatus, including complex operational relations, has previously precluded the existence of functional constructs serving as exact analytical solutions for this class of heat transfer problems. The present study proposes an approach to solving this problem and significantly expands the analytical capabilities in the field of generalized locally nonequilibrium heat transfer problems. Solutions for partially bounded and finite domains of canonical shape are provided as illustrations.

This study addresses the challenge of enhancing the accuracy of Earth's polar motion modeling. Observational data indicate that variations in the parameters of the principal oscillatory modes (Chandler and annual wobbles) exhibit a component synchronous with the precession of the lunar orbit ($\sim 18.61$ years), which remains unaccounted for in standard models incorporating geophysical excitations. To incorporate this effect, a refined dynamic model is proposed and formulated as a system of differential equations with periodic coefficients dependent on the longitude of the Moon's ascending node.
Through numerical simulations based on International Earth Rotation and Reference Systems Service (IERS) data for the period 1976--2025, the optimal parameters of the model are determined: the lunar node coupling coefficient $\chi = 0.07$ and the quality factor $Q = 63$. The inclusion of the long-period lunar forcing is shown to reduce the standard deviation of the model from the observations. In test simulations, the accuracy in determining the pole position improves by an amount corresponding to 3.7 cm on the Earth's surface, with a maximum achievable improvement of up to 5 cm.
These results substantiate the necessity of explicitly incorporating long-period variations linked to the lunar orbit into high-precision models of polar motion.

This study investigates the potential of parallel implementation of the Ant Colony Optimization (ACO) method on SIMT accelerators. Known modifications of the parallel ant colony method have demonstrated effectiveness in solving Traveling Salesman Problem (TSP) and Quadratic Assignment Problem (QAP). However, the need for data synchronization and exchange limits performance, achieving maximum efficiency in coarse-grained algorithms where each thread executes a complete ACO version. With the development and increasing availability of SIMT accelerators, this study proposes a modification of the numerical ant colony optimization method based on matrix formalization of the computational process. The proposed approach extends the applicability of the method to parametric problems aimed at finding optimal parameter values that minimize or maximize the objective function. A parallel computing algorithm has been developed that minimizes information exchange between agents. The algorithm consists of three stages: preparation of matrices for ant-agent movement, determination of ant-agent paths, and updating matrices based on found solutions. Computational complexity reduction is achieved by representing the optimization problem as a parametric graph with decomposition of parameter value sets into sublayers. Among the studied modifications of the ant colony method, ACOCNI and ACOCCyI were considered with an improved probability formula for algorithmic efficiency and hash table application for enhanced exploration phase. The proposed modifications were implemented on GPUs using CUDA technology. Experimental results show more than 15-fold acceleration of the parallel ant colony method when searching for optima of multimodal functions. Future research directions include implementation of the proposed algorithm on heterogeneous computing systems combining SIMT and MIMD components.

This study addresses the complex problem of heat and mass transfer modeling in thermal protection composite materials subjected to heating of high intensity. The study examines the process of binder thermal decomposition, which results in the formation of a gaseous phase and a porous coke residue, followed by gas filtration through this residue and its injection into the gas-dynamic boundary layer. A Stefan-type problem with two moving boundaries defining the decomposition zone is formulated and solved analytically. The velocity of this zone is determined from the heat flux balance. To describe gas generation within the decomposition zone, an approach based on a modified Arrhenius law is proposed. Its parameters are identified using the composite material's reference data (decomposition onset and completion temperatures and densities), thereby eliminating the need for complex, hard-to-formulate full chemical kinetics.
Analytical solutions for temperature fields in all three regions are obtained: the porous coke residue, the active decomposition zone, and the virgin material. Distributions of the composite material density and the gas phase density in the decomposition zone, as well as filtration flow characteristics, are determined. Analysis of the results demonstrates that the temperature distribution in the decomposition zone is essentially nonlinear, while the density distributions are close to linear. The results of this work enable the assessment of mass-dimensional characteristics of thermal protection systems for high-speed aircraft structural elements at the design stage.

A mathematical model is proposed for predicting the creep and creep rupture strength of the hydrogen-charged VT6 titanium alloy at a temperature of 600$^\circ$C. A method for identifying the model parameters has been developed based on data from steady-state creep curves at fixed stress levels and hydrogen concentrations. Creep curves and time to rupture have been calculated for the VT6 alloy at $T=600$$^\circ$C. The adequacy of the model was verified by comparison with experimental data as well as with the results of independent calculations using alternative models. It is shown that the model provides satisfactory prediction accuracy even with significant inherent scatter in the experimental data. Based on the analysis of the identified model parameters, the influence of hydrogen concentration on the rheological properties and fracture mechanism of the material has been investigated, revealing partial embrittlement and a substantial change in nonlinearity indices.

A locally non-equilibrium Navier–Stokes equation, which accounts for the mean free path and relaxation time of microparticles, has been derived based on a modified Newton's law for shear stress in laminar gas flow within a plane-parallel channel. A numerical study of its solution for the case of a harmonic pressure drop along the channel revealed that the velocity variation at every point also exhibits harmonic behavior. It was found that the velocity oscillation amplitude decreases with an increase in the mean free path and relaxation time of the microparticles. For fixed microparticle parameters, the oscillation amplitude decreases with increasing gas viscosity and decreasing channel width. In the limiting case where the channel width becomes comparable to the mean free path, the velocity oscillation amplitude reaches an almost zero value, despite the constant amplitude of the pressure drop oscillations. It is demonstrated that the generation of gas flow oscillations can be utilized to clean the internal surfaces of a methane pyrolysis reactor from carbon deposits, which reduce the efficiency of the process for producing hydrogen and carbon.