Browsing by Author "Aristoff, David, committee member"

Now showing 1 - 4 of 4

Open Access
Barium sensing in hollow cathode plasma using cavity ring-down spectroscopy (CRDS)
(Colorado State University. Libraries, 2024) Antozzi, Seth, author; Yalin, Azer, advisor; Dumitrache, Ciprian, committee member; Aristoff, David, committee member
Hollow cathodes (HCs) are ion propulsion devices commonly paired with Hall Effect Thrusters (HETs), which are devices of increasing importance in the ion propulsion community. Barium Oxide (BaO) cathodes are known to emit barium when operating under high-temperature conditions. Understanding barium densities in the cathode plasma provides experimental guidance for NASA barium modeling, including understanding of the physical characteristics and lifetime of the cathode. Based on modeling work, expected barium densities are ~1010 cm-3. A sensitive diagnostic is required such as CRDS. In this work, the detection of barium from the thermionic emitter of the Mark II 25 A BaO HC using the laser diagnostic technique of cavity ring-down spectroscopy (CRDS) is presented. CRDS detects ground state neutral barium via absorption of the probe laser beam in the vicinity of 553.548 nm (air wavelength). The cathode CRDS measurements are performed along the axis of the cathode since that is the control volume of interest. We report barium density as a function of heater current (plasma off) with results showing an approximately exponential density increase with current. Further parameters of study include keeper current, anode current (with the cathode operating), and propellant flow values. The measured signal-to-noise allows estimation of the barium density detection limit as ~106 cm-3 in the present configuration. An appendix to this work addresses the need for a diagnostic technique to measure krypton neutrals in HC plumes. In the krypton study, we enhance the krypton Two-Photon Absorption Laser Induced Fluorescence (TALIF) technique and apply it to a BaO HC plasma. We utilize a dye laser at 212.6 nm to excite TALIF fluorescence within the plume, with the fluorescence detected at 758.7 nm. We present spatial maps for krypton neutral densities at a cathode flow rate of 7.5 sccm and anode currents of 5A and 13A. These measurements provide insights into facility effects related to cathode coupling and cathode physics, such as the collisional damping of instabilities. Additionally, we discuss how plasma characteristics, including spot versus plume mode, and plasma luminosity, are influenced.
Open Access
In pursuit of industrial like MAXSAT with reduced MAX-3SAT random generation
(Colorado State University. Libraries, 2024) Floyd, Noah R., author; Whitley, Darrell, advisor; Sreedharan, Sarath, committee member; Aristoff, David, committee member
In the modern landscape of MAXSAT, there are two broad classifications of problems: Random MAX-3SAT and Industrial SAT. Random MAX-3SAT problems by randomly sampling variables with a uniform probability and randomly assigning signs to the variable, one clause at a time. Industrial MAX-SAT consists of MAX-3SAT problems as encountered in the real world, and generally have a lower nonlinearity than random MAX-3SAT instances. One of the goals of recent research has been to figure out which rules and structures these industrial problems follow and how to replicate them randomly. This paper builds off of the paper" Reduction-Based MAX-3SAT with Low Nonlinearity and Lattices Under Recombination", implementing its approach to MAX-3SAT clause generation and determining what it can reveal about industrial MAX-13SAT and random MAX-3SAT. This builds off of the transformation from SAT to MAX-SAT problems and hopes to create random MAXSAT problems that are more representative of industrial MAXSAT problems. All this would be in the pursuit of random MAX-3SAT that more accurately maps onto real-world MAX-3SAT instances so that more efficient MAX-3SAT solvers can be produced.
Open Access
Numerical solution of the Black-Scholes equation using finite element methods
(Colorado State University. Libraries, 2023) Anderson, Tyler, author; Bangerth, Wolfgang, advisor; Aristoff, David, committee member; Wang, Tianyang, committee member
The Black-Scholes model is a well known model for pricing financial options. This model takes the form of a partial differential equation (PDE) that, surprisingly, is deterministic. In the special case where the option only has one single underlying asset, what is called the one dimensional version of the Black-Scholes model, there exists an analytical solution. In higher dimensions, however, there is no such analytical solution. This higher dimensional version refers to what is called a Basket-Case Option. This means that to get a solution to this Basket-Case Option PDE, one must employ numerical methods. This thesis will first discuss the stochastic calculus theory necessary to derive the Black-Scholes model, then will explain in detail the time and space discretization used to solve the PDE using a Finite Element Method (FEM). Finally, this thesis will explain some of the results and convergence of this numerical solution.
Open Access
Supercooled liquids and glasses: dynamics, dynamic heterogeneity, and stability
(Colorado State University. Libraries, 2016) Staley, Hannah, author; Bradley, R. Mark, advisor; Szamel, Grzegorz, advisor; Gelfand, Martin, committee member; Aristoff, David, committee member
We used molecular dynamics simulations to study supercooled liquids and glasses. Supercooled liquids are liquids that have been cooled below their freezing temperature. We start the thesis with an introduction on supercooled liquids. We studied several different model glass-formers and compared them by scaling all data to the point where the Stokes-Einstein relation was violated. The Stokes-Einstein relation holds for many liquids, but breaks down at some temperature for most supercooled liquids. In all the systems we studied, we examined dynamic heterogeneity as quantified by the dynamic susceptibility, χ4, and the dynamic correlation length, ξ4. When dynamics are heterogeneous, a liquid breaks up into regions of particles with correlated mobility. The susceptibility is related to the number of particles in such a region, and the dynamic correlation length is related to the size of a region. We broke up our model glass-formers into the categories of strong glass-formers and fragile glass-formers. A strong glass-former has a viscosity, which obeys the Arrhenius relationship, while a fragile glass-former has super-Arrhenius behavior. We compared the systems by relating them at the temperature where the Stokes-Einstein relation was violated. We found that when variables are rescaled to their values at the Stokes-Einstein violation temperature, Ts, the fragile glass-formers all behaved in the same way, and we created plots where the data in all the systems followed the same curve. In the fragile glass-formers, we also found that clusters of correlated particles became compact below Ts. We studied one strong glass-former, and found that it did not match the fragile glass-former curves. However, the Stokes-Einstein violation temperature still appears to be significant in that system, since it appears to mark a change in shape of clusters of correlated particles. However, the clusters did not become compact. We examined the stability of a glass that was created by cooling at different rates. We investigated mechanical stability by measuring the energy and shear modulus of the glass. We also studied the kinetic stability upon heating the glass by examining the average overlap function, a dynamic correlation function. The average overlap function measures how much correlation the positions of particles have with their initial positions after a certain amount of time. We used a stability ratio, S, to probe kinetic stability. Stability is higher in glasses that were prepared by cooling at a slower rate. The different measures of stability have different relationships with initial cooling rate, and we determined that kinetic stability is the best measure of stability.