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University of Oklahoma
1.
Jain, Rishabh.
Probing Flavor Changing Higgs Interactions at LHC and Future Hadron Colliders.
Degree: PhD, 2020, University of Oklahoma
URL: http://hdl.handle.net/11244/324838 
► In this dissertation, we discuss the prospect of discovering flavor changing neutral Higgs (FCNH) interactions with quarks and leptons at current and future hadron colliders.…
(more)
▼ In this dissertation, we discuss the prospect of discovering flavor changing neutral Higgs (FCNH) interactions with quarks and leptons at current and future hadron colliders. Particularly, we have looked for t → c h
0 and φ
0 → τ
± μ
\mp, where φ
0 could be a CP-even scalar \bigg[h
0 (lighter), H
0 (heavier) \bigg ] or a CP-odd pseudo-scalar (A
0). A general two Higgs doublet model (gTHDM) is used to simulate t → c h
0 and φ
0 → τ
± μ
\mp decays. The LHC measurements of the light Higgs boson (h
0) favor
the decoupling limit of gTHDM, in which the couplings of h
0
approach Standard Model values.
In this limit, FCNH couplings of the light Higgs boson h
0 are
naturally suppressed by a small mixing parameter \cos(β-α),
while the FCNH couplings of heavier neutral Higgs bosons H
0, {and} A
0
are sustained by \sin(β-α) ∼ 1. Promising results are found for the LHC
collision energies √{s} = 13 TeV and 14 TeV. In addition, we study the discovery potential of future pp colliders, with √{s} = 27 TeV and 100 TeV. For φ
0 → τ
±μ
\mp,
we evaluate the production rate of physics background from dominant processes (τ
+τ
-, WW, ZZ, Wq, Wg, tt̅) with realistic acceptance
cuts and tagging efficiencies. For t → c h
0, where top is coming from top pair production, we consider h
0 → WW^* → ℓ
+ ℓ
- + \slashed{E}
T and h
0 → τ
+ τ
- → ℓ
+ ℓ
- + \slashed{E}
T and another top decaying hadronically to a b quark and two light jets. For this report we have studied h
0 → WW^* and h
0 → τ
+ τ
- separately. Our analysis suggests a reach of 5σ or better, with integrated luminosity 𝓛 = 3 ab
-1 and √{s} = 13, 14 and 27 TeV for λ
tc ≤ 0.064, under the current ATLAS limits for both light Higgs decay mode separately. For h
0 → WW^* we have also presented the discovery potential at 100 TeV.
Advisors/Committee Members: Kao, Chung (advisor), Petrov, Nikola (committee member), Abbott, Braden (committee member), Baer, Howard (committee member), Mullen, Kieran (committee member).
Subjects/Keywords: Physics; Elementary Particles; High Energy
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APA (6th Edition):
Jain, R. (2020). Probing Flavor Changing Higgs Interactions at LHC and Future Hadron Colliders. (Doctoral Dissertation). University of Oklahoma. Retrieved from http://hdl.handle.net/11244/324838
Chicago Manual of Style (16th Edition):
Jain, Rishabh. “Probing Flavor Changing Higgs Interactions at LHC and Future Hadron Colliders.” 2020. Doctoral Dissertation, University of Oklahoma. Accessed March 03, 2021.
http://hdl.handle.net/11244/324838.
MLA Handbook (7th Edition):
Jain, Rishabh. “Probing Flavor Changing Higgs Interactions at LHC and Future Hadron Colliders.” 2020. Web. 03 Mar 2021.
Vancouver:
Jain R. Probing Flavor Changing Higgs Interactions at LHC and Future Hadron Colliders. [Internet] [Doctoral dissertation]. University of Oklahoma; 2020. [cited 2021 Mar 03].
Available from: http://hdl.handle.net/11244/324838.
Council of Science Editors:
Jain R. Probing Flavor Changing Higgs Interactions at LHC and Future Hadron Colliders. [Doctoral Dissertation]. University of Oklahoma; 2020. Available from: http://hdl.handle.net/11244/324838
University of Oklahoma
2.
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 March 03, 2021.
http://hdl.handle.net/11244/50720.
MLA Handbook (7th Edition):
Broda II, James. “Convergence Rates for Stationary Distributions of Semistochastic Processes.” 2017. Web. 03 Mar 2021.
Vancouver:
Broda II J. Convergence Rates for Stationary Distributions of Semistochastic Processes. [Internet] [Doctoral dissertation]. University of Oklahoma; 2017. [cited 2021 Mar 03].
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
3.
Li, Suyu.
Some sharp inequalities related to Moser-Tridinger-Onofri inequality.
Degree: PhD, 2014, University of Oklahoma
URL: http://hdl.handle.net/11244/10370
► In this dissertation, we focus on the study of sharp inequalities of Moser- Trudinger-Onofri type. We first establish the analog Bliss and Hardy inequal- ities…
(more)
▼ In this dissertation, we focus on the study of sharp inequalities of Moser-
Trudinger-Onofri type. We first establish the analog Bliss and Hardy inequal-
ities with sharp constant involving exponential weight function. One special
case of the inequalities (for n = 2 ) leads to a direct proof of Onofri inequality
on S2. Then we establish the sharp trace inequalities on any smooth bounded
simply connected domain in R2.
Advisors/Committee Members: Zhu, Meijun (advisor), Luo, Yiqi (committee member), Albert, John (committee member), Ozaydin, Murad (committee member), Petrov, Nikola (committee member).
Subjects/Keywords: Mathematics.
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APA (6th Edition):
Li, S. (2014). Some sharp inequalities related to Moser-Tridinger-Onofri inequality. (Doctoral Dissertation). University of Oklahoma. Retrieved from http://hdl.handle.net/11244/10370
Chicago Manual of Style (16th Edition):
Li, Suyu. “Some sharp inequalities related to Moser-Tridinger-Onofri inequality.” 2014. Doctoral Dissertation, University of Oklahoma. Accessed March 03, 2021.
http://hdl.handle.net/11244/10370.
MLA Handbook (7th Edition):
Li, Suyu. “Some sharp inequalities related to Moser-Tridinger-Onofri inequality.” 2014. Web. 03 Mar 2021.
Vancouver:
Li S. Some sharp inequalities related to Moser-Tridinger-Onofri inequality. [Internet] [Doctoral dissertation]. University of Oklahoma; 2014. [cited 2021 Mar 03].
Available from: http://hdl.handle.net/11244/10370.
Council of Science Editors:
Li S. Some sharp inequalities related to Moser-Tridinger-Onofri inequality. [Doctoral Dissertation]. University of Oklahoma; 2014. Available from: http://hdl.handle.net/11244/10370
University of Oklahoma
4.
Bozkurt, Fatma.
NORM RETRIEVAL FROM SPATIOTEMPORAL SAMPLES.
Degree: PhD, 2018, University of Oklahoma
URL: http://hdl.handle.net/11244/316291
► The goal of this dissertation is to investigate norm retrievable frames having dynamical sampling structure, particularly those that fail the phase retrieval con- dition. We…
(more)
▼ The goal of this dissertation is to investigate norm retrievable frames having dynamical sampling structure, particularly those that fail the phase retrieval con- dition. We give several classifications to show how to construct norm retrievable frames dynamically, depending on the properties of the time-evolution operator. We show that norm retrievable frames generated by a single vector from a self- adjoint operator are most of the time phase retrievable frames. However, when we allow more generating vectors, there exist norm retrieval frames that do not do phase retrieval. We used two different subspace approaches to obtain these structures in real Hilbert spaces.
Advisors/Committee Members: Kornelson, Keri (advisor), Remling, Christian (committee member), Petrov, Nikola (committee member), Albert, John (committee member), Runolfsson, Thordur (committee member).
Subjects/Keywords: mathematics; norm retrieval; phase retrieval; dynamical sampling
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APA (6th Edition):
Bozkurt, F. (2018). NORM RETRIEVAL FROM SPATIOTEMPORAL SAMPLES. (Doctoral Dissertation). University of Oklahoma. Retrieved from http://hdl.handle.net/11244/316291
Chicago Manual of Style (16th Edition):
Bozkurt, Fatma. “NORM RETRIEVAL FROM SPATIOTEMPORAL SAMPLES.” 2018. Doctoral Dissertation, University of Oklahoma. Accessed March 03, 2021.
http://hdl.handle.net/11244/316291.
MLA Handbook (7th Edition):
Bozkurt, Fatma. “NORM RETRIEVAL FROM SPATIOTEMPORAL SAMPLES.” 2018. Web. 03 Mar 2021.
Vancouver:
Bozkurt F. NORM RETRIEVAL FROM SPATIOTEMPORAL SAMPLES. [Internet] [Doctoral dissertation]. University of Oklahoma; 2018. [cited 2021 Mar 03].
Available from: http://hdl.handle.net/11244/316291.
Council of Science Editors:
Bozkurt F. NORM RETRIEVAL FROM SPATIOTEMPORAL SAMPLES. [Doctoral Dissertation]. University of Oklahoma; 2018. Available from: http://hdl.handle.net/11244/316291
University of Oklahoma
5.
Padeffke-Kirkland, Maren.
Naturalness in Supersymmetry.
Degree: PhD, 2015, University of Oklahoma
URL: http://hdl.handle.net/11244/14673
► Weak scale supersymmetry solves the Big Hierarchy problem of the Standard Model. But recent severe sparticle mass limits from the LHC accentuate the Little Hierarchy…
(more)
▼ Weak scale supersymmetry solves the Big Hierarchy problem of the Standard Model. But recent severe sparticle mass limits from the LHC accentuate the Little Hierarchy Problem: Why are the W , Z and h masses so small (∼ 100 GeV) when the supersymmetric parameters are at or above the TeV scale? This problem can be addressed quantitatively by studying the fine-tuning of a specific model. Fine-tuning allows for a unique way of giving upper bounds for masses of the superpartners. This dissertation studies a variety of models for their naturalness while satisfying experimental constraints. It is shown that fine-tuning puts most SUSY models under severe pressure: only the Non-Universal Higgs Mass model with two extra parameters (NUHM2) survives the naturalness criteria. Inspired by gauge coupling unification, these models assume gaugino mass unification, however, this may not be required by nature. This text examines how the phenomenology of supersymmetric models changes if non-universal gaugino masses (NUGM) are allowed without impacting naturalness. Within the NUGM model, supersymmetry could be detected from electroweak gaugino production at the LHC in multiple channels. Discovery prospects at the LHC13 vastly improve for the case of low gaugino masses due to observable signals from chargino and/or neutralino states. An International Linear Collider shows rich prospects for production of light electroweak -ino states. Also, direct and indirect searches for WIMPs could offer a means of discovery. In addition, this dissertation explores decoupled sfermions within natural supersymmetry. It is shown that low fine-tuning implies intra-generational degeneracy for decoupled squarks and sleptons.
Advisors/Committee Members: Baer, Howard (advisor), Petrov, Nikola (committee member), Kantowski, Ronald (committee member), Watson, Deborah (committee member), Skubic, Patrick (committee member).
Subjects/Keywords: Physics; Elementary Particles and High Energy.
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APA (6th Edition):
Padeffke-Kirkland, M. (2015). Naturalness in Supersymmetry. (Doctoral Dissertation). University of Oklahoma. Retrieved from http://hdl.handle.net/11244/14673
Chicago Manual of Style (16th Edition):
Padeffke-Kirkland, Maren. “Naturalness in Supersymmetry.” 2015. Doctoral Dissertation, University of Oklahoma. Accessed March 03, 2021.
http://hdl.handle.net/11244/14673.
MLA Handbook (7th Edition):
Padeffke-Kirkland, Maren. “Naturalness in Supersymmetry.” 2015. Web. 03 Mar 2021.
Vancouver:
Padeffke-Kirkland M. Naturalness in Supersymmetry. [Internet] [Doctoral dissertation]. University of Oklahoma; 2015. [cited 2021 Mar 03].
Available from: http://hdl.handle.net/11244/14673.
Council of Science Editors:
Padeffke-Kirkland M. Naturalness in Supersymmetry. [Doctoral Dissertation]. University of Oklahoma; 2015. Available from: http://hdl.handle.net/11244/14673
University of Oklahoma
6.
Ho, Nancy.
Controllability of Linear and Nonlinear Control Systems related through Simulation Relations.
Degree: PhD, 2015, University of Oklahoma
URL: http://hdl.handle.net/11244/23293
► For nonlinear input-disturbance systems that are connected by a simulation relation, we examine to what extent they share certain controllability properties. Specifically our main objective…
(more)
▼ For nonlinear input-disturbance systems that are connected by a simulation relation, we examine to what extent they share certain controllability properties. Specifically our main objective is to determine the conditions under which the following holds: given two control systems F and ~{F} where F is simulated by ~{F} and F is completely controllable, we have that ~{F} is also completely controllable. To this end, we show that under some additional conditions the property of complete controllability is preserved for pointwise graph simulation relations and compact graph simulation relations. Next in an attempt to prove a similar result between a nonlinear system and an almost linear system, but with the simulation relation submanifold being a regular level set of a particular map instead of a graph, we achieve the result of the simulating system ~{F} being at most completely controllable modulo the kernel of a linear map. We show through an example that ~{F} may fail to be completely controllable if it does not fulfill a certain compactness condition. By imposing this compactness condition along with other somewhat restrictive assumptions, we are able to prove a similar result for nonlinear control systems connected through a simulation relation submanifold in the form of a regular level set of a smooth mapping. We then illustrate the features of our final main result with an example.
Advisors/Committee Members: Grasse, Kevin (advisor), Albert, John (committee member), Petrov, Nikola (committee member), Remling, Christian (committee member), Lakshmivarahan, S. (committee member).
Subjects/Keywords: simulation relations; controllability; nonlinear control systems; propagation
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APA (6th Edition):
Ho, N. (2015). Controllability of Linear and Nonlinear Control Systems related through Simulation Relations. (Doctoral Dissertation). University of Oklahoma. Retrieved from http://hdl.handle.net/11244/23293
Chicago Manual of Style (16th Edition):
Ho, Nancy. “Controllability of Linear and Nonlinear Control Systems related through Simulation Relations.” 2015. Doctoral Dissertation, University of Oklahoma. Accessed March 03, 2021.
http://hdl.handle.net/11244/23293.
MLA Handbook (7th Edition):
Ho, Nancy. “Controllability of Linear and Nonlinear Control Systems related through Simulation Relations.” 2015. Web. 03 Mar 2021.
Vancouver:
Ho N. Controllability of Linear and Nonlinear Control Systems related through Simulation Relations. [Internet] [Doctoral dissertation]. University of Oklahoma; 2015. [cited 2021 Mar 03].
Available from: http://hdl.handle.net/11244/23293.
Council of Science Editors:
Ho N. Controllability of Linear and Nonlinear Control Systems related through Simulation Relations. [Doctoral Dissertation]. University of Oklahoma; 2015. Available from: http://hdl.handle.net/11244/23293
University of Oklahoma
7.
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 March 03, 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. 03 Mar 2021.
Vancouver:
Davis C. LOCAL ESCAPE RATE DICHOTOMY FROM A PROBABILITY POINT OF VIEW. [Internet] [Doctoral dissertation]. University of Oklahoma; 2020. [cited 2021 Mar 03].
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
8.
Scarbrough, Kyle.
Oscillation theory for canonical systems, applications, and a couple of other things.
Degree: PhD, 2020, University of Oklahoma
URL: http://hdl.handle.net/11244/325308
► Oscillation theory for canonical systems is developed. This is then applied to various topics related to semibounded systems and the essential spectrum. The correspondence between…
(more)
▼ Oscillation theory for canonical systems is developed. This is then applied to various topics related to semibounded systems and the essential spectrum. The correspondence between self-adjoint relations and self-adjoint operators coming from canonical systems is investigated. An upper bound on the number of solutions of a one-channel difference equation is obtained.
Advisors/Committee Members: Remling, Christian (advisor), Barboza, Bruno (committee member), Albert, John (committee member), Petrov, Nikola (committee member), Przebinda, Tomasz (committee member).
Subjects/Keywords: spectral theory; canonical systems; oscillation theory
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APA (6th Edition):
Scarbrough, K. (2020). Oscillation theory for canonical systems, applications, and a couple of other things. (Doctoral Dissertation). University of Oklahoma. Retrieved from http://hdl.handle.net/11244/325308
Chicago Manual of Style (16th Edition):
Scarbrough, Kyle. “Oscillation theory for canonical systems, applications, and a couple of other things.” 2020. Doctoral Dissertation, University of Oklahoma. Accessed March 03, 2021.
http://hdl.handle.net/11244/325308.
MLA Handbook (7th Edition):
Scarbrough, Kyle. “Oscillation theory for canonical systems, applications, and a couple of other things.” 2020. Web. 03 Mar 2021.
Vancouver:
Scarbrough K. Oscillation theory for canonical systems, applications, and a couple of other things. [Internet] [Doctoral dissertation]. University of Oklahoma; 2020. [cited 2021 Mar 03].
Available from: http://hdl.handle.net/11244/325308.
Council of Science Editors:
Scarbrough K. Oscillation theory for canonical systems, applications, and a couple of other things. [Doctoral Dissertation]. University of Oklahoma; 2020. Available from: http://hdl.handle.net/11244/325308
University of Oklahoma
9.
Wickramarachchi, Priyangika.
Measuring The Trilinear Higgs Couplings at LHC.
Degree: PhD, 2015, University of Oklahoma
URL: http://hdl.handle.net/11244/23317
► The results from the Large Hadron Collider (LHC) indicate that the couplings of the Higgs boson to other particles are consistent with the Standard Model.…
(more)
▼ The results from the Large Hadron Collider (LHC) indicate that the couplings of the Higgs boson to other particles are consistent with the Standard Model. The coupling of the Higgs boson to itself will be the final and ultimate test as to whether this particle is the standard Higgs boson. Both the trilinear Higgs coupling as well as the quartic coupling is needed in order to verify the Higgs potential accurately. Our goal is to determine how well the trilinear Higgs coupling can be determined theoretically. We study the Higgs pair production from gluon fusion at the LHC in the Standard Model and Minimal Supersymmetric Standard Model. We consider the collider energy of the LHC Run 2 with √{s}=13;TeV and 14;TeV to study the production rate of Higgs boson pairs and physics background for final states; hh → bb̅ b b̅ and hh → bb̅τ
+τ
- with realistic acceptance cuts.
Advisors/Committee Members: Kao, Chung (advisor), Baer, Howie (committee member), Kantowski, Ron (committee member), Watson, Deborah (committee member), Petrov, Nikola (committee member).
Subjects/Keywords: Physics
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APA ·
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APA (6th Edition):
Wickramarachchi, P. (2015). Measuring The Trilinear Higgs Couplings at LHC. (Doctoral Dissertation). University of Oklahoma. Retrieved from http://hdl.handle.net/11244/23317
Chicago Manual of Style (16th Edition):
Wickramarachchi, Priyangika. “Measuring The Trilinear Higgs Couplings at LHC.” 2015. Doctoral Dissertation, University of Oklahoma. Accessed March 03, 2021.
http://hdl.handle.net/11244/23317.
MLA Handbook (7th Edition):
Wickramarachchi, Priyangika. “Measuring The Trilinear Higgs Couplings at LHC.” 2015. Web. 03 Mar 2021.
Vancouver:
Wickramarachchi P. Measuring The Trilinear Higgs Couplings at LHC. [Internet] [Doctoral dissertation]. University of Oklahoma; 2015. [cited 2021 Mar 03].
Available from: http://hdl.handle.net/11244/23317.
Council of Science Editors:
Wickramarachchi P. Measuring The Trilinear Higgs Couplings at LHC. [Doctoral Dissertation]. University of Oklahoma; 2015. Available from: http://hdl.handle.net/11244/23317
University of Oklahoma
10.
Bauer, Sean.
ON THE EXISTENCE OF KAM TORI FOR PRESYMPLECTIC VECTOR FIELDS.
Degree: PhD, 2016, University of Oklahoma
URL: http://hdl.handle.net/11244/34745
► We prove the existence of a torus that is invariant with respect to the flow of a presymplectic vector field found in a family of…
(more)
▼ We prove the existence of a torus that is invariant with respect to the flow of a presymplectic vector field found in a family of presymplectic vector fields. Moreover, the flow on this invariant torus is conjugate to a linear flow on a torus with a Diophantine velocity vector. This torus is constructed by iteratively solving functional equations using a Newton method in a space of functions by starting from a torus that is approximately invariant. In contrast to the classical methods of proof, this method does not assume that the system is close to integrable and does not rely on using action-angle variables. The geometry of the problem is used to simplify the equations that come from the Newton method. This method of proof can be implemented into efficient numerical algorithms.
Advisors/Committee Members: Petrov, Nikola (advisor), Grasse, Kevin (committee member), Grigo, Alex (committee member), Lakshmivarahan, S (committee member), Remling, Christian (committee member).
Subjects/Keywords: Dynamical Systems; Presymplectic; KAM
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APA (6th Edition):
Bauer, S. (2016). ON THE EXISTENCE OF KAM TORI FOR PRESYMPLECTIC VECTOR FIELDS. (Doctoral Dissertation). University of Oklahoma. Retrieved from http://hdl.handle.net/11244/34745
Chicago Manual of Style (16th Edition):
Bauer, Sean. “ON THE EXISTENCE OF KAM TORI FOR PRESYMPLECTIC VECTOR FIELDS.” 2016. Doctoral Dissertation, University of Oklahoma. Accessed March 03, 2021.
http://hdl.handle.net/11244/34745.
MLA Handbook (7th Edition):
Bauer, Sean. “ON THE EXISTENCE OF KAM TORI FOR PRESYMPLECTIC VECTOR FIELDS.” 2016. Web. 03 Mar 2021.
Vancouver:
Bauer S. ON THE EXISTENCE OF KAM TORI FOR PRESYMPLECTIC VECTOR FIELDS. [Internet] [Doctoral dissertation]. University of Oklahoma; 2016. [cited 2021 Mar 03].
Available from: http://hdl.handle.net/11244/34745.
Council of Science Editors:
Bauer S. ON THE EXISTENCE OF KAM TORI FOR PRESYMPLECTIC VECTOR FIELDS. [Doctoral Dissertation]. University of Oklahoma; 2016. Available from: http://hdl.handle.net/11244/34745
University of Oklahoma
11.
Chen, Feng.
Adaptive Distributed Source Coding Based on Bayesian Inference.
Degree: PhD, 2015, University of Oklahoma
URL: http://hdl.handle.net/11244/15256
► Distributed Source Coding (DSC) is an important topic for both in information theory and communication. DSC utilizes the correlations among the sources to compress data,…
(more)
▼ Distributed Source Coding (DSC) is an important topic for both in information theory and communication. DSC utilizes the correlations among the sources to compress data, and it has the advantages of being simple and easy to carry out. In DSC, Slepian-Wolf (S-W) and Wyner-Ziv (W-Z) are two important problems, which can be classified as lossless compression and loss compression, respectively. Although the lower bounds of the S-W and W-Z problems have been known to researchers for many decades, the code design to achieve the lower bounds is still an open problem.
This dissertation focuses on three DSC problems: the adaptive Slepian-Wolf decoding for two binary sources (ASWDTBS) problem, the compression of correlated temperature data of sensor network (CCTDSN) problem and the streamlined genome sequence compression using distributed source coding (SGSCUDSC) problem. For the CCTDSN and SGSCUDSC problems, sources will be converted into the binary expression as the sources in ASWDTBS problem for encoding. The Bayesian inference will be applied to all of these three problems. To efficiently solve these Bayesian inferences, message passing algorithm will be applied. For a discrete variable that takes a small number of values, the belief propagation (BP) algorithm is able to implement the message passing algorithm efficiently. However, the complexity of the BP algorithm increases exponentially with the number of values of the variable. Therefore, the BP algorithm can only deal with discrete variable that takes a small number of values and limited continuous variables. For the more complex variables, deterministic approximation methods are used. These methods, such as the variational Bayes (VB) method and expectation propagation (EP) method, can efficiently incorporated into the message passing algorithm.
A virtual binary asymmetric channel (BAC) channel was introduced to model the correlation between the source data and the side information (SI) in ASWDTBS problem, in which two parameters are required to be learned. The two parameters correspond to the crossover probabilities that are 0->1 and 1->0. Based on this model, a factor graph was established that includes LDPC code, source data, SI and both of the crossover probabilities. Since the crossover probabilities are continuous variables, the deterministic approximate inference methods will be incorporated into the message passing algorithm. The proposed algorithm was applied to the synthetic data, and the results showed that the VB-based algorithm achieved much better performance than the performances of the EP-based algorithm and the standard BP algorithm. The poor performance of the EP-based algorithm was also analyzed.
For the CCTDSN problem, the temperature data were collected by crossbow sensors. Four sensors were established in different locations of the laboratory and their readings were sent to the common destination. The data from one sensor were used as the SI, and the data from the other 3 sensors were compressed. The decoding algorithm considers both…
Advisors/Committee Members: Cheng, Samuel (advisor), Verma, Pramode (committee member), Petrov, Nikola (committee member), Tang, ChoonYik (committee member), MacDonald, Gregory (committee member).
Subjects/Keywords: Engineering; Electronics and Electrical.
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APA (6th Edition):
Chen, F. (2015). Adaptive Distributed Source Coding Based on Bayesian Inference. (Doctoral Dissertation). University of Oklahoma. Retrieved from http://hdl.handle.net/11244/15256
Chicago Manual of Style (16th Edition):
Chen, Feng. “Adaptive Distributed Source Coding Based on Bayesian Inference.” 2015. Doctoral Dissertation, University of Oklahoma. Accessed March 03, 2021.
http://hdl.handle.net/11244/15256.
MLA Handbook (7th Edition):
Chen, Feng. “Adaptive Distributed Source Coding Based on Bayesian Inference.” 2015. Web. 03 Mar 2021.
Vancouver:
Chen F. Adaptive Distributed Source Coding Based on Bayesian Inference. [Internet] [Doctoral dissertation]. University of Oklahoma; 2015. [cited 2021 Mar 03].
Available from: http://hdl.handle.net/11244/15256.
Council of Science Editors:
Chen F. Adaptive Distributed Source Coding Based on Bayesian Inference. [Doctoral Dissertation]. University of Oklahoma; 2015. Available from: http://hdl.handle.net/11244/15256
University of Oklahoma
12.
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 ·
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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 March 03, 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. 03 Mar 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 Mar 03].
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
13.
Tajik, Elham.
MODELING AND CONTROL OF MICROGRID COMPONENTS.
Degree: PhD, 2018, University of Oklahoma
URL: http://hdl.handle.net/11244/316764
► Due to the increase in the integration of renewable energy resources into electrical power systems, there are various challenges that modern power systems are facing.…
(more)
▼ Due to the increase in the integration of renewable energy resources into electrical power systems, there are various challenges that modern power systems are facing.
A lot of issues in this subject are discussed under the concept of microgrid and their operational and control concerns.
Power electronic interfaces (converters, inverters) are necessary for connecting generation units based on renewable energy resources to the power grid. Consequently, inverter control is a primary issue in operating microgrids. Fast dynamics of power electronic interfaces results in different operating concerns and strategies for inverter-based generation units as compared to large conventional synchronous generators. To provide simplicity in operating inverter-based generation units, there are various control strategies based on emulating the critical properties of a conventional synchronous generator such as inertia and damping. This dissertation designs a novel operational and control model for controlled power electronic loads and inverter-based generators inspired by synchronous generators' equations and stated in port-Hamiltonian systems' formulation. This inverter generator controller is added to the inverter switching controller to enable the generator to behave in a manner similar to a synchronous generator.
We develop a control methodology based on Interconnection and Damping Assignment Passivity Based Control (IDA-PBC) strategy for the proposed inverter-based generator dynamics. We prove the stability of the designed closed loop system and develop a simulation model for the projected control strategy that includes an example system consisting of a constant impedance load, a π-modeled line and an inverter-based generator.
We also develop a generic port-Hamiltonian model for loads that allows through the appropriate selection of structure and controls the mimicking of the behavior of complex loads that are connected to the grid through controlled power electronic interfaces.
Advisors/Committee Members: Runolfsson, Thordur (advisor), Petrov, Nikola (committee member), Tang, Choon Yik (committee member), Jiang, John (committee member), Moses, Paul (committee member).
Subjects/Keywords: Power Systems; Microgrid; Port-Hamiltonian systems; Constant Power Loads; Virtual Machine; Engineering, Electronics and Electrical.
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APA ·
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CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Tajik, E. (2018). MODELING AND CONTROL OF MICROGRID COMPONENTS. (Doctoral Dissertation). University of Oklahoma. Retrieved from http://hdl.handle.net/11244/316764
Chicago Manual of Style (16th Edition):
Tajik, Elham. “MODELING AND CONTROL OF MICROGRID COMPONENTS.” 2018. Doctoral Dissertation, University of Oklahoma. Accessed March 03, 2021.
http://hdl.handle.net/11244/316764.
MLA Handbook (7th Edition):
Tajik, Elham. “MODELING AND CONTROL OF MICROGRID COMPONENTS.” 2018. Web. 03 Mar 2021.
Vancouver:
Tajik E. MODELING AND CONTROL OF MICROGRID COMPONENTS. [Internet] [Doctoral dissertation]. University of Oklahoma; 2018. [cited 2021 Mar 03].
Available from: http://hdl.handle.net/11244/316764.
Council of Science Editors:
Tajik E. MODELING AND CONTROL OF MICROGRID COMPONENTS. [Doctoral Dissertation]. University of Oklahoma; 2018. Available from: http://hdl.handle.net/11244/316764
University of Oklahoma
14.
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 ·
Chicago ·
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Export
to Zotero / EndNote / Reference
Manager
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 March 03, 2021.
http://hdl.handle.net/11244/319611.
MLA Handbook (7th Edition):
Adekoya, Oreoluwa. “PERIODIC SOLUTIONS OF THE DISPERSION-MANAGED NONLINEAR SCHRODINGER EQUATION.” 2019. Web. 03 Mar 2021.
Vancouver:
Adekoya O. PERIODIC SOLUTIONS OF THE DISPERSION-MANAGED NONLINEAR SCHRODINGER EQUATION. [Internet] [Doctoral dissertation]. University of Oklahoma; 2019. [cited 2021 Mar 03].
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
University of Oklahoma
15.
Gebauer, Joshua.
Assessing Dual-Doppler Vertical Velocity Retrievals from Rapid-Scan Radar Data.
Degree: PhD, 2020, University of Oklahoma
URL: http://hdl.handle.net/11244/326614
► Vertical velocity is the most difficult wind component to accurately retrieve from dual- Doppler observations. Typical radar scans are conducted with shallow elevation angles and…
(more)
▼ Vertical velocity is the most difficult wind component to accurately retrieve from dual-
Doppler observations. Typical radar scans are conducted with shallow elevation angles and
therefore, the radial velocity observations poorly constrain the vertical velocity in retrievals.
Traditional dual-Doppler analysis (DDA) uses the anelastic mass conservation equation as
a constraint to retrieve vertical velocity. However, procedures that integrate the anelastic
mass conservation equation can have large errors in the vertical velocities due to missing
low-level data, errors in boundary specification, and the compounding of horizontal divergence
errors in the integration. In recent years, it has been proposed to use a vertical
vorticity equation as a weak constraint in addition to the mass conservation equation in order
to improve vertical velocity retrievals. Prior observation simulation experiments have
found that the vorticity equation constraint can improve vertical velocity retrievals in situations
with missing low-level data and radar volume scan times that are sufficiently short to
calculate the vorticity tendency accurately.
In this study, the vertical vorticity equation constraint DDA was tested using real
observations from rapid-scan radars. A dual-Doppler dataset of a convective storm was
collected on 4 Sept 2018 with a maximum volume scan time of 30 seconds. An additional
radar was positioned under the storm and conducted near-vertical planned-position indicator
scans (PPIs), which were used as a verification dataset. In general, the vorticity equation
DDA was able to improve vertical velocity retrievels, but the improvement was dependent
on the time between volume scans and the technique used to calculate the vorticity tendency.
When the time between volume scans was 30 seconds, a simple centered difference
of the vorticity calculated from provisional wind retrievals was sufficient for estimating
the vorticity tendency, but with greater time between volume scans this method resulted
in significantly degraded vertical velocities. A technique that used advection correction to
shorten the time difference in the centered difference improved the vertical velocities of
these longer volume scan times, but caused the DDAs with 30 seconds between volume
scans to become slightly worse. A new three-dimensional advection correction technique
that was developed for the vorticity tendency estimation produced slightly better vertical
velocity retrievals than those that used two-dimensional advection correction. One key
difference between these results and those of the prior OSSE experiments is that the improvement
in the retrieved vertical velocities occurred even though there was not a large
data void between the lowest data level and the ground. Additionally, the vorticity equation
constraint DDA was more forgiving to radar data errors as it did not produce unphysical
vertical velocities in a region of sidelobe contamination that was present in the other DDAs.
Considering that observation…
Advisors/Committee Members: Shapiro, Alan (advisor), Corey, Potvin (committee member), Palmer, Robert (committee member), Homeyer, Cameron (committee member), Petrov, Nikola (committee member).
Subjects/Keywords: Radar Analysis; Dual-Doppler; Ensemble Kalman Filter
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APA ·
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MLA ·
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Export
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APA (6th Edition):
Gebauer, J. (2020). Assessing Dual-Doppler Vertical Velocity Retrievals from Rapid-Scan Radar Data. (Doctoral Dissertation). University of Oklahoma. Retrieved from http://hdl.handle.net/11244/326614
Chicago Manual of Style (16th Edition):
Gebauer, Joshua. “Assessing Dual-Doppler Vertical Velocity Retrievals from Rapid-Scan Radar Data.” 2020. Doctoral Dissertation, University of Oklahoma. Accessed March 03, 2021.
http://hdl.handle.net/11244/326614.
MLA Handbook (7th Edition):
Gebauer, Joshua. “Assessing Dual-Doppler Vertical Velocity Retrievals from Rapid-Scan Radar Data.” 2020. Web. 03 Mar 2021.
Vancouver:
Gebauer J. Assessing Dual-Doppler Vertical Velocity Retrievals from Rapid-Scan Radar Data. [Internet] [Doctoral dissertation]. University of Oklahoma; 2020. [cited 2021 Mar 03].
Available from: http://hdl.handle.net/11244/326614.
Council of Science Editors:
Gebauer J. Assessing Dual-Doppler Vertical Velocity Retrievals from Rapid-Scan Radar Data. [Doctoral Dissertation]. University of Oklahoma; 2020. Available from: http://hdl.handle.net/11244/326614
16.
Mickelson, Daniel.
Radiatively-driven Natural Supersymmetry.
Degree: PhD, 2014, University of Oklahoma
URL: http://hdl.handle.net/11244/10493
► Within the framework of supersymmetric theories, a question arises: how can the W, Z, and h masses be so low (∼ 100 GeV) when the…
(more)
▼ Within the framework of supersymmetric theories, a question arises: how can the W, Z, and h masses be so low (∼ 100 GeV) when the superpartner masses are so high (mSUSY > 1−2 TeV)? This is the little hierarchy problem, and can be quantified by studying the fine-tuning of a particular model. Quantifying a model in such a way provides a unique opportunity to give upper bounds on the supersymmetric particle masses. Introduced in this dissertation is the model called Radiatively-driven Natural Supersymmetry, wherein low fine-tuning is achieved while maintaining a light Higgs scalar ≃ 125 GeV. In addition, RNS offers a particle spectrum that evades searches at all current collider experiments, and satisfies cosmological constraints. It is shown that RNS could be discovered with high luminosity at LHC14 in multiple channels, having a soft trilepton + MET signature, a unique same-sign diboson signature accompanied by jets, and gluino cascade decays in the trilepton+jets channel. An International Linear Collider operating at √s = 600 GeV would either discover RNS or rule it out as a feasible model. Dark matter direct and indirect detection experiments also offer a means of discovery, with a 1-ton noble gas detector effectively probing the entirety of RNS parameter space.
Advisors/Committee Members: Baer, Howard (advisor), Milton, Kimball (committee member), Abbott, Braden (committee member), Mason, Bruce (committee member), Petrov, Nikola (committee member).
Subjects/Keywords: Physics; Elementary Particles and High Energy.
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APA ·
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APA (6th Edition):
Mickelson, D. (2014). Radiatively-driven Natural Supersymmetry. (Doctoral Dissertation). University of Oklahoma. Retrieved from http://hdl.handle.net/11244/10493
Chicago Manual of Style (16th Edition):
Mickelson, Daniel. “Radiatively-driven Natural Supersymmetry.” 2014. Doctoral Dissertation, University of Oklahoma. Accessed March 03, 2021.
http://hdl.handle.net/11244/10493.
MLA Handbook (7th Edition):
Mickelson, Daniel. “Radiatively-driven Natural Supersymmetry.” 2014. Web. 03 Mar 2021.
Vancouver:
Mickelson D. Radiatively-driven Natural Supersymmetry. [Internet] [Doctoral dissertation]. University of Oklahoma; 2014. [cited 2021 Mar 03].
Available from: http://hdl.handle.net/11244/10493.
Council of Science Editors:
Mickelson D. Radiatively-driven Natural Supersymmetry. [Doctoral Dissertation]. University of Oklahoma; 2014. Available from: http://hdl.handle.net/11244/10493
. 
Open Access Theses and Dissertations
