Editing Appendix/Ramblings/MyDoctoralStudents (section)

===Years 1982 - 1988===
<!-- 1982 - 1988 -->
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  <td align="center">[http://www.phys.lsu.edu/~tohline/ref_ref.html Pubs.] <font color="red">(rank)</font></td>
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During his first half-a-dozen years on the faculty at LSU, Tohline continued to work closely with Richard Durisen (Indiana University) to examine the onset and nonlinear development of nonaxisymmetric instabilities in differentially rotating polytropes.  <font color="red">Harold A. Williams</font> joined this effort as a graduate student in Tohline's group.  He broadened the study to include configurations having a range of compressibility and different distributions of angular momentum; this became the central thrust of his doctoral dissertation.  Williams also advanced the capabilities of the group's computational tools by implementing a second-order accurate finite-difference scheme to carry out integrations of the governing hydrodynamic equations.  

Over this time period, numerical simulations were carried out, to a large extent, on LSU's IBM main-frame computer.  But, via [https://www.nsf.gov/awardsearch/showAward?AWD_ID=8818225&HistoricalAwards=false NSF funding], the group also was allocated time on Cray hardware at Minnesota's supercomputer center; Tohline and Williams both received training, for example, on Minnesota's newly acquired [https://en.wikipedia.org/wiki/Cray-2 Cray-2].

<font color="red">Izumi Hachisu</font> (Kyoto University, Japan) joined the group in a postdoctoral research position for a couple of years.  Drawing from his own research background, Hachisu provided us with a blueprint for developing a very efficient numerical algorithm for constructing rapidly rotating equilibrium configurations with spheroidal, toroidal, or binary-star geometric shapes &#8212; see our [[AxisymmetricConfigurations/HSCF#Hachisu_Self-Consistent-Field_Technique|relevant chapter discussion]].  Over the past several decades, this ''Hachisu Self-Consistent-Field'' technique has allowed us to construct a wide range of different self-gravitation configurations as initial states for stability analyses and for examining the nonlinear growth of unstable modes using  computational fluid techniques.
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<b>[</b>[https://ui.adsabs.harvard.edu/abs/1985ApJ...298..220T/abstract 19]<b>]</b> <font color="red">(22<sup>nd</sup>)</font><br />
<b>[</b>[https://ui.adsabs.harvard.edu/abs/1987ApJ...315..594W/abstract 22]<b>]</b><br />
<b>[</b>[https://digitalcommons.lsu.edu/gradschool_disstheses/4549/ <math>~\odot</math>]<b>]</b><br />
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<b>[</b>[https://ui.adsabs.harvard.edu/abs/1987ApJ...323..592H/abstract 25]<b>]</b><br />
<b>[</b>[https://ui.adsabs.harvard.edu/abs/1988ApJS...66..315H/abstract 27]<b>]</b><br />
<b>[</b>[https://ui.adsabs.harvard.edu/abs/1990ApJ...361..394T/abstract 33]<b>]</b> <font color="red">(20<sup>th</sup>)</font><br />
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<b>[</b>[https://ui.adsabs.harvard.edu/abs/1986ApJ...305..281D/abstract 20]<b>]</b> <font color="red">(2<sup>nd</sup>)</font><br />
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<b>[</b>[http://www.phys.lsu.edu/faculty/tohline/CiSE/CiSE2007.Vol9No6.pdf Viz]<b>]</b><br />
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A quantitative comparison was made between the results obtained from simulations carried out with two different "finite-difference" CFD codes and one "smoothed particle hydrodynamics" algorithm.
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We obtained the Fortran source code of a volume-rendering algorithm that had been developed by [https://www.gc.cuny.edu/Page-Elements/Academics-Research-Centers-Initiatives/Doctoral-Programs/Computer-Science/Faculty-Bios/Gabor-T-Herman?gclid=Cj0KCQjwxMjnBRCtARIsAGwWnBNa_Gr9qORMGErvo8fpEmKvVnTthkpPFZF5mI9RALHtufJ-o6fnUX0aAuUKEALw_wcB Gabor T. Herman] who, at the time, was in the University of Pennsylvania's radiology department.  With significant assistance from <font color="red">Monika Lee</font> &#8212; our computer systems manager &#8212; the code was tuned to execute on the astronomy group's VAX 11/750 and its attached International Imaging System.  A string of individual digital images was pieced together to generate animation sequences showing the behavior of our time-evolving fluid systems; this was accomplished by operating in tandem:  a Lenco Color Encoder, a Lyon Lamb Mini-VAS animation controller, and a 3/4-inch broadcast-quality Sony U-matic video recorder.  <font color="red">Jeffrey E. Anderson</font> &#8212; an undergraduate student at LSU (1985-89) &#8212; played a key role in operating this set of tools to assist in our analysis of the results of our CFD simulations.
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