Related papers: A Variable Polytrope Index Applied to Planet and M…
The aim of this paper is to discuss the theory of Newtonian and relativistic polytropes with generalized polytropic equation of state. For this purpose, we formulated the general framework to discuss the physical properties of polytrops…
Wrinkling of an inextensible elastic lining of an inner-lined tube under imposed pressure is considered. A simple equation modeling the elastic properties of the lining, the pressure, and the soft-substrate forces is derived. This equation…
With respect to earlier investigations, the theory of multi-component, concentric, copolar, axisymmetric, rigidly rotating polytropes is improved and extended, including subsystems with nonzero density on the boundary and subsystems with…
The condition for pressure isotropy, for spherically symmetric gravitational fields with charged and uncharged matter, is reduced to a recurrence equation with variable, rational coefficients. This difference equation is solved in general…
The bulk composition of an exoplanet is commonly inferred from its average density. For small planets, however, the average density is not unique within the range of compositions. Variations of a number of important planetary…
Materials at high pressures and temperatures are of great interest for planetary science and astrophysics, warm dense matter physics, and inertial confinement fusion research. Planetary structure models rely on our understanding of the…
Physical experiments can characterize the elastic response of granular materials in terms of macroscopic state-variables, namely volume (packing) fraction and stress, while the microstructure is not accessible and thus neglected. Here, by…
A new approach is theoretically proposed to study the glass transition of active pharmaceutical ingredients and a glass-forming anisotropic molecular liquid at high pressures. We describe amorphous materials as a fluid of hard spheres.…
It is shown how the well-known formula for the gravitational energy of self-gravitating regular polytropes of finite mass can be obtained in an elementary way by using Gauss's divergence theorem and the Chandrasekhar virial tensor, without…
In this paper, we have introduced new viable solutions of Einstein-Maxwell field equations by incorporating the features of anisotropic matter distribution in the realm of General theory of Relativity ($GR$). For this procurement, we have…
Envelope methodology is succinctly pitched as a class of procedures for increasing efficiency in multivariate analyses without altering traditional objectives \citep[first sentence of page 1]{cook2018introduction}. This description is true…
The heavy element content of giant exoplanets, inferred from structure models based on their radius and mass, often exceeds predictions based on classical core accretion. Pebble drift, coupled with volatile evaporation, has been proposed as…
Gravitational polarization is examined for equilibrium self-gravitating polytropic sheets perturbed by gravitational field due to test mass sheet. We find equilibrium solutions to the corresponding perturbed Lane-Emden equations for…
We take a unifying and new approach toward polynomial and trigonometric approximation in an arbitrary number of variables, resulting in a precise and general ready-to-use tool that anyone can easily apply in new situations of interest. The…
This contribution investigates the extension of the microplane formulation to the description of transversely isotropic materials such as shale rock, foams, unidirectional composites, and ceramics. Two possible approaches are considered: 1)…
Spherically symmetric relativistic stars with the polytropic equation of state (EoS), which possess the local pressure anisotropy, are considered within the framework of general relativity. The generalized Lane-Emden equations are derived…
We study the structure of static spherical stars made up of a non-relativistic polytropic fluid in linearized higher-curvature theories of gravity (HCG). We first formulate the modified Lane-Emden (LE) equation for the stellar profile…
A new four-parameters family of constitutive functions for spherically symmetric elastic bodies is introduced which extends the two-parameters class of polytropic fluid models widely used in several applications of fluid mechanics. The four…
In this paper we will discuss charged stars with polytropic equation of state, where we will try to derive an equation analogous to the Lane-Emden equation. We will assume that these stars are spherically symmetric, and the electric field…
Context. Clouds have already been detected in exoplanetary atmospheres. They play crucial roles in a planet's atmosphere and climate and can also create ambiguities in the determination of atmospheric parameters such as trace gas mixing…