Andrei G. Bashkirov

Screening of Gravitational Interactions and Its Astrophysical Manifestations

Screening of the Newtonian potential of a moving test body in a homogeneous Maxwellian gas of gravitating bodies is investigated on the basis of the collisionless kinetic equation and the Poisson equation. The modified potential is expressed in terms of the test particle velocity and the gravitational susceptibility of the system. Since all bodies in such a system execute a thermal motion, a renormalized gravitational potential in the system can be determined by way of averaging the test-body potential over the body velocities with the Maxwellian distribution function. It is found that the resultant renormalized potential not only decays faster than the Newtonian potential but also oscillates with the period on order of the Jeans length. A dark matter allowance in the system gives rise to a significant decrease in the oscillation period. The observable oscillations of the tail ends of the correlation functions of galaxies and Abell clusters testify to the oscillating character of the screened potential, and the observable period of these oscillations enables us to estimate the Jeans wavenumber for the dark matter.

Dynamical screening of long-range interactions in nonrelativistic self-gravitating systems

Abstract The problem of long-range nonrelativistic gravitational interactions is revisited. As in the plasma case, the removal of divergences in the collision integral arises from the influence of the surroundings on the effective interactions of particles. A distinguishing feature of the screening of gravitational interactions is that it has a purely dynamic origin and vanishes for immovable particles, in contrast to the plasma case.

Comment on “Stability of Tsallis entropy and instabilities of Rényi and normalized Tsallis entropies: A basis for q -exponential distributions”

It is shown that the Rényi entropy is as stable as the Tsallis entropy at least for the Abe-Lesche counter examples.

Long-range attraction between particles in dusty plasma and partial surface tension of a dusty phase boundary.

Effective potential of a charged dusty particle moving in homogeneous plasma has a negative part that provides attraction between similarly charged dusty particles. A depth of this potential well is great enough to ensure both stability of crystal structure of dusty plasma and sizable value of surface tension of a boundary surface of dusty region. The latter depends on the orientation of the surface relative to the ion flow, namely, it is maximal and positive for the surface normal to the flow and minimal and negative for the surface along the flow. For the most cases of dusty plasma in a gas discharge, a value of the first of them is more than sufficient to ensure stability of lenticular dusty phase void oriented across the counter-ion flow.

Renyi entropy and power-law distributions in natural and human sciences

Traditional Boltzmann‐Gibbs statistic thermodynamics does not provide power-law distributions characterizing complex self-organizing systems [1]. In this work, we propose using a more general approach involving Renyi entropy that makes it possible to adequately describe complex self-organizing systems. Power-law distributions are observed in various fields of natural sciences and in the social and economic activity of mankind [2] and are known as Zipf’s law in linguistics; the Pareto law in economics and sociology of science; the Gutenberg‐Richter law in geophysics; and power-law distributions for critical phenomena, for the intensity of avalanches in a granulated medium, for fragment masses upon impact fragmentation, for the energy spectrum of particles in the atmospheric cascades of cosmic rays, for users of Web sites, etc. On the other hand, the maximum of the Gibbs‐Shannon entropy

Dynamic screening of gravitational interaction and the problem of ephemeris time

The density disturbance in a system of gravitating masses, which is induced by a moving isolated body, gives rise to dynamic screening of the Newtonian potential of this body. When applied to the Solar planetary system, this implies that, because of the motion of the Sun in the Galaxy, the solar gravitational potential turns out to be more weak than the Newtonian potential. The relevant modifications of the basic relations of celestial mechanics leads, in particular, to an increase in the estimated period of the revolution of the Earth around the Sun by approximately 1 s. Such an increase in the ephemeris year compensates by an order of magnitude the observable mean difference between ephemeris time and universal time.