Objectives. COVID-19 has a number of specific characteristics that distinguish it from past pandemics. In addition to the high infection rate, the high spread rate is due to the increased mobility of contemporary populations. The aim of the present work is to construct a mathematical model for the spread of the pandemic and identify patterns under the assumption that Moscow comprises the main source of viral infection in Russia. For this purpose, a twoparameter kinetic model describing the spatial spread of the epidemic is developed. The parameters are determined using theoretical constructions alongside statistical vehicle movement and population density data from various countries, additionally taking into account the development of the first wave on the examples of Russia, Italy and Chile with verification of values obtained from subsequent epidemic waves. This paper studies the development of epidemic events in Russia, starting from the third and including the most recent fifth and sixth waves. Our twoparameter model is based on a kinetic equation. The investigated possibility of predicting the spatial spread of the virus according to the time lag of reaching the peak of infections in Russia as a whole as compared to Moscow is connected with geographical features: in Russia, as in some other countries, the main source of infection can be identified. Moscow represents such a source in Russia due to serving as the largest transport hub in the country.Methods. Mathematical modeling and data analysis methods are used.Results. A predicted time lag between peaks of daily infections in Russia and Moscow is confirmed. Identified invariant parameters for COVID-19 epidemic waves can be used to predict the spread of the disease. The checks were carried out for the wave sequence for which predictions were made about the development of infection for Russia and when the recession following peak would occur. These forecasts for all waves were confirmed from the third to the last sixth waves to confirm the found pattern, which can be important for predicting future events.Conclusions. The confirmed forecasts for the timing and rate of the recession can be used to make good predictions about the fifth and sixth waves of infection of the Omicron variant of the COVID-19 virus. Earlier predictions were confirmed by the statistical data.

A one-dimensional model based on a kinetic-type equation is proposed for studying the dynamic distribution density of virus carriers in time and space while taking into account their distribution from a dedicated center. This model is new and fundamentally different from known models of the diffusion–reaction type. The analytical solution is built; for obtaining a series of calculations, numerical methods are also used. The model and real data from Italy, Russia, and Chile are compared. In addition to the rate of infection, the “rate of recovery” is considered. When the wave of recovery passes through a territory with the greater part of the commonwealth, a conclusion is made about the onset of global recovery, which corresponds to real data. The predictions are proved to have been accurate also for the second wave of the pandemic in Russia. The model is expected to be able also to describe adequately subsequent epidemics instead of only the development of COVID-19.

In this paper, we present the of theoretical calculation and experimental study results of ultrashort pulse emitters with radiating elements based on an oscillator and disk-cone antenna, the excitation source of which is current oscillations in a long line switched by a switch with short switching time τ. The temporal characteristics of the emission field and its spectrum are determined. Depending on parameter l/(cτ) (l is the length of the vibrator arm), various emission modes are shown to be implemented that differ in frequency characteristics and the shape of the radiation pattern. The basic emission regularities are qualitatively explained based on the calculation of the spectrum of eigen oscillations (in the spectral region) and based on the summation of the contributions from elementary currents flowing over the emitter surface (in the time domain).

A generator of repetitive voltage pulses in the form of a damped sine wave with a period of ~6 ns, an amplitude of the first voltage half-wave of up to ~400 kV, and a pulse repetition frequency of up to 60 Hz is described. The generator is powered from a storage battery (7 A h, 36 V) and has several voltage build-up stages.

Описан частотный генератор импульсов напряжения в виде затухающей синусоиды с периодом ~6 нс, амплитудой первой полуволны напряжения до ~ 400 кВ и частотой импульсов до 60 Гц. Генератор питается от аккумуляторной батареи (7 А · ч, 36 В) и имеет несколько ступеней повышения напряжения.

A new design of powerful high-voltage high-current impulse source for nanosecond megavolt charging of short forming lines (SFLs) is proposed. The first stage of the device is based on inductive energy storage. It accumulates energy supplied by the current of magnetic flux compression generator (MCG), whereas the electro-explosive opening switch is used for the energy output into intermediate SFL. In the second stage, we use a Tesla transformer with oil insulation. The results of the earlier experimental study of submegavolt charging of intermediate forming line as well as the results of calculations of the two-stage facility given in this paper demonstrate the feasibility of the device based on MCGs for nanosecond charging of SFL up to about 3 MV.

This study is a contribution into the development of physicotechnical foundations for generation of powerful nanosecond high-current pulses on the basis of explosively driven magnetic flux compression generators. This problem is solved by using inductive storage of energy for matching comparatively low-voltage explosively driven magnetic flux compression generators and high-impedance loads; short forming lines and vacuum diodes. Experimental data of charging of forming lines are given.

A variant of discrete velocity approach for solving the Boltzmann kinetic equation with regular (deterministic) approximation of collision integrals is used in parallel implementation with NVIDIA GPU computing. Some problems, namely a uniform relaxation, nonuniform relaxation in 2D physical space are solved. Speed up of GPU Boltzmann solver is of the order 100 or more times over CPU version of the solver.

The design and parameters of a compact radiator of high-power electromagnetic nanosecond pulses designed for simulation of ultra-wideband exposures in electromagnetic compatibility problems are described. It is shown that the effective pulse power of the radiator is 3 GW in the forward traveling wave and 15 GW in the wave reflected from the reflector. The effective density of the continuous energy spectrum is 17 mJ/MHz at 0.3 GHz.

Приведено описание конструкции и параметров компактного излучателя мощных электромагнитных импульсов наносекундной длительности, предназначенного для моделирования сверхширокополосных воздействий в задачах электромагнитной совместимости. Показано, что эффективная импульсная мощность излучателя составляет в прямой волне 3 ГВт, а в отраженной от рефлектора – 15 ГВт. На частоте 0.3 ГГц эффективная плотность сплошного энергетического спектра излучения равна 17 мДж/МГц.

Experimental results of generating a nanosecond high-current pulse burst by a multiwinding dynamic transformer, which is based on the principle of recuperation of the energy stored in the single primary winding, and the method of the sequential magnetic-flux trapping by several secondary windings are described. The inductive energy storage with an opening switch is used to sharpen current pulses of the generator. Six small electric capacitors are in turn charged up to ∼300 kV for ∼100 ns with a time interval of 10 μs.

The design and characteristics of powerful nanosecond UWB pulse source intended for study of particular electromagnetic compatibility problems are given. For excitation of UWB source we use high voltage drive-pulse generator based on resonance transformer. Power supply is a set of nickel metal hydride rechargeable batteries. Designed source of radiation is characterized by the following parameters: voltage output of the generator is approximately U-G approximate to 550 kV, field range product (FRP = E x R) equals to 300 kV (with reflector 670 kV approx.), effective radiated power (ERP) is approximately 3 GW (15 GW). Peak energy spectrum at the frequency of 0.3 GHz is 17 mJ/MHz. Pulse-repetition frequency is adjusted within 0 to 1 kHz range. Parabolic reflector is about 1.2 x 1.2 x 0.6 m overall. The source as a whole is combined into monoblock of 1 m high and 0.24 m in diameter. Total weight of the source is 65 kg approximately.

We describe an off-line nanosecond charging device for a short forming line; the device has been created on the basis of an inductive energy storage unit. Energy storage is carried out by the current of an explosive magnetic cumulation generator, and the energy output to the load, by means of an electroexplosive current interrupter. The use of a two-stage, instead of a one-stage, magnetic cumulation generator, consisting of a preamplifier and a dynamic transformer, and two smaller-size generators with sequential connection of secondary windings of dynamic transformers, one of which is connected to the inductive storage unit, and the other, to the current interrupter—has made it possible to substantially increase the line charge voltage. As a result, within a time on the order of 100 ns, it was possible to charge a forming line with an electric length of 5 ns to a voltage of ≥1 MV.

A conical working surface is proposed for the cylinder of an internal-combustion engine. This design improves the seal between the piston and the cylinder; reduces frictional losses; reduces fuel and oil consumption; improves engine power and life; improves performance; and reduces environmental impact.

Improvement in the efficiency of piston compression rings is considered. By taking account of the gas dynamics in determining piston-ring geometry and developing a system of piston rings and piston seals for various internal combustion engines, their basic performance and environmental characteristics may be improved.