Difference between revisions of "User:Tohline/H Book"

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=Context=
=Context=


:[http://www.vistrails.org/index.php/User:Tohline/PGE#Principal_Governing_Equations Principal Governing Equations]
* [[User:Tohline/PGE#Principal_Governing_Equations|Principal Governing Equations]]
** [[User:Tohline/PGE/ConservingMass#Continuity_Equation|Continuity Equation]]
** [[User:Tohline/PGE/Euler#Euler_Equation|Euler Equation]]
*** [[User:Tohline/PGE/RotatingFrame#Rotating_Reference_Frame|Rotating Reference Frame]]
** <math>1^\mathrm{st}</math> Law of Thermodynamics
** Poisson Equation


:[http://www.vistrails.org/index.php/User:Tohline/SR Supplemental Relations]
* [[User:Tohline/SR#Supplemental_Relations|Supplemental Relations]]
** [[User:Tohline/SR/PressureCombinations#Total_Pressure|Total Pressure]]
*** [[User:Tohline/SR/Ptot_QuarticSolution#Determining_Temperature_from_Density_and_Pressure|Quartic Temperature Solution]]


:Virial Equations
* Virial Equations


=Applications=
=Applications=
==Spherically Symmetric Configurations==
==Spherically Symmetric Configurations==


If the self-gravitating configuration that we wish to construct is spherically symmetric, then the coupled set of multidimensional, partial differential equations that serve as our [http://www.vistrails.org/index.php/User:Tohline/PGE principal governing equations] can be simplified to a coupled set of one-dimensional, ordinary differential equations.  This is accomplished by expressing each of the multidimensional spatial operators &#8212; gradient (<math>\nabla</math>), divergence (<math>\nabla\cdot</math>), and Laplacian (<math>\nabla^2</math>) &#8212; in spherical coordinates (<math>r, \theta, \varphi</math>) (see, for example, the [http://en.wikipedia.org/wiki/Spherical_coordinate_system#Integration_and_differentiation_in_spherical_coordinates Wikipedia discussion of integration and differentiation in spherical coordinates]) then setting to zero all derivatives that are taken with respect to the angular coordinates <math>\theta</math> and <math>\varphi</math>.  After making this simplification, our governing equations become... [http://www.vistrails.org/index.php/User:Tohline/SphericallySymmetricConfigurations/PGE <more>]
[[User:Tohline/SphericallySymmetricConfigurations/PGE|Introduction]]


===Structure:===
===Structure:===


* <font color="darkblue">'''[http://www.vistrails.org/index.php/User:Tohline/SphericallySymmetricConfigurations/SolutionStrategies Solution Strategies]'''</font>
* <font color="darkblue">'''[[User:Tohline/SphericallySymmetricConfigurations/SolutionStrategies|Solution Strategies]]'''</font>
* Example Solutions:
* Example Solutions:
** [http://www.vistrails.org/index.php?title=User:Tohline/SSC/UniformDensity Uniform-density sphere]
** [[User:Tohline/SSC/UniformDensity|Uniform-density sphere]]
** [http://www.vistrails.org/index.php/User:Tohline/SSC/Polytropes Polytropes]
** [[User:Tohline/SSC/Polytropes|Polytropes]]
** Zero-temperature White Dwarf
** Zero-temperature White Dwarf
** Isothermal sphere
** Isothermal sphere
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===Stability:===
===Stability:===


* <font color="darkblue">'''[http://www.vistrails.org/index.php/User:Tohline/SSC/Perturbations Solution Strategy]'''</font>
* <font color="darkblue">'''[[User:Tohline/SSC/Perturbations|Solution Strategy]]'''</font>
* Example Solutions:
* Example Solutions:
** [http://www.vistrails.org/index.php?title=User:Tohline/SSC/UniformDensity Uniform-density sphere]
** [[User:Tohline/SSC/UniformDensity|Uniform-density sphere]]
** [http://www.vistrails.org/index.php/User:Tohline/SSC/Polytropes Polytropes]
** [[User:Tohline/SSC/Polytropes|Polytropes]]




===<font color="darkblue">'''[http://www.vistrails.org/index.php/User:Tohline/SphericallySymmetricConfigurations Dynamics]:'''</font>===
===<font color="darkblue">'''[[User:Tohline/SphericallySymmetricConfigurations|Dynamics]]:'''</font>===


=Appendices=
=Appendices=


{{LSU_HBook_footer}}
{{LSU_HBook_footer}}

Revision as of 17:38, 21 March 2010


Whitworth's (1981) Isothermal Free-Energy Surface
|   Tiled Menu   |   Tables of Content   |  Banner Video   |  Tohline Home Page   |


Preface from the original version of this HyperText Book (H_Book):

November 18, 1994

Much of our present, basic understanding of the structure, stability, and dynamical evolution of individual stars, short-period binary star systems, and the gaseous disks that are associated with numerous types of stellar systems (including galaxies) is derived from an examination of the behavior of a specific set of coupled, partial differential equations. These equations — most of which also are heavily utilized in studies of continuum flows in terrestrial environments — are thought to govern the underlying physics of all macroscopic "fluid" systems in astronomy. Although relatively simple in form, they prove to be very rich in nature... <more>

Pictorial Table of Contents

Context

  • Virial Equations

Applications

Spherically Symmetric Configurations

Introduction

Structure:


Stability:


Dynamics:

Appendices

Whitworth's (1981) Isothermal Free-Energy Surface

© 2014 - 2021 by Joel E. Tohline
|   H_Book Home   |   YouTube   |
Appendices: | Equations | Variables | References | Ramblings | Images | myphys.lsu | ADS |
Recommended citation:   Tohline, Joel E. (2021), The Structure, Stability, & Dynamics of Self-Gravitating Fluids, a (MediaWiki-based) Vistrails.org publication, https://www.vistrails.org/index.php/User:Tohline/citation