Exact and approximate analytical formulas are derived for the internal structure and global parameters of the spherical non-rotating quasi-incompressible planet. The planet is modeled by a polytrope with a small polytropic index n ≪ 1, and solutions of the relevant differential equations are obtained analytically, to the second order of n. Some solved and unsolved problems of polytropic models ...

The air compr8ssor 1~i th spr8.ying wfl.tP-r into cy1 inders can make its power consumption ann discharF,e temperature decrease but the effect of spraying ••ater to power consumption and discharge tempera~ ture is difficu1t to he quantitatively sho••ed 1dth rliffqrent starting condition. This paper establishs a formula to calculate the polytropic expon8nt in ideal compressing processes of spray...

Context. Strongly stratified hydromagnetic turbulence has recently been identified as a candidate for explaining the spontaneous formation of magnetic flux concentrations by the negative effective magnetic pressure instability (NEMPI). Much of this work has been done for isothermal layers, in which the density scale height is constant throughout. Aims. We now want to know whether earlier conclu...

We give a Lax description for the system of polytropic gas equations. The special structure of the Lax function naturally leads to the two infinite sets of conserved charges associated with this system. We obtain closed form expressions for the conserved charges as well as the generating functions for them. We show how the study of these generating functions can naturally lead to the recursion ...

Gv1 is a genetic locus that coordinately regulates the expression of multiple murine leukemia virus-related endogenous proviral sequences. A quantitative nuclease protection assay for typing Gv1 inheritance has been developed. Use of this assay demonstrates that Gv1 controls transcription of polytropic but not of modified polytropic endogenous proviruses. A combination of genetic techniques wer...

We analyze the stability of Newtonian polytropic static fluid spheres, described by the Lane-Emden equation. In the general case of arbitrary polytropic indices the Lane-Emden equation is a non-linear second order ordinary differential equation. By introducing a set of new variables, the Lane-Emden equation can be reduced to an autonomous system of two ordinary differential equations, which in ...

An analytic solution is presented to the three-dimensional problem of steady axisymmetric fluid flow through an accretion disk. The solution has been obtained through a systematic expansion in the small parameter ǫ = ¯ H/ ¯ R (the ratio of disk thickness to its radial dimension) of the equations of viscous hydrodynamics. The equation of state was assumed to be polytropic. For all values α < 0.6...

Context. Studies of solar and stellar convection often employ simple polytropic setups using the diffusion approximation instead of solving the proper radiative transfer equation. This allows one to control separately the polytropic index of the hydrostatic reference solution, the temperature contrast between top and bottom, and the Rayleigh and Péclet numbers. Aims. Here we extend such studies...