Vol 25, No 4 (2025)

Background and Objectives: Within the framework of Einstein’s general-relativistic theory of gravity, that is, the general theory of relativity (GR), the properties of stationary distributions of a self-gravitating rotating continuous medium in the form of an ideal liquid with a barotropic equation of state p = wε are considered. Here, w = const, p is the pressure, and ε is the energy density of an ideal liquid. Materials and Methods: A stationary space-time compatible with a self-gravitating rotating continuous medium is described by a stationary cylindrical metric ds2 = A(x)dx2 + B(x)dφ2 + C(x)dz2 + 2E(x)dtdφ – D(x)dt2 , 0 ≤ φ ≤ 2π, where the metric coefficients A, B, C, D, E are functions of the radial coordinate x. This metric corresponds to a rotating space-time in which there is a vortex gravitational field. The latter is determined by means of the angular velocity ω of the field of tetrads ei(a) (xk), which are tangent to the considered Riemannian space. Here, the indices i, k are the world indices corresponding to the coordinates of the Riemannian space (base), and the index (a) is a local Lorentz index. For a vortex gravitational field, in contrast to a total gravitational field, it is possible to determine an energy-momentum tensor Tik(ω) satisfying the local conservation law ∇iTik(ω) = 0 relative to the metric of the corresponding static space in which ω = 0 (in the case under consideration, at a coefficient of E = 0). The tensor Tik(ω) has very exotic properties. For example, a weak energy condition is violated in it, since a p(ω) + ε(ω) < 0. For ordinary matter p + ε > 0. This property Tik(ω) contributes to the formation of wormholes in space-time. To study the properties of the considered configuration of a self-gravitating rotating ideal fluid and a vortex gravitational field, the corresponding Einstein gravitational equations are solved. Results: Solutions of Einstein’s gravitational equations in stationary space-time have been obtained with the metric presented above, that is, with a vortex gravitational field and with wormholes in the presence of a self-gravitating rotating ideal fluid with a limiting equation of state p = ε. At the same time, the obtained solutions describe the geometry of space-time of the so-called traversable wormholes, inside which gravitational forces Fg have a finite magnitude. A solution with a passable wormhole, in which Fg = 0,that is, without gravitational force, has also been obtained. In addition, solutions of Einstein’s vacuum equations Rik = 0 in space-time with the metric presented above have been obtained, that is, in the absence of a rotating continuous medium in the presence of only vortex gravitational field. The resulting solution describes the geometry of the wormhole space-time. Conclusion: Since the above-mentioned solution of gravitational equations with a wormhole is a solution to vacuum equations, that is, for empty space without matter, it is possible to suggest the presence of wormholes in outer space that exist a priori and also exist near the Earth.

Background and Objectives: In this paper we consider the peculiarity that arises during the generalized chaotic synchronization regime detection in systems with a complex attractor topology having internal symmetry. Materials and Methods: As the system under study we consider two modified Guckenheimer – Holmes discrete maps coupled unidirectionally. To detect the presence of generalized synchronization we calculate the spectrum of Lyapunov exponents and propose the modification of auxiliary system approach. Results: Considering that the symmetry in the dynamics of the autonomous response system can lead to multistability due to the drive system signal, the correct detection of generalized synchronization with the help of the auxiliary system approach may be complicated. Modification of the generalized synchronization criterion, which allows increasing the reliability of the method in such cases, has been proposed. Conclusion: The results obtained with the help of modified auxiliary system approach are in a good agreement with the calculation of Lyapunov exponents.

Background and Objectives: Triglycerides, as the primary components of fats and oils, play a crucial role in various scientific and industrial fields, including food production, energy, and pharmaceuticals. Their interaction with water molecules is particularly significant, yet many aspects of these interactions remain poorly understood. This study aims to investigate hydrogen bonding in monohydrates of saturated fatty acid triglycerides using molecular dynamics (MD) and density functional theory (DFT) simulations. The objectives include determining the thermodynamic parameters of association, analyzing the influence of hydrocarbon chain length on hydration, and identifying the most stable hydration configurations. Materials and Methods: The study employed classical molecular dynamics (GROMACS) with the AMBER-03 force field and DFT calculations (B3LYP/6-31+G(d) and wB97XD/6-311+G(d,p)) to model hydrogen bonds in monohydrates of triglycerides ranging from triacetin to tristearin (chain lengths of 0 to 16 methylene groups). The MD simulations involved a 4×4×4 nm periodic boundary cell with a triglyceride molecule surrounded by water, run for 500 ps at 300 K and 1 bar. Hydrogen bonds were identified using geometric criteria (distance ≤ 3.5 Å, angle ≤ 30°). DFT calculations optimized molecular structures and calculated thermodynamic parameters, including association energies, enthalpies, and equilibrium constants. Results: The results have revealed that carbonyl groups of the central ester chain are the primary sites for hydrogen bond formation. Monohydrates involving the central chain (Type 1) have exhibited a greater stability than those involving side chains (Type 2). The association energy for Type 1 monohydrates has saturated starting from tricaprylin (chain length of 6). A linear relationship has been observed between the thermodynamic parameter TΔS and the equilibrium constant Kα for Type 1 monohydrates, attributed to the loss of conformational entropy upon hydration. Non-classical hydrogen bonds (C-H···O) have also contributed to the stability of monohydrates, influencing their spatial structure. The study has found that hydration of longer chains requires higher energy to overcome entropy losses. Conclusion: The study has demonstrated that the central carbonyl group of triglycerides is the primary hydration site, with Type 1 monohydrates being more stable than Type 2. The association energy and enthalpy reach saturation for chains longer than tricaprylin, while linear dependencies of TΔS and Kα on chain length highlight the role of conformational entropy in hydration. These findings enhance the understanding of triglyceridewater interactions, providing insights relevant to food science, pharmaceuticals, and the development of lipid-based delivery systems. The combined use of MD and DFT has proved effective for analyzing these complex molecular interactions.

Background and Objectives: The lipid membrane is one of the most important structures of a living cell, representing a barrier with selective permeability. Many biological processes are associated with changes in the concentration of positive and negative ions inside and outsidethe cell. Inthis regard, themembrane ismore widely represented as an electric capacitor. Inmodern studies onthe effect of an alternating field on biomolecular lipids, the existence of a nonlinear capacitance-voltage dependence is also mentioned, which makes the lipid membrane a promising candidate for the role of amemcapacitor. Since the use of practicalmembranemodels is associated with their instability, themolecular dynamics method has become widespread. A similar memory effect was obtained in studies using a coarse-grained model. On all-atom systems, this effect is poorly represented in the literature. The all-atom model more fully describes the interaction of particles, so it would be relevant to compare the coarse-grained and all-atomic membrane-solvent system as models of a memcapacitor under the influence of an alternating electric field. Materials and Methods: The studied system consisted of a lipid membrane immersed in an aqueous KCl solution. Two quantitatively similar systems consisted of 512 lipid molecules, such as dipalmitoylphosphatidylcholine (1,2-Dipalmitoyl-sn-Glycero-3-Phosphocholine), two water compartments of 40 Å and 3 M salt. Two types of force fields were used in the work, a all-atom charmm36m, as well as coarse-grained force fields martni22p and a modified force field – v2.2refPOL+refION. An alternating electric field with a strength of 0.5, 1.0 and 1.5 V/nm with a frequency of 1 GHz was applied to the systems. Molecular dynamics simulations were performed using GROMACS. Results: Under the action of the field, each system has behaved as a “classical” capacitor, where oppositely charged particles have been accumulated on opposite sides of the membrane. The nature of the ion distribution is also similar for the studied systems, positive particles are able to penetrate into the membrane, located inside the hydrophilic structures, and the charge peaks of negative particles are outside the membrane. A significant difference between the all-atom and coarse-grained models is the numerical value of the accumulated charge. Based on the results obtained, we can also talk about the nonlinear dependence of the total charge value in relation to the field strength value and the existence of the hysteresis effect. Conclusion: In this regard, the presented systems can be used to study the memcapacitive properties. 

Background and Objectives: Infra-slow oscillations of brain potentials with a frequency of less than 0.5 Hz, reflect the activity of the autonomic regulation centers and are markers of the psychophysiological state of a person. Such oscillations are characterized by non-stationary dynamics, which complicates their experimental study. Materials and Methods: We have proposed a method for estimating the characteristic time of stationarity of infra-slow oscillations of brain potentials based on the analysis of experimental time series of electroencephalograms. The method includes the stages of dividing the time series into segments, constructing approximating polynomials for each segment, calculating the matrix of Euclidean distances between the coefficients of the polynomials, clustering the segments to determine areas of quasi-stationary dynamics, and analyzing the durations of the combined segments to obtain statistical characteristics. The proposed method can be used to estimate the stationarity time of other electroencephalograms rhythms, as well as the frequency components of the sequence of RR-interval. The method was used to analyze electroencephalograms signals and RR-intervals of 50 healthy volunteers at rest. Results: It has been shown that oscillations in different frequency ranges of the studied signals have different durations of quasi-stationary behavior. In the frequency ranges of 0.05–0.15 Hz and 0.15–0.50 Hz, reflecting the activity of the sympathetic and parasympathetic branches of regulation, respectively, the stationarity time of infra-slow oscillations in electroencephalograms signals was 30 s and 36 s, respectively. Conclusion: The durations of quasi-stationary sections of infra-slow oscillations in electroencephalograms correspond well to the durations of sections of quasi-stationary dynamics of the sequence of RR-interval in the frequency ranges associated with the processes of sympathetic and parasympathetic regulation of the heart rhythm. 

Background and Objectives: Currently, perforated graphene is one of the most discussed representatives of porous 2D nanomaterials from the standpoint of their promising properties and prospects for application in nanoelectronics and nanosensors. In this paper, we consider perforated graphene films with almost round holes with a diameter of 1.2 nm, functionalized with carboxyl (COOH) groups. The aim of the work was to study the chemoresistive response of such films to NO2 gas molecules, which is one of the air pollutants. Materials and Methods: To conduct the study, we used the quantum density functional method in the tight-binding approximation with self-consistent charge calculation. Calculations of the chemoresistive response were carried out in the presence of water molecules on the surface of the functionalized perforated graphene film at a temperature of 300 K. Results: It has been found that the film response value is 87–93% depending on the number of NO2 molecules adsorbed on the surface of the perforated graphene (from 1 to 6). The high chemoresistive sensitivity of the studied films is explained by a sharp decrease in its resistance (by an order of magnitude) when NO2 molecules are deposited. The observed decrease in resistance is explained from the standpoint of changes in the electronic structure of the film and the laws of quantum electron transport in it. Conclusion: The results obtained indicate promising prospects for the use of functionalized perforated graphene films in a gas sensor for detecting pollutants in the air.

Background and Objectives: The article covers the Saratov period in the life of Academician of the Russian Academy of Sciences Lev P. Pitaevskii (1933–2022) in the context of the genealogical line of several generations of Pitaevskiis from the beginning of the 19th century, when L. P. Pitaevskii’s great-great-grandfather Trofim Efimovich bore the surname Pitaev. Detailed biographical information is provided about the academician’s close relatives: Petr I. Pitaevskii, father, Anna S. Feigelson, mother, Lubov’ L. Lukashinskaya, wife. All of them received higher education at Saratov State University. The article provides original materials about L. P. Pitaevskii’s school years and his studies at the Physics Department of Saratov University. Materials and Methods: When writing this article, data from the State Archive of the Russian Federation, the Russian State Archives of Socio-Political History, the State Archive of the Saratov Region, the State Archive of the Modern History of the Saratov Region, the Archive of the Saratov State University, as well as the recollections of people who knew L. P. Pitaevskii closely were used. Conclusion: The high intellectual level of the family in which the future academician was born and raised, his early, clearly expressed desire for scientific creativity have been observed. The political and social peculiarities of the country in the 20th century have been reflected in the biographies of the Pitaevskii’s.