Journal of Applied Mathematics and Mechanics (about journal) Journal of Applied
Mathematics and Mechanics

Russian Academy of Sciences
 Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
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IssuesArchive of Issues2015-6pp.556-565

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Kh.F. Valiyev and A.N. Kraiko, "The dispersion of an ideal gas from a point into a void. A new model of the Big Bang and the expansion of the Universe," J. Appl. Math. Mech. 79 (6), 556-565 (2015)
Year 2015 Volume 79 Issue 6 Pages 556-565
DOI 10.1016/j.jappmathmech.2016.04.001
Title The dispersion of an ideal gas from a point into a void. A new model of the Big Bang and the expansion of the Universe
Author(s) Kh.F. Valiyev (Baranov Central Institute of Aviation Motors, Moscow, Russia)
A.N. Kraiko (Baranov Central Institute of Aviation Motors, Moscow, Russia, akraiko@ciam.ru)
Abstract A self-similar solution of the problem on the dispersion of a finite mass of an ideal (inviscid and non-heat-conducting) gas that is compressed into a point and has infinite energy and finite entropy is obtained within classical (non-relativistic) gas dynamics. In this solution the gas disperses at once into all space, and, as a result, its thermodynamic functions (including the density), unlike the conserved entropy, vanish. The velocity of the gas obtained is equal to the ratio of the distance to the time, which are measured from the point and time of dispersion, and increases from zero to infinity for any time. In self-similar variables the new solution is described by one of the singular points of the corresponding differential equation, rather than by a segment of an integral curve. It satisfies the cosmological principle, which assumes that the Universe is isotropic and homogeneous with respect to the laws that determine its expansion. The problem of the dispersion of an ideal gas from a point into a void when the gas has a mass proportional to its energy and a fixed number of particles of non-zero rest mass is also solved within relativistic gas dynamics without gravity. Here the pressure, internal energy and enthalpy at a non-zero particle number density instantaneously vanish, and the formula for the velocity of the gas is distinguished from the classical only by the restriction of the speed of light. The velocity of the gas satisfies the cosmological principle in the entire expanding Universe, and the particle number density satisfies it outside of the layer adjacent to its boundary. The gravitational correction is then determined in the classical approximation. For more than 200 NASA versions, the distribution of the gas velocity found without this correction agrees with the lifetime of the Universe and the Hubble constant more closely than all the cosmological theories used by NASA.
Received 23 June 2015
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