The purpose of this thesis is to investigate the crossflow and off-the-surface velocity traces on a moderately swept wing at transonic Mach numbers. Computational Fluid Dynamics (CFD) was used to generate the data used to visualize the flow field. This was done for angles of attack of 6, 7, 8 and 10 degrees at a Mach number of 0.8. An overview of flow topology and singular point theory is given as a means to describe the flow field and describe the differences between it at various angles of attack. After performing an investigation of the crossflow velocity traces it was verified that the use of a line of separation in the flow topology as an indication for flow separation is a necessary condition. It was also found that the crossflow topology is more sensitive to shock location than to angle of attack. It has been verified that a line of separation, as defined by Tobak and Peake [ref 1], in the crossflow is an indication that separation may be present on the surface of the wing. Furthermore, shocks complicate the crossflow. In all of the cases the crossflow just aft of a shock becomes much more complex than it was before the shock. New singular points appear and interactions between singular points arise. As angle of attack is increased the flow topology changes critically only in the change from 6 to 7 degrees. This is the range in angle of attack in which a sudden shift in the location of the shock occurs, so it may be postulated that for this wing the flow topology is more sensitive to shock location as opposed to angle of attack. Comparing the topology between the 7, 8 and 10 degree cases, supports this hypothesis as the topology is similar before and after the shock for each case. The flow topology for each case before the shock is much different then the topology just aft of the shock. The investigation of off-the surface traces has shown that as angle of attack is increased the area of separated flow not only grows but also becomes more complex. For the 6 degree angle of attack case, the region of separated flow was concentrated near the surface and as one moved off the surface the flow quickly returned to the attached flow direction with no singular points. This was the case for the 7 degree angle of attack case only the flow did not reattach until after one moved approximately 0.25 feet off the surface. As the angle of attack was increased the distance off the surface in which the flow returned to moving in the downstream direction increased. Furthermore, as angle of attacked was increased the number of singular points and their intensity grew. It was also verified that in all of the cases investigated the presence of a line of separation was an indication of separated flow. Moreover, in all but two cases there were two lines of separation. One located along the furthest outboard and inboard area of the separated region. No lines of separation were observed in or around attached flow, thus the lines of separation may not only indicate that separation is present but in fact give a location for the separated region. / Master of Science

Steady and unsteady flow over a generic Suboff submarine model is studied. The skin-friction magnitudes are measured by using hot-film sensors each connected to a constant temperature anemometer. The local minima in the skin-friction magnitudes are used to obtain the separation locations. Steady static pressure measurements on the model surface are performed at 10° and 20° angles of attack. Steady and unsteady results are presented for two model configurations: barebody and sail-on-side case. The dynamic plunge-pitch-roll model mount (DyPPiR) is used to simulate the pitchup maneuvers. The pitchup maneuver is a linear ramp from 1° to 27° in 0.33 seconds. All the tests are conducted at ReL=5,500,000 with a nominal wind tunnel speed of 42.7±1 m/s. Steady results show that the flow structure on the leeward side of the barebody can be characterized by the crossflow separation. In the sail-on-side case, the separation pattern of the non-sail region follow the barebody separation trend closely. The flow on the sail side is strongly affected by the presence of the sail and the separation pattern is different from the crossflow separation. The flow in the vicinity of the sail-body junction is dominated by the horseshoe type separation. Unsteady results of the barebody and the non-sail region of the sail-on-side case show significant time lags between unsteady and steady crossflow separation locations. These effects produce the difference in separation topology between the unsteady and steady flowfields. A first-order time lag model approximates the unsteady separation locations reasonably well and time lags are obtained by fitting the model equation with the experimental data. The unsteady separation pattern of the sail side does not follow the quasi-steady data with a time lag and the unsteady separation structure is different from the unsteady crossflow separation topology observed for the barebody and the non-sail region of the sail-on-side case. / Master of Science

This research aimed to unite virtues of intrinsically microporous polyimides (PIM-PIs) and thermally treated polymers to develop advanced high-performance membranes with not only high permeability and high selectivity, but mechanical resilience, thermal and chemical stability, and plasticization resistance. Recent research showed that thermal treatment of polymers below or above their degradation temperatures is a potential avenue for improving gas transport properties. Thermally rearranged (TR), thermally crosslinked, or carbon molecular sieve (CMS) membranes have demonstrated promising results in addressing some pressing challenges of gas separation membranes such as chemical stability and plasticization resistance. However, the thermal treatment of PIM-PIs is scarcely studied, and its effect on gas transport properties still remains vague. This Ph.D. work started by investigating the solid-state conversion of PIM-PIs into heterocyclic ring systems upon heat treatment. The PIM-PIs containing functional hydroxyl- and cyano-groups were thermally treated to derive two types of cyclisation systems – conventional polybenzoxazole (PBO) and novel isoindoloquinazolinedione (IQD). Compared to the PIM-PI derived PBO, the novel solid-state conversion of intrinsically microporous cyanoimides into IQD favorably enhanced ultramicropores with up to 80% increase in gas permeability without an expense of gas-pair selectivity. Furthermore, by studying the thermal treatment of non-functionalized and functionalized 6FDA-based polymers a long-neglected contribution of fluorine to the formation of micropores was revealed. It was concluded that the heat treatment induced a continuous fluorine release at 450 °C – crosslinking polymer chains and increasing free volume accessible for gas transport. Finally, for the first time, a hydroxyl-functionalized PIM-PI, 6FDA-HTB, was heat treated by stepwise temperature increase from below, to near and above its degradation temperature to form TR, intermediate and early-stage CMS membranes. This study provided valuable insights on the correlation between the ultra- and micropore development and gas transport properties in PIM-PIs as a function of treatment temperature. Compared to the precursor, the intermediate stage membranes possessed 20-30 times higher CO2 permeability with equivalent CO2/CH4 selectivity. Also, intermediate and early-stage carbon derivatives of 6FDA-HTB exhibited an outstanding 1:1 CO2/CH4 mixed-gas separation results well transcending the 2018 mixed-gas upper bound line. These results deemed further investigation of intermediate stage membranes attractive.

To make decisions, plan, and act appropriately in a complex world, the brain formulates internal models of how the world works. As we change our goals, shift to novel environments, or as the world simply evolves around us, these models must flexibly adapt. Impairments in the formation of such flexible models are present in numerous disorders such as schizophrenia, Parkinson’s, and Alzheimer’s Disease and plague even the most sophisticated artificial agents. Therefore, understanding how the brain structures efficient internal models is of critical importance. Previous findings indicate that the information extracted from past experiences is organized and encoded into relational structured knowledge by the prefrontal cortex (PFC) and the medial temporal lobe (MTL). This process requires balancing two complementary computations in response to overlap. The first is to generalize the commonalities shared across overlapping experiences. The second is to separate overlapping experiences that fundamentally differed along a critical dimension, such as their outcomes, required actions, or time. How the brain balances these functions when faced with overlap remains poorly understood. In this thesis, I proposed that the analysis of the geometry of neural representational spaces offers valuable insights into the brain’s solution to optimally disambiguate and generalize overlapping experiences. I tested this proposal through the analysis of three functional magnetic resonance imaging (fMRI) experiments leveraging data-driven multivariate techniques to probe the dimensionality, structure, and content of these spaces. The first experiment (chapter 2) explored how PFC subregions respond to partially overlapping spatial environments during goal-directed virtual navigation. Based on previous research conducted in our lab that showed prefrontal activity in response to spatial overlap, we analyzed the dimensionality, structure, and content of prefrontal representations while participants learned a virtual navigation task. These analyses demonstrated compressed and highly orthogonalized codes early in learning that shifted over time towards more integrated and schematic codes. Critically, both prospective and retrospective information was bound to the representations of overlapping routes, with greater weight given to prospective information early in learning to help separate overlap. Based on these results, I advanced the idea that PFC subregions tune the geometry of their representations based on task demands and argued that prefrontal attention acts as a filter to promote both the separation and generalization of overlap. Building on the first experiment, a second study (chapter 3) focused on the re-analysis of a high-resolution fMRI study centered on the MTL that examined how MTL subregions handle prospective spatial overlap when planning routes in the same task. Based on previous research in our lab, we knew that the parahippocampal cortex (PHC) and hippocampal subfields CA1 and CA3/DG likely play a role in disambiguating overlapping routes during planning. We probed the geometry of their representations using the same methods used in experiment 1. The results demonstrated a segregation of roles between compressed schematic codes in PHC and expanded orthogonalized codes in CA3/DG that formed over the course of learning in response to overlap. Importantly, the degree of pattern separation observed in CA3/DG depended on the amount of initial overlap. These findings lead to the conclusion that generalization and separation are balanced in the MTL by distributing these functions to different subregions. Furthermore, the results suggest that MTL integration is supported by compression, whereas its separation is achieved via expansion. The third experiment (chapter 4) further examined how PFC and MTL regions balance generalization and separation processes when faced with abstract overlap between context-dependent rules. An analysis of the geometry of representational spaces in a context-dependent rule learning task found that successful rule learning was characterized by maintaining a balance between high and low dimensional spaces over learning. This equilibrium likely enabled the formation of relational knowledge representations that captured the latent structure of the task rules. Importantly, the only level of abstraction observed was one that perfectly matched the maximal amount of abstraction necessary to perform the task, and this structure only appeared later in learning in the hippocampus relative to extra-hippocampal regions. These results suggest that the brain employs an efficient and flexible coding scheme to respond to task demands. The results also suggest an important interplay between prefrontal and hippocampal codes over the course of learning. These three experiments demonstrate the promise that representational geometries offer in understanding the computations of the brain. Specifically, the results show that the flexible equilibrium between generalization and separation is accompanied by the fine-tuning of the dimensionality, structure, and content of representational spaces across a distributed network of MTL and PFC subregions. In the conclusion chapter, I discuss how these insights fit into existing frameworks regarding efficient and distributed codes.

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