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2017-07-06T19:27:35Z

Jrivera: 1 revision: Joel edits

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2017-07-06T19:27:34Z

Jrivera: 1 revision: Joel edits

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=Tiled Menu=

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==Context==

{| class="wikitable" style="margin-right: auto; margin-left: 0px; border-style: solid; border-width: 2px border-color: black;"

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! style="height: 150px; width: 150px; background-color:lightgreen; border-right:2px solid black;" |[[User:Tohline/PGE#Principal_Governing_Equations|Principal Governing Equations]] (PGEs)
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! style="height: 150px; width: 150px; border-right:2px dashed black;" |[[User:Tohline/PGE/ConservingMass#Continuity_Equation|Continuity]]
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! style="height: 150px; width: 150px; border-right:2px dashed black;" |[[User:Tohline/PGE/Euler#Euler_Equation|Euler]]
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! style="height: 150px; width: 150px; border-right:2px dashed black;" |1st Law of Thermodynamics
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! style="height: 150px; width: 150px;"|Poisson
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{| class="wikitable" style="margin-right: auto; margin-left: 0px; border-style: solid; border-width: 3px border-color: black"
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! style="height: 150px; width: 150px; background-color:#ffff99; border-right:2px solid black;" |[[User:Tohline/SR#Supplemental_Relations|Equation of State]] (EOS)
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! style="height: 150px; width: 150px; " |[[User:Tohline/SR/PressureCombinations#Total_Pressure|Total Pressure]]
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==Spherically Symmetric Configurations==

{| class="wikitable" style="margin-right: auto; margin-left: 0px; border-style: solid; border-width: 2px border-color: black;"
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! style="height: 150px; width: 150px; background-color:lightgreen;" |[[User:Tohline/SphericallySymmetricConfigurations/PGE#Spherically_Symmetric_Configurations_.28Part_I.29|One-Dimensional PGEs]]
|}

===Equilibrium Structures===

{| class="wikitable" style="margin-right: auto; margin-left: 75px; border-style: solid; border-width: 2px border-color: black;"

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! style="height: 150px; width: 150px; background-color:lightgreen; border-right:2px solid black;" |[[User:Tohline/SphericallySymmetricConfigurations/SolutionStrategies#Spherically_Symmetric_Configurations_.28Part_II.29|Hydrostatic Balance Equation]]
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! style="height: 150px; width: 310px; text-align:center; border-right:2px dashed black;" |<div align="center">{{ User:Tohline/Math/EQ_SShydrostaticBalance01 }}</div>
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! style="height: 150px; width: 150px;" |[[User:Tohline/SphericallySymmetricConfigurations/SolutionStrategies#Solution_Strategies|Solution Strategies]]
|}
 
{| class="wikitable" style="margin-right: auto; margin-left: 75px; border-style: solid; border-width: 3px border-color: black"
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! style="height: 150px; width: 150px; background-color:#ffff99; border-right:2px solid black;" |[[User:Tohline/SSC/Structure/IsothermalSphere#Isothermal_Sphere|Isothermal Sphere]]
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! style="height: 150px; width: 310px; text-align:center; border-right:2px dashed black;" |<div align="center">{{ User:Tohline/Math/EQ_SSLaneEmden02 }}</div>
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! style="height: 150px; width: 150px;" |[[User:Tohline/SphericallySymmetricConfigurations/SolutionStrategies#Numerical|via Direct Numerical Integration]]
|}
 
{| class="wikitable" style="margin-right: auto; margin-left: 75px; border-style: solid; border-width: 3px border-color: black"
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! style="height: 150px; width: 150px; background-color:#ffff99; border-right:2px solid black;" |[[User:Tohline/SSC/Structure/Polytropes#Polytropic_Spheres|Isolated Polytropes]]
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! style="height: 150px; width: 310px; text-align:center; border-right:2px dashed black;" |<div align="center">{{ User:Tohline/Math/EQ_SSLaneEmden01 }}</div>
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! style="height: 150px; width: 150px; border-right:2px dashed black;" |[[User:Tohline/SSC/Structure/Polytropes#Known_Analytic_Solutions|Known Analytic Solutions]]
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! style="height: 150px; width: 150px; border-right:2px dashed black;" |[[User:Tohline/SphericallySymmetricConfigurations/SolutionStrategies#Numerical|via Direct Numerical Integration]]
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! style="height: 150px; width: 150px; " |[[User:Tohline/SphericallySymmetricConfigurations/SolutionStrategies#SCF|via Self-Consistent Field (SCF) Technique]]
|}
 
{| class="wikitable" style="margin-right: auto; margin-left: 75px; border-style: solid; border-width: 3px border-color: black"
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! style="height: 150px; width: 150px; background-color:#ffff99; border-right:2px solid black; " |[[User:Tohline/SSC/Structure/WhiteDwarfs#White_Dwarfs|Zero-Temperature White Dwarf]]
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! style="height: 150px; width: 150px; background-color:#ffeeee;" |[[User:Tohline/SSC/Structure/WhiteDwarfs#Chandrasekhar_mass|Chandrasekhar Limiting Mass]]
|}
 
{| class="wikitable" style="margin-right: auto; margin-left: 75px; border-style: solid; border-width: 3px border-color: black"
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! style="height: 150px; width: 150px; background-color:#ffff99; border-right:2px solid black;" |Pressure-Truncated Configurations
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! style="height: 150px; width: 150px; background-color:#ffeeee; border-right:2px dashed black;" |[[User:Tohline/SSC/Structure/BonnorEbert#Pressure-Bounded_Isothermal_Sphere|Bonnor-Ebert (Isothermal) Spheres]]
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! style="height: 150px; width: 150px; border-right:2px dashed black;" |[[User:Tohline/SSC/Structure/PolytropesEmbedded#Embedded_Polytropic_Spheres|Polytropes]]
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! style="height: 150px; width: 150px; border-right:2px dotted black;" |[[User:Tohline/Appendix/Ramblings/Turning_Points#Turning_Points|Equilibrium Sequence Turning-Points]]
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! style="height: 150px; width: 150px; " |[[File:MassVsRadiusCombined02.png|150px|Equilibrium sequences of Pressure-Truncated Polytropes]]
|}
 
{| class="wikitable" style="margin-right: auto; margin-left: 75px; border-style: solid; border-width: 3px border-color: black"
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! style="height: 150px; width: 150px; background-color:#ffff99; border-right:2px solid black;" |[[User:Tohline/SSC/Structure/BiPolytropes#BiPolytropes|Composite Polytropes]] (Bipolytropes)
|
! style="height: 150px; width: 150px; background-color:#ffeeee; border-right:2px dashed black;" |[[User:Tohline/SSC/Structure/LimitingMasses#Sch.C3.B6nberg-Chandrasekhar_Mass|Schönberg- Chandrasekhar Mass]]
|
! style="height: 150px; width: 150px; border-right:2px dashed black;" |[[User:Tohline/SSC/Structure/BiPolytropes/Analytic5_1#BiPolytrope_with_nc_.3D_5_and_ne_.3D_1|Analytic <math>~(n_c, n_e)</math> = <math>~(5,1)</math>]]
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! style="height: 150px; width: 150px; border-right:2px dashed black;" |[[User:Tohline/SSC/Structure/BiPolytropes/Analytic1_5#BiPolytrope_with_nc_.3D_1_and_ne_.3D_5|Analytic <math>~(n_c, n_e)</math> = <math>~(1,5)</math>]]
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! style="height: 150px; width: 150px; " |[[User:Tohline/SSC/Stability/InstabilityOnsetOverview#Turning_Points_along_Sequences_of_Pressure-Truncated_Polytropes|Equilibrium Sequence Turning-Points]]
|}

===Stability Analysis===

{| class="wikitable" style="margin-right: auto; margin-left: 75px; border-style: solid; border-width: 3px border-color: black"
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! style="height: 150px; width: 150px; background-color:lightgreen; border-right:2px solid black;" |Radial Pulsation Equation
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! style="height: 150px; width: 150px; border-right:2px dotted black;" |[[User:Tohline/SSC/Perspective_Reconciliation#Reconciling_Eulerian_versus_Lagrangian_Perspectives|Example Derivations & Statement of Eigenvalue Problem]]
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! style="height: 150px; width: 150px; border-right:2px dotted black;" |[[File:ImageOfDerivations06GoodJeansBonnor.png|120px|thumb|center|Jeans (1928) or Bonnor (1957)]]
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! style="height: 150px; width: 150px; border-right:2px dotted black;" |[[File:ImageOfDerivations07GoodLedouxWalraven.png|120px|thumb|center|Ledoux & Walraven (1958)]]
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! style="height: 150px; width: 150px; border-right:2px dashed black;" |[[File:ImageOfDerivations08GoodRosseland.png|120px|thumb|center|Rosseland (1969)]]
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! style="height: 150px; width: 150px;" |[[User:Tohline/SSC/SoundWaves#Sound_Waves|Relationship to Sound Waves]]
|}
 
{| class="wikitable" style="margin-right: auto; margin-left: 75px; border-style: solid; border-width: 3px border-color: black"
|-
! style="height: 150px; width: 150px; background-color:#ffff99; border-right:2px solid black; " |Uniform-Density Configurations
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! style="height: 150px; width: 150px; background-color:#ffeeee; border-right:2px dotted black; " |[[User:Tohline/SSC/UniformDensity#The_Stability_of_Uniform-Density_Spheres|Sterne's Analytic Sol'n of Eigenvalue Problem]]
|
! style="height: 150px; width: 150px; " |[[File:Sterne1937SolutionPlot1.png|150px|Equilibrium sequences of Pressure-Truncated Polytropes]]
|}
 
{| class="wikitable" style="margin-right: auto; margin-left: 75px; border-style: solid; border-width: 3px border-color: black"
|-
! style="height: 150px; width: 150px; background-color:#ffff99; border-right:2px solid black;" |[[User:Tohline/SSC/Structure/IsothermalSphere#Isothermal_Sphere|Pressure-Truncated Isothermal Spheres]]
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! style="height: 150px; width: 620px; text-align:center; border-right:2px dashed black;" |<div align="center">{{ User:Tohline/Math/EQ_RadialPulsation03 }}</div>
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! style="height: 150px; width: 150px; border-right:2px dotted black;" |[[User:Tohline/SSC/Stability/Isothermal#Radial_Oscillations_of_Pressure-Truncated_Isothermal_Spheres|via Direct Numerical Integration]]
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! style="height: 150px; width: 310px; border-right:2px dashed black;" |[[File:TaffVanHorn1974Fundamental.gif|280px|Fundamental-Mode Eigenvectors]]
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! style="height: 150px; width: 150px; background-color:#ffeeee;" |[[User:Tohline/SSC/Structure/BonnorEbert#Pressure-Bounded_Isothermal_Sphere|Yabushita's Analytic Sol'n for Marginally Unstable Configurations]]
|}
 
{| class="wikitable" style="margin-right: auto; margin-left: 75px; border-style: solid; border-width: 3px border-color: black"
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! style="height: 150px; width: 150px; background-color:#ffff99; border-right:2px solid black;" |[[User:Tohline/SSC/Structure/Polytropes#Polytropic_Spheres|Polytropes]]
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! style="height: 150px; width: 620px; text-align:center; border-right:2px dashed black;" |<div align="center">{{ User:Tohline/Math/EQ_RadialPulsation02 }}</div>
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! style="height: 150px; width: 150px; border-right:2px dotted black;" |[[User:Tohline/SSC/Stability/n3PolytropeLAWE#Radial_Oscillations_of_n_.3D_3_Polytropic_Spheres|Isolated n = 3 Polytrope]]
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! style="height: 150px; width: 150px; border-right:2px dashed black;" |[[File:Schwarzschild1941movie.gif|140px|Schwarzschild's Modal Analysis]]
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! style="height: 150px; width: 150px; border-right:2px dashed black;" |[[User:Tohline/SSC/Stability/n3PolytropeLAWE#Radial_Oscillations_of_n_.3D_3_Polytropic_Spheres|Pressure-Truncated Configurations]]
|
! style="height: 150px; width: 150px; background-color:#ffeeee;" |[[User:Tohline/SSC/Stability/InstabilityOnsetOverview#Analyses_of_Radial_Oscillations|Our Analytic Sol'n for Marginally Unstable Configurations]]
|}
 

===Nonlinear Dynamical Evolution===

{| class="wikitable" style="margin-right: auto; margin-left: 75px; border-style: solid; border-width: 3px border-color: black"
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! style="height: 150px; width: 150px; background-color:#ffff99;;" |[[User:Tohline/SSC/FreeFall#Free-Fall_Collapse|Free-Fall Collapse]]
|}
 
{| class="wikitable" style="margin-right: auto; margin-left: 75px; border-style: solid; border-width: 3px border-color: black"
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! style="height: 150px; width: 150px; background-color:#ffff99; border-right:2px solid black;" |Collapse of Isothermal Spheres
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! style="height: 150px; width: 150px; border-right:2px dashed black;" |[http://adsabs.harvard.edu/abs/1993ApJ...416..303F via Direct Numerical Integration]
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! style="height: 150px; width: 150px;" |Self-Similar Solution
|}
 
{| class="wikitable" style="margin-right: auto; margin-left: 75px; border-style: solid; border-width: 3px border-color: black"
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! style="height: 150px; width: 150px; background-color:#ffff99;" |[[User:Tohline/Apps/GoldreichWeber80#Homologously_Collapsing_Stellar_Cores|Collapse of an Isolated n = 3 Polytrope]]
|}
 

=See Also=

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