Polytropic process

Abstract: Presented are several results on the formation of singularities in solutions to the three-dimensional Euler equations for a polytropic, ideal fluid under various assumptions on the initial data. In particular, it is shown that a localized fluid which is initially compressed and outgoing, on average, will develop singularities regardless of the size of the initial disturbance.

Abstract: The equations of motion for steady-state spherical symmetric flow of matter into or out of a condensed object (e.g. neutron stars, ‘black holes’, etc.) are displayed and solved for simple polytropic gases. It appears that infalling matter may be heated as hot as 1012K and that X-ray luminosities of the order of 1037 erg s−1 could result. The two fluid (electrons and ions separately) approach is also examined and it is shown that electrostatic fields of the order of 105 V m−1 are required near the surface of the object. Such fields are not strong enough to significantly modify the space-time metric.

Abstract: The standard approach to the analysis of the pulsations of a driven gas bubble is to assume that the pressure within the bubble follows a polytropic relation of the form p=p0(R0/R)3κ, where p is the pressure within the bubble, R is the radius, κ is the polytropic exponent, and the subscript zero indicates equilibrium values. For nonlinear oscillations of the gas bubble, however, this approximation has several limitations and needs to be reconsidered. A new formulation of the dynamics of bubble oscillations is presented in which the internal pressure is obtained numerically and the polytropic approximation is no longer required. Several comparisons are given of the two formulations, which describe in some detail the limitations of the polytropic approximation.