Issue 5, 2025

The method of "Large particles" in mathematical modeling of Kelvin–Helmholtz instability in air

S. I. Kosyakov$^{1,2}$, S. N. Kulichkov$^{1,2}$, M. N. Zakirov$^1$

The application of the well–known "Large particles" method in mathematical modeling of the simplest type of shear flows - a two-dimensional unsteady plane mixing layer is considered. The results of direct numerical simulation of the Kelvin-Helmholtz instability development at the interface of two layers of air of different densities moving with a tangential velocity shift in a field of strong external acceleration are described. The reliability of the calculation results is confirmed by comparing them with analytical calculations, with the results of numerical solution of a similar problem, as well as with experimental data. Based on the results of calculations, a new functional dependence of the increase in the width of the mixing layer on time, external acceleration, the difference in the densities of the air layers and the velocity difference at the contact boundary is obtained. This dependence is obtained for large values of acceleration values, velocity differences, and density at the gap. It will be useful for predicting the expansion of mixing zones in various currents with a tangential velocity gap, which are ubiquitous both in technology and in the atmosphere – for example, at the initial section of the jet, at the initial stage of mixing in a cylindrical vortex, with the development of wavy clouds or instability of a clear sky in the atmosphere.

S. I. Kosyakov$^{1,2}$, S. N. Kulichkov$^{1,2}$, M. Z. Nafisovich$^1$

Currently, a significant effect of the expansion of the front region of intense nonlinear acoustic waves created in the atmosphere by pulsed point sources of various nature has not been fully explained – the recorded width of the front region is several orders of magnitude larger than it follows from theoretical concepts. To explain such a significant effect, a hypothesis has been put forward about the possibility of developing Kelvin-Helmholtz instability inside the front region of the wave with a shear flow caused by a mass velocity gradient in the front region itself. The paper substantiates the proposed hypothesis. For this purpose, direct (without using any semi-empirical models) numerical simulation of the Kelvin-Helmholtz instability inside a physically infinitesimal volume of air in the front region of an intense nonlinear acoustic wave is performed. The homogeneous plane motion of compressed air in a wave is considered. It is shown for the first time that the development of Kelvin-Helmholtz instability at different distances from the source should have geometric similarity due to the fact that the process develops in an ideal environment. It does not matter whether the width of the front area increases as the wave moves away from the source or it increases due to an increase in its energy.

D. V. Selezneva

In the oil and gas industry, carbon dioxide injection into the reservoir is considered a promising method for enhancing oil recovery: when dissolved in hydrocarbons, the viscosity of oil decreases and a swelling process occurs, which improves the efficiency of displacement. At certain values of pressure and temperature, a three-phase equilibrium can form in the system - two liquid phases (enriched in carbon dioxide and enriched in hydrocarbons) and a gas phase, which seriously complicates the use of classical iterative algorithms for calculating phase equilibria with stability tests. In this paper, the method of direct minimization of the Gibbs free energy at fixed values of pressure and temperature was used to determine the boundaries of the regions of two-phase and three-phase equilibrium; in addition, the viscosities of each phase were calculated using the Lorenz-Bray-Clark model, which made it possible to quantitatively estimate the decrease in the viscosity of the oil phase.

Structural properties of host galaxies of light-weight supermassive black holes based on new data from "Hubble" space telescope

L. -. Osipova$^1$, K. -. Grishin$^2$, I. -. Chilingarian$^2$

In this paper, two-dimensional and one-dimensional photometric modeling of new Hubble Space Telescope data was performed for galaxies hosting intermediate-mass black holes (IMBHs), as well as for objects from an extended sample with black hole masses up to one million solar masses. Using the resulting models, the stellar mass of each galaxy bulge was estimated, and the positions of the galaxies were determined on the black hole mass–bulge mass scaling relation. The location of these galaxies on this relation provides constraints on black hole growth processes in the low-mass regime.

P. S. Sozinova, N. N. Shakhvorostova

We report observations of methanol emission at 84-GHz toward 32 infrared dark cloud (IRDC) sources at various evolutionary stages. Data were obtained using the 20-meter radiotelescope located in Onsala, Sweden, during 2019-2020. Among these 32 sources, the 5$_{-1}$---4$_{0} E$ methanol emission was detected in 24. These objects do not overlap with any previously observed 84-GHz sources, making all our detections novel. Based on our findings, five sources were identified in which emission of class I methanol masers was observed. Additionally, we compare the 84-GHz observations with previous 44-GHz measurements toward the same sources, revealing a correlation between emission at both frequencies and notable similarities in their spectral profiles.

A. V. Borisov$^1$, A. O. Shishanin$^2$

In this methodological note, we consider the thermodynamic properties of a simple system with an infinite number of degrees of freedom --- a quantum string equivalent to an infinite set of oscillators with frequencies multiples of the fundamental frequency $\omega$. We calculate the partition function, average energy, and heat capacity of the string as functions of temperature. Using the Laplace transform of the partition function, we show that the statistical weight of a string state with energy $E = N \hbar\omega $ is equal to the number of partitions $p(N)$ of a natural number $N$ into a sum of natural numbers, and we reproduce (up to a numerical coefficient) the well-known in number theory Hardy--Ramanujan asymptotic formula for $p(N)$ provided $N\gg 1$. We show that quantizing a string is also equivalent to quantizing a one-dimensional field theory describing, in particular, a superposition of standing electromagnetic waves.

V. V. Hramkov$^1$, D. R. Aliev$^1$, V. O. Skulkin$^1$, A. A. Vorontsova$^1$, E. A. Gerdt$^1$

The research aim is investigation of the curium affection on neutron-physical and thermophysical characteristics of VVER-1200 and BN-600. The fuel assemblies neutron-physical and thermophysical models have been created for the calculations to be made. Curium was added to the common fuel homogeneously in the proportions from 0,1 to 20 % as CmO2 oxide. Characteristics considered are: neutron multiplication factor, neutron spectrum, temperature distribution. A stronger effect on the reactivity is observed of the VVER-1200 model – Keff decreases by 3,85%. The maximum decrease of BN-600 neutron multiplication factor is 3%. Adding curium increases the neutron flux density of VVER-1200. Also curium does a considerable positive effect on the fast reactor’s reactivity, that creates a possibility of using Cm as a fuel. The maximum fuel temperature decreases by 500 grad, when curium is added.

S. Yu. Glazov, A. A. Kovalev

In this paper, the dependence of the plasma wave frequency on the wave vector and the density of plasma excitations in the electron gas of a two-dimensional graphene superlattice are theoretically investigated. The calculations are performed based on the quantum theory of plasma waves in the random phase approximation taking into account the umklapp processes. The plasmon frequency estimate for the currently theoretically studied superlattices based on graphene on a striped substrate yields ω ∼ 10$^13$ c$^−1$. A comparison of the plasmon dispersion laws of graphene and quantum semiconductor superlattices is performed.

S. Yu. Glazov, E. I. Dudareva

The effect of a constant homogeneous electric field on the penetration of a field of periodically charged planes and filaments into a two-dimensional electron gas of a two-dimensional superlattice is studied. In the presence of a constant quantizing electric field, the potential oscillates with frequencies that are multiples of the Stark frequency. In the case of a non-degenerate electron gas, the amplitude of the constant component of the potential is found.

A. N. Golodukhina

Optical microresonators with high quality-factor are an advanced platform for carrying out actual scientific research in the field of quantum optics and photonics. Self-injection locking (SIL) effect is an example of phenomena realized on the platform of such resonators. SIL effect allows for narrowing the width of the emission line to the order of units of kHz. In this work, we studied features of self-injection locking regime in the presence of stimulated Raman scattering in the system. It was found that in the presence of Stokes optical microcomb the output emission linewidth turns out to be an order of magnitude higher than expected values.

L. -. Boudjemila

Solar cells are very fragile, and exposure to extreme weather conditions may cause micro-cracks, leading to a degradation in their performance. Therefore, a perovskite material combined with a self-healing polymer can form a composite with a dual continuous interwoven network. This composite undergoes healing through synergistic grain growth and solid diffusion processes at moderately elevated temperatures of 333 K. The ions can migrate to fill gaps or fissures, and their ionic mobility allows for the reorganization of the crystal structure, potentially restoring electrical connectivity. Various experimental techniques have been optimized in order to achieve better efficiency of the PSCs in atmospheric condition by varying the concentrations of the self-healing polymer incorporated into the perovskite material to find the suitable one. The I-V measurements show a reduction of loss in efficiency from 40% to only 4% of the damaged solar cell. This approach can provide potential protection against efficiency loss due to micro-fissures while also benefiting from the optoelectrical properties of the perovskite material.