Related papers: A Variable Polytrope Index Applied to Planet and M…
In this paper we consider a class of second order singular homogeneous differential equations called the Lane-Emden-type with time singularity in the drift coefficient. Lane-Emden equations are singular initial value problems that model…
A general class of models is proposed that is able to estimate the whole predictive distribution of a dependent variable $Y$ given a vector of explanatory variables $\xb$. The models exploit that the strength of explanatory variables to…
Although current sensitivity limits are such that true Solar System analogs remain challenging to detect, numerous planetary systems have been discovered that are very different from our own Solar System. The majority of systems harbor a…
We obtain two equations (following from two different approaches) for the density profile in a self-gravitating polytropic cylindrically symmetric and rotating turbulent gas disk. The adopted physical picture is appropriate to describe the…
In order to simulate rigidly rotating polytropes we have simulated systems of $N$ point particles, with $N$ up to 1800. Two particles at a distance $r$ interact by an attractive potential $-1/r$ and a repulsive potential $1/r^2$. The…
This article aims to propose a novel analytical model for anisotropic multi-layer elliptical structures incorporating graphene layers. The multi-layer structure is formed of various magnetic materials. An external magnetic bias has been…
We show that density models describing multiple observables with (i) hard boundaries and (ii) dependence on external parameters may be created using an auto-regressive Gaussian mixture model. The model is designed to capture how observable…
Lane Emden differential equation of the polytropic gas sphere could be used to construct simple models of stellar structures, star clusters and many configurations in astrophysics. This differential equation suffers from the singularity at…
In the mechanics of inviscid conservative fluids, it is classical to generate the equations of dynamics by formulating with adequate variables, that the pressure integral calculated in the time-space domain corresponding to the motion of…
In the present paper we study warm inflationary universe models in the context of a polytropic gas. We derive the characteristics of this model in slow-roll approximation and develop our model in two cases, 1- For a constant dissipative…
Galactic dynamo models have generally relied on input parameters that are very challenging to constrain. We address this problem by developing a model that uses observable quantities as input: the galaxy rotation curve, the surface…
A polytropic process describes the transition of a fluid from one state to another through a specific relationship between the fluid density and temperature. The value of the polytropic index that governs this relationship determines the…
Exploring exoplanets has transformed our understanding of the universe by revealing many planetary systems that defy our current understanding. To study their atmospheres, spectroscopic observations are used to infer essential atmospheric…
Combining isotopic constraints from meteorite data with dynamical models of planet formation proves to be advantageous in identifying the best model for terrestrial planet formation. Prior studies have shown that the probability of…
Despite the increase in observational data on exoplanets, the processes that lead to the formation of planets are still not well understood. But thanks to the high number of known exoplanets, it is now possible to look at them as a…
We present numerical support for the hypothesis that macroscopic observables of dense granular media can be evaluated from averages over typical blocked configurations: we construct the corresponding measure for a class of…
In this paper we study anisotropic spherical polytropes within the framework of general relativity. Using the anisotropic Tolman-Oppenheimer-Volkov (TOV) equations, we explore the relativistic anisotropic Lane-Emden equations. We find how…
The influence on macroscopic work hardening of small, spherical, elastic particles dispersed within a matrix is studied using an isotropic strain gradient plasticity framework. An analytical solution, based on a recently developed yield…
Using a numerical approach based on the coupling of the discrete and finite element methods, we explore the variation of the bulk modulus K of soft particle assemblies undergoing isotropic compression. As the assemblies densify under…
An iterative method is presented for solving the problem of a uniformly rotating, self-gravitating ring without a central body in Newtonian gravity by expanding about the thin ring limit. Using this method, a simple formula relating mass to…