Strain-stream model of epidemic spread in application to COVID-19.

Abstract: The recently developed model of the epidemic spread of two virus strains in a closed population is generalized to the situation typical for the couple of strains delta and omicron, when there is a high probability of omicron infection soon enough after recovering from delta infection. This model can be considered as a kind of combination of SIR and SIS models for the case of competition of two strains of the same virus with different contagiousness in a population. The obtained equations and results can be directly implemented for practical calculations of the replacement of strains of the SARS-CoV-2 virus.

Second sum rule for the hot plasma permittivity.

Based on linear response theory, Kramers-Kronig relations, and diagram techniques of perturbation theory, it is shown that the second sum rule is satisfied for hot plasma permittivity. An explicit analytical expression for the second sum rule in the limit of weak nonideality is derived.

Virial theorem for an inhomogeneous medium, boundary conditions for the wave functions, and stress tensor in quantum statistics.

On the basis of the stationary Schrödinger equation, the virial theorem in an inhomogeneous external field for the canonical ensemble is proved. It is shown that the difference in the form of virial theorem is conditioned by the value of the wave-function derivative on the surface of the volume, surrounding the system under consideration. The stress tensor in such a system is determined by the average values of the wave-function space derivatives.

Diffusion in a time-dependent external field.

The problem of diffusion in a time-dependent (and generally inhomogeneous) external field is considered on the basis of a generalized master equation with two times, introduced by Trigger and co-authors [S. A. Trigger, G.

Active and passive Brownian motion of charged particles in two-dimensional plasma models.

The dynamics of charged Coulomb grains in a plasma is numerically and analytically investigated. Analogous to recent experiments, it is assumed that the grains are trapped in an external parabolic field. Our simulations are based on a Langevin model, where the grain-plasma interaction is realized by a velocity-dependent friction coefficient and a velocity-independent diffusion coefficient.

Kinetic theory of Jeans instability.

Kinetic treatment of the Jeans gravitational instability, with collisions taken into account, is presented. The initial-value problem for the distribution function which obeys the kinetic equation, with the collision integral conserving the number of particles, is solved. Dispersion relation is obtained and analyzed.

Fokker-Planck equation for Boltzmann-type and active particles: transfer probability approach.

A Fokker-Planck equation with velocity-dependent coefficients is considered for various isotropic systems on the basis of probability transition (PT) approach. This method provides a self-consistent and universal description of friction and diffusion for Brownian particles. Renormalization of the friction coefficient is shown to occur for two-dimensional and three-dimensional cases, due to the tensorial character of diffusion.

Rotational kinetics of absorbing dust grains in neutral gas.

We study the rotational and translational kinetics of massive particulates (dust grains) absorbing the ambient gas. Equations for microscopic phase densities are deduced resulting in the Fokker-Planck equation for the dust component. It is shown that although there is no stationary distribution, the translational and rotational temperatures of dust tend to certain values, which differ from the temperature of the ambient gas.

Nonhomogeneity of dusty crystals and plasma diagnostics.

Real dusty crystals are inhomogeneous due to the presence of external forces. We suggest approximations for calculations of different types of inhomogeneous dust crystals (DC's) (chain and DC's with a few slabs) in the equilibrium state. The results are in a good agreement with experimental results and can be used as an effective diagnostic method for many dusty systems.

Statistical theory of dusty plasmas: microscopic equations and Bogolyubov-Born-Green-Kirkwood-Yvon hierarchy.

Basic principles of statistical theory of dusty plasmas are formulated with regard for electron and ion absorption by dust particles. Rigorous microscopic equations are introduced and employed to derive the BBGKY hierarchy and kinetic equations. The charging processes are shown to induce a considerable modification of both microscopic and kinetic equations for plasma particles and grains.

Stationary velocity and charge distributions of grains in dusty plasmas.

Within the kinetic approach the velocity and the charge distributions of grains in stationary dusty plasmas are calculated and the relations between the effective temperatures of such distributions and plasma parameters are established. It is found that the effective temperature which determines the velocity grain distribution could be anomalously large due to the action of accelerating ionic bombarding force. The possibility to apply the results obtained to the explanation of the increasing grain temperature in the course of Coulomb-crystal melting by reduction of the gas pressure is discussed.