Difference between revisions of "User:Tohline/Appendix/Ramblings/ForPJ April2021"

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* [[User:Tohline/ThreeDimensionalConfigurations/BinaryFission#Fission_Hypothesis_of_Binary_Star_Formation|Fission Hypothesis of Binary Star Formation]]
* [[User:Tohline/ThreeDimensionalConfigurations/BinaryFission#Fission_Hypothesis_of_Binary_Star_Formation|Fission Hypothesis of Binary Star Formation]]
* [[User:Tohline/ThreeDimensionalConfigurations/ChallengesPt2#COLLADA-Based_Representation|COLLADA-based Representation of Riemann Type 1 Ellipsoid]]
* [[User:Tohline/ThreeDimensionalConfigurations/ChallengesPt2#COLLADA-Based_Representation|COLLADA-based Representation of Riemann Type 1 Ellipsoid]]
==Challenges to Young, Applied Mathematicians==
<font color="red">'''Note from J. E. Tohline to Students with Good Mathematical Skills'''</font>:  The astronomy community's understanding of the ''Structure, Stability, and Dynamics'' of stars and galaxies would be strengthened if we had, in hand, closed-form analytic solutions to the following well-defined mathematical problems.  (Solutions can be obtained ''numerically'' with relative ease, but here the challenge is to find a closed-form analytic solution.)  As is true with most meaningful scientific research projects, it is not at all clear whether each of these problems ''has'' a solution.  In my judgment, however, it seems plausible that a closed-form solution can be discovered in each case and such a solution would be of sufficient interest to the astronomical community that it would likely be publishable in a professional astronomy or physics journal.  At the very least, each of these projects represents an opportunity for a graduate student, an undergraduate, or even a talented high-school student (perhaps in connection with a mathematics science fair project?) to hone her/his research skills in applied mathematics.  Also, I would be thrilled to include a solution to any one of these problems &#8212; along with full credit to the solution's author &#8212; as a chapter in this online H_Book.  Having retired from LSU, I am not in a position to financially support or formally advise students who are in pursuit of a higher-education degree.  I would nevertheless be interested in sharing my expertise &#8212; and, perhaps, developing a collaborative relationship &#8212; with individuals who are interested in pursuing answers to the questions posed by this identified set of problems.
* [[User:Tohline/MathProjects/EigenvalueProblemN1|Find Analytic Solutions to an Eigenvalue Problem]]


=See Also=
=See Also=

Revision as of 15:00, 17 April 2021


For PJ in April 2021

Whitworth's (1981) Isothermal Free-Energy Surface
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Potentially Relevant Initial Links

Challenges to Young, Applied Mathematicians

Note from J. E. Tohline to Students with Good Mathematical Skills: The astronomy community's understanding of the Structure, Stability, and Dynamics of stars and galaxies would be strengthened if we had, in hand, closed-form analytic solutions to the following well-defined mathematical problems. (Solutions can be obtained numerically with relative ease, but here the challenge is to find a closed-form analytic solution.) As is true with most meaningful scientific research projects, it is not at all clear whether each of these problems has a solution. In my judgment, however, it seems plausible that a closed-form solution can be discovered in each case and such a solution would be of sufficient interest to the astronomical community that it would likely be publishable in a professional astronomy or physics journal. At the very least, each of these projects represents an opportunity for a graduate student, an undergraduate, or even a talented high-school student (perhaps in connection with a mathematics science fair project?) to hone her/his research skills in applied mathematics. Also, I would be thrilled to include a solution to any one of these problems — along with full credit to the solution's author — as a chapter in this online H_Book. Having retired from LSU, I am not in a position to financially support or formally advise students who are in pursuit of a higher-education degree. I would nevertheless be interested in sharing my expertise — and, perhaps, developing a collaborative relationship — with individuals who are interested in pursuing answers to the questions posed by this identified set of problems.

See Also

Whitworth's (1981) Isothermal Free-Energy Surface

© 2014 - 2021 by Joel E. Tohline
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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