Конференции ИВТ СО РАН

Abstracts

It is interesting the receiving of the large significances of density for corresponding medium, for example, for the problem of laser thermonuclear synthesis [1]. At monograph [2] there is a united method for mathematical description of compression gases to the large significances (including a infinity) of density. In particular, there are the corresponding value boundary problems, which description power compression of different volumes initial homogeneous and resting gas (including non one-dimensional and interesting for the real physics experiments). Also it takes into strong consideration of the flow particulars and composites the flows of different dimension. It proves the theorems about existing and uniqueness solutions of states value boundary problems and analyses the properties of this solutions. In particular, it proves that for any analytical surface an initial homogeneous and resting no zero mass of gas existences, which may be compression to the infinite density on this surface.

On the basis of methods from [2] there are obtaining the following new results at a mathematical description a power compression of gas. It proves the theorems about existing and uniqueness solutions of Kraiko’s problem about shockless conversion “from resting – to resting” and a problem about receiving the concrete distributions of gas parameters. Also there are universal asymptotic laws of a shockless compression of the many dimensional gas layers. These laws define more precisely the known conclusion about unstable of such flows near final moment of shock less power compression. It is created calculation algorithms, which account the known particulars of considering flows. A using these algorithms gives a chance to calculate a shockless compression of resting and homogeneous plane, cylindrical, spherical and non one dimensional layers at the density, which is grater than initials in ten or hundred of thousand once. It is the investigation of shock less compression the hydrogen with the real isentropic in conditions a conversion from molecular state to atomic state, when hydrogen is no normal gas. It states the sound characteristics in the flows of heat-conductive gas in case balancing radiation and Compton’s mechanism of photons dissipative. There are the analogues of centered Riemann’s waves in case of an one and a two dimensional flows of heat conductive and non-viscous gas. Also there are the composite flows, which describe power compression layers of heat-conductive and non-viscous gas. Due to the traveling waves the structure of shock wave is determined.

Due to the obtained results it is conclusion, that this theory makes possible an accuracy mathematical modeling of the real physical experiments for a receiving of the large significances a density of required continuous medium with the conception of shock less compression and gives the recommendations at a construction the concreted target for thermonuclear synthesis.

The research is supported by the Russian Foundation for Basic Research (the projects 02-01-01122, 04-01-00205).

[1] Zababahin E.I., Zababahin I.E. The phenomena unlimited cumulating. Moscow: Nauka, 1988 (in Russian).

[2] Bautin S.P. The mathematical theory of shockless power compression ideal gases. Novosibirsk: Nauka, 1997 (in Russian).

Note. Abstracts are published in author's edition

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