A future for Ukrainian science.

As the war in Ukraine enters its fourth month, Russian forces continue to destroy the nation's scientific institutions and infrastructure, signaling Russia's intent to obliterate the future for Ukraine. In Kharkiv, for instance, the renowned Institute of Physics and Technology and its newly built Neutron Source nuclear facility have been heavily damaged. Even the Plant Production Institute with its underground national seed bank-one of the world's largest-has been bombed.

Electron density fluctuations in collisional dusty plasma with variable grain charge.

The kinetic theory of electric fluctuations in a collisional weakly ionized dusty plasma is formulated with due regard to the grain charging dynamics. The correlation functions of electron and ion density are obtained by considering their collisions with neutrals described within the Bhatnagar-Gross-Krook model. The electron density correlation spectra in isothermal and nonisothermal plasma are calculated for various values of grain density, grain size, and ion collisionality.

Interaction force between two finite-size charged particles in weakly ionized plasma.

The results of numerical studies of the interaction forces between two finite-size charged spherical conductive particles embedded into weakly ionized strongly collisional isothermal plasma-like medium are presented. The studies are performed for the case of particles with fixed electric charge under the assumption that particles do not absorb electrons and ions from the surrounding plasma (colloidal particles) as well as for particles charged by plasma currents (grains). In the first case the Poisson-Boltzmann model was used and in the second the dynamics of grain charging is described in the drift-diffusion approximation.

Statistical description of Coulomb-like systems.

The solution of the problem of the partition function calculation for a Coulomb-like system is proposed. The quantum-field-theory approach is used to give a statistical description of a system of interacting particles with due regard to arbitrary spatially inhomogeneous configurations. Formation of structures in a Coulomb-like system is analyzed and applied to the case of of dusty crystals and two-dimensional colloidal crystals.

Stochastic processes crossing from ballistic to fractional diffusion with memory: exact results.

We address the now classical problem of a diffusion process that crosses over from a ballistic behavior at short times to a fractional diffusion (subdiffusion or superdiffusion) at longer times. Using the standard non-Markovian diffusion equation we demonstrate how to choose the memory kernel to exactly respect the two different asymptotics of the diffusion process. Having done so we solve for the probability distribution function (pdf) as a continuous function which evolves inside a ballistically expanding domain.

Screening of dust grains in a weakly ionized gas: effects of charging by plasma currents.

Screening and charging of a grain in a weakly ionized plasma background are studied within the drift-diffusion approximation. The computations evidence that the account of grain charging results in a distinct qualitative change in the screened field as compared to the thermodynamically equilibrium case of a grain with a constant charge. The stationary grain charge as well as the field within the sheath around the grain are shown to be almost independent of the type of boundary conditions (for relatively low ionization rates and small grain sizes), whereas the asymptotical behavior of the effective field is rather sensitive to them.

Anisotropic diffusion across an external magnetic field and large-scale fluctuations in magnetized plasmas.

The problem of random motion of charged particles in an external magnetic field is studied under the assumption that the Langevin sources produce anisotropic diffusion in velocity space and the friction force is dependent on the direction of particle motion. It is shown that in the case under consideration, the kinetic equation describing particle transitions in phase space is reduced to the equation with a Fokker-Planck collision term in the general form (non-isotropic friction coefficient and nonzero off-diagonal elements of the diffusion tensor in the velocity space). The solution of such an equation has been obtained and the explicit form of the transition probability is found.

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.