scholarly journals On Self-Gravitating Polytropic Cylinders and Slabs

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.

Physical Characteristics of a Polytrope Index 5 with Finite Radius

1981 ◽  
Vol 4 (2) ◽  
pp. 205-208
Author(s):  
J. O. Murphy
Keyword(s):  
Discrete System ◽  
Physical Structure ◽  
Density Variation ◽  
Uniform Density ◽  
Finite Radius ◽  
Polytropic Model ◽  
Emden Equation ◽  
Infinite Extent ◽  
Physical Features ◽  
Polytrope Index

In astrophysics the polytropic law with index n is commonly used as a means of imposing a simple and ordered physical structure on a gaseous (or smoothed discrete) system. In many instances it would be preferable to be able to introduce a polytropic density variation analytically into the basic theory rather than numerically at the computational phase. It is perhaps unfortunate that the three well known classical analytical E type solutions of the Lane-Emden equation for n = 0, 1 and 5 all have some constraining physical features; specifically, the polytrope n = 0 has uniform density and hence arbitrary radius, when n = 1 the mass and radius are independent of each other and the solution cannot be transformed homologically, and because the first zero ξ1 = ∞ for n = 5 the corresponding polytropic model has infinite extent and central condensation. In contrast, and unlike most stars, the two finite radius models have central condensations which ~ 1.

scholarly journals A pointwise inequality for the fourth-order Lane–Emden equation

2015 ◽  
Vol 8 (7) ◽  
pp. 1541-1563 ◽  
Author(s):  
Mostafa Fazly ◽  
Jun-cheng Wei ◽  
Xingwang Xu
Keyword(s):  
Fourth Order ◽  
Emden Equation

scholarly journals On a class of fourth order linear recurrence equations

1984 ◽  
Vol 7 (1) ◽  
pp. 131-149 ◽  
Author(s):  
Sui-Sun Cheng
Keyword(s):  
Fourth Order ◽  
Linear Recurrence ◽  
Order Linear ◽  
Basic Properties ◽  
Recurrence Equations

This paper is concerned with sequences that satisfy a class of fourth order linear recurrence equations. Basic properties of such sequences are derived. In addition, we discuss the oscillatory and nonoscillatory behavior of such sequences.

THE REISSNER-SAGOCI PROBLEM FOR A LONG CYLINDER OF FINITE RADIUS

1966 ◽  
Vol 19 (2) ◽  
pp. 123-129 ◽  
Author(s):  
I. N. SNEDDON ◽  
R. P. SRIVASTAV ◽  
S. C. MATHUR
Keyword(s):  
Finite Radius ◽  
Long Cylinder

scholarly journals Emden’s Polytropes: Gas Globes In Hydrostatic Equilibrium

2013 ◽  
Vol 12 (1) ◽  
pp. 99-127
Author(s):  
M N Anandaram
Keyword(s):  
Mass Distribution ◽  
Equilibrium Structure ◽  
Review Article ◽  
Hydrostatic Equilibrium ◽  
Graphical Form ◽  
Polytropic Index ◽  
Tabular Form ◽  
Program Code ◽  
Emden Equation ◽  
Python Script

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.

Statistics and parallaxes

1978 ◽  
Vol 48 ◽  
pp. 7-29
Author(s):  
T. E. Lutz
Keyword(s):  
Experimental Design ◽  
Statistical Methods ◽  
Review Paper ◽  
Systematic Errors ◽  
Past Experience ◽  
Random Errors ◽  
Trigonometric Parallaxes ◽  
Systematic And Random Errors

This review paper deals with the use of statistical methods to evaluate systematic and random errors associated with trigonometric parallaxes. First, systematic errors which arise when using trigonometric parallaxes to calibrate luminosity systems are discussed. Next, determination of the external errors of parallax measurement are reviewed. Observatory corrections are discussed. Schilt’s point, that as the causes of these systematic differences between observatories are not known the computed corrections can not be applied appropriately, is emphasized. However, modern parallax work is sufficiently accurate that it is necessary to determine observatory corrections if full use is to be made of the potential precision of the data. To this end, it is suggested that a prior experimental design is required. Past experience has shown that accidental overlap of observing programs will not suffice to determine observatory corrections which are meaningful.

The restoration of blurred electron micrographs

1986 ◽  
Vol 44 ◽  
pp. 180-181
Author(s):  
Bridget Carragher ◽  
David A. Bluemke ◽  
Michael J. Potel ◽  
Robert Josephs
Keyword(s):  
Cross Section ◽  
Electron Micrographs ◽  
Relative Motion ◽  
Finite Thickness ◽  
Image Plane ◽  
Helical Axis ◽  
Thin Sections ◽  
Structural Details

We have investigated the feasibility of restoring blurred electron micrographs. Two related problems have been considered; the restoration of images blurred as a result of relative motion between the specimen and the image plane, and the restoration of images which are rotationally blurred about an axis. Micrographs taken while the specimen is drifting result in images which are blurred in the direction of motion. An example of rotational blurring arises in micrographs of thin sections of helical particles viewed in cross section. The twist of the particle within the finite thickness of the section causes the image to appear rotationally blurred about the helical axis. As a result, structural details, particularly at large distances from the helical axis, will be obscured.

Children’s Recall of Approximations to English

1973 ◽  
Vol 16 (2) ◽  
pp. 201-212 ◽  
Author(s):  
Elizabeth Carrow ◽  
Michael Mauldin
Keyword(s):  
Language Development ◽  
Fourth Order ◽  
Third Order ◽  
Memory Processes ◽  
The Third ◽  
General Index ◽  
General Linguistic

As a general index of language development, the recall of first through fourth order approximations to English was examined in four, five, six, and seven year olds and adults. Data suggested that recall improved with age, and increases in approximation to English were accompanied by increases in recall for six and seven year olds and adults. Recall improved for four and five year olds through the third order but declined at the fourth. The latter finding was attributed to deficits in semantic structures and memory processes in four and five year olds. The former finding was interpreted as an index of the development of general linguistic processes.

Potential Uses of Vinegar as a Medicine and Related in vivo Mechanisms

2016 ◽  
Vol 86 (3-4) ◽  
pp. 127-151 ◽  
Author(s):  
Zeshan Ali ◽  
Zhenbin Wang ◽  
Rai Muhammad Amir ◽  
Shoaib Younas ◽  
Asif Wali ◽  
...  
Keyword(s):  
Chemical Structure ◽  
Review Paper ◽  
Heart Diseases ◽  
Folk Medicine ◽  
Active Role ◽  
Current Review ◽  
Different Types ◽  
Positive Effect

While the use of vinegar to fi ght against infections and other crucial conditions dates back to Hippocrates, recent research has found that vinegar consumption has a positive effect on biomarkers for diabetes, cancer, and heart diseases. Different types of vinegar have been used in the world during different time periods. Vinegar is produced by a fermentation process. Foods with a high content of carbohydrates are a good source of vinegar. Review of the results of different studies performed on vinegar components reveals that the daily use of these components has a healthy impact on the physiological and chemical structure of the human body. During the era of Hippocrates, people used vinegar as a medicine to treat wounds, which means that vinegar is one of the ancient foods used as folk medicine. The purpose of the current review paper is to provide a detailed summary of the outcome of previous studies emphasizing the role of vinegar in treatment of different diseases both in acute and chronic conditions, its in vivo mechanism and the active role of different bacteria.

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