This paper investigates the long-time behaviour of solutions to the $$\varepsilon $$ -perturbed Fokker–Planck–Kolmogorov (FPK) equation in the context of ship roll dynamics under stochastic sea excitation. Starting from a stochastic model of a ship navigating in a transverse sea, we derive the associated FPK equation governing the time evolution of the joint probability density function (PDF) of the roll angle, angular velocity, and wave-induced excitation. The theoretical analysis focuses on the asymptotic behaviour of the PDF as time tends to infinity, demonstrating that the probability of capsize stabilises and eventually becomes time-invariant. This result offers new insights into the probabilistic stability of ships subjected to random sea conditions. To support these theoretical findings, we implement a finite-difference numerical scheme that accurately captures the transient dynamics and confirms convergence towards the steady-state distribution. The simulations validate the analytical predictions and underline the robustness of the proposed approach for long-term stability assessments in marine engineering applications.

Concepts regarding the mechanisms of defect formation in material structures are examined. Problems of the kinetic theory of strength and the impact of thermal fluctuations on the initiation of microcracks and the accumulation of irreversible damage in materials are analyzed. An approach to constructing mathematical models of the damage accumulation kinetics using hypothetical schemes of quasi-chemical reaction is proposed.

Background. The inverse electromagnetic problems of inhomogeneity reconstruction in a dielectric body by the near-field measurements arise, for example, in the early diagnosis of breast cancer by microwave tomography. The solution of such inverse problems is the basis for the development of a technique for detecting inhomogeneities using microwave devices. The efficiency of the technique depends on the inverse problem solution accuracy. Therefore, the development of new, more accurate methods for solving the inverse problem of microwave tomography is highly relevant. Aim. This study is aimed at the development of a method for solving the electromagnetic inverse problem of microwave tomography using near-field measurements, i.e., restoring the structure of an inhomogeneous dielectric body from values of an electromagnetic field outside this body using a measuring setup. Methods. The inverse problem is solved by a two-step method for determining the inhomogeneity of a body, in which the current function inside the body is first found and then the permittivity function is calculated. The method is non-iterative and does not require a good initial approximation. Results. A two-step method has been used to solve the inverse problem of microwave tomography. The numerical results are presented. Inhomogeneous bodies in the shape of a hemisphere have been investigated. Experimental results are presented. Conclusions. The efficiency of the proposed technique for detecting inhomogeneities in a dielectric body by microwave tomography is demonstrated. The calculation and experimental data are reported.

Optimization parameters of a cyclic thermal de-icing system (DIS) are formulated. A method of optimization multiparametric calculation has been developed. The use of this technique is proposed in the conditions of the most intense icing of the structure in question to determine the best operating parameters of the de-icing system. The use of the obtained parameters reduces the DIS’ energy consumption, which can reduce the weight of the batteries powering it and increase the efficiency of both aircraft and wind turbines in icing conditions.

The radiation patterns of mid-infrared graphene antenna arrays with N = 256 emitters have been simulated in the CST MWS software package at the resonant frequencies of the surface plasmon polariton fundamental mode in micro- and nanosized rectangular graphene elements for different values of the chemical potential. It has been shown that, with an increase in the chemical potential, the operating frequencies are retuned towards higher mid-IR frequencies, the radiation pattern width at the half-power level decreases, and the direction of the main lobe of the radiation pattern changes; i.e., electronic scanning of the main beam of the radiation pattern occurs.

The synthesis of a catalyst carrier precursor by sub- and supercritical water oxidation of metallic aluminum followed by iron oxide deposition has been investigated. The dependences of the physicochemical properties of the samples on temperature, reaction time, and supercritical fluid density have been examined. Conclusions have been drawn about the optimum reaction parameters ensuring the maximum specific surface of the samples.

Using the constructed Lagrange function $$L$$ and calculated dissipative function $$\dot {Q}$$ , a general system of dynamic equations has been obtained to describe the motion of a cylindrical body completely immersed in a fluid. It is assumed that the body is hinged at its one end where the origin of coordinates is selected. The free end can make almost any motions and is elastically held by a spring at an arbitrary point. The problem is solved in a spherical coordinate system in which differential equations of motion are derived in terms of two independent angular variables $$\theta $$ and $$\varphi $$ taking into account the viscosity $$\eta $$ of a continuum.

To develop new 6G and beyond terahertz (THz) wireless communication systems with the high-throughput and data rate, the direction of polarization of emitted THz waves should be effectively controlled, whereas most methods are technologically complex and expensive. The implementation of THz antennas and devices based on 2D materials, e.g., graphene, solves the problem of the effective control. The possibility is studied of controlling the polarization of THz and IR radiation of plasmonic antennas based on rectangular graphene nanoribbons by changing the chemical potential (applying an external electric field). This important scientific problem related to the design of THz antennas can largely be solved by modeling in the CST MWS 2023 electrodynamic modeling program. Plasmon THz antennas based on rectangular graphene nanoribbons have been chosen as objects of study and the possibility of emitting waves of two orthogonal polarizations has been shown. Methods for controlling the polarization of THz and IR radiation of such antennas have been identified, which are based on choosing the operating frequencies corresponding to the plasmon resonances of the surface plasmon-polariton modes and metallization of a dielectric substrate. The possibility of controlling the polarization of THz and IR radiation allows the creation of both new elements of plasmonic antenna arrays and new communication technologies, including future 6G networks.

The paper presents the results of a theoretical study of the dispersion characteristics of electromagnetic waves (EMW) existing in a transversely magnetized antiferromagnetic (AFM) semiconductor with loss. An AFM semiconductor is an infinite bi-gyrotropic medium, the effective material parameters of which are twice negative in several frequency ranges. It was found that these frequency bands are in the terahertz range, and there are four backward EMEs in them, two of which are TE waves, and the other two are TM waves.

Abstract—For deeply supercooled bulk water, known are anomalies of thermodynamic quantities near the Widom line, the locus of increased fluctuations of entropy and density. In this work, we measured the reflected power of microwave radiation at the frequency of 18 GHz from a silicate sorbent sample moistened with a hydrogen peroxide solution. In the experiment, we observed variations in the recorded reflected radiation power in the range of –46 to –47°C determined by structural changes in the liquid. Thus, it is shown that fluctuations of water parameters near the Widom line manifest themselves in changes not only in thermodynamic, but also in electrophysical quantities.