In the weakly inviscid regime parametrically driven surface gravity-capillary waves generate oscillatory viscous boundary layers along the container walls and the free surface. Through nonlinear rectification these generate Reynolds stresses which drive a streaming flow in the nominally inviscid bulk; this flow in turn advects the waves responsible for the boundary layers. The resulting system is described by amplitude equations coupled to a Navier-Stokes-like equation for the bulk streaming flow, with boundary conditions obtained by matching to the boundary layers, and represents a novel type of pattern-forming system. The coupling is responsible for new types of secondary instabilities of standing waves leading to chaotic dynamics, and in appropriate regimes can lead to the presence of relaxation oscillations. These are present because in the nearly inviscid regime the streaming flow decays much more slowly than the waves, and resemble a class of oscillations discovered by Simonelli and Gollub [J. Fluid Mech. 199 (1989), 349] in a domain with an almost square cross-section.

Coloniality, in which organisms are composed of repeated discrete structural units that are physically connected to each other, is a major evolutionary innovation. Since the first colonial animals appeared during the Cambrian Period, coloniality has independently evolved in several animal lineages including cnidarians, hemichordates, chordates, bryozoans, entoprocts, and annelids. Despite the prevalence of this trait, the mechanisms underlying broadscale biogeographic trends in coloniality remain untested. In this dissertation, I examined two global-scale biogeographic patterns related to coloniality in ascidians, a diverse group of chordates. In addition to this work, I also examined colonial animals through the lens of pedagogy. In Chapter 1, I investigated mechanisms underlying the latitudinal gradient in colonial ascidian richness. Using publicly available species occurrence data and abundance data from two large experimental networks, I demonstrate that this gradient is robust and likely driven by ecological mechanisms. In Chapter 2, I explored the relationship between coloniality and Rapoport’s rules, the correlation between latitude and species’ latitudinal or bathymetric ranges. Using species occurrence data, I show that ascidians demonstrate Rapoport’s bathymetric rule possibly due to biogeographic variation in coloniality. Together, these findings indicate the need for more rigorous testing of the mechanisms underlying broad biogeographic patterns. In Chapter 3, I examined taxonomic bias in the animal diversity present in introductory biology course materials. Vertebrates, especially mammals, were overrepresented in textbooks and lecture slides, relative to their actual diversity. In contrast, invertebrates, including many groups of colonial animals, were underrepresented to varying degrees.

This dissertation undertakes a comprehensive exploration of computational methods for studying and optimizing plasma processes, focusing specifically on the behavior and characteristics of atmospheric plasmas under various ignition waveforms. Leveraging somaFOAM, an in-house plasma solver based on OpenFOAM, this research delves into the effects of different voltage profiles—including sinusoidal, unipolar, bipolar, and sinusoidal damped waveforms—on plasma stability and efficiency. While atmospheric plasmas provide potential novel applications in medical, surface treatment, water purification, and decontamination of surfaces, the main limitation is the inherent instability of atmospheric plasma due to the high breakdown voltage. Furthermore, its traditional mode of operation, which consists of filamentary discharges, can be counterproductive to surface treatment as the filaments current are discretized, now allowing for fine control of the system when the sensitivity of the surface needs to be considered, alongside the nonuniform mode of operation. As such, atmospheric pressure glow discharges, operating in the radio frequency regime, allow for modular control of the plasma intensity while allowing the surface to be treated uniformly. Further study is of interest to supplant and replace depending on the application filamentary discharges. However, a systematic understanding of the controlling parameters within the plasma is required to have a stable glow discharge, as the ignition of an atmospheric glow discharge is inherently difficult due to the high power required to operate at atmospheric pressure. As such, it is interesting to study modes of control to ignite a stable plasma while simultaneously maximizing its reactivity, as these properties are inverse to each other.

As such, the first project aims to consider control of the input parameters by utilizing different ignition waveforms at the same cycled-averaged power to study the effects of utilizing different waveforms on plasma stability and reactivity. However, as the feedstock gases also affect the characterization of the waveforms, two feedstock gases, argon and helium, are utilized to establish independence or dependence on the feedstock gas while at the same time studying the benefits of each feedstock gas, helium provides ease of operation and characterization, argon has been touted as a low-cost alternative which also promises ease of operation in comparison to other feedstock gas. Analysis is provided to determine whether the plasma operates in the α or γ mode of operation. However, further research is required, such as determining the criticality of the waveforms utilized to operate the plasma while at the same time investigating the effects of dielectric barrier discharges to maximize reactivity within the system, as previous research in the kilohertz regime seems to indicate that dielectrics can stabilize the plasma operation.

The second project further investigates argon plasma as research also considers the potential for scalability of the plasma, for which argon provides an opportunity. α-γ relationship between the voltage and current, the relationship between the γ mode of operation and a plasma dominated by secondary electron emissions followed by the study of the electron profiles as a relationship of stability, the relationship between the bulk voltage and input voltage for the pulsed waveforms for power coupling are studied for bare electrodes in order to provide a comprehensive picture of the plasma characterization, allowing for a deeper study of the plasma physics compared to the first project which one touched to a surface level as the interest was to determine the effects of the waveform coupled with the feedstock gas. At the same time, the addition of dielectric elements is considered within the dielectric gap to characterize the addition of such elements into the plasma and whenever such a strategy to maximize reactivity and stability is feasible. The third project, inspired upon the numerical downtime of utilizing modeling techniques in the second project, intends to use dynamic mode decomposition as a data-driven method to obtain a prediction that is adequate for purposes of analysis and characterization of the plasma without the computational downtime, utilizing a domain of parametrized solutions to train the model. Three cases are evaluated, with the first case at the boundary of the solution domain, the second case within the domain of the solution, and the third case partially outside the domain of the solution to evaluate edge cases and cases within the domain of the solution to determine the strength and weaknesses of the prediction, to be able to utilize data-driven techniques with existing databases to be able to characterize the plasma without the computational burden encountered with modeling techniques, allowing for just-in-time data results, improving efficiency.

The different projects presented here aim to comprehensively describe atmospheric plasmas and their characterization under different feedstock gases and input waveforms in order to propose a new way to maximize stability and reactivity simultaneously, utilizing a control approach to achieve this. At the same time, as parametrization techniques are computationally expensive, a data-driven technique could be seen as another tool to minimize computational downtime while obtaining results that can be utilized to understand the plasma characterization, allowing for a more efficient control mode of the plasma.