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Maxwell's vacuum equations can be presented as follows:
where E is electrical field; D = PE - electrical induction and at the same time electrical polarization of PV , H'=m0H-- magnetic field (according to modern vocabulary H-- magnetic field); e0=8,855×10-12m-3kg-1s4A2; m0 = 1,257×10-6mkgs-2A-2; B' =PM- magnetic induction B/m0 ratio and simultaneously magnetic polarization of PV; r--- electric charge density; J= r v --electric current density; v--- average velocity of electric current carriers.
Heaviside's vacuum equations can be presented as follows:
where EG --- gravitational field; DG =PG--- gravitational induction and at the same time gravitational polarization of PV; H'G=m0GHG- spin field; e0G=1/4pG= 1,193×109m-3kgs2; G=6,672×10-11m3kg-1s-2 - gravitational constant; m0G=1/e0Gc2 = 0,9329×10-26mkg-1; c=2,998×108ms-1 --- the speed of light (the speed of the gravitation waves is assumed to be equal to the speed of light) B'G= PS --- spin induction BG/m0G ratio and spin polarization of PV; rG--- the density of the mass; JG=rG v -the density of the gravitational current; v --- the speed of the gravitational current carriers. Thus PV is characterized by four polarizations: PE --- the density of the electric dipoles of PV; PM --- the density of the magnetic moments of PV; PG ---the density of the gravitational dipoles of PV; PS -- the density of the spin moments (spins) of PV or the density of the angular momentum of PV.
According to (1--4) polarizations PE and PM are related as well as PG and PS polarizations, but the two pairs of polarizations PE PM and PG PS are completely independent of each other.
For the century of the physics development important changes have occured in the concepts of the polarizational properties of the matter and PV. The connection between the magnet and the spin polarization in the matter is established. First it was discovered in the classic ferromagnetics and paramagnets in the gyromagnetic Barnett effects (1909) and Einstein-de-Gaaz effects (1911 ). Then this connection was confirmed in the other materials using paramagnetic and nuclear resonance techniques. In the modern physics PV is considered to be a quark medium ("vacuum is not the void") in which s-quarks and s-antiquarks are connected into dipoles . Apparently, PV is the neutral medium . This medium can be nothing else than the polarization medium.
Since PV quarks have electrical charges and mass, magnetic and spin moments, electrical and gravitational polarizations can be related in PV as well as magnet and spin polarizations. This connection between PV polarizations can be introduced to the Maxwell's vacuum equations (2) and Heaviside's vacuum equations (4).
But on the other hand the correction of the experimentally proved Maxwell's equations and quantum electrodynamics equations (based on Maxwell's equations) will necessarily lead to the unobserved physical phenomena.
The authors have found a solution of this problem : the connection between electric and gravitational, magnetic and spin polarization was assumed to exist only in the local areas. So in PV theory an object has appeared that was called VD.
The mathematical model of the vacuum domains based on the discussed notions can be presented as follows:
where "cross" coefficients e1=0; m1=0 outside the area V of the vacuum domain and e1¼ 0, m1¼ 0 inside the area V of the vacuum domain; e, m, s --- the relative electrical and magnetic permeabilities and the conductivity of the matter respectively; eG, mG, sG --- the relative gravitational and spin permeabilities and gravitational conductivity of the matter respectively (eG, mG are approximately equal to 1, sG is small); s1 --- electrogravitational conductivity of the matter (s1 is small); J0 = r0v; J0G= r0Gv; r0, r0G --- mobile electric charges and masses respectively.
Outside VD the group of Lorentz transforms is observed, since equations
(5--8) --- are relativistic. In the nonrelativistic approximation (v <<c)
E'= E + [vB];
E'G =EG + [vBG], (9)
where E', E'G --- electric and gravitational fields in the moving bases.
Inside the domains the energy conservation law, the law of the conservation of momentum and the law of the conservation of the impulse are observed.
The investigation of the physical properties of VD can be reduced to the solution of the boundary problems with the terminal conditions on the boundaries of the given area V of VD and on the infinity (like the boundary conditions in the problems of electrodynamics).
Though the basic equations (5), (7) of the model are invariable in any problems, additional equations (6) and (8) can be changed and modified in particular problems in accordance with the electric theory of the matter and the continuum mechanics.
In the physical and mathematical model of VD many problems arise. Some of them are already solved [15,16]. All the physical properties of the anomalous phenomena shown in table 1 can be easily explained (except for the technical difficulties of the field problems solution). Thus the assumption is confirmed that all these phenomena are the consequence of the physical properties of VD. According to the model all the mentioned physical properties of VD can be expressed simultaneously. As far as this fact is concerned, the present model is essentially different from the known model of the ball lightning , in which some physical properties of the ball lightning such as rotation are ignored.
We can't present all the results of the analysis of the physical properties of the anomalous phenomena based on VD model, since it will take too long, but we shall consider some results.
"Self-luminescence" of vacuum domains takes place because gravispin waves energy is transformed into electromagnet waves energy. This effect is studied in the publication that dates back to 1995 . The complete conversion of the energy of one type of waves into the other takes place inside VD at the distance
where l --- wave length; ae=e1 /(e0e0G)-1/2; am=m1 /(m0m0G)-1/2 (ae, am£ 1).
The electrical discharges and the gas rotation inside VD , one of the forms of explosions, levitation and the magnetic field of the domains are connected with the polarization of VD that arise as a result of the effect of the Earth fields. For example, for the spherical domain these polarizations are expressed as follows:
- electrical polarization of the domain
- gravitational polarization of the domain
- magnetic polarization of the domain
- spin polarization of the domains
where E0 --- electric field (130 V/m); E0G--- gravitational field (9,83 m/s2); H0 ---magnetic field (19,5 A/m); H0S --- spin field (1013kg/m×) of the Earth
The polarization of VD allows to calculate the potential energy of VD
W = WE + WG + WM + WS, (15)
where WE=-E0( PE V); WG=-E0G(PGV); WM=-H0(PM V); WS=-H0S(PSV); V --- the volume of the spheric domain.
The potential energy allows to determine the force that acts upon VD
F =-‹W. (16)
Thus if we know the virtual mass we obtain the formula to determine the law of VD motion. It should be noted that this formula is valid in any media.
The initial mechanical stress that acts upon the gas and the solid can be determined proceeding from the continuum theory by L.I.Sedov , according to which
where t--- the tangential stress of the asymmetric stress tensor.
The tangential stress can be as large as hundreds of the atmospheres when VD is moving rapidly in the direction of the change in the magnetic and spin field of the Earth (for example, in tornado)
When VD penetrates into the matter, it acquires the electric monocharge
When VD penetrates into the matter with this monocharge it causes the electric current of the free electric charges that aim at the neutralization of the monocharge. This current is responsible for the liberation of the heat energy
where r'=-ae×h0-1rG ; R --- domain radius.
Heat energy is connected with the contact explosions of VD. The density of the heat energy can be as high as WT/ V@ 106J/m3 with VD diameter of 1 km and more.
4. TORNADO OUTBREAKS AS AN EXAMPLE OF ACTIVIZATION OF THE FUNCTIONS OF VACUUM DOMAINS.
Solutions of particular problems of VD model show that VDs play a significant role in geophysical processes and in the Earth geological change . Moreover, the consideration of hypotheses implied by the model allow us to propose that the influence of vacuum domains upon the formation of the Earth and even Solar System is even more large.
We can assume that VDs are formed in the Sun as a result of decomposition of absolute physical vacuum, which is characterized in our model by the coefficients e1=0, m1=0, into the pair of PV modifications characterized by the coefficients +e1¼ 0, +m1¼ 0 ,and -e1¼ 0, -m1¼ 0 or -e1¼ 0, \ +m1¼ 0 and +e1¼ 0, -m1¼ 0 (this assertion arises if we assume the Terletsky quadrigue of particles and antiparticles to be a basic unit of absolute physical vacuum. We may also suppose that these modifications carry some part of thermonuclear synthesis energy away from the Sun, thus making the continuous course of this reaction possible.. A combination of the two PV modifications outside of Sun, producing absolute physical vacuum, must result in giving off the captured Solar Energy in the of a "photon explosion". Possibly, the explosion of the "Tunguska meteorite" in 1908 is an example of such event.
According to the physical essence of the model such explosions may take place in any media of the Earth, including atmosphere, water, lithosphere, etc. , serving as a form of additional solar energy influx to the Earth.
The electric and magnetic fields as well as additional angular momentum of the Earth may also have connection with the VD penetrating deep into the Earth. The additional angular momentum may, in it's turn, contribute to the Earth spin field. Certainly, such processes must take place on the other planets of the Solar system. Basing on the model (namely, on the Heaviside equations) one simply shows that the spin field serves as one of the factors of interaction of the Sun and planets (causing planets to orbit the Sun in the plane of the Sun's ecliptic, causing first seven planets to rotate in the same direction etc.)
Let us discuss in detail the role of VD's in the process of sharp increase of number and power of tornadoes. The two times growth of annual number of tornadoes in the second part of our century must be considered as a part of general rearrangement of the Earth climate machine. The relation between self-luminous formations local non-homogeneities of physical vacuum, discovered by authors , allowed us to propose a new model of physical processes and energy supply of tornadoes. This model contributed to establish a relation, so far unknown, between the geology-geophysical quality of the territory and the rate of tornado occurrence . The new approaches to the study of tornadoes  also point at the relation between the energetic discontinuities in lithosphere ( such as formation and renovation of tectonic faults ) and the initiation of tornadoes. Thus we propose a new non-meteorological approach to the study of these violent processes, now growing stronger.
The possibilities of the physics of vacuum domains especially in it's gravidynamic component, provide a foundation for the developed approach [15,26]. As it follows from the model, visibe or invisible energy-containing formations such as ball lightnings, pulsing electromagnetic emissions, luminous strips etc. Are the effects of the energy transformation inside VDs. The cross relations between Maxwell and Heaviside equations, described above, for the volume occupied by a natural self-luminous formation, allow to get quantitative estimates for the effects of gravitational polarization. Such polarization creates, in some volume, a gravitation dipole, positive in it's bottom part and negative in it's top part. Thus VDs induce a local variation of the gravitation field, which manifests itself in macroscopic processes of lifting up large masses by a tornado funnel.
Representing a tornado funnel as a "rope-like" vacuum domain , one can obtain that the source of the air rotation forces develops because of spin polarization of self-luminous formation under the action of the Earth magnetic field and it's regional anomalies. Therefore the huge atmospheric vortex processes arise as a result of spin polarization ( recall the gyromagnetic effect of Einstein-de-Gaas), which has vector sum equal to zero if the magnetic field is absent. As our estimates show , the volume occupied by a vacuum domain possesses the gyromagnetic property exceeding ferromagnetics by several orders of magnitude . Taking in mind the general property of vacuum domains to be an energy transformer of four fields i.e. electric, magnetic, gravitational, and spin fields one finds a possibility to explain rich but so far unexplained phenomenology of physical processes associated with tornadoes .
Picture 3 . Earthquake epicenters and tornadoes in California and Nevada.
But as it is pointed out in , , the tornado outbreaks conform to the localization and periodization of processes in geology-geophysical environment . Many years study of the properties and space-time distribution of self-luminous formations [3,5,11] revealed vigorous relations between origination, existence and disappearance of vacuum domains and the energetic discontinuities in lithosphere and ionosphere. Particularly, for Altai mountain region, a spatial incompatibility was established for the frequencies of vacuum domains and the earthquake epicenters; with the maxima of the encounters of the natural self-luminous formations being spatially separated from seismically charged regions  a similar regularity was also established for the tornado outbreaks and the earthquake epicenters in California and Nevada . The strips of maximal tornado density (fig.3) are considerably distant from that of the the earthquake epicenters density. This effect, to be studied further, gives evidence of ( like in the Vladivostok tornado case) the role of lithosphere energetic discontinuities in in the generation of tornadoes and indicates the activation of vertical energy transfers in the Earth hulls
The physical and mathematical model of VD does not contradict with the modern quantum field theory. On the contrary, with this theory one can derive the macroscopic consequences of this microscopic theory. In fact, within the scopes of the model PV is considered to be a polarization medium.
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