UMD Theses and Dissertations
Permanent URI for this collectionhttp://hdl.handle.net/1903/3
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Item The complexity of simulating quantum physics: dynamics and equilibrium(2021) Deshpande, Abhinav; Gorshkov, Alexey V; Fefferman, Bill; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Quantum computing is the offspring of quantum mechanics and computer science, two great scientific fields founded in the 20th century. Quantum computing is a relatively young field and is recognized as having the potential to revolutionize science and technology in the coming century. The primary question in this field is essentially to ask which problems are feasible with potential quantum computers and which are not. In this dissertation, we study this question with a physical bent of mind. We apply tools from computer science and mathematical physics to study the complexity of simulating quantum systems. In general, our goal is to identify parameter regimes under which simulating quantum systems is easy (efficiently solvable) or hard (not efficiently solvable). This study leads to an understanding of the features that make certain problems easy or hard to solve. We also get physical insight into the behavior of the system being simulated. In the first part of this dissertation, we study the classical complexity of simulating quantum dynamics. In general, the systems we study transition from being easy to simulate at short times to being harder to simulate at later times. We argue that the transition timescale is a useful measure for various Hamiltonians and is indicative of the physics behind the change in complexity. We illustrate this idea for a specific bosonic system, obtaining a complexity phase diagram that delineates the system into easy or hard for simulation. We also prove that the phase diagram is robust, supporting our statement that the phase diagram is indicative of the underlying physics. In the next part, we study open quantum systems from the point of view of their potential to encode hard computational problems. We study a class of fermionic Hamiltonians subject to Markovian noise described by Lindblad jump operators and illustrate how, sometimes, certain Lindblad operators can induce computational complexity into the problem. Specifically, we show that these operators can implement entangling gates, which can be used for universal quantum computation. We also study a system of bosons with Gaussian initial states subject to photon loss and detected using photon-number-resolving measurements. We show that such systems can remain hard to simulate exactly and retain a relic of the "quantumness" present in the lossless system. Finally, in the last part of this dissertation, we study the complexity of simulating a class of equilibrium states, namely ground states. We give complexity-theoretic evidence to identify two structural properties that can make ground states easier to simulate. These are the existence of a spectral gap and the existence of a classical description of the ground state. Our findings complement and guide efforts in the search for efficient algorithms.Item Bioinspired sensing and control for underwater pursuit(2019) Free, Brian Anderson; Paley, Derek A; Aerospace Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Fish in nature have several distinct advantages over traditional propeller driven underwater vehicles including maneuverability and flow sensing capabilities. Taking inspiration from biology, this work seeks to answer three questions related to bioinspired pursuit and apply the knowledge gained therein to the control of a novel, reaction-wheel driven autonomous fish robot. Which factors are most important to a successful pursuit? How might we guarantee capture with underwater pursuit? How might we track the wake of a flapping fish or vehicle? A technique called probabilistic analytical modeling (PAM) is developed and illustrated by the interactions between predator and prey fish in two case studies that draw on recent experiments. The technique provides a method for investigators to analyze kinematics time series of pursuit to determine which parameters (e.g. speed, flush distance, and escape angles) have the greatest impact on metrics such as probability of survival. Providing theoretical guarantees of capture become complicated in the case of a swimming fish or bioinspired fish robot because of the oscillatory nature fish motion. A feedback control law is shown to result in forward swimming motion in a desired direction. Analysis of this law in a pursuit scenario yields a condition stating whether capture is guaranteed provided some basic information about the motion of the prey. To address wake tracking inspiration is taken from the lateral line sensing organ in fish, which is sensitive to hydrodynamic forces in the local flow field. In experiment, an array of pressure sensors on a Joukowski foil estimates and controls flow-relative position in a Karman vortex street using potential flow theory, recursive Bayesian filtering, and trajectory-tracking, feedback control. The work in this dissertation pushes the state of the art in bioinspired underwater vehicles closer to what can be found in nature. A modeling technique provides a means to determine what is most important to pursuit when designing a vehicle, analysis of a control law shows that a robotic fish is capable of pursuit engagements with capture guarantees, and an estimation framework demonstrates how the wake of a swimming fish or obstacle in the flow can be tracked.Item REPUTATION DYNAMICS IN MARKETING CONTEXTS(2019) Ukanwa Zeiger, Kalinda Ukanwa; Godes, David; Rust, Roland T.; Business and Management: Marketing; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)This dissertation is an examination of the impact of dynamic consumer reputation effects on firm decision-making in the marketplace. Essay I is a study of the impact of firm interventions on competitive reputation building among consumers on an online platform. Specifically, I model an actor’s decision to upload pirated content in order to build his reputation, despite facing threats from copyright lawsuits (firm interventions seeking to deter uploading activity) and intense competition on the platform. We propose a novel theory that explains what could occur in this scenario: high-reputation consumers will decrease their reputation-building activity, but their low-reputation competition may see an opportunity to enhance their reputation and increase activity. We argue that because competition for reputation is active on the site, the lawsuits may deter uploading in the short-run but may actually lead to more piracy over the long-run. Our findings support the theory: while high-reputation publishers decrease the likelihood of uploading as lawsuits increase, low-reputation uploaders do the opposite: they upload more. Essay II is an examination of the impact that a consumer group's reputation can have on firm decision-making. Specifically, we investigate 1) conditions under which a non-prejudiced firm may discriminate in service against its consumers based on group reputation, and 2) how subsequent consumer word-of-mouth can impact demand and profits over time. This mixed-methods study shows that discrimination can be profitable in the short-run but can backfire in the long-run due to the effects of consumer word-of-mouth and firm competition. Results indicate that high consumer heterogeneity in quality (i.e., their profitability to the firm) and low measurement error in detecting consumer quality attenuate the magnitude of service discrimination. The authors provide managerial recommendations on reducing service discrimination's profit-damaging effects. This research emphasizes the long-term benefits of switching to a service policy that does not use group reputation information. This dissertation contributes to the general marketing literature by providing new insights into how the reputation of the consumer, a sparsely researched area, can have direct impact on the firm in its decision-making.Item COLLISION DYNAMICS OF HIGHLY ORIENTED SUPER ROTOR MOLECULES FROM AN OPTICAL CENTRIFUGE(2017) Murray, Matthew J.; Mullin, Amy S; Chemical Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Sophisticated optical methods provide some of the most promising tools for complete control of a molecule’s energy and orientation, which enables a more complete understanding of chemical reactivity and structure. This dissertation investigates the collision dynamics of molecular super rotors with oriented angular momentum prepared in an optical centrifuge. Molecules with anisotropic polarizabilities are trapped in the electric field of linearly polarized light and then angularly accelerated from 0 to 35 THz over the duration of the optical pulse. This process drives molecules to extreme rotational states and the ensemble of molecules has a unidirectional sense of rotation determined by the propagation of the optical field. High resolution transient IR absorption spectroscopy of the super rotor molecules reveals the dynamics of collisional energy transfer. These studies show that high energy CO2 and CO rotors release large amounts of translational energy through impulsive collisions. Time-evolution of the translational energy distribution of the CO2 J=0-100 state shows that depletion from low J states involves molecules with sub-thermal velocities. Polarization-dependent Doppler profiles of CO rotors show anisotropic kinetic energy release and reveal a majority population of molecular rotors in the initial plane of rotation. Experimental modifications improved signal to noise levels by a factor of 10, enabling new transient studies in the low-pressure, single-collision regime. Polarization-dependent studies show that CO2 rotors in the J=54-100 states retain their initial angular momentum orientation, and that this effect increases as a function of rotational angular momentum. These studies show that rotating molecules behave like classical gyroscopes. Polarization-dependent measurements of CO2 rotors in the presence of He and Ar buffer gases show that CO2 super rotors are more strongly relaxed by He collisions, demonstrating the importance of rotational adiabaticity in the relaxation process. Quantum scattering calculations of the He-CO2 and Ar-CO2 collision systems were performed to interpret the qualitative features of the experimental results. This work provides a detailed mechanistic understanding of the unique collisional dynamics of super rotor molecules.Item STRUCTURAL AND FUNCTIONAL STUDIES OF CYCLIC K48-LINKED DIUBIQUITIN(2016) Sundar, Adithya; Fushman, David; Biochemistry; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)K48-linked di-ubiquitin exists in a dynamic equilibrium between open and closed states. The structure of K48-Ub2 in the closed conformation features a hydrophobic interface formed between the two Ub domains. The same hydrophobic residues at the interface are involved in binding to ubiquitin-associated (UBA) domains. Cyclization of K48-Ub2 should limit the range of conformations available for such interactions. Interestingly, cyclic K48-linked Ub2 (cycUb2) has been found in vivo and can be isolated in vitro to study its structure and dynamics. In this study, a crystal structure of cycUb2 was obtained, and the dynamics of cycUb2 were characterized by solution NMR. The crystal structure of cycUb2, which is in agreement with solution NMR data, is closed with the hydrophobic patches of each Ub domain buried at the interface. Despite its structural constraints, cycUb2 was still able to interact with UBA domains, albeit with lower affinity.Item The Control of a Mathematical Analog of a Tentacle(2015) Xu, Xin; Levine, William S; Electrical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)A 2-dimensional dynamic analog of squid tentacles was presented. The tentacle analog consists of a multi-cell structure, which can be easily replicated to a large scale. Each cell of the model is a quadrilateral with unit masses at the corners. Each side of the quadrilateral is a spring-damper system in parallel. The spring constants are the controls for the system. The dynamics are subject to the constraint that the area of each quadrilateral must remain constant. The system dynamics was analyzed, and various equilibrium points were found with different controls. Then these equilibrium points were further determined experimentally, demonstrated to be asymptotically stable. A simulation built in MATLAB was used to find the convergence rates under different controls and damping coefficients. Finally, a control scheme was developed and used to drive the system to several configurations observed in real tentacle.Item Flight Dynamics Simulation Modeling and Control of a Large Flexible Tiltrotor Aircraft(2014) Juhasz, Ondrej; Celi, Roberto; Aerospace Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)A high order rotorcraft mathematical model is developed and validated against the XV-15 and a Large Civil Tiltrotor (LCTR) concept. The mathematical model is generic and allows for any rotorcraft configuration, from single main rotor helicopters to coaxial and tiltrotor aircraft. Rigid-body and inflow states, as well as flexible wing and blade states are used in the analysis. The separate modeling of each rotorcraft component allows for structural flexibility to be included, which is important when modeling large aircraft where structural modes affect the flight dynamics frequency ranges of interest, generally 1 to 20 rad/sec. Details of the formulation of the mathematical model are given, including derivations of structural, aerodynamic, and inertial loads. The linking of the components of the aircraft is developed using an approach similar to multibody analyses by exploiting a tree topology, but without equations of constraints. Assessments of the effects of wing flexibility are given. Flexibility effects are evaluated by looking at the nature of the couplings between rigid-body modes and wing structural modes and vice versa. The effects of various different forms of structural feedback on aircraft dynamics are analyzed. A proportional-integral feedback on the structural acceleration is deemed to be most effective at both improving the damping and reducing the overall excitation of a structural mode. A model following control architecture is then implemented on full order flexible LCTR models. For this aircraft, the four lowest frequency structural modes are below 20 rad/sec, and are thus needed for control law development and analysis. The impact of structural feedback on both Attitude-Command, Attitude-Hold (ACAH) and Translational Rate Command (TRC) response types are investigated. A rigid aircraft model has optimistic performance characteristics, and a control system designed for a rigid aircraft could potentially destabilize a flexible one. The various control systems are flown in a fixed-base simulator. Pilot inputs and aircraft performance are recorded and analyzed.Item Dynamics and Control of Non-smooth Systems with Applications to Supercavitating Vehicles(2011) Nguyen, Vincent Phuc; Balachandran, Balakumar; Mechanical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The subject matter of this dissertation relates to the dynamics of non-smooth vehicle systems, and in particular, supercavitating vehicles. These high-speed underwater vehicles are designed to have sustained vaporous or ventilated gas cavities that form over the entire vehicle. In terms of the modeling, the system non-smoothness is caused by the interaction forces generated when the vehicle contacts the cavity. These planing interactions can cause stable and unstable dynamics, some of which could be limit-cycle dynamics. Here, planing forces are considered on the basis of non-cylindrical cavity shapes that include shifts induced by the cavitator angle of attack. Incorporating these realistic physical effects into a vehicle system model generates a unique hydrodynamic non-smoothness that is characterized by non-constant switching boundaries and non-constant switched dynamics. Nonlinear stability analyses are carried out, Hopf bifurcations of equilibrium solutions are identified, and stabilizing control is investigated. Also considered is partially cavitating system dynamics, where active fin forces are used to support the vehicle. Non-steady planing is also considered, which accounts for vehicle motions into the cavity, and this planing provides a damping-like component in the planing force formulation. Modeled with non-steady planing is a physical time delay relating to the fact that the cavity, where planing occurs, is based on the previous cavitator position and orientation data. This delay is found to be stabilizing for certain values of speed. Maneuvering is considered by using inner-loop and outer-loop control schemes. A feedback inner-loop scheme helps reject fast planing instabilities, while a numeric optimal control approach is used to generate outer-loop commands to guide the vehicle through desired maneuvers. The maneuvers are considered for operations with tight body to cavity clearance, and in which planing is prevalent. Simple search algorithms along with a penalty method for handling the constraints are found to work the best due to the complexity of the non-smooth system dynamics.Item Black Hole Dynamics and Gravitational Radiation in Galactic Nuclei(2009) Lauburg, Vanessa; Miller, Michael C.; Astronomy; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)In this dissertation, we present new channels for the production of gravitational radiation sources: mergers of black holes in the nuclear star clusters found in many small galaxies, and mergers and tidal separations of black hole binaries in galaxies that host supermassive black holes. Mergers between stellar-mass black holes will be key sources of gravitational radiation for ground-based detectors. However, the rates of these events are highly uncertain, because we can not observe these binaries electromagnetically. In this work, we show that the nuclear star clusters found in the centers of small galaxies are conducive environments for black hole mergers. These clusters have large escape velocities, high stellar densities, and large numbers of black holes that will have multiple close encounters, which often lead to mergers. We present simulations of the three-body dynamics of black holes in this environment and estimate that, if many nuclear star clusters do not have supermassive black holes, tens of events per year will be detectable with Advanced LIGO. Larger galaxies that host supermassive black holes can produce extreme-mass ratio inspiral (EMRI) events, which are important sources for the future space-based detector, LISA. Here, we show that tidal separation of black hole binaries by supermassive black holes will produce a distinct class of EMRIs with near-zero eccentricities, and we estimate that rates from tidal separation could be comparable to or larger than those from the traditionally-discussed two-body capture formation scenario. Before tidal separation can occur, a binary encounters multiple stars as it sinks through the nucleus toward the supermassive black hole. In this region, velocities are high, and interactions with stars can destroy binaries through ionization. We investigate wide ranges in initial mass function and internal energy of the binaries, and find that tidal separations, mergers, and ionizations are all likely outcomes for binaries near the galactic center. Tidally separated binaries will contribute to the LISA detection rate, and mergers will produce tens of events per year for Advanced LIGO. We show, therefore, that galactic nuclei are promising hosts of gravitational wave sources for both LISA and LIGO.Item Dynamics of Free Piston Stirling Engines(2009) Choudhary, Farhan; Balachandran, Balakumar; Mechanical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Free piston Stirling engines (FPSEs) are examples of closed cycle regenerative engines, which can be used to convert thermal energy into mechanical energy. FPSEs are multi-degree-of-freedom dynamical systems that are designed to operate in a periodic manner. Traditionally, the designed periodic orbits are meta-stable, making the system operation sensitive to disturbances. A preferred operating state would be an attracting limit cycle, since the steady-state dynamics would be unique. In this thesis, it is investigated as to how to engineer a Hopf bifurcation of an equilibrium solution in a FPSE. Through a combination of weakly nonlinear analysis and simulations, it is shown that it is possible to engineer a Hopf bifurcation in a FPSE system. Through the analyses, reduced-order-models are developed on the basis of Schmidt formulations and nodal analysis. This thesis effort could serve as a platform for designing FPSEs which take advantage of nonlinear phenomena in either the beta or double acting alpha configuration.