Issue 3, 2026

Optical methods for determining the relationship between the biophysical constant of osmolarity and the parameters of aqueous biological solutions.

J. A. Guseva$^1$, V. V. Davydov$^2$, D. S. Provodin$^3$, D. V. Davydova$^4$

The early diagnosis of chronic kidney disease is critically important due to the asymptomatic progression of the condition in its initial stages and its increasing prevalence. This study substantiates the need to develop novel, accessible, and non-invasive diagnostic approaches based on optical technologies. A method based on refractometric measurement of urine refractive index is proposed, enabling the quantitative evaluation of key physicochemical parameters. Reliable linear relationships between urine osmolality, density, and temperature were established. The method demonstrates high measurement accuracy (±0.0001) and stability over a wide temperature range (288–303 K), making it a competitive and cost-effective alternative to traditional diagnostic techniques such as urinalysis strips, urinometry, and osmometry. Regression equations were developed to estimate osmolality based on density ($\mathrm{Os} = 33.128\rho - 33.107$) and density based on refractive index ($\rho = 2.4322n - 2.2444$). The results confirm the feasibility of using refractometry as a tool for rapid, non-invasive assessment of kidney function and early detection of CKD. The proposed approach simplifies routine clinical analysis and has the potential for implementation in both laboratory and point-of-care settings.

Evolution of three-dimensional contrast structure in an inhomogeneous medium with weak advection

A. A. Bykov, Q. Q. Gan

The subject of the work is a three-dimensional initial-boundary value problem for the quasi-linear reaction-advection-diffusion (RAD) equation with a small parameter for the advection and diffusion terms. The presence of a small parameter provides the possibility of the existence of solutions such as a contrast structure (CS), for which there are large areas with a small field gradient (CS spots), separated by narrow regions with a large field gradient (internal transition layers, ITL). The solution to the problem is constructed in the form of an asymptotic series in powers of a small parameter. We find a zero-order solution from a nonlinear initial-boundary value problem for a family of ordinary differential equations, for all subsequent orders we find the solution from linear inhomogeneous boundary value problems. A distinctive feature of this work is that we present a study of the case we found, for which the position of the ITL, and, accordingly, the solution of the zero-order equations of the asymptotic series described by the Hamilton-Jacobi equation, those. a family of Cauchy problems for a nonlinear system of ordinary differential equations, parameterized by a two-dimensional vector field defining a point on the surface of the CS front at the initial time. In previous work on multidimensional contrast structures, the zero-order solution to the non-stationary RAD problem was not found explicitly. We will show that in leading (zero) order the Hamiltonian potential is calculated as an integral of the source density function. The surface of the transition layer evolves in the same way as the surface of the permanent eikonal for the problem of wave propagation in an inhomogeneous medium in the short-wave approximation, although the physical models have nothing in common. Next we will show that in the first order of the asymptotic series the speed of movement of the ITL is determined by the gradient of the medium parameters and the Gaussian curvature of the ITL. The time of destruction of the contrast structure was found. We will also find an explicit solution to the problem of the movement of ITLs in a medium with weak inhomogeneity and show that on the surface of the ITL in the zeroth order of the asymptotic series a break line is formed, which in the first order is transformed into a cylindrical or conical surface with a small but finite radius of curvature.

TEOREMS ON THE INTEGRALS ARISING IN PROBLEMS OF NONLINEAR ELECTRODYNAMICS OF VACUUM

M. E. Abishev$^1$, M. S. Seidaliyeva$^2$, V. I. Denisov$^3$, I. P. Denisova$^4$

In a number of important problems of nonlinear electrodynamics of the vacuum, specific integrals with a variable upper limit arise. Integrals of this kind have not been considered in the scientific literature. In this work, theorems are proved that establish relationships between these integrals.

LOGARITHMIC POTENTIAL AND THE BOUNDARY EFFECTS IN THE PROBLEM OF A PLATE CAPACITOR

A. V. Kurilin

The solution of the Laplace equation in a two-dimensional case for a plate capacitor is analyzed. Analytical formulas for the potential and the field strength corresponding to a uniform charge distribution over two dielectric plates of finite width are derived. The case of an infinitely thin charge layers in two-dimensional space is also considered. The results of numerical calculations in the Mathcad program are presented. Graphs and the field line patterns are constructed, allowing for edge effects in the classical model of a uniform electrostatic field.

Numerical simulation of spatial configurations of a series of amino acids by solving the Schrödinger equation

I. A. Shatskov

The numerical method of K. E. Plokhotnikov for solving the Schrödinger equation is applied to spatial configurations of eleven proteinogenic amino acids (glycine, alanine, valine, leucine, isoleucine, proline, serine, threonine, cysteine, tyrosine, tryptophan) in their canonical PubChem geometries. The method combines stochastic Monte-Carlo discretization of configuration space with a finite-difference approximation of the kinetic energy operator. A scheme of valence-electron positioning with delocalization along covalent bonds and with the number of valence electrons fixed by the group number of the periodic table is employed. For all 11 structures, the relative deviation of the discrete-Hamiltonian eigenvalue Ω_I from the reference total-energy estimate E_ref is below 0.02 %, and Ω_I lies in the middle part of the spectrum in all cases. Tryptophan is examined as the most complex example (135 quantum particles; configuration-space dimension 405).

Classification problem for imbalanced data

R. R. Valiev

A binary classification problem for diagnostics of railway infrastructure objects using multiparametric condition and operation data is considered. The data set is strongly imbalanced: observations corresponding to normal track condition considerably outnumber observations associated with dangerous defects. Several classifiers and resampling approaches are compared using synthetic data sets and a real data set containing 107597 objects and 145 features. The XGBoost algorithm demonstrates the most stable performance among the considered methods. Special attention is paid to the choice of the probabilistic classification threshold, which controls the trade-off between missed defects and false alarms. The threshold is shown to vary with the month of observation, indicating temporal heterogeneity of the data. Feature-importance analysis is used to identify parameters that have the largest influence on defect prediction.

A. V. Borisov

In this methological paper, we show that, by considering the Schr¨odinger and Pauli equations for the wave function of a particle as the Lagrange equations of classical field theory, it is possible, on the basis of Noether’s theorem, to obtain Noether charges (constants of motion) in the form of quantum-mechanical expectation values of the observables of thep article, to which are associated self-adjoint operators of energy, momentum and angular momentum, as well as the law of conservation of probability.

Structural changes in naturally aged titanium nickelide alloys

E. A. Brovkina$^1$, T. Yu. Kiseleva$^1$, V. V. Snegirev$^2$, A. G. Khundjua$^1$

The effect of prolonged natural aging on the structure and characteristics of martensitic transformations in three-component titanium nickelide alloys doped with niobium, vanadium, silicon and copper was studied by X-ray analysis of polycrystals. Titanium nickelide products are used in medicine as implants and are implanted into the human body for many years and decades, which entails the requirement for the immutability of the material's characteristics over a long period of operation in order to avoid tragic consequences. It was found that an increase in the duration of isothermal aging of alloys at room temperature from 3 to 6 years to 45 years had an effect on the structural and phase state of each alloy studied. Alloys Ti46Ni46Cu8, Ni51Ti45Si4, Ti46Ni46Nb8, Ti44Ni44Nb12 exhibit a rather weak change in the crystalline state. The alloys of the TiNi-V system (Ti48Ni48V4 and Ti46Ni46V8) in naturally aging samples exhibit the greatest instability at the crystal structure level, which raises the question of the utmost attention to the safety of using titanium nickelide products and alloys based on it for medical purposes.

Analysis of Pulsating Gas-Dynamic Flows Using Proper Orthogonal Decomposition

V. D. Petri$^1$, I. E. Ivanov$^1$, I. A. Kryukov$^2$

This work is devoted to the development of algorithmic tools for extracting stable structures (modes, coherent structures) associated with oscillations in unsteady gas-dynamic fields. The research area related to modal decomposition is actively developing, since it has a number of advantages over traditional methods for processing data obtained from numerical or physical experiments. This work uses one of the well-established methods of modal analysis, namely Proper Orthogonal Decomposition (POD). The method consists in representing the pulsating part of a field as a sum of products of temporal and spatial modes (basis functions), each of which approximates the field in the sense of the best quadratic approximation; this makes it possible to interpret such modes as the most significant flow structures within the chosen measure. Finding the basis functions on a grid is based on methods of linear algebra and is reduced to finding the right and left singular vectors of the singular value decomposition (SVD) of a matrix containing field distributions at fixed time instants. The algorithm was tested on a model problem. Numerical studies were then carried out for two-dimensional flows arising when a gas medium flows around bodies of different shapes (a square cylinder and a NACA 0012 airfoil), in regimes where a von Karman vortex street is formed.

Model of the control and management system for a linear electron accelerator based on EPICS

M. Yu. Kopatch$^{1,3}$, A. N. Ermakov$^{2,3}$

A linear electron accelerator was physically launched at the Skobeltsyn Institute of Nuclear Physics with the assistance of the MSU Laboratory of Electron Accelerators to solve problems of fundamental and applied research. This work is devoted to the initial stage of the development of an accelerator control and monitoring system based on the EPICS software package. The created model of the monitoring and control system consists of several controllers used in industrial accelerators, as well as third-party controllers. Within the framework of the model, information is collected and transmitted between controllers and a control computer, and control logic based on virtual finite state machines is implemented.An algorithm has been developed to include new controllers based on the Modbus data transmission protocol in the system for flexible modernization of the future control system.