Issue 4, 2026

Bandwidth restrictions of a waveguide with a periodic impedance boundary

A. A. Bykov

A mathematical model for a rectangular waveguide with an impedance boundary condition is formulated and substantiated. The model is based on the application of the Galerkin boundary method. It is assumed that the surface impedance is not a constant, but is given as a function of the coordinates on the surface. The solution is represented as a linear combination of coordinate functions, each of which exactly satisfies Maxwell's equations inside a cylindrical domain. The set of coordinate functions at the border forms a complete system. The coefficients are found from the condition of orthogonality of the surface residual to the system of a projection functions. Because of using the Galerkin method the projection functions coincide with the system of coordinate functions. To calculate the guided waves of a rectangular waveguide with an impedance boundary, a homotopy method is proposed and justified. The decomposition of the solution into a power series in a small parameter is also constructed.

Entropy-Regularized Attention Mechanisms in a Wavefunction Ansatz for the Variational Monte Carlo Algorithm

R. A. Rudamenko, A. M. Savchenko

In the problem of finding the ground state of a many-electron system, variational quantum Monte Carlo (VMC) reformulates the task as the optimization of a parameterized wave-function ansatz in real space. The quality and stability of VMC optimization are largely determined by the expressivity of the ansatz and by the numerical robustness of the training procedure, including the construction of samples from the wave-function distribution $|\Psi_{\theta}|^{2}$. In this work, we consider neural-network approaches to wave-function parameterization aimed at modeling electronic correlations and propose to use neural attention mechanisms as a universal module for nonlocal correlation transformations. Special attention is paid to the entropic origin of attention normalization: the standard softmax corresponds to Shannon entropy regularization, whereas generalized entropies, in particular those of Tsallis and Sharma--Mittal, make it possible to move toward sparse normalization families such as $\alpha$-entmax. Pilot computational experiments were carried out for the Be atom and compared with experimental reference data. For the baseline softmax case, stable training trajectories were obtained. We also performed an experiment in which softmax was replaced by entmax; in the current implementation, this revealed numerical difficulties during training and thus identified the practical limits of a direct substitution of the attention normalization scheme. The paper formulates the theoretical foundations and practical recommendations for this approach and outlines further directions for the development of entropy-regularized attention mechanisms in neural-network wave-function ans\"atze for VMC.

A mathematical model of an acoustic signal as a superposition of components with an unknown a priori shape

M. N. Zakirov

A method for analyzing acoustic signals is presented based on their representation as a superposition of repeating components of a fixed but a priori unknown shape, having different amplitudes and time delays, and additive noise. The method allows you to find duplicate fragments in the signal and evaluate their parameters. Unknown parameters are determined by minimizing the discrepancy between the model and experimental signals. The proposed approach can be used to improve methods of acoustic sounding of the atmosphere, since the delay times of reflected signals are related to the height of the reflecting layers, and their amplitudes characterize the intensity of reflection. The method is also applicable to the study of other media with a plane-parallel layered structure.

Comparison of Statistical Models and Gradient Boosting for Reconstructing Missing Values in a Time Series of Atmospheric Carbon Dioxide Concentration

A. I. Baliuk

The problem of reconstructing missing values in a time series of carbon dioxide concentration using atmospheric and meteorological observation data is considered. The paper describes the statistical SARIMAX model, as well as Lasso regression as a method for preliminary selection of significant exogenous variables. The main part of the paper is devoted to the gradient boosting model and its comparison with statistical models. It is shown that the quality of missing-value reconstruction using the SARIMAX model depends on the set of exogenous variables. The gradient boosting model built on an extended feature space demonstrated the best performance in reconstructing missing values of carbon dioxide concentration. The obtained results can be used for working with time series of geophysical parameters.

V. V. Binkovskii, S. D. Mostovoy

In this paper, the classical XY model on a three-dimensional kagome lattice with ABC stacking is investigated using the Monte Carlo method. The ground states of the system are determined depending on the in-plane anisotropy parameter $\alpha = J_{\text{up}}/J_{\text{down}}$ and the interlayer interaction $J_z$. Phase diagrams are constructed and the types of phase transitions are established. It is shown that for small $|J_z|$ a first-order transition to a $120^\circ$ structure is realized, while for large $|J_z|$ a second-order transition to collinear ordering occurs. In a narrow region near the critical value $|J_z^{\text{c}}|$, phase competition is observed.

A. V. Rakhmanov, S. D. Mostovoy

The paper presents a simulation of evaporation in a two-dimensional system of particles interacting via the Lennard-Jones potential. The establishment of thermal equilibrium is studied; the temperature of the system is determined using both kinetic and statistical approaches, and a relation between the initial particle velocity and the temperature is established. A local heating method is proposed to simulate evaporation and to calculate the latent heat of vaporization. It is shown that the obtained latent heat values at different temperatures agree with a theoretical power-law dependence. Additionally, the vapor pressure and heat capacity of the system are calculated; their temperature dependences qualitatively follow the Antoine equation and the behavior of heat capacity near a phase transition. The results confirm the applicability of the Lennard-Jones potential for describing first-order phase transitions.

A physico-mathematical model of the transformation of an intense nonlinear acoustic wave in the atmosphere into a weak sound disturbance

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

As a result of numerous experiments, it has been established that an intense pulsed nonlinear acoustic wave forming in the atmosphere transforms into a weak sound disturbance with a significant expansion of the frontal region. At the same time, the width of the front area of the wave is an order of magnitude larger than theoretical concepts. The paper solves the problem of developing a mathematical model of such a transformation. The model is based on the hypothesis of the development of Kelvin-Helmholtz instability in neighboring physically infinitesimally small volumes of air during their compression in the front region of the wave. As a result of the resulting pulsations, the Lagrangian of the air flow is disrupted and an exchange of mass, momentum, and energy occurs between groups of neighboring physically infinitesimally small volumes, which leads to an expansion of the front region of the wave. The control volume method is used to derive the model equations. The left sides of the obtained equations represent classical unsteady Eulerian differential equations. The right-hand sides of the equations contain source terms of a pulsation nature. The verification of the developed model was carried out on the problem of the spherically symmetric propagation of an air wave from an explosion of a TNT charge. Satisfactory agreement of the calculation results with experimental data is shown.

On the Dallenbach Absorber Theory

V. V. Medvedev$^1$, T. M. Linkova$^2$

Light-absorbing devices based on interference coatings was considered using the example of Dallenbach absorber.The theory of Dallenbach absorber is generalized to the case where the extinction coefficient varies in the transverse direction while the refractive index remains constant. Analytical conditions for perfect absorption under normal wave incidence are derived. The analytical theory is presented in the assumption of a substrate made of perfect electric conductor (PEC).

Calorimetric MEMS gas flow rate sensor based on high-aspect-ratio platinum conductors

E. V. Stekolshikov$^{1,2}$, M. A. Lyakh$^{1,2}$, I. V. Uvarov$^1$

A calorimetric gas flow sensor is presented. The sensing element consists of three platinum wires of 1 mm in length and 130 nm in thickness. They are suspended above a channel etched in a silicon wafer. The central wire serves as a heater, while the side wires act as thermistors and measure the flow velocity. The sensing element is fabricated using microelectromechanical systems (MEMS) technology, and the wires are released in a gas discharge plasma. The sensor is calibrated using a specially developed electronic module that records the change in the resistance of thermistors under the nitrogen flow in a glass tube. The sensor demonstrates the sensitivity of 11.7 mV/(m/s) for flow velocity up to 3 m/s.

Theory and modeling of ordering kinetics in binary alloys

R. Z. Kahidze$^1$, A. V. Nazarov$^{1,2}$

A microscopic theory of ordering kinetics in binary alloys is developed on the basis of the vacancy diffusion mechanism. In contrast to the mean-field approximation, the present approach consistently takes into account two-particle correlations by employing an approximation scheme analogous to that proposed by Kirkwood. A closed kinetic equation is derived for PAB, the probability of finding unlike atoms on neighboring lattice sites. It is shown that, for a square lattice, the equilibrium state is described by a cubic equation, whose roots are obtained analytically using Cardano’s formula. The kinetic equation is solved in closed form; it is found that relaxation proceeds significantly more slowly for the equiatomic composition than for non-equiatomic systems. This result provides a qualitative explanation for the experimentally observed retention of the disordered state in high-entropy alloys, even after prolonged annealing treatments.