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

The dynamics of a three-qubit multiphoton Tavis–Cummings model is investigated. The model comprises an isolated qubit and two qubits, each trapped in an independent single-mode ideal resonator. The trapped qubits resonantly interact with the thermal or vacuum field of their respective resonators via multi-photon processes, with their initial states being genuinely entangled Greenberger–Horne–Zeilinger and genuinely entangled Werner states.
An exact solution for the model is obtained in the form of an evolution operator derived from the time-dependent Schrödinger equation. Using this operator, the exact solution of the Liouville–von Neumann equation for the density matrix is constructed, and entanglement measures—negativity and fidelity—are computed.
The numerical results reveal a stark contrast depending on the field type. For vacuum resonator fields, increasing the multi-photon order $m$ does not stabilize entanglement but merely reduces the oscillation period of negativity and fidelity. In contrast, for thermal fields, a higher $m$ increases the maximum fidelity and effectively stabilizes the qubit entanglement.
Thus, the multi-photon order serves as an effective mechanism for controlling qubit entanglement specifically in the presence of thermal resonator fields.

This study investigates an inverse problem of determining the convolution kernel in an integro-differential parabolic equation with a uniformly elliptic operator in divergence form. The overdetermination condition is specified at a fixed interior point of the domain. By applying the Fourier method, the problem is reduced to a nonlinear Volterra integral equation of the second kind. Utilizing the contraction mapping principle in specially constructed weighted spaces, we prove a theorem on the global existence and uniqueness of a solution to the inverse problem. An estimate for its conditional stability is also established. The results are applied to the one-dimensional case of the heat equation with constant coefficients.

A nonhomogeneous second-order equation of mixed parabolic-hyperbolic type is studied in a rectangular domain. The Dezin problem is considered. The problem consists in finding a solution to the equation that satisfies an interior-boundary condition relating the value of the unknown function on the line of type change to the value of the normal derivative on the boundary in the hyperbolic subdomain, as well as nonhomogeneous boundary conditions of the first kind on the lateral sides.
Using a substitution, the problem is reduced to an equivalent one with homogeneous boundary conditions, which allows us, without loss of generality, to consider the latter hereafter.
The solution is constructed as a sum of a Fourier series in the orthonormal system of eigenfunctions of the corresponding one-dimensional spectral problem. A criterion for the uniqueness of the solution is established. For the case where this criterion is violated, a nontrivial solution to the homogeneous problem is constructed, and a necessary and sufficient condition for the solvability of the nonhomogeneous problem is obtained.
While justifying the convergence of the constructed series, the small denominators problem arises, depending on the aspect ratio of the rectangle in the hyperbolic part of the domain. Sufficient conditions on the problem parameters are obtained that ensure the non-vanishing of these denominators. Under these conditions and certain smoothness requirements on the right-hand side of the equation, the absolute and uniform convergence of both the series itself and the series for its derivatives involved in the equation is proved. Thus, uniqueness and existence theorems for the solution are proved; the solution is written in explicit form.

The induction of compressive residual stresses on the surfaces of stress concentrators is widely used to enhance the fatigue life of aircraft components. However, a method for fatigue life assessment under flight-cycle elastic loading in the presence of residual stresses remains a subject of discussion. In this study, such a method is proposed and applied to an aircraft engine mounting bracket eyelet with residual stresses induced on its contact cylindrical surface.
The near-surface eigenstrain distribution is determined using by the Davidenkov–Birger method with a reconstruction formula derived by the authors and is introduced into a finite-element model via initial strains in multilayered shell elements. The distributions of residual stresses caused by eigenstrains and of stresses induced by maximum operational loads during a flight cycle are calculated. Residual stresses shift the critical point from the surface into the interior of the component without appreciably altering the operational stresses.
To estimate the fatigue crack initiation life under flight-cycle loading, an evolutionary model proposed by the authors is employed. Two sets of material parameters for the evolutionary model are identified from experimental fatigue curves; one set captures sensitivity to load irregularity, whereas the other does not. Fatigue curves for the case where the fatigue failure origin lies beneath the eigenstrain layer are simulated by shifting the test results obtained from non-surface-treated specimens.
Calculations for different representations of the flight cycle and different near-surface eigenstrain distributions show that simplifying either the cycle or the eigenstrain distribution leads to less conservative (overestimated) fatigue life predictions. This effect is not captured by calculations that employ cycle-counting (rainflow) history schematization, reduction of individual multiaxial loading cycles to equivalent uniaxial cycles, and linear summation of their damage contributions. In the model, fatigue failure originating beneath the residual stress layer is predicted to be a less dangerous event than failure initiating at the surface.

This study addresses the development and validation of advanced models for hydrogen production via catalytic hydrocarbon decomposition, with a particular focus on methane decomposition. A structural simulation model was implemented in the MATLAB/Simulink environment based on the Langmuir–Hinshelwood kinetic model. The model explicitly accounts for adsorption and desorption of reactants and products on the catalyst surface, as well as surface reactions between adsorbed intermediates. By incorporating mass and energy balance equations, the framework enables the prediction of reactant and product concentrations, reaction temperature profiles, and heat transfer between the reaction mixture and the thermal control medium. A neural network model was also developed and trained using data from 38 experiments involving 12 different catalyst compositions. This data-driven model captures nonlinear dependencies between catalyst composition, operating conditions, and process efficiency, thereby enhancing predictive performance in dynamic environments. Comparative analysis against experimental data demonstrated that the structural model achieves higher accuracy (mean absolute error, MAE = 3.35 %) relative to the neural network model, which exhibited a slightly higher prediction error. The integration of physics-based simulation and machine learning approaches provides both interpretability and adaptability, highlighting the potential of hybrid modeling strategies for optimizing hydrogen production technologies. The results contribute to the broader development of advanced simulation tools for hydrogen energy applications, supporting efficiency improvements, real-time process control, and the transition toward sustainable energy systems.

This study considers a mathematical model of a computing node represented as an infinite-server queueing system with a Poisson arrival flow and a service rate depending on the number of customers in the system. This effect is referred to as service rate degradation. Mathematically, degradation is described by a positive non-increasing function that determines the dependence of the service rate of each customer on the total number of customers being served in the system.
The application of this approach allows for more accurate modeling resource contention in computing systems and enables appropriate selection of architectural parameters when designing new systems or optimizing existing ones. At the same time, the dependence of the service rate on the number of customers significantly complicates the model and the equations describing its operation, which necessitates the development of new research methods.
To analyze the proposed model, the method of asymptotic diffusion analysis is applied under the limiting condition of a high-intensity input flow. The method is implemented in three stages and allows one to obtain analytical expressions for the main probabilistic characteristics of the system under study.
The proposed method is approximate and asymptotic. However, numerical experiments and comparison with pre-limit results for the model with a Poisson arrival flow demonstrate small errors and a wide range of applicability of the method (with respect to the model parameters).

This study investigates a modification of the Ant Colony Optimization (ACO) method for solving parametric problems. The considered approach is based on path search by ant agents in a parametric graph, where vertices correspond to parameter values and the path determines the resulting set of values. The proposed matrix modification of ACO represents the algorithm in terms of matrix operations with predominant use of fixed-length loops. The optimal graph structure involves splitting the values of each parameter into layers with a maximum of five vertices per layer.
To accelerate computations, AVX instructions of the central processing unit are employed in inner loops. However, with five vertices per layer, the use of AVX instructions proves inefficient since it requires the number of vertices to be a multiple of four. Consequently, a transposed modification of the matrix method is developed, oriented toward graphs containing 100 or more vertices per layer, which enables efficient utilization of AVX instructions.
The proposed modifications were evaluated on various hardware platforms, including Intel and AMD processors. It is established that 12th and 13th generation Intel processors are more than twice as efficient as 8th and 9th generation processors. The AMD processor demonstrates high performance when executing classical ACO but falls behind Intel processors when using matrix modifications.
Various graph structures with 100, 1000, and 10000 vertices per layer solving the same problem were analyzed. The highest efficiency was achieved by the matrix modification of ACO combining AVX instructions and OpenMP directives: the execution time of 500 iterations for 500 ant agents is 5–6 ms per parameter. Different matrix modifications yield similar results, which is explained by the high computational cost of ant agent path search, which is difficult to vectorize using AVX.

This study investigates the characteristic properties of the Schwarz iterative algorithm as applied to three-dimensional elastostatics problems for multiply connected bodies. Within the framework of the boundary state method, the algorithm is shown to provide an economical basis dimension, uniquely fast convergence (2–3 iterations), and a significant reduction in computational resource requirements compared to the direct approach. The problem of the stress-strain state of a biconus with a spherical cavity at various displacement values is considered. The influence of geometric singularities (conical points, a curvilinear edge) on the convergence of the algorithm and the stress distribution is revealed. Based on an analysis of stress intensity, the necessity of constructing special solutions for a correct assessment of the state of the medium near geometric features is substantiated.