Department Library


Jacob Fields (Senior Thesis, July 2020, Advisor: David Neilsen )


Gamma-ray bursts (GRBs) are the most luminous electromagnetic phenomena in the universe, but much remains unknown about them. Many models invoked to explain their highly variable light curves are based on complicated dynamics and interactions involving the GRB progenitor but assume simple circumstellar environments. Many long GRBs, however, show late time optical and x-ray flares that may be an indication of a much richer environment. Relativistic hydrodynamics simulations are used to study a family of initial data with a relativistic blast wave encountering a dense circumstellar shell of matter, similar to what an aging star expelling the outer layers of its atmosphere might generate. The possibility that some of this late time curve variability results from these interactions is tested. A characterization of the profiles of the resulting reverse shocks and a preliminary analysis of the subsequent radiation are presented. The results suggests a noticeable increase in the synchrotron spectrum immediately following the interaction and possible infrared and optical emissions due to black-body shortly afterward.


Jonathan Bassett (Senior Thesis, April 2018, Advisor: David Neilsen )


We study the effects of spinning bodies on the chaotic properties of the three-body problem in general relativity. We use the post-Newtonian Hamiltonian to order 2 with the leading-order spin-orbit Hamiltonian. We study a system composed of a binary star system in a circular orbit and an incoming star. We generalize previous work by adding spin to each of the objects. The parameter space includes both regions with predictable behavior and regions with chaotic behavior, but the spin of the stars does not significantly alter the size of chaotic regions. Spin does not appear to have a significant effect on chaos in the relativistic three-body problem for this system.

William Black (Senior Thesis, April 2018, Advisor: David Neilsen )


Supermassive black holes (SMBHs) are orphans—since no known progenitors exist, their origins are mysterious. They are so massive that even if the first stars collapsed into black holes, they would struggle to even come close to supermassive sizes. I investigate whether primordial black holes (PBHs), formed by overdensities in the Big Bang, could be the progenitors of SMBH. I use the cosmology code Enzo to simulate the growth of single solar mass PBHs over the course of ~325 Myr to see if the PBHs can reach supermassive sizes. Additionally, I compare Bondi accretion to viscous accretion. I use two methods to test whether PBHs could grow fast enough to become SMBHs. First: comparison to the growth of their surrounding halos—if a PBH is roughly 10^3 M⊙ by the time its halo is 10^8 M⊙, PBH–SMBH evolution is possible. Second: comparison to observed early SMBHs. If our PBHs reach similar sizes by similar times, PBH–SMBH evolution could be a viable pathway for those early observed SMBHs. Aside from the main results, I discovered that Bondi accretion and viscous accretion result in drastically different accretion rates. While black holes growing with Bondi accretion grew on order 10^-4, black holes with viscous accretion grew on order 10^+4. This is likely due to the dependence of Bondi accretion on simulation resolution. Given sufficiently dense seeding points, I found that the growth of PBHs does match the growth needed to reach supermassive sizes. The PBHs reached 10^3 M⊙ by the time their halos were 10^8 M⊙, so they do have the potential to reach the sizes of many observed SMBHs. Their extrapolated growth barely fell short of observed early SMBHs, but if 10–100 M⊙ PBHs were seeded, their growth trajectory would be on track to reach the sizes of early SMBHs.


Jacob Tinnin (Senior Thesis, August 2017, Advisor: David Neilsen )


Moving boundary conditions, such as a pinwheel in water, are extremely difficult to simulate by conventional computational fluid dynamics methods. Lattice Boltzmann methods are a relatively new simulation technique for fluids in complex geometries and are efficient and highly parallelizable. These methods derive from a discretization of the kinetic Boltzmann equation. While boundary conditions for differential equations with complex geometries can be difficult to find, the lattice Boltzmann method is particle-based, and boundary conditions are easily specified and modified at any point during the simulation. We present several examples of systems that are very difficult to simulate by other methods. These results confirm the utility of the lattice Boltzmann in addition to its efficiency and parallelizability.


Forrest Glines (Senior Thesis, April 2016, Advisor: David Neilsen )


Simulating binary star mergers in full relativistic magnetohydrodynamics with general relativity is computationally expensive, with production level simulations taking up to two months using traditional algorithms. These speeds are insufficient to explore the parameter space of binary star mergers. Following recent trends in chip manufacture, CPU speeds are unlikely to increase and speed up simulation times. In order to shorten simulation times new algorithms that take advantage of newer, faster computing architectures such as GPUs are required. This thesis presents GMHD, a relativistic magnetohydrodynamics code that runs on NVIDIA GPUs faster than other codes on CPUs. It implements a high-resolution shock-capturing algorithm using the piecewise-parabolic method and a total variation bounded method based on the Osher-Chakrabarthy method. The accuracy of the fluid methods are tested simulating the shock tube problem and the Kelvin-Helmholtz instability. Both methods accurately mode solution. This thesis also presents tests demonstrating the weak and strong scalability of the code tests to hundreds of GPUs. GMHD shows the viability and usefulness of using GPUs and forms a basis for future work on large scale simulations of binary mergers.

Eli McArthur (Senior Thesis, June 2016, Advisor: David Neilsen )


Minor perturbations resulting from a brief period of inflation at the time of the universe's birth seeded the growth of all structure in the universe. Using Enzo, a research code optimized for running cosmological simulations, we simulate the formation of the universe. We take into account the most current cosmological parameters and plot star formation rates of the universe for halos of varying mass from the beginning of time until today. By simulating star formation of the early universe, we verify that initially minuscule dark matter pockets resulting from inflationary perturbations attract more and more matter as the universe expands. The resulting halos vary in size and have varying degrees of star formation. Additionally, this analysis paves the way for future members of the scientific community to test a new way of identifying population III stars in the cosmic microwave background.


Jared Jay (Senior Thesis, April 2015, Advisor: David Neilsen )


We study the chaotic properties of the three-body problem in general relativity and examine the effects of successive post-Newtonian Hamiltonian correction terms. We set up a planar, two-parameter, three-body system consisting of a circular binary and an incoming star, and integrate the system many times, varying the two initial parameters by small amounts. We study the cases of equal masses and unequal masses. We observe that the initial parameter space contains regions of fairly predictable behavior and regions of chaotic behavior at all levels of approximation to relativity. This is strong evidence that the three-body exhibits the same chaos in general relativity as in Newtonian gravity.

Hugh Morgan (Senior Thesis, April 2015, Advisor: David Neilsen )


The gravitational three-body problem is non-analytic and exhibits chaotic behavior. Three-body interactions are common in particle-dense regions such as globular clusters and they may explain the origins of supermassive black holes. We investigate interactions in general relativity and compare them to the well understood, chaotic three-body problem in Newtonian gravity. Using the post-Newtonian equations, an approximation to general relativity, we analyzed three-body problems consisting of a binary system and a far-away, third object. We found that the system is indeed chaotic using the post-Newtonian equations. We also found that including gravitational radiation led to more black hole formations than Newtonian gravity. We also investigated possible relativistic effects on systems discovered by the Kepler Space Telescope. Particularly we looked at massive planets in tight orbits orbits and tried to refine the mass bounds of stability for the three-body systems using the post-Newtonian equations. We found that including the relativistic approximation does not significantly change the mass bounds and consumes significantly more computer resources.


Brody Bassett (Senior Thesis, August 2012, Advisor: David Neilsen )



Heather Harper (Capstone, April 2010, Advisor: David Neilsen )


We model the electromagnetic emissions of a binary neutron star merger. We use the ideal gas equation of state and rely on thermal and bremsstrahlung radiation as the sources of emission. We calculate the intensity of this radiation through radiative transfer to produce numerical and graphical data. As the merger progresses we see high intensity areas increase in the center of the stars and fluctuations in the outer areas, including the formation and disappearance of luminous appendages. Right before the collapse of the merger into a black hole, we see four distinct high intensity arms develop a halo around the center of the stars. This halo may be caused by gravitational forces and angular momentum effects. We also see a sharp drop in hard gamma emissions at the later stages of the merger which could be connected to a gamma ray burst.

Thomas McConkie (Senior Thesis, August 2010, Advisor: David Neilsen )


Whalen et al. [1] conducted a survey which analyzed the effect of radiative feedback by one primordial star on subsequent star formation. Their study found results deviating from previous one-dimensional modeling. We extended the survey by performing two-dimensional simulations of cosmological minihalo evaporation using the astrophysical fluid hydrodynamic code ZEUS-MP. This code was run varying primordial star size (25 - 80 M⊙), halo to star distance (150 - 1000 pc), and halo central density(1.43 - 1569 cm−3). We find that the ionization front of the star penetrates nearby halos to varying degrees according to their central density and proximity to the star. The degree of penetration may prevent, postpone, delay or have no effect on star formation.

Gregory Sutherland (Senior Thesis, May 2010, Advisor: David Neilsen )


We study the impact of the second order Post-Newtonian corrections on chaos in the three-body problem. We had second order code that was generated using Maple and converted to Fortran. The code was giving unexpected results so we wanted to find any errors and fix them. So we generated second order equations from the Hamiltonian using Mathematica instead. Then we converted those equations to Fortran language and put them into the supercomputer. We then compared the outcomes with those from the previous code. We found that there were differences between the two. We were able to verify the new code as accurate and can now do future work being able to trust in the newly generated code.


J.J. Campbell (Capstone, December 2008, Advisor: David Neilsen )


In classical Newtonian gravity, the three-body problem is known to be chaotic for general initial data. We investigate the existence of chaos for the three- body problem in general relativity using the first post-Newtonian approxima- tion. Our initial data consists of a third object entering a binary pair and is parameterized by an impact parameter and phase angle. The Hamiltonian equations of motion are integrated using adaptive methods and we extract gauge-independent quantities at infinity. We present results that characterize chaos in general relativity.


Nicholas Nelson (Senior Thesis, April 2007, Advisor: David Neilsen )


Potential numerical methods for solving the general relativistic magnetohydrodynamic (GRMHD) fluid equations are investigated. Specifically, a one dimensional central weighted essentially non-oscillatory (CWENO) scheme without a staggered grid and a one dimensional weighted essentially non-oscillatory (WENO) scheme are discussed in the context of solving the relativistic fluid equations. The implementation of CWENO and WENO are described, and both are applied to standard test problems. The modified CWENO scheme is found to be unstable in tests using the GRMHD fluid equations and Burger’s equation. When solving the general relativistic perfect fluid equations, WENO is stable and has sharp resolution of shocks.

Joseph Smidt (Senior Thesis, August 2007, Advisor: David Neilsen )


We perform two-dimensional simulations of cosmological minihalo evaporation in the vicinity of a Population III star to determine if its ultraviolet (UV) radiation promotes or quenches star formation in nearby primordial clouds. We find that the ionization front of the star penetrates nearby halos to varying degrees according to their central density and proximity to the star. UV photons easily destroy diffuse clouds but cannot affect the cores of denser, more evolved structures. In intermediate cases, the radiation drives shocks enriched with H2, a key coolant in primeval gas, into the core. These shocks enhance density and cooling rates in the halo core, accelerating its collapse into a new star. Radiative feedback by one primordial star on subsequent star formation can thus be positive, negative, or neutral.

David Tanner (Senior Thesis, August 2007, Advisor: David Neilsen )


The three-body problem is explored in general relativity using the second order post- Newtonian approximation. The results are compared to Newtonian gravity. The three bodies are set up as a binary system with an incoming body. The system is evolved through time for a large two dimensional space of initial values. Several properties for both the Newtonian and relativistic systems are mapped onto the initial-value space and analyzed. The two sets of maps show regions of similarity and contrast. The relativistic system's chaotic behavior diverges most significantly from the Newtonian system when the three bodies undergo relativistic interactions.