Related papers: A Variable Polytrope Index Applied to Planet and M…
The hardness of materials plays an important role in material design. There are numerous experimental methods to measure the hardness of materials, but theoretical prediction of hardness is challenging. By investigating the correlation…
The so-called "global polytropic model" is based on the assumption of hydrostatic equilibrium for the solar system, or for a planet's system of statellites (like the jovian system), described by the Lane-Emden differential equation. A…
Molecular clouds are supported by thermal pressure, magnetic pressure, and turbulent pressure. Each of these can be modeled with a polytropic equation of state, so that overall the total pressure is the sum of the individual components. We…
Physical conditions deep within planets and exoplanets have yet to be measured directly, but indirect methods can calculate them. The polytropic models are one possible solution to this problem. In the present paper, we assume that the…
The aim of this study is to construct a simple stellar model with non-uniform polytropic index. We find that the Emden equation cannot deal with the polytrope gas sphere with non-uniform polytropic index in a real star, and then we…
A fundamental assumption in the so-called "global polytropic model" is hydrostatic equilibrium for a system of planets or statellites. By solving the Lane-Emden differential equation for such a system in the complex plane, we find…
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…
The perturbation method is applied to numerical solution of the Lane-Emden Equation of arbitrary index n, and the global parameters of polytropes are found as function of polytropic index n.
The porosity structure of a granular body is an important characteristic that affects evolutionary changes in the body. We conducted compression experiments using fluffy granular samples with various particle sizes, shapes, and…
A new method for direct evaluation of both crystalline structure, bulk modulus B_0, and bulk-modulus pressure derivative B'_0 of solid materials with complex crystal structures is presented. The explicit and exact results presented here…
Polytropic models play a very important role in galactic dynamics and in the theory of stellar structure and evolution. However, in general, the solution of the Lane-Emden equation can not be given analytically but only numerically. In the…
We study the primordial Universe in a cosmological model where inflation is driven by a fluid with a polytropic equation of state $p = \alpha\rho + k\rho^{1 + 1/n}$. We calculate the dynamics of the scalar factor and build a Universe with…
A general formalism developed few years ago to model polytropic Newtonian stars with anisotropic pressure is applied to model stars for which, both, radial and tangential pressure satisfy polytropic equations of state. We obtain the…
In the past few years, the number of confirmed planets has grown above 2000. It is clear that they represent a diversity of structures not seen in our own solar system. In addition to very detailed interior modeling, it is valuable to have…
We propose a novel mathematical method to construct an exact polytropic sphere in self-gravitating hydrostatic equilibrium, improving the non-linear Poisson equation. The central boundary condition for the present equation requires a ratio…
A general formalism to find the density profile of a slowly rotating stellar object in modified gravity is presented. We derive a generic Lane-Emden equation and its analytical solution for a wide class of modified theories of gravity.
A polytropic quark star model is suggested in order to establish a general framework in which theoretical quark star models could be tested by observations. The key difference between polytropic quark stars and the polytropic model studied…
This paper models the increase of density of a virgin loose granular sample submitted to a progressive axisymmetric compression (either isotropic or anisotropic) as an irreversible process which destroys the larger voids; a statistical…
We construct spherical, hydrostatic models of dense molecular cores and Bok globules consisting of two distinct, spatially separate gas components: a central, isothermal region surrounded by a negative-index, polytropic envelope. The clouds…
Polytropic stars are useful tools for learning about stellar structure without the complexity of comprehensive stellar models. These models rely on a certain power-law correlation between the star's pressure and density. This paper proposes…