A class of translation-invariant Gibbs measures for models with a continuum of spin values on a Cayley tree was examined. The results show that the problem of describing such measures reduces to studying positive solutions of a nonlinear integral equation of Hammerstein type. A connection between the solutions of the integral equation and the properties of a corresponding polynomial was established. A theorem on the existence and uniqueness of a positive solution of the Hammerstein equation for an arbitrary tree order 𝑘 ≥ 2 was proved. Explicit formulas for the solutions were obtained via the roots of a polynomial of degree 𝑘 + 1, constructively describing the set of translation-invariant Gibbs measures.
The influence of pore space characteristics of terrigenous reservoir rocks on two-phase flows was investigated. Computational experiments were carried out using the lattice Boltzmann method on a series of digital models of natural sandstones with various filtration and capacity properties. It was established that pore space heterogeneity, which is described by the standard deviation of pore size distribution, emerges as a key factor determining displacement efficiency. The negative impact of increasing heterogeneity on displacement efficiency and front stability was shown. A map of the influence of the capillary number on displacement efficiency, depending on standard deviation and permeability, was created. The results are of fundamental importance for the mechanics of multiphase flows in porous media and can be used in predicting hydrocarbon field development measures.
This article describes different modeling options for mixing the hot lubricant of the upstream pad of a fluid film bearing and the fresh lubricant of the oil-feeding inter-pad groove. The outcomes of the mixing process affect the lubricant temperature distribution near the leading edge of the next pad located downstream. Ultimately, this distribution determines the thermal state of the lubricant film, the output characteristics, and the power losses of the bearing. The fixed pad thrust bearing of a centrifugal or screw compressor was investigated. The mixing simulation was reduced to different boundary conditions for the truncated Navier–Stokes equation of motion, which are also part of the general periodic thermoelastohydrodynamic (PTEHD) mathematical model of bearing operation. The results of the numerical calculations of the thrust bearing characteristics under different flow boundary conditions were compared with those obtained using other programs. For these purposes, the numerically implemented Sm2px3Txt calculation program was employed. Based on the results, conclusions were drawn about the need for a sufficient flow of the fresh lubricant in the oil supply groove to compensate for lateral leaks of the pad and when the thrust bearing operation mode becomes more complicated, for example, if the gap decreases, the rotational speed increases, or the thrust collar moves.
The stability of the Hodgkin–Huxley model was examined with respect to the following three ionic parameters: the equilibrium potentials of potassium, sodium, and leak ions. A two-parameter bifurcation analysis of the Hodgkin–Huxley model was performed in the plane of the equilibrium potentials of potassium and sodium. Regions of stable and unstable steady states were identified. The Hopf bifurcation boundary was located. Using numerical continuation, the influence of the leak potential on shifts in the detected bifurcation values was investigated, and the two-dimensional stability maps were extended into a three-dimensional parameter space. The results clarify the role of the three equilibrium potentials in the modulation of the excitability of the Hodgkin–Huxley system and contribute to a better understanding of the dynamical consequences of ionic disturbances such as hyperkalemia, hyponatremia, and leak-channel dysfunction.
The spectra of grid operators in some finite element method (FEM) schemes for solving twodimensional problems of elasticity theory were investigated. It was revealed that, for a number of classical FEM schemes, a mutual influence between the spectra of volumetric and shear deformations may occur, which can lead to undesirable effects such as volumetric and shear locking. The analysis of the spectral errors in the FEM schemes demonstrated the effectiveness of the reduced integration technique and underscored the importance of fulfilling the group properties of grid differential operators that ensure consistent approximation of partial derivatives. A number of numerical schemes with improved spectral properties were described. The results were illustrated by the solutions of model problems.
In this study, the effectiveness of topological optimization methods for designing adhesive joints in multilayer structures was evaluated. Five types of joints were examined: vertical beam joints, variable cross-section beam joints, inclined joints, horizontal joints, and joints with local boundary conditions. A modified RAMP method, combined with the finite element method, was proposed for optimizing adhesive zones. A comparative study with the SIMP method, selected based on an analysis of existing scientific literature using artificial intelligence, was conducted.
Using physical experiment and direct numerical simulation, principal patterns were revealed in the evolution of the structure of swirling flows in smooth straight pipes at the Reynolds numbers from 240 to 1640. Swirling was generated by a vane swirler. Changes in the swirl ratio, streamwise velocity, and its root-mean-square fluctuation with an increase in the distance from the swirler were analyzed. The Reynolds numbers at which the early signs of laminar-turbulent transition occur in the flow were identified: a rapid growth of velocity fluctuations and the onset of intermittency in velocity oscillograms. The physical mechanisms underlying the transition to turbulence in the vicinity of the pipe axis and near the pipe wall were found and described.
This article presents the results of a numerical study on the dynamics of gas bubbles in a viscous liquid under the action of gravity. The rise of a single bubble, two bubbles starting at the same level relative to the vessel bottom, and bubbles rising one after another were examined. The bubble motion was described using a mathematical model based on the Navier–Stokes and continuity equations, and the position of the moving interface was tracked using the volume of fluid (VOF) method. The partial differential equations with appropriate initial and boundary conditions were solved by the finite volume method implemented in the OpenFOAM software package. Validation of the model and verification of the numerical algorithms were performed by solving a test problem and comparing the results with known data. The effect of the initial shape of the bubble on its rising velocity was assessed. The hydrodynamic interaction between two identical bubbles with different initial positions relative to each other was investigated. It was demonstrated that the merging of two bubbles is facilitated by a decrease in pressure within the region between them, the entry of one bubble into the hydrodynamic wake of another, and sufficient contact time for thinning of the liquid film separating them.
This article focuses on methods of developing machine translation systems for low-resource languages, such as Turkic languages. A hybrid approach combining data augmentation and transfer learning was proposed. Data augmentation was achieved via morphotranslation of parallel corpora from closely related languages and paraphrasing based on the “Turklang” linguistic knowledge graph, enabling the generation of synthetic parallel data through an intermediate ontological representation. The BERT architecture was selected as both encoder and decoder. The training data comprised parallel corpora of approximately 30 million sentence pairs. The experimental part included training and evaluation of both one-way and multilingual models for six of the most low-resource Turkic–Russian language pairs: Crimean Tatar, Khakas, Tuvan, Altaic, Kumyk, and Yakut. The training was performed on a small portion of the collected data to ensure data volume balance between different languages. The results show that the multilingual model, trained using data augmentation and transfer learning, significantly improves BLEU, SacreBLEU, and ChrF scores compared to the one-way models.
The effect of microcapsules modified with graphene oxide for the production of self-healing concrete on the strength of heavy concrete at different curing ages (3, 7, and 28 days) and on the strength recovery coefficient was examined. The experimental results were analyzed using orthogonal statistical method. Microscopic observations confirmed that the microcapsule rupture releases the active core and forms significant amounts of a healing binder to fill cracks. The experimental analysis showed that the strength recovery coefficient Kx increases with self-healing time. The optimal ratio of graphene/additive in concrete was determined, and recommendations for its content, depending on the area of application of the concrete, were made.
The rigor and reproducibility of topographic studies are ensured by geomorphometry. This field, which has a developed physical and mathematical theory and a powerful toolkit of computational methods, combines various disciplines, such as photogrammetry, geoinformatics, and computational mathematics. Geomorphometric modeling of Antarctic oases, the unique ice-free territories in Antarctica, is necessary to better understand the quantitative characteristics of their topography and support the broader use of morphometric data in polar research.This article focuses on the Schirmacher Oasis, a typical Antarctic oasis located in Queen Maud Land, East Antarctica. Geomorphometric modeling and mapping of the region were carried out for the first time. As input data, a fragment of the Reference Elevation Model of Antarctica (REMA), a digital elevation model (DEM) of the entire Antarctica, with a grid spacing of 8 m was used. From the REMA DEM fragment, digital terrain models were derived, and maps of the following eleven key morphometric variables were generated: slope, aspect, horizontal curvature, vertical curvature, minimal curvature, maximal curvature, catchment area, topographic wetness index, stream power index, total insolation, and wind exposition index. Interpretations of the obtained maps were given, and their possible use was described. The study is part of the project to create a physical geographical thematic scientific reference geomorphometric atlas of ice-free Antarctic territories.
This article overviews the current status and unresolved issues of network calculus (NC) theory, a promising approach for analyzing network models. NC provides a mathematical framework to compute guaranteed upper bounds on traffic delays and data amounts in the buffer of network devices in order to ensure the high quality of service in critical systems such as industrial and on-board networks, real-time systems, and cloud infrastructures. The theoretical foundations of deterministic NC, including (min, +) and (max, +) algebras, are summarized. The concepts of arrival and service curves are outlined. Existing NC methods are described and compared for their applicability and limitations. Particular attention is given to the latest advances in the use and study of NC, including stochastic NC, methods that take into account flow multiplexing, integration with queuing theory methods, and applications of NC models and methods in new areas such as Time-Sensitive Networking, 5G/6G mobile networks, wireless networks, and cloud computing. The most significant challenges and future research directions in the field are discussed.
A new mathematical model of porous functionally graded (PFG) conical sector micro/nanoplates with temperature-dependent properties was developed based on the modified couple stress theory. The variational iteration method was employed to solve the nonlinear differential equations describing the bending of flexible conical (annular) sector plates under thermomechanical loading. The proposed method yielded an almost exact solution while requiring much less computational time compared to the finite difference and finite element methods.
This article focuses on the implementation of a lightweight model of a friction pendulum bearing in the finite-element model of a base-isolated structure. The proposed approach appears as an alternative to a high-fidelity finite-element model. The model considers the slider moving on the sliding surface as a material point with three degrees of freedom. The equations of motion for the slider are derived by leveraging the Lagrangian formalism. The three-degrees-of-freedom model is compared with other available analytical approaches that can be employed to define the response of friction pendulum bearings, mainly unidirectional formulations. From the numerical experiments, the dynamic response of a structure with and without base isolation is obtained using a finite-element analysis. Acceleration time series, recorded during an earthquake, are employed as an input. The numerical results, in terms of displacement and acceleration evolutions, demonstrate the positive effect of seismic isolation on mitigating the risk of failure in the structure.
The propulsive motion of a cylindrical flapping wing with an elliptical cross-section in a viscous incompressible fluid is investigated to develop an analytical model for predicting the cruising speed of such a wing without resorting to computationally expensive numerical methods. The mathematical formulation of the problem is based on the unsteady Navier–Stokes equations. The wing motion is described as a planar translational-rotational oscillation with prescribed velocities. The problem is solved using an asymptotic approach, under the assumption of high-frequency and low-amplitude oscillations. A structural formula is derived that describes the variation of the cruising speed in relation to the angle of translational oscillations, the phase shift between translational and rotational oscillations, the amplitude of rotational oscillations, and the aspect ratio of the elliptical cross-section. The consistency of the results with known analytical solutions for a circular cylinder is demonstrated. The limits of the model’s applicability with respect to the oscillation frequency are considered.
A mathematically rigorous formulation of contact problems in the theory of plates and shells is justified. An overview of the recently solved static and dynamic problems, their analytical and numerical solutions, is carried out, and the results of the obtained solutions are analyzed. Additionally, examples are provided of such problems where the correct determination of contact stress distribution is fundamentally important.
The effects of implanting As+ , Mn+ , In+ ions and pulsed light annealing on the formation of recrystallized relief periodic microstructures from the molten phase on the surface of a silicon (Si) plate for their potential application in solar energy conversion was studied.
This article is devoted to improving the technique for constructing interpretable regression models in which parameters are estimated using the ordinary least squares method. A definition of quite interpretable linear regressions is provided. The main requirements for such regressions include the consistency between the signs of the parameter estimates and the substantive meanings of the variables, the significance of the estimates, the low degree of multicollinearity, and the high quality of approximation. Whether a model belongs to the class of quite interpretable regressions or not depends on its significance level. In terms of mixed 0-1 integer linear programming, which has made progress in recent years due to computational advances, an optimization problem is formulated for constructing quite interpretable linear regressions with a fairly large number of linear constraints. The problem is proved to be solvable under certain conditions. The proposed mathematical framework can be successfully applied to processing big data, as the number of constraints in the formulated problem does not depend on the sample size, unlike existing foreign analogues.
Advancements in robotics have expanded a use of unmanned aerial vehicle (UAV) swarms in critical tasks such as disaster response, including search and rescue operations during floods, hurricanes, landsliding, and earthquakes. Swarm formation control stands as a critical challenge in UAV swarm control. In this article, a simple and resource-efficient method for addressing collisions within swarm formations during outdoor missions is proposed, along with a set of formations designed for various task requirements. The proposed algorithm is implemented using the Robot Operating System (ROS) for a swarm of ten PX4-LIRS UAVs. Experiments conducted in the Gazebo simulator demonstrated the algorithm’s effectiveness, with the quantitative results presented through mean and standard deviations of the absolute positioning error measurements.
Binary alloy solidification involves the transition of a liquid mixture of two metals into a solid phase and presents several complex challenges that researchers aim to address. These problems can be categorized into issues related to thermodynamics, diffusion, and macro- and microstructural evolution during the cooling process. The Sivashinsky equation is a fourth-order nonlinear partial differential equation that arises in the mathematical modeling of binary alloy solidification problems. In this article, we apply the Fourier spectral method combined with the Euler method to numerically solve the 2D Sivashinsky equation with periodic boundary conditions. A numerical study of the Sivashinsky equation is important because its analytical solution does not exist, except for trivial solutions. The error estimation of the approximate solution is provided. Furthermore, we show, both theoretically and numerically, that the proposed method preserves the decreasing mass condition of the obtained numerical solutions. Finally, to validate the theoretical results, three examples with different initial conditions are investigated.
