MULTI-BAND BOSE HUBBARD MODELS AND EFFECTIVE THREE-BODY INTERACTIONS

Experiments with ultracold atoms in optical lattice have become a versatile testing ground to study diverse quantum many-body Hamiltonians. A single-band Bose-Hubbard (BH) Hamiltonian was first proposed to describe these systems in 1998 and its associated quantum phase-transition was subsequently observed in 2002. Over the years, there has been a rapid progress in experimental realizations of more complex lattice geometries, leading to more exotic BH Hamiltonians with contributions from excited bands, and modified tunneling and interaction energies. There has also been interesting theoretical insights and experimental studies on “un- conventional” Bose-Einstein condensates in optical lattices and predictions of rich orbital physics in higher bands. In this thesis, I present our results on several multi- band BH models and emergent quantum phenomena. In particular, I study optical lattices with two local minima per unit cell and show that the low energy states of a multi-band BH Hamiltonian with only pairwise interactions is equivalent to an effec- tive single-band Hamiltonian with strong three-body interactions. I also propose a second method to create three-body interactions in ultracold gases of bosonic atoms in a optical lattice. In this case, this is achieved by a careful cancellation of two contributions in the pair-wise interaction between the atoms, one proportional to the zero-energy scattering length and a second proportional to the effective range. I subsequently study the physics of Bose-Einstein condensation in the second band of a double-well 2D lattice and show that the collision aided decay rate of the con- densate to the ground band is smaller than the tunneling rate between neighboring unit cells. Finally, I propose a numerical method using the discrete variable repre- sentation for constructing real-valued Wannier functions localized in a unit cell for optical lattices. The developed numerical method is general and can be applied to a wide array of optical lattice geometries in one, two or three dimensions.

Using a Combination of Phylogenetic Comparative and Paleobotanical Methods to Elucidate Patterns of Lineage Selection in Rosales (Plantae: Anthophyta)

An increasing focus in evolutionary biology is on the interplay between mesoscale ecological and evolutionary processes such as population demographics, habitat tolerance, and especially geographic distribution, as potential drivers responsible for patterns of diversification and extinction over geologic time. However, few studies to date connect organismal processes such as survival and reproduction through mesoscale patterns to long-term macroevolutionary trends. In my dissertation, I investigate how mechanism of seed dispersal, mediated through geographic range size, influences diversification rates in the Rosales (Plantae: Anthophyta). In my first chapter, I validate the phylogenetic comparative methods that I use in my second and third chapters. Available state speciation and extinction (SSE) models assumptions about evolution known to be false through fossil data. I show, however, that as long as net diversification rates remain positive – a condition likely true for the Rosales – these violations of SSE’s assumptions do not cause significantly biased results. With SSE methods validated, my second chapter reconstructs three associations that appear to increase diversification rate for Rosalean genera: (1) herbaceous habit; (2) a three-way interaction combining animal dispersal, high within-genus species richness, and geographic range on multiple continents; (3) a four-way interaction combining woody habit with the other three characteristics of (2). I suggest that the three- and four-way interactions represent colonization ability and resulting extinction resistance in the face of late Cenozoic climate change; however, there are other possibilities as well that I hope to investigate in future research. My third chapter reconstructs the phylogeographic history of the Rosales using both non-fossil-assisted SSE methods as well as fossil-informed traditional phylogeographic analysis. Ancestral state reconstructions indicate that the Rosaceae diversified in North America while the other Rosalean families diversified elsewhere, possibly in Eurasia. SSE is able to successfully identify groups of genera that were likely to have been ancestrally widespread, but has poorer taxonomic resolution than methods that use fossil data. In conclusion, these chapters together suggest several potential causal links between organismal, mesoscale, and geologic scale processes, but further work will be needed to test the hypotheses that I raise here.

Shock Train/Boundary-Layer Interaction in Rectangular Scramjet Isolators

Numerous studies of the dual-mode scramjet isolator, a critical component in preventing inlet unstart and/or vehicle loss by containing a collection of flow disturbances called a shock train, have been performed since the dual-mode propulsion cycle was introduced in the 1960s. Low momentum corner flow and other three-dimensional effects inherent to rectangular isolators have, however, been largely ignored in experimental studies of the boundary layer separation driven isolator shock train dynamics. Furthermore, the use of two dimensional diagnostic techniques in past works, be it single-perspective line-of-sight schlieren/shadowgraphy or single axis wall pressure measurements, have been unable to resolve the three-dimensional flow features inside the rectangular isolator. These flow characteristics need to be thoroughly understood if robust dual-mode scramjet designs are to be fielded. The work presented in this thesis is focused on experimentally analyzing shock train/boundary layer interactions from multiple perspectives in aspect ratio 1.0, 3.0, and 6.0 rectangular isolators with inflow Mach numbers ranging from 2.4 to 2.7. Secondary steady-state Computational Fluid Dynamics studies are performed to compare to the experimental results and to provide additional perspectives of the flow field. Specific issues that remain unresolved after decades of isolator shock train studies that are addressed in this work include the three-dimensional formation of the isolator shock train front, the spatial and temporal low momentum corner flow separation scales, the transient behavior of shock train/boundary layer interaction at specific coordinates along the isolator's lateral axis, and effects of the rectangular geometry on semi-empirical relations for shock train length prediction. A novel multiplane shadowgraph technique is developed to resolve the structure of the shock train along both the minor and major duct axis simultaneously. It is shown that the shock train front is of a hybrid oblique/normal nature. Initial low momentum corner flow separation spawns the formation of oblique shock planes which interact and proceed toward the center flow region, becoming more normal in the process. The hybrid structure becomes more two-dimensional as aspect ratio is increased but corner flow separation precedes center flow separation on the order of 1 duct height for all aspect ratios considered. Additional instantaneous oil flow surface visualization shows the symmetry of the three-dimensional shock train front around the lower wall centerline. Quantitative synthetic schlieren visualization shows the density gradient magnitude approximately double between the corner oblique and center flow normal structures. Fast response pressure measurements acquired near the corner region of the duct show preliminary separation in the outer regions preceding centerline separation on the order of 2 seconds. Non-intrusive Focusing Schlieren Deflectometry Velocimeter measurements reveal that both shock train oscillation frequency and velocity component decrease as measurements are taken away from centerline and towards the side-wall region, along with confirming the more two dimensional shock train front approximation for higher aspect ratios. An updated modification to Waltrup \& Billig's original semi-empirical shock train length relation for circular ducts based on centerline pressure measurements is introduced to account for rectangular isolator aspect ratio, upstream corner separation length scale, and major- and minor-axis boundary layer momentum thickness asymmetry. The latter is derived both experimentally and computationally and it is shown that the major-axis (side-wall) boundary layer has lower momentum thickness compared to the minor-axis (nozzle bounded) boundary layer, making it more separable. Furthermore, it is shown that the updated correlation drastically improves shock train length prediction capabilities in higher aspect ratio isolators. This thesis suggests that performance analysis of rectangular confined supersonic flow fields can no longer be based on observations and measurements obtained along a single axis alone. Knowledge gained by the work performed in this study will allow for the development of more robust shock train leading edge detection techniques and isolator designs which can greatly mitigate the risk of inlet unstart and/or vehicle loss in flight.

The Emergence of Spanish Impressionism and its Interaction with French Impressionism in Music at the Turn of the Twentieth Century: selections from the solo and collaborative piano repertoire

French Impressionism is a term which is often used in discussing music originating in France towards the end of the nineteenth century. The term Spanish Impressionism could also be used when discussing Spanish music written by the Spanish composers who studied and worked in Paris at the same time as their French counterparts. After all, Spanish music written during this time exhibits many of the same characteristics and aesthetics as French music of the same era. This dissertation will focus on the French and Spanish composers writing during that exciting time. Musical impressionism emphasizes harmonic effects and rhythmic fluidity in the pursuit of evocative moods, sound pictures of nature or places over the formalism of structure and thematic concerns. The music of this time is highly virtuosic as well as musically demanding, since many of the composers were brilliant pianists. My three dissertation recitals concentrated on works which exhibited the many facets of impressionism as well as the technical and musical challenges. The repertoire included selections by Spanish composers Manuel de Falla, Isaac Albéniz, Enrique Granados, Joaquín Turina, and Joaquín Rodrigo and French composers Claude Debussy and Maurice Ravel. The recitals were on April 30, 2013, February 23, 2014 and October 11, 2015. They included solo piano works by Granados and Albéniz, vocal works by Debussy, Ravel, de Falla, Turina and Rodrigo, piano trios by Granados and Turina, instrumental duos by Debussy, Ravel and de Falla, and a two-piano work of Debussy transcribed by Ravel. All three recitals were held in Gildenhorn Recital Hall at the University of Maryland and copies of this dissertation and recordings of each recital may be found through the Digital Repository at the University of Maryland (DRUM).

Structural characterization of interaction of K11 and K63 mixed-linkage polyubiquitin chains with the tUIMs of epsin1

Ubiquitylation or covalent attachment of ubiquitin (Ub) to a variety of substrate proteins in cells is a versatile post-translational modification involved in the regulation of numerous cellular processes. The distinct messages that polyubiquitylation encodes are attributed to the multitude of conformations possible through attachment of ubiquitin monomers within a polyubiquitin chain via a specific lysine residue. Thus the hypothesis is that linkage defines polyubiquitin conformation which in turn determines specific recognition by cellular receptors. Ubiquitylation of membrane surface receptor proteins plays a very important role in regulating receptor-mediated endocytosis as well as endosomal sorting for lysosomal degradation. Epsin1 is an endocytic adaptor protein with three tandem UIMs (Ubiquitin Interacting Motifs) which are responsible for the highly specific interaction between epsin and ubiquitylated receptors. Epsin1 is also an oncogenic protein and its expression is upregulated in some types of cancer. Recently it has been shown that novel K11 and K63 mixed-linkage polyubiquitin chains serve as internalization signal for MHC I (Major Histocompatibility Complex I) molecule through their association with the tUIMs of epsin1. However the molecular mode of action and structural details of the interaction between polyubiquitin chains on receptors and tUIMs of epsin1 is yet to be determined. This information is crucial for the development of anticancer therapeutics targeting epsin1. The molecular basis for the linkage-specific recognition of K11 and K63 mixed-linkage polyubiquitin chains by the tandem UIMs of the endocytic adaptor protein epsin1 is investigated using a combination of NMR methods.

Developmental Neural Correlates of Social Interaction

Children develop in a sea of reciprocal social interaction, but their brain development is predominately studied in non-interactive contexts (e.g., viewing photographs of faces). This dissertation investigated how the developing brain supports social interaction. Specifically, novel paradigms were used to target two facets of social experience—social communication and social motivation—across three studies in children and adults. In Study 1, adults listened to short vignettes—which contained no social information—that they believed to be either prerecorded or presented over an audio-feed by a live social partner. Simply believing that speech was from a live social partner increased activation in the brain’s mentalizing network—a network involved in thinking about others’ thoughts. Study 2 extended this paradigm to middle childhood, a time of increasing social competence and social network complexity, as well as structural and functional social brain development. Results showed that, as in adults, regions of the mentalizing network were engaged by live speech. Taken together, these findings indicate that the mentalizing network may support the processing of interactive communicative cues across development. Given this established importance of social-interactive context, Study 3 examined children’s social motivation when they believed they were engaged in a computer-based chat with a peer. Children initiated interaction via sharing information about their likes and hobbies and received responses from the peer. Compared to a non-social control, in which children chatted with a computer, peer interaction increased activation in mentalizing regions and reward circuitry. Further, within mentalizing regions, responsivity to the peer increased with age. Thus, across all three studies, social cognitive regions associated with mentalizing supported real-time social interaction. In contrast, the specific social context appeared to influence both reward circuitry involvement and age-related changes in neural activity. Future studies should continue to examine how the brain supports interaction across varied real-world social contexts. In addition to illuminating typical development, understanding the neural bases of interaction will offer insight into social disabilities such as autism, where social difficulties are often most acute in interactive situations. Ultimately, to best capture human experience, social neuroscience ought to be embedded in the social world.

The Effect of Supportive Social Interaction Priming on Children's Prosocial Comforing Responses to Distressed Others

The ability to sensitively care for others’ wellbeing develops early in ontogeny and is an important developmental milestone for healthy social, emotional, and moral development. One facet of care for others, prosocial comforting, has been linked with important social outcomes such as peer acceptance and friendship quality, underscoring the importance of determining factors involved in the ability to comfort. Although social support has been linked with a number of important social outcomes, no study has directly examined whether felt social support can foster children’s positive behavior toward others. The purpose of the current investigation was to use an experimental priming paradigm to demonstrate that felt social support a) enhances children’s ability to respond prosocially to the distress of others and b) decreases children’s expressions of personal distress when faced with the distress of another person. Participants were 94 4-year-old children (M = 53.56 months, SD = 3.38 months; 52 girls). Children were randomly assigned to either view pictures of mothers and children in close, personal interactions (supportive social interaction condition), happy women and children in separate pictures, presented side-by-side (happy control condition), or pictures of colorful overlapping shapes (neutral control condition). Each set of 20 pictures was presented in the context of a categorization computer game that participants played 4 times throughout the course of the study. Immediately following the first three computer games, children were given the opportunity to comfort someone who was distressed; twice it was the adult experimenter working with the child, and once it was an unseen infant crying over a monitor that participants had been trained to use. Comforting behaviors and distress/arousal were coded in 10-second time segments and yielded a global comforting score and a distress proportion score for each task. Results indicated that priming condition had no effect on either prosocial comforting behavior or expressions of personal distress. I discuss these null findings in light of the available literatures on priming mental representations in children and on prosocial comforting, and suggest some future directions for continued investigation in both fields.

INVESTIGATIONS INTO MECHANISMS UNDERLYING EXTREME WAVE FORMATIONS AND COMPUTATIONALLY INTENSIVE SIMULATIONS

Various mechanisms have been proposed to explain extreme waves or rogue waves in an oceanic environment including directional focusing, dispersive focusing, wave-current interaction, and nonlinear modulational instability. The Benjamin-Feir instability (nonlinear modulational instability), however, is considered to be one of the primary mechanisms for rogue-wave occurrence. The nonlinear Schrodinger equation is a well-established approximate model based on the same assumptions as required for the derivation of the Benjamin-Feir theory. Solutions of the nonlinear Schrodinger equation, including new rogue-wave type solutions are presented in the author's dissertation work. The solutions are obtained by using a predictive eigenvalue map based predictor-corrector procedure developed by the author. Features of the predictive map are explored and the influences of certain parameter variations are investigated. The solutions are rescaled to match the length scales of waves generated in a wave tank. Based on the information provided by the map and the details of physical scaling, a framework is developed that can serve as a basis for experimental investigations into a variety of extreme waves as well localizations in wave fields. To derive further fundamental insights into the complexity of extreme wave conditions, Smoothed Particle Hydrodynamics (SPH) simulations are carried out on an advanced Graphic Processing Unit (GPU) based parallel computational platform. Free surface gravity wave simulations have successfully characterized water-wave dispersion in the SPH model while demonstrating extreme energy focusing and wave growth in both linear and nonlinear regimes. A virtual wave tank is simulated wherein wave motions can be excited from either side. Focusing of several wave trains and isolated waves has been simulated. With properly chosen parameters, dispersion effects are observed causing a chirped wave train to focus and exhibit growth. By using the insights derived from the study of the nonlinear Schrodinger equation, modulational instability or self-focusing has been induced in a numerical wave tank and studied through several numerical simulations. Due to the inherent dissipative nature of SPH models, simulating persistent progressive waves can be problematic. This issue has been addressed and an observation-based solution has been provided. The efficacy of SPH in modeling wave focusing can be critical to further our understanding and predicting extreme wave phenomena through simulations. A deeper understanding of the mechanisms underlying extreme energy localization phenomena can help facilitate energy harnessing and serve as a basis to predict and mitigate the impact of energy focusing.