View source for User:Tohline/H BookTiledMenu

__FORCETOC__ 
<!-- __NOTOC__ will force TOC off -->

=Tiled Menu=

{{LSU_HBook_header}}

==Context==

{| class="wikitable" style="margin-right: auto; margin-left: 0px; border-style: solid; border-width: 2px border-color: black;"
<!-- |+ style="text-align:left; height:40px;" | <font size="+2">'''CONTEXT'''</font> -->
|- 
! style="height: 150px; width: 150px; background-color:lightgreen; border-right:2px solid black;" |[[User:Tohline/PGE#Principal_Governing_Equations|<b>Principal<br />Governing<br />Equations</b>]]<br />(PGEs)
|
! style="height: 150px; width: 150px; border-right:2px dashed black;" |[[User:Tohline/PGE/ConservingMass#Continuity_Equation|Continuity]]
|
! style="height: 150px; width: 150px; border-right:2px dashed black;" |[[User:Tohline/PGE/Euler#Euler_Equation|Euler]]
|
! style="height: 150px; width: 150px; border-right:2px dashed black;" |1<sup>st</sup> Law of<br />Thermodynamics
|
! style="height: 150px; width: 150px;"|Poisson
|}
<p>&nbsp;</p>
{| class="wikitable" style="margin-right: auto; margin-left: 0px; border-style: solid; border-width: 3px border-color: black"
|- 
! style="height: 150px; width: 150px; background-color:#ffff99; border-right:2px solid black;" |[[User:Tohline/SR#Supplemental_Relations|<b>Equation<br />of State</b>]]<br />(EOS)
|
! style="height: 150px; width: 150px; " |[[User:Tohline/SR/PressureCombinations#Total_Pressure|Total<br />Pressure]] 
|}


==Spherically Symmetric Configurations==

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


===Equilibrium Structures===

{| class="wikitable" style="margin-right: auto; margin-left: 75px; border-style: solid; border-width: 2px border-color: black;"
<!-- |+ style="text-align:left; height:40px;" | <font size="+2">'''CONTEXT'''</font> -->
|- 
! style="height: 150px; width: 150px; background-color:lightgreen; border-right:2px solid black;" |[[User:Tohline/SphericallySymmetricConfigurations/SolutionStrategies#Spherically_Symmetric_Configurations_.28Part_II.29|<b>Hydrostatic<br />Balance<br />Equation</b>]]
|
! style="height: 150px; width: 310px; text-align:center; border-right:2px dashed black;" |<div align="center">{{ User:Tohline/Math/EQ_SShydrostaticBalance01 }}</div>
|
! style="height: 150px; width: 150px;" |[[User:Tohline/SphericallySymmetricConfigurations/SolutionStrategies#Solution_Strategies|Solution<br />Strategies]]
|}
<p>&nbsp;</p>
{| 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|<b>Isothermal<br />Sphere</b>]]
|
! style="height: 150px; width: 310px; text-align:center; border-right:2px dashed black;" |<div align="center">{{ User:Tohline/Math/EQ_SSLaneEmden02 }}</div>
|
! style="height: 150px; width: 150px;" |[[User:Tohline/SphericallySymmetricConfigurations/SolutionStrategies#Numerical|via<br />Direct<br />Numerical<br />Integration]]
|}
<p>&nbsp;</p>
{| 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/Polytropes#Polytropic_Spheres|<b>Isolated<br />Polytropes</b>]]
|
! style="height: 150px; width: 310px; text-align:center; border-right:2px dashed black;" |<div align="center">{{ User:Tohline/Math/EQ_SSLaneEmden01 }}</div>
|
! style="height: 150px; width: 150px; border-right:2px dashed black;" |[[User:Tohline/SSC/Structure/Polytropes#Known_Analytic_Solutions|Known<br />Analytic<br />Solutions]]
|
! style="height: 150px; width: 150px; border-right:2px dashed black;" |[[User:Tohline/SphericallySymmetricConfigurations/SolutionStrategies#Numerical|via<br />Direct<br />Numerical<br />Integration]]
|
! style="height: 150px; width: 150px; " |[[User:Tohline/SphericallySymmetricConfigurations/SolutionStrategies#SCF|via<br />Self-Consistent<br />Field (SCF)<br />Technique]]
|}
<p>&nbsp;</p>
{| 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/WhiteDwarfs#White_Dwarfs|<b>Zero-Temperature<br />White Dwarf</b>]]
|
! style="height: 150px; width: 150px; background-color:#ffeeee;" |[[User:Tohline/SSC/Structure/WhiteDwarfs#Chandrasekhar_mass|Chandrasekhar<br />Limiting<br />Mass]]
|}
<p>&nbsp;</p>
{| 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;" |<b>Pressure-Truncated<br />Configurations</b>
|
! style="height: 150px; width: 150px; background-color:#ffeeee; border-right:2px dashed black;" |[[User:Tohline/SSC/Structure/BonnorEbert#Pressure-Bounded_Isothermal_Sphere|Bonnor-Ebert<br />(Isothermal)<br />Spheres]]
|
! style="height: 150px; width: 150px; border-right:2px dashed black;" |[[User:Tohline/SSC/Structure/PolytropesEmbedded#Embedded_Polytropic_Spheres|Polytropes]]
|
! style="height: 150px; width: 150px; border-right:2px dotted black;" |[[User:Tohline/Appendix/Ramblings/Turning_Points#Turning_Points|Equilibrium<br />Sequence<br />Turning-Points]]
|
! style="height: 150px; width: 150px; " |[[File:MassVsRadiusCombined02.png|150px|Equilibrium sequences of Pressure-Truncated Polytropes]]
|}
<p>&nbsp;</p>
{| 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/BiPolytropes#BiPolytropes|<b>Composite<br />Polytropes</b>]]<br />(Bipolytropes)
|
! style="height: 150px; width: 150px; background-color:#ffeeee; border-right:2px dashed black;" |[[User:Tohline/SSC/Structure/LimitingMasses#Sch.C3.B6nberg-Chandrasekhar_Mass|Sch&ouml;nberg-<br />Chandrasekhar<br />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<br /><br /><math>~(n_c, n_e)</math><br /> = <br /><math>~(5,1)</math>]]
|
! 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<br /><br /><math>~(n_c, n_e)</math><br /> = <br /><math>~(1,5)</math>]]
|
! style="height: 150px; width: 150px; " |[[User:Tohline/SSC/Stability/InstabilityOnsetOverview#Turning_Points_along_Sequences_of_Pressure-Truncated_Polytropes|Equilibrium<br />Sequence<br />Turning-Points]]
|}


===Stability Analysis===

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


===Nonlinear Dynamical Evolution===

{| 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;;" |[[User:Tohline/SSC/FreeFall#Free-Fall_Collapse|<b>Free-Fall<br />Collapse</b>]]
|}
<p>&nbsp;</p>
{| 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;" |<b>Collapse of<br />Isothermal<br />Spheres</b>
|
! style="height: 150px; width: 150px; border-right:2px dashed black;" |[http://adsabs.harvard.edu/abs/1993ApJ...416..303F via<br/>Direct<br />Numerical<br />Integration]
|
! style="height: 150px; width: 150px;" |Self-Similar<br />Solution
|}
<p>&nbsp;</p>
{| 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;" |[[User:Tohline/Apps/GoldreichWeber80#Homologously_Collapsing_Stellar_Cores|<b>Collapse of<br />an Isolated<br />n = 3<br />Polytrope</b>]]
|}
<p>&nbsp;</p>

=See Also=


{{LSU_HBook_footer}}