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==Other Less Challenging or Less Well-Defined Research Projects==
===Stability of Bipolytropic Configurations===
Using primarily analytic techniques, our objective is to evaluate the free energy of spherically symmetric, bipolytropic configurations (''aka'' composite polytropes), then, use variations in the free energy function to identify equilibrium states (scalar virial theorem) and to assess the relative dynamical stability of the states.
* Early discussions with LSU graduate student, [[SSC/VirialStability#Discussion_with_Kundan_Kadam|Kundan Kadam]]; see also [[SSC/Structure/BiPolytropes/Analytic00#BiPolytrope_with_nc_.3D_0_and_ne_.3D_0|construction of <math>(n_c, n_e) = (0, 0)</math> bipolytrope]]
* Outline of [[SSC/Virial/PolytropesEmbeddedOutline#Outline|Work Completed, to Date]], on the free energy of pressure-truncated polytropes
* Relevant to &hellip;

<table border="0" cellpadding="1" align="center" width="100%">
<tr><td width="4%" align="left">&nbsp;&nbsp;&nbsp;</td>
<td align="left">[[SSC/Structure/LimitingMasses#Sch.C3.B6nberg-Chandrasekhar_Mass|Sch&ouml;nberg-Chandrasekhar Mass]]</td></tr>
<tr><td width="4%" align="left">&nbsp;&nbsp;&nbsp;</td>
<td align="left">[[SSC/Structure/BiPolytropes/Analytic51#Derivation_by_Eggleton.2C_Faulkner.2C_and_Cannon_.281998.29|Stellar Evolution from Main Sequence to Red Giant]]</td></tr>
<tr><td width="4%" align="left">&nbsp;&nbsp;&nbsp;</td>
<td align="left">[[SSC/Structure/LimitingMasses#Bounded_Isothermal_Sphere_.26_Bonnor-Ebert_Mass|Bonnor-Ebert Spheres]]</td></tr>
<tr><td width="4%" align="left">&nbsp;&nbsp;&nbsp;</td>
<td align="left">[[Appendix/Ramblings/OriginOfPlanetaryNebulae|Origin of Planetary Nebulae]]</td></tr>
</table>

===Gravitational-Wave Signals from Core-Collapse Supernovae===
To date, gravitational radiation has not been directly detected by any scientific instrument on Earth.  The advancement of detector techniques in association with the development of new observatories worldwide &#8212; such as [http://www.ligo.org/ LIGO] and [http://wwwcascina.virgo.infn.it/ VIRGO] &#8212; promises to change this situation in the near future.  When gravitational-wave signals are detected from core-collapse supernovae, the expectation is that these signals &#8212; primarily tracing out wave amplitude as a function of time &#8212; will exhibit a great deal of structure, reflecting several different phases of the collapse.  We propose to construct a semi-analytic signal template to help the gravitational-wave community more fully understand the underlying physics that is fundamentally responsible for generating the (anticipated) signal's characteristic features.
* [[ProjectsUnderway/CoreCollapseSupernovae#A_Template_for_Gravitational_Wave_Signals_from_Core-Collapse_Supernovae|A Template for Gravitational-Wave Signals from Core-Collapse Supernovae]]
* Relevant to &hellip;

<table border="0" cellpadding="1" align="center" width="100%">
<tr><td width="4%" align="left">&nbsp;&nbsp;&nbsp;</td>
<td align="left">[[SSC/Dynamics/FreeFall#Free-Fall_Collapse|Gravitational Free-Fall Collapse]]</td></tr>
<tr><td width="4%" align="left">&nbsp;&nbsp;&nbsp;</td>
<td align="left">[[Apps/GoldreichWeber80#Homologously_Collapsing_Stellar_Cores|Homologous Collapse of Stellar Cores]] (Goldreich &amp; Weber 1980)</td></tr>
</table>

===Musings Regarding Dark Matter and Dark Energy===
[Joel E. Tohline recollection on 3/8/2015]  It was during my first year (July 1978 – June 1979) as a J. Willard Gibbs Instructor in the Astronomy Department at Yale University that I started wondering whether the nearly ubiquitous display of “flat rotation curves” in disk galaxies might be explained, not via the dark matter hypothesis, but by invoking a 1/r force-law for gravity at large distances.  My reasoning was simple:
# I was uncomfortable with the “dark matter” hypothesis, which smelled to me like the story of ether, all over again.
# If Isaac Newton had been handed Vera Rubin’s observations &#8212; which showed that orbital velocities were approximately constant with distance &#8212; instead of Kepler's observations &#8212; which showed that orbital velocities behaved as <math>~v \propto r^{-1/2}</math> &#8212; he likely would have hypothesized that the gravitational acceleration due to a central point mass is proportional to <math>~r^{-1}</math> instead of <math>~r^{-2}</math>.
While I put quite a lot of thought into this idea in the late '70s and early '80s &#8212; and I still give it some thought from time to time because I consider the astrophysics community's fundamental understanding of "dark matter" and now, too, "dark energy" to be weak &#8212; I produced only two publications on the topic, neither of which was in a refereed archival journal:
* [http://adsabs.harvard.edu/abs/1983IAUS..100..205T Stabilizing a Cold Disk with a 1/r Force Law]
* [http://www.phys.lsu.edu/~tohline/vita/Tohline.C5.pdf Does Gravity Exhibit a 1/r Force on the Scale of Galaxies?]
From time to time, I plan to post here some of the research notes that I have generated on this topic over the years, as well as recollections of discussions of the topic that I have had with professional colleagues.  I begin by posting a scanned copy of one of my most cherished possessions from my time at Yale.
* [http://www.phys.lsu.edu/~tohline/TinsleyNotes1978.pdf Notes from Beatrice Tinsley] showing that she, too, had given some thought to the implications of a 1/r force-law for gravity in 1978.

* [[DarkMatter/VeraRubin|Early interactions with Vera Rubin]].

* [[DarkMatter/UniformSphere|Attraction associated with a uniform-density sphere]] &#8212; my derivation in the early '80s, with the kind assistance of LSU Professor Attipat K. Rajagopal.

* [[DarkMatter/CK2015|Remarks on Christodoulou &amp; Kazanas (2015)]] 

* [[Appendix/Ramblings/StrongNuclearForce|Radial Dependence of the Strong Nuclear Force]]