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University of Oklahoma
1.
Peccarelli, Nicholas.
Nonlinear Equalization and Digital Pre-Distortion Techniques for Future Radar and Communications Digital Array Systems.
Degree: PhD, 2020, University of Oklahoma
URL: http://hdl.handle.net/11244/324399 
► Modern radar (military, automotive, weather, etc.) and communication systems seek to leverage the spatio-spectral efficiency of phased arrays. Specifically, there is an increasingly large demand…
(more)
▼ Modern radar (military, automotive, weather, etc.) and communication systems seek to leverage the spatio-spectral efficiency of phased arrays. Specifically, there is an increasingly large demand for fully-digital arrays, with each antenna element having its own transmitter and receiver. Further, in order to makes these systems realizable, low-cost, low-complexity solutions are required, often sacrificing the system's linearity. Lower linearity paired with the inherent lack of RF spacial filtering can make these highly digital systems vulnerable to high-power interferering signals – potentially introducing spectral regrowth and/or gain compression, distorting the signal-of-interest.
Digital linearization solutions such as Digital Pre-Distiortion (DPD) and Nonlinear Equalization (NLEQ) have been shown to effectively mitigate nonlinearities for transmitters and receivers, respectively. Further, DPD and NLEQ seek to extend the effective dynamic range of digital arrays, helping the systems reach their designed dynamic range improvement of 10log
10(N)~dB, where N is the number of transmitters/receivers. However, the performance of these solutions is ultimately determined by training model and waveform. Further, the nonlinear characteristics of a system can change with temperature, frequency, power, time, etc., requiring a robust calibration technique to maintain a high-level of nonlinear mitigation.
This dissertation reviews the different types of nonlinear models and the current NLEQ and DPD algorithms for digital array systems. Further, a generalized calibration waveform for both NLEQ and DPD is proposed, allowing a system to maximize its dynamic range over power and frequency. Additionally, an it{in-situ} calibration method, leveraging the inherent mutual coupling in an array, is proposed as a solution to maintaining a high level of performance in a fielded digital array system over the system's lifetime. The combination of the proposed training waveform and it{in-situ} calibration technique prove to be very effective at adaptively creating a generalized solution to extending the dynamic range of future low-cost digital array systems.
Advisors/Committee Members: Fulton, Caleb (advisor), Goodman, Nathan (committee member), Sigmarsson, Hjalti (committee member), McDaniel, Jay (committee member), Grigo, Alexander (committee member).
Subjects/Keywords: Nonlinear Equalization; Phased Array; Radar; Signal Processing
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APA (6th Edition):
Peccarelli, N. (2020). Nonlinear Equalization and Digital Pre-Distortion Techniques for Future Radar and Communications Digital Array Systems. (Doctoral Dissertation). University of Oklahoma. Retrieved from http://hdl.handle.net/11244/324399
Chicago Manual of Style (16th Edition):
Peccarelli, Nicholas. “Nonlinear Equalization and Digital Pre-Distortion Techniques for Future Radar and Communications Digital Array Systems.” 2020. Doctoral Dissertation, University of Oklahoma. Accessed February 25, 2021.
http://hdl.handle.net/11244/324399.
MLA Handbook (7th Edition):
Peccarelli, Nicholas. “Nonlinear Equalization and Digital Pre-Distortion Techniques for Future Radar and Communications Digital Array Systems.” 2020. Web. 25 Feb 2021.
Vancouver:
Peccarelli N. Nonlinear Equalization and Digital Pre-Distortion Techniques for Future Radar and Communications Digital Array Systems. [Internet] [Doctoral dissertation]. University of Oklahoma; 2020. [cited 2021 Feb 25].
Available from: http://hdl.handle.net/11244/324399.
Council of Science Editors:
Peccarelli N. Nonlinear Equalization and Digital Pre-Distortion Techniques for Future Radar and Communications Digital Array Systems. [Doctoral Dissertation]. University of Oklahoma; 2020. Available from: http://hdl.handle.net/11244/324399
University of Oklahoma
2.
Sheaib, Dania.
Dynamics and Stability of Buoyancy-Induced Flows.
Degree: PhD, 2019, University of Oklahoma
URL: http://hdl.handle.net/11244/319610
► The present dissertation tackles two different problems in fluid mechanics. In the first problem, we study the stability of free or natural convection of a…
(more)
▼ The present dissertation tackles two different problems in fluid mechanics. In the first problem, we study the stability of free or natural convection of a compressible fluid over a heated plate underlying a semi-infinite vertical slot and underlying a closed vessel. For both settings, we show linear and non-linear stability of the reference solution by constructing respective Lyapunov functions and using LaSalle's Invariance Principle. The construction of the Lyapunov function is motivated by the assumption that the fluid particles evolve according to a Markov chain. In the second problem, we study the flow dynamics of a viscous stably stratified fluid in a channel with time-periodic temperature variations applied at the sidewalls. Seeking solutions in the form of simple harmonic oscillations, we obtain analytical temperature and velocity profiles for the one-dimensional time-dependent flow. We then use these solutions to study the possibility of resonance of the fluid flow with the periodic oscillations of the externally supplied temperatures at the walls. Results indicate the existence of resonance depicted as prominent peaks of physical quantities at certain frequencies of the external temperature oscillations.
Advisors/Committee Members: Grigo, Alexander (advisor), Nikola, Petrov (advisor), Albert, John (committee member), Marfurt, Kurt (committee member), Remling, Christian (committee member).
Subjects/Keywords: Navier-Stokes Equations; Dynamics; Stability; Buoyancy-Induced Flows; Natural Convection; Steady Flow; Horizontal Plate; Time-dependent Flow; Vertical Channel; Stratified Fluid; Lyapunov Function; Resonance; Prandtl Number
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APA (6th Edition):
Sheaib, D. (2019). Dynamics and Stability of Buoyancy-Induced Flows. (Doctoral Dissertation). University of Oklahoma. Retrieved from http://hdl.handle.net/11244/319610
Chicago Manual of Style (16th Edition):
Sheaib, Dania. “Dynamics and Stability of Buoyancy-Induced Flows.” 2019. Doctoral Dissertation, University of Oklahoma. Accessed February 25, 2021.
http://hdl.handle.net/11244/319610.
MLA Handbook (7th Edition):
Sheaib, Dania. “Dynamics and Stability of Buoyancy-Induced Flows.” 2019. Web. 25 Feb 2021.
Vancouver:
Sheaib D. Dynamics and Stability of Buoyancy-Induced Flows. [Internet] [Doctoral dissertation]. University of Oklahoma; 2019. [cited 2021 Feb 25].
Available from: http://hdl.handle.net/11244/319610.
Council of Science Editors:
Sheaib D. Dynamics and Stability of Buoyancy-Induced Flows. [Doctoral Dissertation]. University of Oklahoma; 2019. Available from: http://hdl.handle.net/11244/319610
University of Oklahoma
3.
Broda II, James.
Convergence Rates for Stationary Distributions of Semistochastic Processes.
Degree: PhD, 2017, University of Oklahoma
URL: http://hdl.handle.net/11244/50720
► The primary objects of study in this dissertation are semistochastic processes. The types of semistochastic processes we consider are continuous-time and continuous-state processes consisting of…
(more)
▼ The primary objects of study in this dissertation are semistochastic processes. The types of semistochastic processes we consider are continuous-time and continuous-state processes consisting of intervals of deterministic evolution punctuated by random disturbances of random severity. A natural question regarding such processes is whether they admit stationary distributions. While partial answers to this question exist in the literature, the primary aim of this dissertation is to supplement the criteria for existence with bounds on convergence rates. This requires careful analysis of the associated Markov semigroups and infinitesimal generators. We obtain our bounds on convergence rates by establishing minorization and drift conditions. Specific examples are considered in cases of bounded and unbounded state spaces.
We also discuss a method of exact computation for the stationary distributions of a certain class of semistochastic processes. An important example to which we can apply our work concerns the modelling of the carbon content of an ecosystem.
Advisors/Committee Members: Petrov, Nikola (advisor), Grigo, Alexander (advisor), Ellis, Stephen (committee member), Albert, John (committee member), Wang, Ying (committee member).
Subjects/Keywords: Carbon Dynamics; Catastrophes; Kicked Flows; Semistochastic Processes
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APA (6th Edition):
Broda II, J. (2017). Convergence Rates for Stationary Distributions of Semistochastic Processes. (Doctoral Dissertation). University of Oklahoma. Retrieved from http://hdl.handle.net/11244/50720
Chicago Manual of Style (16th Edition):
Broda II, James. “Convergence Rates for Stationary Distributions of Semistochastic Processes.” 2017. Doctoral Dissertation, University of Oklahoma. Accessed February 25, 2021.
http://hdl.handle.net/11244/50720.
MLA Handbook (7th Edition):
Broda II, James. “Convergence Rates for Stationary Distributions of Semistochastic Processes.” 2017. Web. 25 Feb 2021.
Vancouver:
Broda II J. Convergence Rates for Stationary Distributions of Semistochastic Processes. [Internet] [Doctoral dissertation]. University of Oklahoma; 2017. [cited 2021 Feb 25].
Available from: http://hdl.handle.net/11244/50720.
Council of Science Editors:
Broda II J. Convergence Rates for Stationary Distributions of Semistochastic Processes. [Doctoral Dissertation]. University of Oklahoma; 2017. Available from: http://hdl.handle.net/11244/50720
University of Oklahoma
4.
Davis, Connor.
LOCAL ESCAPE RATE DICHOTOMY FROM A PROBABILITY POINT OF VIEW.
Degree: PhD, 2020, University of Oklahoma
URL: http://hdl.handle.net/11244/325312
► We will discuss a dichotomy pertaining to escape rates in dynamical systems. This dichotomy pertains to the limiting behavior of the escape rate as it…
(more)
▼ We will discuss a dichotomy pertaining to escape rates in dynamical systems.
This dichotomy pertains to the limiting behavior of the escape rate as it is
compared to the size of a shrinking hole (the local escape rate). In this case, it
has been shown, with some robustness, that under certain mixing conditions
on the system this limiting behavior is determined by the periodicity of of
the set to which the hole shrinks. We will use a blocking argument to obtain
error estimates for truncation of the limit described above. These will allow
for the result that the double limit describing the local escape rate to be taken
along different paths. Finally, we will discuss a result that ties the escape rate
conditioned on being in the hole, to the usual escape rate.
Advisors/Committee Members: Grigo, Alexander (advisor), Yang, Fan (advisor), Wang, Ying (committee member), Albert, John (committee member), Duerfeldt, Adam (committee member), Petrov, Nikola (committee member).
Subjects/Keywords: Mathematics.; Ergodic Theory; Dynamical Systems
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APA (6th Edition):
Davis, C. (2020). LOCAL ESCAPE RATE DICHOTOMY FROM A PROBABILITY POINT OF VIEW. (Doctoral Dissertation). University of Oklahoma. Retrieved from http://hdl.handle.net/11244/325312
Chicago Manual of Style (16th Edition):
Davis, Connor. “LOCAL ESCAPE RATE DICHOTOMY FROM A PROBABILITY POINT OF VIEW.” 2020. Doctoral Dissertation, University of Oklahoma. Accessed February 25, 2021.
http://hdl.handle.net/11244/325312.
MLA Handbook (7th Edition):
Davis, Connor. “LOCAL ESCAPE RATE DICHOTOMY FROM A PROBABILITY POINT OF VIEW.” 2020. Web. 25 Feb 2021.
Vancouver:
Davis C. LOCAL ESCAPE RATE DICHOTOMY FROM A PROBABILITY POINT OF VIEW. [Internet] [Doctoral dissertation]. University of Oklahoma; 2020. [cited 2021 Feb 25].
Available from: http://hdl.handle.net/11244/325312.
Council of Science Editors:
Davis C. LOCAL ESCAPE RATE DICHOTOMY FROM A PROBABILITY POINT OF VIEW. [Doctoral Dissertation]. University of Oklahoma; 2020. Available from: http://hdl.handle.net/11244/325312
University of Oklahoma
5.
Roberts, Brett.
The Role of Surface Drag in Supercell Tornadogenesis and Mesocyclogenesis: Studies Based on Idealized Numerical Simulations.
Degree: PhD, 2017, University of Oklahoma
URL: http://hdl.handle.net/11244/50736
► Idealized numerical simulations of supercell thunderstorms have been employed for several decades to study tornadogenesis, providing valuable insights that have helped shape our current understanding…
(more)
▼ Idealized numerical simulations of supercell thunderstorms have been employed for several decades to study tornadogenesis, providing valuable insights that have helped shape our current understanding of the process. Until the past several years, however, most of these simulations used a free-slip lower boundary condition, effectively disregarding the effects of surface drag. In this study, 50-m (tornado-resolving) idealized simulations of a supercell thunderstorm are performed using the Advanced Regional Prediction System (ARPS) with parameterized surface drag. Analyses of the dynamics of low-level mesocyclogenesis and tornadogenesis are conducted.
Two sets of experiments are performed and analyzed in this study. First, a pair of experiments is performed to identify mechanisms by which drag affects storm behavior. In the first experiment (full-wind drag), surface drag is applied to the full wind components; in the second experiment (environmental drag), drag is applied only to the background environmental wind, with storm-induced perturbations unaffected. In the full-wind drag experiment, a tornado develops around 25 min into the simulation and persists for more than 10 min; in the environmental drag experiment, no tornado occurs. An important mechanism leading to tornadogenesis in the full-wind drag experiment is the generation of near-ground crosswise horizontal vorticity by drag on the storm scale as inflow air accelerates into the low-level mesocyclone; this vorticity is subsequently exchanged into the streamwise direction and eventually tilted into the vertical. Preceding tornadogenesis, the low-level mesocyclone in the full-wind drag experiment also intensifies and lowers rapidly toward the ground, which does not occur in the environmental drag experiment. Circulation budgets for material circuits enclosing the low-level mesocyclone reveal substantial generation of new circulation by surface drag in the full-wind drag experiment, while the mesocyclone circulation in the environmental-drag experiment is primarily barotropic in origin.
A second set of experiments is performed in which the drag coefficient (Cd) is varied over a range of values appropriate for water and land. The initial low-level mesocyclone lowers toward the ground, intensifies, and produces a tornado in all experiments with Cd > 0, with the intensification occurring earlier for larger Cd; in the no-drag experiment, the low-level mesocyclone remains comparatively weak during this period. Circulation budgets for material circuits initialized around the mesocyclone again implicate surface drag acting in the inflow region as having generated important new circulation. Although a greater relative contribution from drag is seen as Cd increases, the difference between the last two experiments (Cd = 0.02, Cd = 0.05) is minimal and the tornado in the latter experiment is weaker, suggesting an upper limit on the drag coefficient for the favorability of this circulation-generating mechanism. Later in the simulations, after precipitation-driven…
Advisors/Committee Members: Xue, Ming (advisor), Bluestein, Howard (committee member), Dawson, Daniel (committee member), Shapiro, Alan (committee member), Grigo, Alexander (committee member).
Subjects/Keywords: Physics, Atmospheric Science.; supercells; tornadoes; numerical weather prediction; severe storms
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APA ·
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APA (6th Edition):
Roberts, B. (2017). The Role of Surface Drag in Supercell Tornadogenesis and Mesocyclogenesis: Studies Based on Idealized Numerical Simulations. (Doctoral Dissertation). University of Oklahoma. Retrieved from http://hdl.handle.net/11244/50736
Chicago Manual of Style (16th Edition):
Roberts, Brett. “The Role of Surface Drag in Supercell Tornadogenesis and Mesocyclogenesis: Studies Based on Idealized Numerical Simulations.” 2017. Doctoral Dissertation, University of Oklahoma. Accessed February 25, 2021.
http://hdl.handle.net/11244/50736.
MLA Handbook (7th Edition):
Roberts, Brett. “The Role of Surface Drag in Supercell Tornadogenesis and Mesocyclogenesis: Studies Based on Idealized Numerical Simulations.” 2017. Web. 25 Feb 2021.
Vancouver:
Roberts B. The Role of Surface Drag in Supercell Tornadogenesis and Mesocyclogenesis: Studies Based on Idealized Numerical Simulations. [Internet] [Doctoral dissertation]. University of Oklahoma; 2017. [cited 2021 Feb 25].
Available from: http://hdl.handle.net/11244/50736.
Council of Science Editors:
Roberts B. The Role of Surface Drag in Supercell Tornadogenesis and Mesocyclogenesis: Studies Based on Idealized Numerical Simulations. [Doctoral Dissertation]. University of Oklahoma; 2017. Available from: http://hdl.handle.net/11244/50736
University of Oklahoma
6.
Sunkula, Mahesh.
GEOMETRIC QUANTIZATION OF A SEMI-GLOBAL MODEL OF A FOCUS-FOCUS SINGULARITY.
Degree: PhD, 2019, University of Oklahoma
URL: http://hdl.handle.net/11244/321110
► Quantization of a classical mechanical system is an old problem in physics. In classical mechanics, the evolution of the system is given by a Hamiltonian…
(more)
▼ Quantization of a classical mechanical system is an old problem in physics.
In classical mechanics, the evolution of the system is given by a Hamiltonian vector field
on a symplectic manifold (``phase space'').
Geometric quantization is a procedure to construct a quantum system
using the geometry of the classical phase space.
A completely integrable system is a symplectic manifold with a moment map.
If the moment map has singularities, the geometric quantization of such system becomes difficult to construct.
In such case one needs to use tools from algebraic geometry (sheaves, cohomologies, etc.) to quantize such a system.
The non-degenerate singularities of moment maps have been completely classified.
In this dissertation we study a 4-dimensional symplectic manifold with a moment map
that has a non-degenerate singularity of the so-called focus-focus type.
A simple mechanical system with such a singularity is the spherical pendulum
(a point mass moving without resistance on the surface of a sphere under the influence of the Earth's gravity field).
We compute the geometric quantization of a focus-focus singularity
by constructing a fine resolution and computing the corresponding
sheaf cohomology groups.
Advisors/Committee Members: Petrov, Nikola (advisor), Albert, John (committee member), S, Lakshmivarahan (committee member), Grigo, Alexander (committee member), Remling, Christian (committee member).
Subjects/Keywords: Geometric Quantization; Symplectic Geometry; Mathematical Physics
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APA (6th Edition):
Sunkula, M. (2019). GEOMETRIC QUANTIZATION OF A SEMI-GLOBAL MODEL OF A FOCUS-FOCUS SINGULARITY. (Doctoral Dissertation). University of Oklahoma. Retrieved from http://hdl.handle.net/11244/321110
Chicago Manual of Style (16th Edition):
Sunkula, Mahesh. “GEOMETRIC QUANTIZATION OF A SEMI-GLOBAL MODEL OF A FOCUS-FOCUS SINGULARITY.” 2019. Doctoral Dissertation, University of Oklahoma. Accessed February 25, 2021.
http://hdl.handle.net/11244/321110.
MLA Handbook (7th Edition):
Sunkula, Mahesh. “GEOMETRIC QUANTIZATION OF A SEMI-GLOBAL MODEL OF A FOCUS-FOCUS SINGULARITY.” 2019. Web. 25 Feb 2021.
Vancouver:
Sunkula M. GEOMETRIC QUANTIZATION OF A SEMI-GLOBAL MODEL OF A FOCUS-FOCUS SINGULARITY. [Internet] [Doctoral dissertation]. University of Oklahoma; 2019. [cited 2021 Feb 25].
Available from: http://hdl.handle.net/11244/321110.
Council of Science Editors:
Sunkula M. GEOMETRIC QUANTIZATION OF A SEMI-GLOBAL MODEL OF A FOCUS-FOCUS SINGULARITY. [Doctoral Dissertation]. University of Oklahoma; 2019. Available from: http://hdl.handle.net/11244/321110
University of Oklahoma
7.
Adekoya, Oreoluwa.
PERIODIC SOLUTIONS OF THE DISPERSION-MANAGED NONLINEAR SCHRODINGER EQUATION.
Degree: PhD, 2019, University of Oklahoma
URL: http://hdl.handle.net/11244/319611
► We study the existence, uniqueness and stability of solutions to the initial-value problem for the periodic dispersion-managed nonlinear Schrödinger (DMNLS) equation, an equation that models…
(more)
▼ We study the existence, uniqueness and stability of solutions to the initial-value problem for the periodic dispersion-managed nonlinear Schrödinger (DMNLS) equation, an equation that models the propagation of periodic, nonlinear, quasi-monochromatic electromagnetic pulses in a dispersion-managed fiber. The periodic DMNLS equation we derive is the same as the non-periodic DMNLS equation (\ref{eq:1.2}), except with a subtle difference in the operator T
(s)=T
D(s)= e
-iD(s)\partialx2. The periodic function D(s) still controls the dispersive properties of the optical fiber.
With respect to the Cauchy problem for the periodic DMNLS equation, under certain assumptions on the variable dispersion, we use a Strichartz estimate (Theorem \ref{th:3.2}) on the family of operators T
D(s) to prove global well-posedness for initial data in H
r for non negative integer values of r.
Lastly, we prove results on the existence and stability of ground state solutions by considering the convergence of minimizing sequences for certain variational problems. In the case α>0, the convergence follows from the Rellich-Kondrachov Theorem; in the case α=0, we use a concentration-compactness argument due to Kunze, but with significant modifications.
Advisors/Committee Members: Albert, John (advisor), Crowther, Kathleen (committee member), Grigo, Alexander (committee member), Petrov, Nikola (committee member), Remling, Christian (committee member).
Subjects/Keywords: Dispersion-managed; Dispersion; Nonlinear; Schrodinger; Periodic dispersion managed nonlinear schrodinger equation
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APA ·
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APA (6th Edition):
Adekoya, O. (2019). PERIODIC SOLUTIONS OF THE DISPERSION-MANAGED NONLINEAR SCHRODINGER EQUATION. (Doctoral Dissertation). University of Oklahoma. Retrieved from http://hdl.handle.net/11244/319611
Chicago Manual of Style (16th Edition):
Adekoya, Oreoluwa. “PERIODIC SOLUTIONS OF THE DISPERSION-MANAGED NONLINEAR SCHRODINGER EQUATION.” 2019. Doctoral Dissertation, University of Oklahoma. Accessed February 25, 2021.
http://hdl.handle.net/11244/319611.
MLA Handbook (7th Edition):
Adekoya, Oreoluwa. “PERIODIC SOLUTIONS OF THE DISPERSION-MANAGED NONLINEAR SCHRODINGER EQUATION.” 2019. Web. 25 Feb 2021.
Vancouver:
Adekoya O. PERIODIC SOLUTIONS OF THE DISPERSION-MANAGED NONLINEAR SCHRODINGER EQUATION. [Internet] [Doctoral dissertation]. University of Oklahoma; 2019. [cited 2021 Feb 25].
Available from: http://hdl.handle.net/11244/319611.
Council of Science Editors:
Adekoya O. PERIODIC SOLUTIONS OF THE DISPERSION-MANAGED NONLINEAR SCHRODINGER EQUATION. [Doctoral Dissertation]. University of Oklahoma; 2019. Available from: http://hdl.handle.net/11244/319611
. 
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