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.

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. 

Let 𝜏 be a faithful normal semifinite trace on a von Neumann algebra ℳ. The block projection operator 𝒫̃_𝑛 (𝑛 ≥ 2) on the *-algebra 𝑆(ℳ, 𝜏 ) of all 𝜏 -measurable operators is investigated. It is shown that 𝑓(𝒫̃_𝑛(𝐴)) ≥ 𝒫̃_𝑛(𝑓(𝐴)) for any operator monotone function 𝑓 on R⁺ and 𝐴 ∈ 𝑆(ℳ, 𝜏 )⁺. For an operator convex function 𝑓 on R⁺, we have 𝑓(𝒫̃_𝑛(𝐴)) ≤ 𝒫̃_𝑛(𝑓(𝐴)) for 𝐴 ∈ 𝑆(ℳ, 𝜏 )⁺. Conditions are established under which 𝒫̃_𝑛(𝐴) belongs to the class 𝑆₀(ℳ, 𝜏 ) of 𝜏 -compact operators, to the class 𝐹(ℳ, 𝜏 ) of elementary operators, to the classes 𝐿_𝑝(ℳ, 𝜏 ) of operators 𝜏 -integrable with 𝑝-th power, or to the ℳ algebra itself. If 𝐴, 𝐵 ∈ 𝑆(ℳ, 𝜏 ) and 𝒫̃_𝑛(𝐵) is a left (right) inverse for the operator 𝐴, then 𝒫̃_𝑛(𝐵) is also a left (respectively, right) inverse for the operator 𝒫̃_𝑛(𝐴).

In this study, a methodology is proposed to account for vertical well imperfection, depending on the degree of reservoir penetration, in a two-dimensional vertically averaged numerical flow model of a heterogeneous reservoir. Verification modeling is performed on a rectangular finite-volume grid using the open-source MATLAB Reservoir Simulation Toolbox (MRST). In the averaged two-dimensional model, wells are represented as point sources with productivity indices calculated from the wellbore radius. Accounting for well imperfection is reduced to determining the effective wellbore radius by established analytical methods and local numerical upscaling of the wellbore radius in the nearwellbore region, which appears as a relatively simple tool for constructing a two-dimensional reservoir model. Based on a comparison of the two- and three-dimensional numerical solutions for the problem of well interference, a significant superiority of local numerical upscaling over analytical models is demonstrated.

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.

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.

A comprehensive study, combining density functional theory (DFT) calculations and experimental investigations, of the quasi-one-dimensional antiferromagnet RbFeSe₂ is carried out. The non-spinpolarized ab initio calculations show that its metallic conductivity is above the N´eel temperature 𝑇_𝑁 = 248 K, with no gap in the electron density of states at the Fermi energy. The experimental four-probe conductivity measurements yet reveal an insulating behavior throughout the temperature range of 4–300 K. Following these measurements, an X-ray diffraction analysis is conducted. Its results demonstrate a severe degradation of the sample after air exposure (7–9 min), with the reduction in selenium occupancy by more than 20 % below stoichiometric values and the formation of elemental selenium phase (𝑃₃221 space group). The discrepancy between theoretical predictions and the obtained experimental results is attributed to the rapid air-induced oxidation leading to structural defects and electron localization. The results obtained highlight the critical importance of rigorous atmospheric control when studying iron chalcogenides, provide quantitative insights into the degradation mechanisms affecting electronic properties, and indicate that standard DFT approaches may overestimate metallicity in quasi-one-dimensional systems, particularly when structural defects are present.

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.

This article presents a mathematical model and algorithm for analyzing the stress–strain state (SSS) of elastic-plastic plates with a central circular hole in a three-dimensional setting. The developed algorithm can be applied to any boundary conditions, dependencies, and materials for which experimental stress–strain diagrams are available. The model is based on the deformation theory of plasticity and was implemented using a combination of the finite element method (FEM) and the method of I.A. Birger’s variable elasticity parameters. To obtain reliable results, the type finite elements (FE) and their number in a three-dimensional setting were investigated, along with the convergence of the solutions on a mesh of tetrahedral and hexahedral FE for a plate with and without a hole in the center. The hexahedral FE was found to be the most optimal. Computational examples for a rectangular plate clamped along the contour and subjected to a constant load were provided. The plate material considered is pure aluminum described by the stress–strain diagram developed by Y. Ohashi and S. Murakami.

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. 

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.

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.