27 research outputs found
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
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 is verified. Using representations of , the
virtual link group is defined. Also representations of welded braid group
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: . 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 the length of the lower
central series of is equal to 2, or
.Comment: 31 page
Groups of virtual trefoil and Kishino knots
In the paper of Yu. A. Mikhalchishina for an arbitrary virtual link three
groups , , and 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 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