Odessa National Polytechnic University

Diffusion is regarded as one of mechanisms, which leads to leakages through the fuel cladding during the long-term storage of spent nuclear fuel. The schematization of the diffusion process through a circular cylindrical cladding of fuel elements, where axial and circumferential diffusion flows are neglected, is considered. Fundamental properties of leakages through a cylindrical cladding of fuel elements associated with the effect of sorption, desorption, and diffusion are investigated; it is shown that the diffusion through the cladding material is the main limiting factor for leakages, whereas sorption and the effect of desorption are limited due to the saturation property. A mathematical model how to assess the maximum possible leakage of radioactive materials through the cladding of fuel elements due to diffusion processes during the long-term storage of spent nuclear fuel is proposed. This model is presented in the form of a system of differential equations with initial and boundary conditions that make it possible to determine the concentration of radioactive materials inside the fuel cladding taking into account radioactive decay, the concentration of radioactive material in the fuel cladding material during diffusion, and the concentration of radioactive material in the volume outside the fuel cladding. The solution of differential equations, which represent a mathematical model of the leakage of radioactive materials through the cladding of a fuel element during the long-term dry storage of spent nuclear fuel, was performed using the straight line method. A qualitative analysis of the patterns of leakage of radioactive materials was carried out and the influence of the initial concentration and half-life of radioactive materials was established. A quantitative analysis of possible leakages of radioactive material through the cladding of a fuel element during the long-term storage of spent nuclear fuel has been carried out on the basis of computer modeling using specially developed original software.

One possible data encryption scheme is related to stream ciphers, which use a sufficiently long pseudo-random sequence. To increase the cryptographic strength of the cipher, linear shift algorithms (generated by linear recurrent sequences such as the Fibonacci sequence and its generalizations) are additionally used. Two such generalizations are convolved Fibonacci numbers {F_n^(s)}_n=1^∞ and k-sections of the Fibonacci sequence {Φ_n,k}_n=1^∞ ( Φ_n,k=F_nk/F_k). This article considers a further generalization of Fibonacci numbers, namely convolutions of k-sections of the Fibonacci sequence {Φ_n,k^(s)}_n=1^∞. These numbers are defined by the relations: Φ_n,k^(1)=∑_j=0^n-1Φ_j+1,kΦ_n-j,k , Φ_n,k^(s)=∑_j=0^n-1Φ_j+1,kΦ_n-j,k^(s-1) , s=2,3,... Moreover, Φ_n,1=F_n, Φ_n,1^(s)=F_n^(s). An explicit formula for the representation of convolutions of k-sections of the Fibonacci sequence and a Binet type formula is established: Φ_n,k^(s)=5^-s(F_k)^-2s-1∑_j=0^s(-1)^(k-1)jn+2s jn+s-1-j n-1 F_k(n+2s-2j). Several consequences were also obtained for F_n and F_n^(s), based on the connection between the derivatives of Chebyshev polynomials of the second kind U_n(z) and their derivatives, as well as the connection for convolutions of k-sections of the Fibonacci sequence with derivatives of Chebyshev polynomials of the second kind via Lucas numbers L_k. Note that the sequences {Φ_n,k^(s)}_n=1^∞ for k=3,4,... and s=1,2,.. are not included in the OEIS encyclopedia.

The theory of macroscopic fluctuations in systems with flux is presented within the framework of thermodynamics. It is shown that the Onsager-Casimir reciprocal relations are satisfied only in equilibrium systems and do not take place in the case of non-equilibrium ones. It is emphasized that the Langevin fluctuation-dissipation theorem (FDT) is a mathematical formula that does not require any physical justification and which allows solving the problem of internal and external fluctuations. It is shown that the behavior of internal and external fluctuations differs fundamentally. In particular, fluctuations induced by external noise play a decisive role near the points of dissipative instabilities.

The article considers the problem of improving the efficiency of finishing machining of mechanical engineering parts with wear-resistant composite coatings based on a clad titanium carbide (TiC-NiP-Cu) system. During the work, a universal, comprehensive methodology was developed to determine the optimal machining parameters for parts with both plasma composite coatings and other surface layers of various chemical compositions. Optimal grinding parameters for the TiC-NiP-Cu coating have been determined and scientifically substantiated. It has been proven that the proposed parameters enable reliable control of the thermal and stress-strain states of the surface layer. The study accounts for the use of tools with different characteristics (including diamond and electrocorundum wheels), as well as the specifics of machining with cooling lubricants and dry machining. In addition, a direct relationship has been established between the initial parameters of plasma spraying and the optimal parameters for subsequent grinding, enabling maximum specific productivity without compromising adhesion strength. The developed approach is based on the objective of maximizing specific productivity, which is strictly limited by permissible values for residual stresses and the adhesion strength of the coating to the substrate. Furthermore, the necessity of a gradual reduction in the actual depth of cut as the allowance is removed has been experimentally confirmed, thereby ensuring defect-free machining and preventing delamination of the sprayed layer. The application of the developed methodology and the recommended parameters ensures the achievement of the specified qualitative characteristics of the surface (roughness, absence of grinding burns) while maintaining the maximum possible specific productivity of the machining.

The article considers an approach to substantiating the functional structure of a software tool for automated verification of gas turbine engine regulator protection algorithms and functions. The relevance of the study is driven by the need to safely and reproducibly verify critical start-up and shut-down transients, as direct engine testing is risky and difficult to standardize. The aim of the study is to substantiate the functional structure of a prospective software tool intended for visual and formal scenario authoring, execution, and documentation of automated verification scenarios. The research methodology is based on the systematic analysis of regulatory functions, the generalization of typical protection algorithms, the definition of requirements for automated test scenarios, and the formalization of the main groups of functional nodes. A classification of protection algorithms is proposed: parametric, dynamic, diagnostic, reconfiguration, and self-test algorithms. It is shown that the software tool should provide a minimal verification workflow: initial condition setting, generation of test inputs, processing of analog and discrete signals, verification of logical and timing conditions, registration of regulator response, interaction with a bench simulator, and report generation. The expediency of representing a verification scenario as a set of functional nodes is substantiated. The main node groups include flow control, variables and data, mathematical and logical processing, time control, command generation, equipment interaction, file operations, logging, reporting, validation, and error handling. A generalized scenario structure and criteria for evaluating the results are proposed. The results obtained can serve as a basis for further development of software tools for the automated verification of gas turbine engine regulators as part of a bench-simulation complex.