Doctor of Philosophy, The Ohio State University, 2024, Physics

The field of cold atom physics has been invigorated by the recent emergence of quantum droplets, self-bound mixtures of two Bose-Einstein condensates (BEC) which are stable without external confinement. Despite being composed of ultradilute gases, quantum droplets are similar to a liquid in that they are capable of remaining self-bound even when they are deformed. In this thesis, we delve into the potential of leveraging this deformability. Through solutions of the Gross–Pitaevskii (GP) equations, we demonstrate that quantum droplets can be manipulated into diverse topological configurations. This opens the door to experiments showcasing the many interesting quantum effects stemming from the interplay of topology and quantum mechanics. We also show that droplets can function as confining traps for other gases, allowing for the creation of composite BEC systems which are also self-bound. Extending this notion further, we introduce the concept of quantum gas meta-materials and show how the droplet can be used to construct a whole host of new structures which exhibit novel quantum effects, akin to meta-materials in solid-state systems. In addition to the work on quantum droplets, we will discuss recent cold atom experiments involving images of quantum clusters. These images reveal an underlying geometric structure in the wavefunction. We discuss our algorithm to extract the "optimal configuration" from this geometric structure, and show that it can be used to identify changes in the groundstate of the cluster.

Committee: Yuan-Ming Lu (Advisor); Tin-Lun Ho (Advisor); Ilya Gruzberg (Committee Member); Christopher Hirata (Committee Member); Jay Gupta (Committee Member) Subjects: Condensed Matter Physics; Quantum Physics; Theoretical Physics

Doctor of Philosophy, The Ohio State University, 2007, Electrical Engineering

Flow control refers to the ability to manipulate fluid flow so as to achieve a desired change in its behavior, which offers many potential technological benefits, such as reducing fuel costs for vehicles and improving effectiveness of industrial processes. An interesting case of flow control is cavity flow control, which has been the motivation of this study: When air flow passes over a shallow cavity a strong resonance is produced by a natural feedback mechanism, scattering acoustic waves that propagate upstream and reach the shear layer, and developing flow structures. These cause many practical problems including damage and fatigue in landing gears and weapons bays in aircrafts. Presently there is a lack of sufficient mathematical analysis and control design tools for flow control problems. This includes mathematical models that are amenable to control design. Recently reduced-order modeling techniques, such as those based on proper orthogonal decomposition (POD) and Galerkin projection (GP), have come to interest. However, a main issue with these models is that the effect of boundary conditions, which is where the control input is, gets embedded into system coefficients. This results in a form quite different from what one deals with in standard control systems framework, which is a set of ordinary differential equations (ODE) where the input appears as an explicit term. Another issue with the standard POD/GP models is that they do not yield to systems that have any apparent structure in their coefficients. This leaves one with little choice other than to neglect the nonlinearities of the models and employ standard linear control theory based designs. The research presented in this thesis makes an effort at closing the gaps mentioned above by 1) presenting a reduced-order modeling method utilizing a novel technique for input separation on POD/GP models, 2) introducing a technique based on averaging theory and center manifold theory so as to reveal certain struct (open full item for complete abstract)

Committee: Andrea Serrani (Advisor) Subjects: