Emden’s Polytropes: Gas Globes In Hydrostatic Equilibrium

The theory of polytropes dealing with the hydrostatic equilibrium structure of gas globes had its origin in Emden’s publication, Gaskugeln a century ago (1907). This review article has been written for students of physics and astrophysics not only to understand the theory of polytropes as the simplest of stellar models but also computationally solve the Lane-Emden equation for polytropes. Anyone can easily obtain values of normalized temperature, density, pressure and mass distribution as a function of the normalized radius or mass in any polytrope model in tabular form as well as in graphical form using the program code. Explanation of the algorithm to write a code is provided (python script on request). A graphical description of how the polytropic index determines the structure of the polytrope is also given.

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Stellar Structure in a Newtonian Theory with Variable G

Physics ◽

10.3390/physics3040071 ◽

2021 ◽

Vol 3 (4) ◽

pp. 1123-1132

Author(s):

Júlio C. Fabris ◽

Túlio Ottoni ◽

Júnior D. Toniato ◽

Hermano Velten

Keyword(s):

Spatial Dependence ◽

Equilibrium Structure ◽

Hydrostatic Equilibrium ◽

Stellar Structure ◽

Polytropic Index ◽

Gravitational Coupling ◽

Matter Distribution ◽

Newtonian Theory ◽

Emden Equation ◽

Variable G

A Newtonian-like theory inspired by the Brans–Dicke gravitational Lagrangian has been recently proposed by us. For static configurations, the gravitational coupling acquires an intrinsic spatial dependence within the matter distribution. Therefore, the interior of astrophysical configurations may provide a testable environment for this approach as long as no screening mechanism is evoked. In this work, we focus on the stellar hydrostatic equilibrium structure in such a varying Newtonian gravitational coupling G scenario. A modified Lane–Emden equation is presented and its solutions for various values of the polytropic index are discussed. The role played by the theory parameter ω, the analogue of the Brans–Dicke parameter, in the physical properties of stars is discussed.

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A numerical method for computing optimum radii of host stars and orbits of planets, with application to Kepler-11, Kepler-90, Kepler-215, HD 10180, HD 34445 and TRAPPIST-1

International Journal of Modern Physics C ◽

10.1142/s0129183121500285 ◽

2020 ◽

pp. 2150028

Author(s):

V. S. Geroyannis

Keyword(s):

Numerical Method ◽

Planetary System ◽

Hydrostatic Equilibrium ◽

Polytropic Index ◽

Spherical Shells ◽

Polytropic Model ◽

Emden Equation ◽

Exoplanetary Systems ◽

Planetary Orbits ◽

Host Stars

In the so-called “global polytropic model”, we assume planetary systems in hydrostatic equilibrium and solve the Lane–Emden equation in the complex plane. We thus find polytropic spherical shells providing accommodation to planetary orbits. On the basis of this model, we develop a numerical method which can compute optimum values for the polytropic index of the global polytropic model that simulates the planetary system, for the orbits of the planets, and for the host star radius. We apply our method to the exoplanetary systems Kepler-11, Kepler-90, Kepler-215, HD 10180, HD 34445 and TRAPPIST-1.

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Thiolation of Biopolymers for Developing Drug Delivery Systems with Enhanced Mechanical and Mucoadhesive Properties: A Review

Polymers ◽

10.3390/polym12081803 ◽

2020 ◽

Vol 12 (8) ◽

pp. 1803

Author(s):

Vivek Puri ◽

Ameya Sharma ◽

Pradeep Kumar ◽

Inderbir Singh

Keyword(s):

Mechanical Properties ◽

Drug Delivery ◽

Efficient Method ◽

Drug Delivery Systems ◽

Delivery Systems ◽

Review Article ◽

Present Review ◽

Tabular Form ◽

Thiolated Polymers ◽

Drug Delivery Applications

Biopolymers are extensively used for developing drug delivery systems as they are easily available, economical, readily modified, nontoxic, biodegradable and biocompatible. Thiolation is a well reported approach for enhancing mucoadhesive and mechanical properties of polymers. In the present review article, for the modification of biopolymers different thiolation methods and evaluation/characterization techniques have been discussed in detail. Reported literature on thiolated biopolymers with enhanced mechanical and mucoadhesive properties has been presented conspicuously in text as well as in tabular form. Patents filed by researchers on thiolated polymers have also been presented. In conclusion, thiolation is an easily reproducible and efficient method for customization of mucoadhesive and mechanical properties of biopolymers for drug delivery applications.

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Induced energy polarization of the vacuum and the Coma cluster

Canadian Journal of Physics ◽

10.1139/cjp-2013-0294 ◽

2013 ◽

Vol 91 (12) ◽

pp. 1114-1120 ◽

Cited By ~ 2

Author(s):

A. Raymond Penner

Keyword(s):

Mass Distribution ◽

Velocity Dispersion ◽

Hydrostatic Equilibrium ◽

Coma Cluster ◽

Measured Velocity ◽

Virial Mass ◽

Intracluster Gas ◽

Good Agreement

The theory of an induced energy polarized vacuum is applied to the Coma cluster. The theoretical virial mass distribution of the cluster is determined and found to be in good agreement with previous virial mass estimates. A more concentrated intracluster gas profile than one based on the assumption that the gas is in hydrostatic equilibrium and isothermal does, however, lead to better agreement with measured shear values in the inner regions. The theory also leads to good agreement with measured velocity dispersion values in the case of the galaxies of the cluster being in radial orbits.

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On Self-Gravitating Polytropic Cylinders and Slabs

Mapana Journal of Sciences ◽

10.12723/mjs.48.5 ◽

2019 ◽

Vol 18 (1) ◽

pp. 67-92

Author(s):

Mandyam N Anandaram

Keyword(s):

Fourth Order ◽

Review Paper ◽

Finite Thickness ◽

Gas Distribution ◽

Finite Radius ◽

Emden Equation ◽

Python Script ◽

Basic Properties ◽

Richardson Method ◽

Long Cylinder

In this review paper the 2-D Lane-Emden equation (LEEq) model of a self-gravitating gas distribution in the form of an infinitely long cylinder shaped polytrope of finite radius is obtained and its basic radial properties are outlined. Similarly reviewed is the derivation of the 1-D LEEq model of an infinitely wide planar polytrope of finite thickness and its basic properties across thickness are discussed. These two polytropes are solved numerically along with the 3-D models for comparison using the 2 nd order Euler-Richardson method (ERM) and their index based parameters are determined. The Python script used in these computations has been shown to be not only fast but is capable of matching fourth order performance. However, these models are found to have finite radii for all polytropic indices unlike the restricted spherical analogs and have astrophysical applications. Distortion due to rotation in polytropic rings has also been computed using ERM.

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Implementasi Middleware Pada Evomo Dengan Metode Web Service Restfull Dan Pengujian CI/CD, Coverage Serta Simulasi Protokol Grafana

Jurnal Tekno Insentif ◽

10.36787/jti.v15i2.507 ◽

2021 ◽

Vol 15 (2) ◽

pp. 110-121

Author(s):

Syafrial Fachri Pane ◽

Amri Yanuar ◽

Alit Fajar Kurniawan ◽

Maulyanda Az

Keyword(s):

Data Analysis ◽

Web Service ◽

Research Methodology ◽

Monitoring Data ◽

Data Monitoring ◽

Graphical Form ◽

Program Code ◽

Graphic Data ◽

Analysis Process ◽

System Program

ABSTRAK Penelitian ini membantu dalam melakukan proses analisis data monitoring dalam bentuk grafik, memanfaatkan CI/CD pipeline dalam melakukan implementasi CI/CD dapat memberikan kenyamanan dalam melakukan develop dan mengurangi bug, dari hasil implementasi CI/CD didapatkan hasil statements 93,33%, branch 100%, functions 87,88%, lines 94,92%. Grafik data disiapkan oleh grafana dalam bentuk script iframe diterapkan pada code program sistem. Penelitian ini menggunakan metodologi penelitian yang dapat menyatakan bahwa sistem yang dibangun dapat berfungsi dengan baik. Jadi, penelitian ini mampu menjawab permasalahan yang terjadi pada sistem Evomo. ABSTRACT This research helps in carrying out the monitoring data analysis process in graphical form, utilizing the CI/CD pipeline in implementing CI/CD can provide convenience in developing and reducing bugs. functions 87.88%, lines 94.92%, Graphic data prepared by grafana in the form of iframe script applied to the system program code. This study uses a research methodology that can state that the system built can function properly. So, this research is able to answer the problems that occur in the Evomo system.

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The Shrink-Fit of a Cylindrical Shell Onto a Discontinuous Rigid Mandrel

Journal of Applied Mechanics ◽

10.1115/1.3423490 ◽

1974 ◽

Vol 41 (4) ◽

pp. 959-962 ◽

Cited By ~ 3

Author(s):

D. B. Bogy

Keyword(s):

Thin Shell ◽

Shell Theory ◽

Numerical Results ◽

Graphical Form ◽

Tabular Form ◽

Arbitrary Length ◽

Axisymmetric Contact Problem ◽

Shrink Fit ◽

Limiting Case ◽

Thin Shell Theory

This axisymmetric contact problem is solved using Kirchhoff-Love thin shell theory for a mandrel with a gap and for a plug, either of arbitrary length. The limiting case of a very long gap is of particular significance and is also solved. Representative numerical results are presented in graphical form and sufficient numerical results are presented in tabular form to permit easy computation of any desired aspect of the solution.

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Rigidly rotating gravitationally bound systems of point particles, compared to polytropes

International Journal of Modern Physics C ◽

10.1142/s0129183120500904 ◽

2020 ◽

Vol 31 (06) ◽

pp. 2050090

Author(s):

Yngve Hopstad ◽

Jan Myrheim

Keyword(s):

Continuum Limit ◽

Minimum Energy ◽

Index Formula ◽

Attractive Potential ◽

Polytropic Index ◽

Emden Equation ◽

Point Particles ◽

Polytropic Gas ◽

Energy Formula ◽

The Continuum

In order to simulate rigidly rotating polytropes, we have simulated systems of [Formula: see text] point particles, with [Formula: see text] up to 1800. Two particles at a distance [Formula: see text] interact by an attractive potential [Formula: see text] and a repulsive potential [Formula: see text]. The repulsion simulates the pressure in a polytropic gas of polytropic index [Formula: see text]. We take the total angular momentum [Formula: see text] to be conserved, but not the total energy [Formula: see text]. The particles are stationary in the rotating coordinate system. The rotational energy is [Formula: see text] where [Formula: see text] is the moment of inertia. Configurations, where the energy [Formula: see text] has a local minimum, are stable. In the continuum limit [Formula: see text], the particles become more and more tightly packed in a finite volume, with the interparticle distances decreasing as [Formula: see text]. We argue that [Formula: see text] is a good parameter for describing the continuum limit. We argue further that the continuum limit is the polytropic gas of index [Formula: see text]. For example, the density profile of the nonrotating gas approaches that computed from the Lane–Emden equation describing the nonrotating polytropic gas. In the case of maximum rotation, the instability occurs by the loss of particles from the equator, which becomes a sharp edge, as predicted by Jeans in his study of rotating polytropes. We describe the minimum energy nonrotating configurations for a number of small values of [Formula: see text].

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