Many systems of physical interest are difficult to manage computationally because of the intrinsic nature of the equations that govern them. Many of these systems of equations are stiff, meaning that the standard approach to solving them is with implicit methods, because explicit methods either are unstable or require timesteps too small to be computationally efficient. Presented here is a study of explicit methods that decouple stability from accuracy under certain conditions, allowing for larger timesteps to be taken.

An integral field unit fiber array spectrograph was used to observe the emission spectra of radical species (C2, C3, CH, CN, and NH2) in multiple comets. The resultant azimuthal and radial division maps produced from the reduced data provide a unique method of analyzing features with these radicals in the comae, as well as how they behave over time. A Monte Carlo model was developed in order to simulate the behavior of particles from the outer nucleus and coma of each comet depending on various parameters including rotational period, outflow velocity, and active area location. The results from the model were used to constrain the physical parameters of three comets: 10P/Tempel 2, C/2009 P1 (Garradd), and 168P/Hergenrother.

Maintaining Space Domain Awareness (SDA) of satellites in low Earth orbit (LEO) requires effective methods of tracking and characterization. Optical measurements of these objects are generally sparse due to limited access intervals and high angular rates. Light pollution and geographic obstructions may also preclude consistent observations. However, a mobile small aperture telescope grants the ability to minimize such environmental effects, thereby increasing capture likelihoods for objects within this regime. By enhancing LEO satellite visibility in this way, extensive orbital and visual data are obtainable. An 8-inch Meade LX200GPS telescope equipped with a Lumenera SKYnyx2-0M CCD camera comprises the system that conducted observations of LEO. From 22 sessions spanning four months, 76 objects were imaged to provide a data set of 313 streak frames for initial orbit and photometric analyses. An Assumed Circular Orbit formulation provided considerable refinements in semimajor axis and eccentricity, up to one order of magnitude, when compared to a Gauss Extended method. Regarding the use of initial orbits for future pass predictions, the Assumed Circular Orbit angular positions indicated improvements up to 97.4% in accuracy and 65.7% in consistency over Gauss Extended. A photometric study placed the brightest observed visual magnitude at 3.60 mag, and the faintest visible at 9.47 mag. By converting brightness to a physical size, detected objects were approximately 23.8 meters at the largest and 40.6 centimeters at the smallest. Angles and brightness measurements of LEO satellites with mobile platforms may thus benefit the SDA effort.

<p>We present a numerical study of gas accretion into galaxies using the SPH code, Gasoline. Numerical tests on shock treatment in Gasoline are run to evaluate how well cosmological-scale, high Mach number shocks are treated. We find that shock solutions are far too noisy, and in specific density and metallicity regimes, this seeds a phase separation instability of hot and cold gas. We propose this instability as the source of cold blobs seen in many numerical simulations. We find that improved shock behavior is primarily attained through increased viscosity parameters. Analysis is also performed on four cosmological simulations from the McMaster Unbiased Galaxy Simulations (MUGS) (Stinson et al. 2010). In agreement with recent literature, we find cold flows of gas seeded by dark matter filaments stretching far into the inner galaxy in all analyzed galaxies. Tracking of star and gas particles is performed, and we find that cold mode accretion makes up between 40% and 60% of total gas accretion. As well, we find that cold gas is in general very quickly formed into stars, and that between 40% and 70% of total star mass comes from cold gas accretion.</p> / Master of Science (MSc)

<p>In this thesis we present a procedure by which synthetic photometry of a hydrodynamic model of star or star-like object can be calculated in a regime where the photosphere is not radially resolved. In order to properly model the unresolved photosphere, we present a method where pressure and density are integrated outward from the outermost resolved radius of the star and then interpolated in temperature-surface gravity space between a set of MARCS \citep{Gustafsson2008a} stellar atmosphere models. These interpolations are accurate to within 10\% of expected temperature values and are determined by minimizing the difference between the integrated pressure, density and surface gravity and that of the atmosphere model. Using the Monte Carlo Radiative Transfer code \texttt{radmc3d}\citep{Dullemond2012}, we produce blackbody spectra of stars and photometric light curves of equal and unequal mass detached binaries and a contact binary. Stellar blackbody spectra are accurate to better than 1\%. Resultant light curves have less scatter than existing methods, such as \texttt{shellspec}\citep{Budaj2004} and show the expected morphology. Our method allows for imaging directly from hydrodynamic simulations, with minimal user set-up. This procedure is designed with the intent of producing simulated photometry of stellar merger models.</p> / Master of Science (MSc)

Comets, remnants of the solar system's formation, exhibits partially unexplained outbursts that are closely tied to the physical structure of the nucleus. To investigate outbursts, we employed pore network modeling techniques, such as the Bower-Watson algorithm and Voronoi diagrams, to better represent the nucleus' complex porous structure and simulate gas transfer processes. We examined heat diffusion in the comet's subsurface and its influence on crystallization. The extra heat generated by crystallization can shift the crystalline front deeper into the nucleus, accelerating subsurface evaporation rates. This process results in the formation of a thicker ice mantle with reduced porosity on the surface, trapping evaporated gas in the underlying layers. As gas pressure accumulates over time, the mantle eventually succumbs to the buildup. By applying percolation theory, we identified the critical point at which trapped gas breaks through the surface, ultimately leading to a better understanding of comet outburst formation.

<p>We use numerical simulations to examine the fragmentation of protostellar discs via gravitational instability (GI), a proposed formation mechanism for gas-giant planets and brown dwarfs. To accurately model heating and cooling, we have implemented radiative transfer (RT) in the TreeSPH code Gasoline, using the flux-limited diffusion approximation coupled to photosphere boundary cooling. We present 3D radiation hydrodynamics simulations of discs that are gravitationally unstable in the inner 40 AU; these discs do not fragment because the cooling times are too long. In prior work, one of these discs was found to fragment; however, we demonstrate that this resulted from an over-estimate of the photosphere cooling rate. Fragmentation via GI does not appear to be a viable formation mechanism in the inner 40 AU.</p> <p>We also present simulations of GI in the outer regions of discs, near 100 AU, where we find GI to be a viable formation mechanism. We give a detailed framework that explains the link between cooling and fragmentation: spiral arms grow on a scale determined by the linear gravitational instability, have a characteristic width determined by the balance of heating and cooling, and fragment if this width is less than twice their Hill radius. This framework is consistent with the fragmentation and initial fragment masses observed in our simulations. We apply the framework to discs modelled with the commonly-used beta-prescription cooling and calculate the critical cooling rate for the first time, with results that are consistent with previous estimates measured from numerical experiments.</p> <p>RT is fundamentally important in the star formation process. Non-ionizing radiation heats the gas and prevents small-scale fragmentation. Ionizing radiation from massive stars is an important feedback mechanism and may disrupt giant molecular clouds. We present methods and tests for our implementation of ionizing radiation, using the Optically-Thin Variable Eddington Tensor method.</p> / Doctor of Philosophy (PhD)

The apparent rarity of taxonomic A-class asteroids poses a significant paradox for understanding asteroid differentiation and the dynamical evolution of the early solar system. Based on results from asteroid taxonomic surveys, and on the abundances and mineralogy of different achondrite meteorites, it appears that olivine-dominated mantle remnants are missing from both the asteroid population and in meteorite collections. Several scenarios to explain this paradox have been proposed: (1) olivine mantle material has been stripped away by collisions and only remains as small fragments (< ~5 km), (2) A-class asteroids are abundant but have been altered in some way masking their presence, or (3) differentiated asteroids did not form thick olivine-rich mantles. We have approached these questions through the collection of taxonomic and observational data on known A-class asteroids, and the geochemical characterization of olivine grains from pallasite and ureilite igneous meteorites. Examination of four taxonomic surveys reveals discrepancies in the classification of A-class objects. Recent data with spectral coverage to 2.45 μm have reclassified some asteroids previously thought to belong to the class. Data complied from these taxonomies reveal only 17 A-class asteroids out of ~2100 individual objects surveyed (<1%). Physical and orbital characteristics of A-class asteroids indicate that the majority are small (<13 km) collisional fragments that reside in orbits interior to, or within the inner main-belt. Photometric observations of five A-class asteroids obtained during this study have constrained the rotational periods of, 246 Asporina, 289 Nenetta, 446 Aeternitas, 1600 Vyssotsky, and the Mars-crossing asteroid 1951 Lick. Robust photometric data for 446 Aeternitas collected over three apparitions yielded a precise rotation period (15.737496 ± 0.000005 h) and a pole orientation of Β = 49º, and λ = 342º. A shape model produced from these data revealed that 446 Aeternitas has a distinctly angular shape suggestive of a collisional fragment. Olivine compositions between our pallasite meteorites span a narrow range (Fa10.5 - Fa13.4), while the ureilite olivine compositions, generally more fayalitic, display wide variations in the eight examined meteorites (Fa8.5 - Fa22.1). Major and trace element behavior in olivines from pallasite meteorites is consistent with a model of slow, in situ cooling and crystallization, allowing for near-equilibrium exchange between crystallizing olivines and coexisting silicate and FeNi melt, preserving near-uniform olivine major element compositions, and limited trace element variation. Trace element signatures of ureilite silicates (olivine and pigeonite) show large variations, consistent with residual solids from fractional melting processes. Ureilite olivines are uniformly more enriched in both compatible lithophile and siderophile elements (Ca, Li, Sc, V, Cr, Ni, and Mn) than pallasite olivines. corroborating models for ureilite petrogenesis as low-degree partial melting residues in the absence of an FeNi melt phase. Uniformity of elemental signatures among different pallasites point to a chemically homogeneous parent body.

A conventional large aperture telescope required for binary star research is typically cost prohibitive. A prototype active optics system was created and fitted to a telescope frame using relatively low cost components. The active optics system was capable of tipping, tilting, and elevating the mirrors to align reflected star light. The low cost mirror position actuators have a resolution of 31 nm, repeatable to within 16 nm. This is accurate enough to perform speckle analysis for the visible light spectrum. The mirrors used in testing were not supported with a whiffletree and produced trefoil-like aberrations which made phasing two mirrors difficult. The active optics system was able to successfully focus and align the mirrors through manual adjustment. Interference patterns could not be found due to having no method of measuring the mirror surfaces, preventing proper mirror alignment and phasing. Interference from air turbulence and trefoil-like aberrations further complicated this task. With some future project additions, this system has the potential to be completely automated. The success of the active optics actuators makes for a significant step towards a fully automated sparse aperture telescope.

This thesis approaches the task of designing a control system for the Parallel Actuator Mount developed by Dr. John Ridgely and Mr. Garrett Gudgel. It aims to create a base framework that directly controls the telescope and can be expanded to accept external command. It incorporates lower priced components and develops more easily approachable software with great functionality. An open-loop method for velocity control is established. Developing repeatable tests is a major focus. Testing finds the control methods developed result in velocity error of less than 5% and position error of less than 1.5% despite several mechanical issues and inaccuracies. Design guidelines are established that allow for the easy implementation of a Parallel Actuator Mount on other systems. This paper proves that the Parallel Actuator Mount is a potentially viable system for aiming a telescope when an astronomer does not require full sky coverage. The tests showed too much error to fully recommend the system as built and tested, but there are paths to increase accuracy of the system without greatly increasing the complexity or cost. The inclusion of a method of feedback, including a plate solver and an inertial measurement unit, would greatly improve the system. It may also be of use to modify the software to include a variable time step for the velocity control.