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- {{ User:Tohline/Math/EQ_SSLaneEmden01 }} <!-- As we have discussed in [[User:Tohline/SSC/Structure/IsothermalSphere#Governing_Relations|a separate chapter]], th78 KB (11,084 words) - 20:29, 11 July 2020
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- ==Ramblings== <li>[[User:Tohline/Appendix/Ramblings/DirectionCosines|Direction Cosines]]</li>18 KB (2,190 words) - 17:10, 28 May 2021
- In what follows, we borrow heavily from Chapter VIII of [<b>[[User:Tohline/Appendix/References#LL75|<font color="red">LL75</font>]]</b>], as it provides an exc We begin with the set of [[User:Tohline/PGE#Principal_Governing_Equations|principal governing equations]] that prov19 KB (2,695 words) - 21:06, 8 March 2017
- ...st expression results from enlisting the [[User:Tohline/Appendix/Ramblings/PowerSeriesExpressions#Binomial|binomial theorem]].) For simplicity, in the discussion that follo ...development that was used to underpin work of the group at [[User:Tohline/Appendix/CGH/ZebraImaging#UT_Southwestern_Medical_Center_at_Dallas|UT's Southwestern21 KB (3,242 words) - 16:51, 31 March 2020
- In an [[User:Tohline/SSC/Perturbations#2ndOrderODE|accompanying discussion]], we derived the so- {{User:Tohline/Math/EQ_RadialPulsation01}}28 KB (4,231 words) - 20:50, 28 February 2017
- We discuss this topic in a [[User:Tohline/Appendix/Ramblings/BordeauxSequences#Spheroid-Ring_Systems|separate, accompanying chapter]]. ...Wong (1973, Annals of Physics, 77, 279)], which we have separately [[User:Tohline/Apps/Wong1973Potential#Wong.27s_.281973.29_Analytic_Potential|discussed in148 KB (21,556 words) - 00:05, 17 December 2020
- ...state, that is, {{User:Tohline/Math/VAR_Pressure01}} is related to {{User:Tohline/Math/VAR_Density01}} through the relation, ...l sound speed. Comparing this {{User:Tohline/Math/VAR_Pressure01}}-{{User:Tohline/Math/VAR_Density01}} relationship to19 KB (2,922 words) - 23:02, 8 March 2019
- In an [[User:Tohline/SSC/Perturbations#2ndOrderODE|accompanying discussion]], we derived the so- {{User:Tohline/Math/EQ_RadialPulsation01}}49 KB (7,239 words) - 16:39, 11 April 2017
- ...ion] that governs the propagation of sound waves. Here we build on [[User:Tohline/SSC/SoundWaves#Sound_Waves|our separate, introductory discussion of sound w We begin with the set of [[User:Tohline/PGE#Principal_Governing_Equations|principal governing equations]] that prov47 KB (7,037 words) - 21:12, 8 March 2017
- ...] and [http://adsabs.harvard.edu/abs/1988ApJS...66..315H I. Hachisu, J. E. Tohline & Y. Eriguchi (1987, ApJ, 323, 592 - 613)] have mapped out the full seq ...rature and, therefore, has heretofore been under-appreciated. In a [[User:Tohline/Apps/Wong1973Potential#Wong.27s_.281973.29_Analytic_Potential|separate, acc197 KB (28,120 words) - 21:04, 16 July 2020
- ...cartesian, spherical or cylindrical coordinates. Specifically for [[User:Tohline/2DStructure/ToroidalGreenFunction#Axisymmetric_Systems|axisymmetric systems ...n derived by [http://adsabs.harvard.edu/abs/1999ApJ...527...86C Cohl & Tohline (1999)] — involving different integrand expressions and no summation166 KB (23,360 words) - 18:41, 4 October 2018
- ...ch no equilibrium configurations exist. As we have summarized in a [[User:Tohline/SSC/Structure/BonnorEbert#Following_Bonnor.27s_Presentation|related discuss In an [[User:Tohline/SSC/Structure/BonnorEbert#Pressure-Bounded_Isothermal_Sphere|accompanying d123 KB (18,556 words) - 19:29, 8 May 2019
- Referring back to our separate discussion of the [[User:Tohline/2DStructure/ToroidalGreenFunction#Basic_Elements_of_a_Toroidal_Coordinate_S Now that I think about it, this is all a bit silly because from the [[User:Tohline/2DStructure/ToroidalGreenFunction#Basic_Elements_of_a_Toroidal_Coordinate_S63 KB (9,332 words) - 16:46, 20 August 2018
- ...tric, equilibrium structures that have been derived elsewhere. The [[User:Tohline/SphericallySymmetricConfigurations/PGE#Spherically_Symmetric_Configurations ...anner outlined by the "structural solution strategy" we have called [[User:Tohline/SphericallySymmetricConfigurations/SolutionStrategies#Solution_Strategies|T81 KB (12,156 words) - 20:16, 6 July 2017
- =Ramblings: Marginally Unstable Bipolytropes= ...c indexes, as labeled, over the range <math>1 \le n \le 6</math>. ([[User:Tohline/SSC/Stability/InstabilityOnsetOverview#Turning_Points_along_Sequences_of_Pr110 KB (16,431 words) - 21:56, 11 December 2018
- <font size="+2"><b>Summary</b></font><p></p>Joel E. Tohline (May, 2017) ...color="maroon">Eigenfunction of the Neutral Mode:</font> In a [[User:Tohline/SSC/Stability/InstabilityOnsetOverview#Analyses_of_Radial_Oscillations|sepa176 KB (23,976 words) - 22:41, 26 May 2017
- ...operties of the underlying equilibrium models have been reviewed in [[User:Tohline/SSC/Structure/BiPolytropes/Analytic1_5#BiPolytrope_with_nc_.3D_1_and_ne_.3D {{ User:Tohline/Math/EQ_RadialPulsation02 }}73 KB (10,895 words) - 23:45, 7 January 2019
- ...c indexes, as labeled, over the range <math>1 \le n \le 6</math>. ([[User:Tohline/SSC/Stability/InstabilityOnsetOverview#Turning_Points_along_Sequences_of_Pr ...ro to infinity. Figure 2, whose content is essentially the same as [[User:Tohline/SSC/Structure/BiPolytropes/Analytic5_1#Model_Sequences|Figure 1 of this sep135 KB (19,927 words) - 22:35, 15 May 2019
- ...will assume that {{User:Tohline/Math/VAR_Density01}} is related to {{User:Tohline/Math/VAR_Enthalpy01}} through the relation, {{User:Tohline/Math/EQ_Polytrope03}}97 KB (13,913 words) - 22:37, 30 July 2019