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Chronology of Research Endeavors


Looking back, it seems clear to me that the technical book that has had the most influence on my research career has been [EFE], that is, Chandrasekhar's (originally, 1969) Ellipsoidal Figures of Equilibrium. Chandrasekhar evaluated the relative stability of a wide variety of astrophysically interesting (usually Newtonian self-gravitating), rotating equilibrium configurations by employing his own exceptional mathematical skills and those of his students — notably, Norman Lebovitz. When I entered graduate school at UC, Santa Cruz in 1974, [EFE] was the set of glasses through which most astronomers examined stability. Having access to only meager computing resources, Chandrasekhar's descriptions of the onset of instabilities, or evolution between nearly adjacent states, was usually limited to linear-amplitude deviations from equilibrium. From the beginning, I have been interested in using (steadily improving) computational resources to repeat, then extend the analyses found in [EFE] … (1) to configurations with non-homogeneous and compressible structures; and (2) into the nonlinear regime.

The MediaWiki-formatted text that you are reading — titled, The Structure, Stability, & Dynamics of Self-Gravitating Fluids — is my attempt to explain in detail what has been learned as a result of our (and the broader astrophysics community's) extension of the foundation work presented in [EFE]. The chapters of this ever-developing book that, on any date, I consider ready for public consumption can be found on the MediaWiki page that I refer to as the Tiled Menu. The graduate students who have come through my group over the years have made important contributions to the healthy development of this research field. The Outline of Research Activities that is presented, below, highlights and summarizes these contributions.

Doctoral Students Tohline Has Advised

Doctoral Students Whom Tohline has Advised at LSU:   See also
Year of Ph.D. Student Name ED Jointly Advised? Quarter-Sized Mosaic Image
1988 Harold A. Williams  
1989 Dimitris M. Christodoulou  
1992 John W. Woodward  
1994 Horst Väth w/ Detlev Koester (Univ. of Kiel, Germany)
1996 Kimberly C. (Barker) New  
1998 Saied Andalib  
1998 Erik Young w/ Ganesh Chanmugam (LSU Physics & Astronomy)
1999 Paul Fisher  
1999 John E. Cazes  
1999 Howard S. Cohl  
2001 Eric I. Barnes  
2001 Patrick M. Motl w/ Juhan Frank (LSU Physics & Astronomy)
2004 Shangli Ou  
2006 Ravi Kumar Kopparapu  
2006 Richard P. Muffoletto w/ John Tyler (LSU Computer Science)
2010 Wes P. Even  
2010 Jay M. Call  
2011 Dominic C. Marcello  
2014 Zachary D. Byerly  

ED = Electronic Dissertation


NOTE: In order to see a larger version of the primary image — or its annotated thumbnail companion, shown here, on the right — click once on the image, then click a second time on Full Resolution.

Outline of Research Activities

Color Coding
(star formation)
(galaxy dynamics)
(sources of gravitational radiation)
Computational Fluid Dynamics (CFD)
algorithm development
Visualization Tools Other

Here, a brief summary is presented of contributions that we have made toward advancing the astrophysics community's understanding of the structure, stability, & dynamics of self-gravitating fluids. The role that individual LSU graduate students have made to this story has been highlighted. The colored bar on the left identifies, in broad terms, the category of research that is being described in each paragraph; the Color Coding table shown immediately above explains what broad category is associated with each color.

Years 1976 - 1978

  Pubs. (rank)

Tohline's dissertation research under the guidance of Peter Bodenheimer (UCSC) and David Black (NASA/Ames Research Center) was an early attempt to examine whether of not isothermal gas clouds whose mass exceeds the Jeans mass spontaneously fragment during a phase of free-fall collapse. The adopted Eulerian computational hydrodynamics scheme was first-order donor-cell based on the 2D (axisymmetric, cylindrical-coordinate) scheme described by Black & Bodenheimer (1976) but extended by Tohline to a 3D grid; a typical simulation was carried out on the CDC 7600 at NASA/Ames and involved 303 ∼ 3 × 104 grid cells.

[4] (15th)
[7] (14th)


At each integration time step of a simulation, the self-consistently determined, time-dependent Newtonian gravitational potential was determined by combining (1) an FFT technique in the azimuthal coordinate direction, with (2) a Buneman Cyclic Reduction technique in R and Z.


Richard Durisen — a NASA/Ames postdoc at the time — said to me something along the lines of, "Hey! When you finish developing that hydrocode, let's get together and examine the dynamical stability of rapidly rotating, equilibrium configurations."

Years 1978 - 1982

  Pubs. (rank)

While at Yale University (1978 - 1980) and at Los Alamos National Laboratory (1980 - 1982), Tohline worked closely with Richard Durisen (Indiana University) to examine the onset and nonlinear development of nonaxisymmetric instabilities in differentially rotating, n = 3/2 polytropes whose internal angular momentum distribution was that of an n' = 0 sequence. Generally speaking, unstable eigenfrequencies matched earlier predictions (by other groups) based on linear stability analyses; unstable eigenfunctions displayed a two-armed spiral character. As the amplitude of unstable modes grew to nonlinear amplitude, the developed spiral arms were able to effectively redistribute angular momentum, preventing fragmentation/fission of the configurations.

Over this time period, numerical simulations were carried out on the IBM 360/95 at the NASA/Goddard Institute for Space Studies and on an early Cray at Los Alamos, where computational efficiencies were gained by taking advantage of the Cray's vector hardware capabilities.

Upon receipt of an invitation from journal editors, while at Los Alamos, Tohline published a review of the field titled, "Hydrodynamic Collapse."


[9] (9th)

[10] (13th)


Nelson Caldwell — a Yale graduate student at the time — showed Tohline some of his early work focused on the observationally determined properties of elliptical galaxies that display prominent dust lanes. Additional discussions led to a collaboration between Caldwell, Tohline, and Gregory Simonson — also a Yale graduate student at the time — in which the observed orientation of dust lanes can be explained in terms of dissipative settling of gas disks and, as a consequence, can be used to deduce the underlying geometry (e.g., oblate or prolate spheroidal) of each galaxy's mass distribution. With guidance from Tohline, Simonson completed a Yale University doctoral dissertation in which this settling model was extended to the context of polar rings in spiral galaxies.

When Tohline presented a seminar in the Department of Astronomy at Indiana University on the topic of "dust lanes in elliptical galaxies," Durisen asked what would happen to a settling gas disk if the underlying galaxy mass distribution was tumbling end over end — e.g., a cigar spinning about its shortest axis. The ensuing discussions led to a fruitful collaboration between Durisen and Tohline in which it became clear that steady-state warped disks could result. (After Tohline moved to LSU, extensions of this research work resulted in collaborative publications with several LSU graduate students — D. Christodoulou, K. New, H. Väth — and in Paul Fisher's doctoral dissertation research project.)

Years 1982 - 1988

  Pubs. (rank)

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. Harold A. Williams 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 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 Cray-2.

Izumi Hachisu (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 — see our 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.

[19] (22nd)

[33] (20th)

[20] (2nd)



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.


We obtained the Fortran source code of a volume-rendering algorithm that had been developed by Gabor T. Herman who, at the time, was in the University of Pennsylvania's radiology department. With significant assistance from Monika Lee — our computer systems manager — 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. Jeffrey E. Anderson — an undergraduate student at LSU (1985-89) — played a key role in operating this set of tools to assist in our analysis of the results of our CFD simulations.

Creation of NSF Supercomputing Centers

Taken from §1.2.2 of the 1995 Report of the Task Force on the Future of the NSF Supercomputer Centers Program:

Four Centers* were established in 1985, and a fifth added in 1986, all providing “vector supercomputing services” for the research community and training for the many researchers who lacked experience with these systems. These Centers were points of convergence where researchers learned to think in the new computational paradigm and to explore new vistas in resolution, accuracy, and parametric description of their problems.

Experiments in allocating resources, developing software support services, and starting standardized graphics and database descriptions to accelerate scientific visualization were all initiated during this phase.

Additionally, each Center established relationships with universities, both geographically close and far, to form consortia of members who had a stake in the resources of the Centers and in their future development. An important feature of these relationships was the formation of peer-review allocation boards, in which experts in computational science could direct attention to the performance of user’s computer codes. Special attention was given to improvements of those codes with low performance. Direct interactions with experts at the Centers frequently facilitated significant performance improvements.

*Footnote [4]: The original four centers were (1) The National Center for Supercomputing Applications (NCSA) at the University of Illinois, Urbana-Champaign, (2) The Cornell Theory Center (CTC), (3) The John von Neuman Center (JvNC), a consortium located at Princeton University, (4) The San Diego Supercomputer Center (SDSC), located at the University of California, San Diego and operated by General Atomics. The fifth — added in 1986 — was the Pittsburgh Supercomputing Center (PSC), directed by the University of Pittsburgh and Carnegie Mellon University and operated by Westinghouse.

Years 1988 - 1994

  Pubs. (rank)

Using the HSCF-technique, John W. Woodward constructed geometrically thick, axisymmetric accretion disk structures having a range of disk-to-central-object mass ratios. He used CFD techniques to determine which configurations were dynamically stable and which were dynamically unstable toward the development of nonaxisymmetric disk structure.

Over this time period, we requested and received NSF allocations of supercomputing time at the Cornell Theory Center. The CTC's main "vector" hardware resource consisted of a group of Floating Point Systems (FPS) array processors attached to an IBM main-frame. The CTC was our Center of choice because LSU also had decided to attach several FPS array processors to its IBM main-frame. We gained a great deal of early insight regarding the development of parallel computing algorithms through Woodward's extensive interactions with the CTC's technical staff, especially Francesca Verdier.

[38] (19th)





Building on the foundation ideas developed earlier in collaboration with Caldwell and Simonson, Dimitris M. Christodoulou used a so-called tilted-ring model of approximately a dozen warped spiral galaxy disks to decipher the geometric shape — whether oblate- or prolate-spheroidal — of each galaxy's underlying dark matter halo. In an effort to better understand how the warped structure of spiral disks develop over time, Christodoulou also used the group's CFD code to model the settling of disks that are initially flat, but tilted at some nonzero angle with respect to the equatorial plane of the potential well defined by an underlying, axisymmetric halo. (Due to constraints imposed by available computational resources, only disks with initially thick geometric structures were modeled dynamically; there was insufficient grid resolution to realistically model thin disks.)


As he was completing his dissertation research, Woodward took it upon himself to rewrite our 2nd-order-accurate CFD code so that it ran efficiently on the Department of Physics & Astronomy's new, 8K-node SIMD-architecture MasPar MP1 computer. Our 3D, cylindrical-coordinate-based simulations nicely mapped to the MasPar's architecture if we adopted a spatial grid resolution of 64 (in Z) × 128 (in R) — that is, 8K meridional-plane grid zones — × 128 azimuthal zones "stacked in memory."


In collaboration with Tohline, Sandeep Dani — a graduate student in LSU's Department of Mechanical Engineering — developed an efficient algorithm for rendering curvilinear volume data on our SIMD-architecture MasPar MP1 computer; Dani's doctoral dissertation advisors in Mechanical Engineering, Warren N. Waggenspack Jr. and David E. Thompson, also were key players in this collaboration.

A NeXTcube was added to our equipment ranks. Having a built-in RGB-to-NTSC signal converter, the NeXT replaced our Lenco Color Encoder; it also provided a friendly programming environment through which Woodward (and others) was able to completely automate the sequence of steps required to generate a video from a stack of digital images.

Richard Durisen (Indiana University) hooked up with a scientific visualization specialist, J. B. Yost, at Illinois's NCSA to produce a high-quality movie that used multiple, translucent isodensity surfaces to beautifully illustrate results from a CFD simulation on which we had collaborated. This was an extremely artistic as well as scientifically instructive animation. It served as motivation for our group's continued development of improved visualization tools and techniques.

Years 1994 - 2000

  Pubs. (rank)

Our earlier CFD modeling of rapidly rotating polytropes showed that configurations that are sufficiently rapidly rotating will be subject to a dynamical bar-mode instability. John E. Cazes showed that the nonlinear development of this instability usually results in the formation of a dynamically stable, self-gravitating structure that appears to be a compressible analog of a Riemann ellipsoid. Often, differential fluid flows inside the bar were supersonic and exhibited mild standing shocks near the ends of the bar, so the structure of each bar was necessarily expected to change on a secular time scale. After introducing a mechanism for slowly cooling the bar, Cazes observed that the bar became steadily more elongated and tended to develop a pair of off-axis density maxima. This suggested — but did not convincingly show — that as star-forming clouds slowly contract, they can smoothly transition from stable bar-like structures to binary protostellar configurations.

In an effort to ascertain whether the results obtained from Woodward's earlier CFD-based examination of the stability of toroidal configurations were consistent with the results of linear stability analyses previously published by other groups, Saied W. Andalib completed a project — in close collaboration with Christodoulou — titled, "A Survey of the Principal Modes of Nonaxisymmetric Instability in Self-Gravitating Accretion-Disk Models." Andalib also developed a technique for constructing 2D equilibrium structures of compressible and differentially rotating disks that exhibit nonlinear distortions in the azimuthal coordinate direction. (A very similar technique is described in the 1996 publication by Korycansky & Papaloizou.) The variety of model geometries that were obtained with this new tool helped us place in better context the range of distorted models that developed spontaneously during John Cazes' simulations.

Over this time period, we continued to receive NSF allocations of supercomputing time, but we shifted from the CTC to the San Diego Supercomputing Center (SDSC) for two reasons: (1) It appeared to us that it would be relatively easy for us to migrate the parallel version of our CFD code — which had been developed using MasPar Fortran — to the SDSC's Cray T3D (then T3E) because PGHPF (Portland Group's High-Performance Fortran) was a supported compiler on the Cray platforms. (2) The SDSC's new Advanced Scientific Visualization Laboratory (Vislab) was providing access to visualization tools on its Silicon Graphics Onyx2, such as Alias|Wavefront. At approximately the same time, a virtually identical computing environment was developed at the DoD's new Major Shared Resource Center (MSRC) in Stennis, MS; after being introduced to the MSRC's managers by Warren N. Waggenspack Jr. (LSU, Mechanical Engineering), we also received an allocation of time on these computing resources via the DoD's Programming Environment & Training (PET) program.

In relatively short order we figured out that the PGHPF compiler did not generate efficient executable code on the MIMD-architecture Cray T3E. Patrick M. Motl rewrote the CFD code using explicit message-passing instructions (MPI) and realized a significant speedup of the executable code.





[51] (25th)

[53] (6th)



Building on the foundation ideas developed earlier in collaboration with Caldwell and Simonson, and, in effect, extending Christodoulou's earlier CFD simulations, Paul Fisher used our MasPar-based CFD code to model the secular settling of thin galaxy disks toward the equatorial plane of spheroidal halos. The observed behavior of these settling disks was unexpected, as the underlying equatorial plane of the halo did not seem to serve as a preferred plane. This discrepancy may have resulted from artificial constraints on the disk's velocity field that were unintentionally imposed at the time by our CFD algorithm.


Using the HSCF technique, Kimberly C. B. New (now, Scott) constructed equilibrium models of synchronously rotating, equal-mass binary stars along various physically relevant sequences: White dwarf sequences having various total masses, and Newtonian neutron star (NS) sequences having different possible NS equations of state. Each equilibrium sequence was composed of binaries having varying separations, allowing for detached, contact, or common-envelope structures. She then used our MasPar-based CFD code to follow in a self-consistent manner the time-evolutionary motion of these extended fluid systems in order to determine along each equilibrium sequence which, if any, configurations were dynamically unstable toward merger.


Howard S. Cohl made two key contributions to the development of our Poisson solver: (1) A parallel implementation of a data-transpose technique to facilitate, on our SIMD-architecture MasPar, fast execution of an iterative scheme to evaluate the Newtonian gravitational potential throughout the interior volume of the grid; and (2) a compact cylindrical Green's function (CCGF) expansion that much more effectively facilitates an accurate evaluation of potential values along the exterior boundary of our cylindrical-coordinate grid.

Comment from Tohline:  As has been detailed in an accompanying chapter on this CCGF paper, over my professional career this has proven to be the publication with the most citations from research groups outside of the astrophysics community. Howard Cohl deserves full credit for the important discovery presented in this paper; I simply tagged along as his physics doctoral dissertation advisor and harshest skeptic.


In collaboration with Monika Lee, and at three different sites — see accompanying table — John Cazes and Howard Cohl developed a heterogeneous computing environment (HCE) through which our two primary computational tasks (CFD simulation and visualization) were performed simultaneously on two separate computing platforms, each of which was configured to handle the assigned task in an optimum fashion. Communication between the tasks (the link) was accomplished over existing local area networks.

TASK:    CFD Simulation the link Visualization
Platform data transfer process control Platform
MasPar MP1 NFS cross-mounted disks unix sockets Sparcstation
@ SDSC & @ Stennis
Cray T3E ftp remote shell script SGI Onyx

Spring 2000 Sabbatical at Caltech


At the invitation of Kip Thorne (physics) and Anneila Sargent (astronomy), Tohline spent the spring 2000 semester on sabbatical leave at Caltech. A collaboration with Lee Lindblom and Caltech graduate student, Michele Vallisneri, quickly developed. Together, this trio modeled the nonlinear development of the Rossby mode (r-mode) instability in a rapidly rotating neutron star. (See associated You Tube Video.)

Numerical simulations were carried out using the MPI-based version of LSU's CFD code — developed by LSU graduate student, Patrick Motl — modified to include a physically relevant post-Newtonian driving term.

[57] (5th)

Years 2000 - 2005

  Pubs. (rank)

In collaboration with Lee Lindblom (Caltech) and Tohline, Shangli Ou simulated the secular development of the so-called Dedekind bar-mode instability in rapidly rotating, initially axisymmetric polytropes. The numerical simulations were carried out using the MPI-based version of LSU's CFD code — developed by LSU graduate student, Patrick Motl — modified to include a physically relevant post-Newtonian driving term.

With guidance from Tohline, Ou also used the group's MPI-based CFD code — without post-Newtonian driving terms — to simulate the development of: (1) a one-armed spiral instability in low-T/|W| postbounce supernova cores (in collaboration with Christian D. Ott and Adam Burrows); (2) an unexpected dynamical instability in differentially rotating neutron stars; and (3) an elliptical instability in rotating fluid bars and ellipsoidal stars (in collaboration with Patrick Motl).

[66] (10th)


[67] (11th)
[71] (18th)


Suppose the compressible analog of a Riemann ellipsoid that developed during one of Cazes' simulations (see above, under Years 1994 - 2000) is scaled up in size to represent a dynamically stable, spinning gaseous bar at the center of a (barred) spiral galaxy. Individual stars that form from this gaseous bar will be injected into the galaxy with a velocity vector that corresponds to the velocity vector that the gas has at the location where the star formed. But because the "point-like" star will not be influenced by the gas pressure after its formation, the star must follow a trajectory that is different from the gas streamlines. Using n-body simulations, Eric I. Barnes identified the families of stellar orbits that become occupied by stars that are formed from such steady-state bars.


With Juhan Frank as his primary doctoral advisor and Tohline as secondary advisor, Patrick M. Motl made significant improvements to the group's CFD code (see above, under Years 1994 - 2000) and used the code to simulate mass-transfer in unequal-mass, semi-detached binary systems. Both stars had polytropic equations of state but, otherwise, the initially synchronously rotating model configurations were chosen to represent white dwarf pairs. Numerous evolutions were followed from the onset of mass transfer to (i) merger, (ii) tidal disruption, or (iii) detachment.

Spring 2010 Sabbatical at U. Utah


Tohline spent the spring 2010 semester on sabbatical leave at the University of Utah's Scientific Computing & Imaging (SCI) Institute, at the invitation of Chris Johnson (institute director) and Cláudio T. Silva (computer science); Silva is now at the Tandon School of Engineering at NYU. Tohline became immersed in the research activities of the SCI Institute in an effort to take advantage of and build upon significant advances that have been made by computer scientists in the arena of scientific visualization. The software tool of choice was VisTrails, a provenance-based research environment developed by Silva in close collaboration with Juliana Freire (computer science). Under the tutelage of two graduate students in the VisTrails group — Erik Anderson and Emanuele Santos — Tohline learned how to effectively use this infrastructure to quantitatively analyze the results of his group's astrophysical fluid simulations, and gained a much clearer understanding of how modern visualization tools can provide a critical foundation for archival scientific journal publications of the future.

[PCS] (29th)

Tiled Menu

Appendices: | VisTrailsEquations | VisTrailsVariables | References | Ramblings | VisTrailsImages | myphys.lsu | ADS |