On The Kinetic Stage Of Instability Of The Electron Beam - Solar Wind Plasma System

Within the framework of quasilinear theory it has been found that when radio bursts of III type are generated by the inhomogeneous system of electron beam - solar wind plasma, only time of development of the primary stage of instability, i.e., agnetohydrodynamic, is more than the total time of relaxation of an electron beam derived within the homogeneous model. During the development of hydrodynamic instability the electron beam is spread from the Sun to the distance of 4 astonomical unities. The hydrodynamic stage is followed by the development of kinetic instability leading, ultimately, to the formation of horizontal plateau in the beam region at the tail of Maxwell distribution. Parameters of the plateau, such as its length and height, have been calculated as characteristic parameters of an electron beam generated by the active solar bursts. In the development of kinetic beam instability more than a half of kinetic energy of the beam is transmitted to plasma oscillations.Comment: 5 pages, 1 figur

The Procedure Of Examination Of The Stability Of Boundary Between Plasma And The Magnetic Field In Electroneutral Approach

A procedure that allows study of unstable stability of a boundary layer between plasma and a magnetic field has been developed. Layer equilibrium for one reason or another is not set but follows from strict solution of kinetic equation with self-consistent electromagnetic field. Nicolson's solution was used as equilibrium solution. The non-equilibrium component to the distribution function was found and on this basis tensor of dielectric permeability simulating the medium was (boundary layer) is calculated. This tensor essentially differs from the known tensor for magnetoactive plasma. Equations for electric field perturbation were obtained from the Maxwell's equations completed with the derived constitutive equation. The technique of determination of dispersion characteristics of perturbations of a boundary layer was proposed. The theory is applicable to thermal nonrelativistic plasma.Comment: 15 pages, 1 figur

Frequency Characteristics Of Acoustic-Gravity Eigenwaves Of The Nonadiabatic Atmosphere

The main objective of the given work consists in the account of the basic mechanisms, which decline processes in atmosphere from adiabaticity approach, and in the study of effect non-adiabaticity on the swing of eigenmodes of atmosphere at various altitudes. The dispersion equation is solved, dispersion curves for acoustic and gravity branches are explored. The increment of growth of eigenmodes at various altitudes of atmosphere is explored. Frequencies (real part) both for acoustic, and for gravity branches acoustic-gravity waves (AGW) in nonadiabatic atmosphere, coinciding with frequencies of the adiabatic model for the same wave vectors at low altitudes, smoothly decrease with altitude. It leads to decrease of a phase velocity for both branches at larger altitudes in a real atmosphere in comparison with predicted by the adiabatic model.Comment: 8 pages, 12 figure

Representations of virtual braids by automorphisms and virtual knot groups

In the present paper the representation of the virtual braid group $VB_n$ into the automorphism group of free product of the free group and free abelian group is constructed. This representation generalizes the previously constructed ones. The fact that these already known representations are not faithful for $n \geq 4$ is verified. Using representations of $VB_n$, the virtual link group is defined. Also representations of welded braid group $WB_n$ are constructed and the welded link group is defined.Comment: 30 pages, 7 figure

The Landau Damping Effect and Complex-valued Nature of Physical Quantities

Within the framework of the hypothesis offered by authors about complex-valued nature of physical quantities, the effect of the Landau damping has been explored with assumption that not only frequency can be a small imaginary component but also a wave vector. The numerical solution of the obtained dispersion equation testifies that uncollisional damping is accompanied in a certain region of space by antidumping of waves, and in particular situations antidumping may prevail over damping. It is possible that this effect may explain the experimental difficulties connected with inhibition of instabilities of plasma in the problem of controllable thermonuclear fusion.Comment: 6 pages, 1 tabl

On The Procedure Of Examination Of Instability Of The Shock Front Relatively Acousto-Gravitational Perturbations

The dispersing equation was derived from system of the hydrodynamic equations that take into account the gravity, and from boundary conditions of shock front. The dispersing equation made it possible to study unstable stability of front not only relative to sound vibrations, but also to explore the gravitational branch of acousto-gravitational waves. Within the framework of the model under study there appeared a possibility to examine the interval of frequencies in which wave disturbances of the aerosphere induced by shock waves from land-based sources are energized.Comment: 5 pages, 1 figur

About Exact Solution Of The Kinetic Equation For Current Sheath

In the offered paper the kinetic theory of equilibrium and stability of the nonelectroneutral current sheaths formed at arbitrary values of medium parameters was developed. Equilibrium distribution function of a current sheath (Harris's function) considering anisotropy of temperature of plasma along and across the layers is summarized. The procedure of examination of a current sheath stability with due regard to plasma polarization effect is offered. Tensor of dielectric permeability is calculated and dispersion equation for investigation of possible instability modes of non-electroneutral current sheath is derived. Non-electroneutral equilibrium solution for a current sheath in the magnetospheric tail is derived and its instability is explored. A possible mechanism of magnetic field annihilation in the magnetospheric tail and acceleration of charged particles in the process of magnetospheric substorm development is considered.Comment: 19 pages, 11 figure

On the lower central series of Baumslag-Solitar groups

We find the lower central series for residually nilpotent Baumslag-Solitar groups, and find the intersection of all terms of the lower central series. Also, we find non-abelian Bauslag-Solitar groups for which the lower central series has length 2. For some Baumslag-Solitar groups a connection is found between the intersection of all subgroups of finite index and the intersection of all terms of the lower central series.Comment: 14 page

On residually nilpotence of group extensions

We study the following question: under what conditions extension of one residually nilpotent group by another residually nilpotent group is residually nilpotent? We prove some sufficient conditions under which this extension is residually nilpotent. Also, we study this question for semi-direct products and, in particular, for extensions of free group by infinite cyclic group: $F_n \rtimes_{\varphi} \mathbb{Z}$. We find conditions under which this group is residually nilpotent, find conditions under which this group has long lower central series. In particular, we prove that for $n=2$ the length of the lower central series of $F_n \rtimes_{\varphi} \mathbb{Z}$ is equal to 2, $\omega$ or $\omega^2$.Comment: 31 page

Groups of virtual trefoil and Kishino knots

In the paper of Yu. A. Mikhalchishina for an arbitrary virtual link $L$ three groups $G_{1,r}(L)$, $r>0$, $G_{2}(L)$ and $G_{3}(L)$ were defined. In the present paper these groups for the virtual trefoil are investigated. The structure of these groups are found out and the fact that some of them are not isomorphic to each other is proved. Also we prove that $G_3$ distinguishes the Kishino knot from the trivial knot. The fact that these groups have the lower central series which does not stabilize on the second term is noted. Hence we have a possibility to study these groups using quotients by terms of the lower central series and to construct representations of these groups in rings of formal power series. It allows to construct an invariants for virtual knots.Comment: 21 page