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University of Kansas
1.
Valle, Chris.
Shor's Algorithm and Grover's Algorithm in Quantum Computing.
Degree: MA, Mathematics, 2011, University of Kansas
URL: http://hdl.handle.net/1808/7674 
► In this paper we will analyse two quantum algorithms that sparked interest in the potential of quantum computers. The first is Lov Grover's algorithm which…
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▼ In this paper we will analyse two quantum algorithms that sparked interest in the potential of quantum computers. The first is Lov Grover's algorithm which may be used to conduct a type of database search. The second is Peter Shor's algorithm which may be used to factor large numbers and provides an exponential speed up over the best current classical algorithms. In the context of these two algorithms we will discuss the benefits and weaknesses of quantum computation. We will show that in exchange for a quantum computer's greater speed we must accept an inherent level of uncertainty in our results.
Advisors/Committee Members: Xu, Hongguo (advisor), Van Vleck, Erik (cmtemember), Huang, Weizhang (cmtemember).
Subjects/Keywords: Mathematics; Computer science; Physics; Algorithm; Grover; Quantum computer; Shor; Superposition
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APA (6th Edition):
Valle, C. (2011). Shor's Algorithm and Grover's Algorithm in Quantum Computing. (Masters Thesis). University of Kansas. Retrieved from http://hdl.handle.net/1808/7674
Chicago Manual of Style (16th Edition):
Valle, Chris. “Shor's Algorithm and Grover's Algorithm in Quantum Computing.” 2011. Masters Thesis, University of Kansas. Accessed February 28, 2021.
http://hdl.handle.net/1808/7674.
MLA Handbook (7th Edition):
Valle, Chris. “Shor's Algorithm and Grover's Algorithm in Quantum Computing.” 2011. Web. 28 Feb 2021.
Vancouver:
Valle C. Shor's Algorithm and Grover's Algorithm in Quantum Computing. [Internet] [Masters thesis]. University of Kansas; 2011. [cited 2021 Feb 28].
Available from: http://hdl.handle.net/1808/7674.
Council of Science Editors:
Valle C. Shor's Algorithm and Grover's Algorithm in Quantum Computing. [Masters Thesis]. University of Kansas; 2011. Available from: http://hdl.handle.net/1808/7674
University of Kansas
2.
Eifler, Douglas.
Evolutionary Dynamics of Protean Evasion.
Degree: MA, Mathematics, 2015, University of Kansas
URL: http://hdl.handle.net/1808/19534
► Pursuit and evasion are among the most widespread interactions in which animals engage. Effective evasion may be promoted by adopting various protean behaviors (erratic, unpredictable,…
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▼ Pursuit and evasion are among the most widespread interactions in which animals engage. Effective evasion may be promoted by adopting various protean behaviors (erratic, unpredictable, and confusing) that may serve to confuse pursuers and increase their reaction time. In this study, pursuers and evaders were modeled as particles moving at a constant speed, with strategy-dependent feedback control rules for direction. The effectiveness of three evasion strategies (pure evasion, random movement and zigzagging) was examined. Different versions of random movement and zigzagging were assessed, using simulations that determined capture time for each version when confronted by a pure pursuit pursuer. Monte Carlo simulations were used in a discrete-time evolutionary game to examine competition among evasion strategies when pitted against pure pursuit players of varying speed and maneuverability. The evolutionary dynamics converge to a pure strategy of zigzag evasion. Directions for future work on evasion are presented.
Advisors/Committee Members: Pasik-Duncan, Bozenna (advisor), Bayer, Margaret (cmtemember), Duncan, Tyrone (cmtemember), Van Vleck, Erik (cmtemember).
Subjects/Keywords: Mathematics; Ecology; Behavioral sciences; antipredator; evasion; game; pursuit; simulation; zigzag
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APA (6th Edition):
Eifler, D. (2015). Evolutionary Dynamics of Protean Evasion. (Masters Thesis). University of Kansas. Retrieved from http://hdl.handle.net/1808/19534
Chicago Manual of Style (16th Edition):
Eifler, Douglas. “Evolutionary Dynamics of Protean Evasion.” 2015. Masters Thesis, University of Kansas. Accessed February 28, 2021.
http://hdl.handle.net/1808/19534.
MLA Handbook (7th Edition):
Eifler, Douglas. “Evolutionary Dynamics of Protean Evasion.” 2015. Web. 28 Feb 2021.
Vancouver:
Eifler D. Evolutionary Dynamics of Protean Evasion. [Internet] [Masters thesis]. University of Kansas; 2015. [cited 2021 Feb 28].
Available from: http://hdl.handle.net/1808/19534.
Council of Science Editors:
Eifler D. Evolutionary Dynamics of Protean Evasion. [Masters Thesis]. University of Kansas; 2015. Available from: http://hdl.handle.net/1808/19534
3.
Dorn, Timothy.
Shearing Flows in Liquid Crystal Models.
Degree: PhD, Mathematics, 2012, University of Kansas
URL: http://hdl.handle.net/1808/10322
► The liquid crystal phase is a phase of matter between the solid and liquid phase whose flow is characterized by a velocity field and a…
(more)
▼ The liquid crystal phase is a phase of matter between the solid and liquid phase whose flow is characterized by a velocity field and a director field which describes locally the orientation of the liquid crystal. In this work we explore shearing flows in two related continuum models of liquid crystals. The first is a phenomenological model of frictional forces in a geological fault, which is motivated by the second model, the Leslie-Ericksen continuum theory of liquid crystals.
Advisors/Committee Members: Liu, Weishi (advisor), Oh, Myunghyun (cmtemember), Stanislavova, Milena (cmtemember), Van Vleck, Erik (cmtemember), Shi, JiCong (cmtemember).
Subjects/Keywords: Mathematics; Materials science
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APA (6th Edition):
Dorn, T. (2012). Shearing Flows in Liquid Crystal Models. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/10322
Chicago Manual of Style (16th Edition):
Dorn, Timothy. “Shearing Flows in Liquid Crystal Models.” 2012. Doctoral Dissertation, University of Kansas. Accessed February 28, 2021.
http://hdl.handle.net/1808/10322.
MLA Handbook (7th Edition):
Dorn, Timothy. “Shearing Flows in Liquid Crystal Models.” 2012. Web. 28 Feb 2021.
Vancouver:
Dorn T. Shearing Flows in Liquid Crystal Models. [Internet] [Doctoral dissertation]. University of Kansas; 2012. [cited 2021 Feb 28].
Available from: http://hdl.handle.net/1808/10322.
Council of Science Editors:
Dorn T. Shearing Flows in Liquid Crystal Models. [Doctoral Dissertation]. University of Kansas; 2012. Available from: http://hdl.handle.net/1808/10322
University of Kansas
4.
Kolasinski, Avary Justice.
Surface and bulk moving mesh methods based on equidistribution and alignment.
Degree: PhD, Mathematics, 2019, University of Kansas
URL: http://hdl.handle.net/1808/29886
► In this dissertation, we first present a new functional for variational mesh generation and adaptation that is formulated by combining the equidistribution and alignment conditions…
(more)
▼ In this dissertation, we first present a new functional for variational mesh generation and adaptation that is formulated by combining the equidistribution and alignment conditions into a single condition with only one dimensionless parameter. The functional is shown to be coercive which, when employed with the moving mesh partial differential equation method, allows various theoretical properties to be proved. Numerical examples for bulk meshes demonstrate that the new functional performs comparably to a similar existing functional that is known to work well but contains an additional parameter. Variational mesh adaptation for bulk meshes has been well developed however, surface moving mesh methods are limited. Here, we present a surface moving mesh method for general surfaces with or without explicit parameterization. The development starts with formulating the equidistribution and alignment conditions for surface meshes from which, we establish a meshing energy functional. The moving mesh equation is then defined as the gradient system of the energy functional, with the nodal mesh velocities being projected onto the underlying surface. The analytical expression for the mesh velocities is obtained in a compact, matrix form, which makes the implementation of the new method on a computer relatively easy and robust. Moreover, it is analytically shown that any mesh trajectory generated by the method remains nonsingular if it is so initially. It is emphasized that the method is developed directly on surface meshes, making no use of any information on surface parameterization. A selection of two-dimensional and three-dimensional examples are presented.
Advisors/Committee Members: Huang, Weizhang (advisor), Gavosto, Estela (cmtemember), Miedlar, Agnieszka (cmtemember), Shontz, Suzanne (cmtemember), Van Vleck, Erik (cmtemember).
Subjects/Keywords: Applied mathematics; Mathematics; Discretization; Mesh adaptation; Numerical analysis; Partial differential equations; Scientific computing; Surface moving mesh methods
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APA (6th Edition):
Kolasinski, A. J. (2019). Surface and bulk moving mesh methods based on equidistribution and alignment. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/29886
Chicago Manual of Style (16th Edition):
Kolasinski, Avary Justice. “Surface and bulk moving mesh methods based on equidistribution and alignment.” 2019. Doctoral Dissertation, University of Kansas. Accessed February 28, 2021.
http://hdl.handle.net/1808/29886.
MLA Handbook (7th Edition):
Kolasinski, Avary Justice. “Surface and bulk moving mesh methods based on equidistribution and alignment.” 2019. Web. 28 Feb 2021.
Vancouver:
Kolasinski AJ. Surface and bulk moving mesh methods based on equidistribution and alignment. [Internet] [Doctoral dissertation]. University of Kansas; 2019. [cited 2021 Feb 28].
Available from: http://hdl.handle.net/1808/29886.
Council of Science Editors:
Kolasinski AJ. Surface and bulk moving mesh methods based on equidistribution and alignment. [Doctoral Dissertation]. University of Kansas; 2019. Available from: http://hdl.handle.net/1808/29886
University of Kansas
5.
Li, Xianping.
Anisotropic Mesh Adaptation for the Finite Element Solution of Anisotropic Diffusion Problems.
Degree: PhD, Mathematics, 2011, University of Kansas
URL: http://hdl.handle.net/1808/9755
► Anisotropic diffusion problems arise in many fields of science and engineering and are modeled by partial differential equations (PDEs) or represented in variational formulations. Standard…
(more)
▼ Anisotropic diffusion problems arise in many fields of science and engineering and are modeled by partial differential equations (PDEs) or represented in variational formulations. Standard numerical schemes can produce spurious oscillations when they are used to solve those problems. A common approach is to design a proper numerical scheme or a proper mesh such that the numerical solution satisfies discrete maximum principle (DMP). For problems in variational formulations, numerous research has been done on isotropic mesh adaptation but little work has been done for anisotropic mesh adaptation. In this dissertation, anisotropic mesh adaptation for the finite element solution of anisotropic diffusion problems is investigated. A brief introduction for the related topics is provided. The anisotropic mesh adaptation based on DMP satisfaction is then discussed. An anisotropic non-obtuse angle condition is developed which guarantees that the linear finite element approximation of the steady state problem satisfies DMP. A metric tensor is derived for use in mesh generation based on the anisotropic non-obtuse angle condition. Then DMP satisfaction and error based mesh adaptation are combined together for the first time. For problems in variational formulations, two metric tensors for anisotropic mesh adaptation and one for isotropic mesh adaptation are developed. For anisotropic mesh adaptation, one metric tensor (based on Hessian recovery) is semi-a posterior and the other (based on hierarchical basis error estimator) is completely a posterior. The metric tensor for isotropic mesh adaptation is completely a posterior. All the metric tensors incorporate structural information of the underlying problem into their design and generate meshes that adapt to changes in the structure. The application of anisotropic diffusion filter in image processing is briefly discussed. Numerical examples demonstrate that anisotropic mesh adaptation can significantly improve computational efficiency while still providing good quality result. More research is needed to investigate DMP satisfaction for parabolic problems.
Advisors/Committee Members: Huang, Weizhang (advisor), Duncan, Tyrone E. (cmtemember), Han, Jie (cmtemember), Van Vleck, Erik (cmtemember), Xu, Hongguo (cmtemember).
Subjects/Keywords: Mathematics; Anisotropic diffusion; Anisotropic mesh adaptation; Discrete maximum principle; Finite element; Mesh adaptation; Variational problem
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APA (6th Edition):
Li, X. (2011). Anisotropic Mesh Adaptation for the Finite Element Solution of Anisotropic Diffusion Problems. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/9755
Chicago Manual of Style (16th Edition):
Li, Xianping. “Anisotropic Mesh Adaptation for the Finite Element Solution of Anisotropic Diffusion Problems.” 2011. Doctoral Dissertation, University of Kansas. Accessed February 28, 2021.
http://hdl.handle.net/1808/9755.
MLA Handbook (7th Edition):
Li, Xianping. “Anisotropic Mesh Adaptation for the Finite Element Solution of Anisotropic Diffusion Problems.” 2011. Web. 28 Feb 2021.
Vancouver:
Li X. Anisotropic Mesh Adaptation for the Finite Element Solution of Anisotropic Diffusion Problems. [Internet] [Doctoral dissertation]. University of Kansas; 2011. [cited 2021 Feb 28].
Available from: http://hdl.handle.net/1808/9755.
Council of Science Editors:
Li X. Anisotropic Mesh Adaptation for the Finite Element Solution of Anisotropic Diffusion Problems. [Doctoral Dissertation]. University of Kansas; 2011. Available from: http://hdl.handle.net/1808/9755
University of Kansas
6.
Yu, Yufei.
An Adaptive Moving Mesh Finite Element Method and Its Application to Mathematical Models from Physical Sciences and Image Processing.
Degree: PhD, Mathematics, 2019, University of Kansas
URL: http://hdl.handle.net/1808/30071
► Moving sharp fronts are an important feature of many mathematical models from physical sciences and cause challenges in numerical computation. In order to obtain accurate…
(more)
▼ Moving sharp fronts are an important feature of many mathematical models from physical sciences and cause challenges in numerical computation. In order to obtain accurate solutions, a high resolution of mesh is necessary, which results in high computational cost if a fixed mesh is used. As a solution to this issue, an adaptive mesh method, which is called the moving mesh partial differential equation (MMPDE) method, is described in this work. The MMPDE method has the advantage of adaptively relocating the mesh points to increase the densities around sharp layers of the solutions, without increasing the mesh size. Moreover, this strategy can generate a nonsingular mesh even on non-convex and non-simply connected domains, given that the initial mesh is nonsingular. The focus of this thesis is on the application of the MMPDE method to mathematical models from physical sciences and image segmentation. In particular, this thesis includes the selection of the regularization parameter for the Ambrosio-Tortorelli functional, a simulation of the contact sets in the evolution of the micro-electro mechanical systems, and a numerical study of the flux selectivity in the Poisson-Nernst-Planck model. Sharp interfaces take place in all these three models, bringing interesting features and rich phenomena to study.
Advisors/Committee Members: Huang, Weizhang (advisor), Huang, Weizhang (cmtemember), Keshmiri, Shawn (cmtemember), Liu, Weishi (cmtemember), Tu, Xuemin (cmtemember), Van Vleck, Erik (cmtemember).
Subjects/Keywords: Applied mathematics
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APA ·
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APA (6th Edition):
Yu, Y. (2019). An Adaptive Moving Mesh Finite Element Method and Its Application to Mathematical Models from Physical Sciences and Image Processing. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/30071
Chicago Manual of Style (16th Edition):
Yu, Yufei. “An Adaptive Moving Mesh Finite Element Method and Its Application to Mathematical Models from Physical Sciences and Image Processing.” 2019. Doctoral Dissertation, University of Kansas. Accessed February 28, 2021.
http://hdl.handle.net/1808/30071.
MLA Handbook (7th Edition):
Yu, Yufei. “An Adaptive Moving Mesh Finite Element Method and Its Application to Mathematical Models from Physical Sciences and Image Processing.” 2019. Web. 28 Feb 2021.
Vancouver:
Yu Y. An Adaptive Moving Mesh Finite Element Method and Its Application to Mathematical Models from Physical Sciences and Image Processing. [Internet] [Doctoral dissertation]. University of Kansas; 2019. [cited 2021 Feb 28].
Available from: http://hdl.handle.net/1808/30071.
Council of Science Editors:
Yu Y. An Adaptive Moving Mesh Finite Element Method and Its Application to Mathematical Models from Physical Sciences and Image Processing. [Doctoral Dissertation]. University of Kansas; 2019. Available from: http://hdl.handle.net/1808/30071
University of Kansas
7.
Brucal-Hallare, Maila.
Solutions of Lattice Differential Equations over Inhomogeneous Media.
Degree: PhD, Mathematics, 2012, University of Kansas
URL: http://hdl.handle.net/1808/18632
► This thesis investigates one-dimensional spatially-discrete reaction-diffusion equations with a diffusion term that involves nearest-neighbor coupling and with a reaction-term that is a smooth-cubic nonlinearity. Specifically,…
(more)
▼ This thesis investigates one-dimensional spatially-discrete reaction-diffusion equations with a diffusion term that involves nearest-neighbor coupling and with a reaction-term that is a smooth-cubic nonlinearity. Specifically, we consider two nontrivial examples of lattice differential equations (LDEs) on Z that are related to the (homogeneous) lattice Nagumo equation. The LDEs that we consider are used to model natural phenomena defined over an inhomogeneous medium, namely: (1) a lattice Nagumo equation with a negative diffusion coefficient. Such is still a well-posed problem in the LDE setting and has been shown to arise from a discrete model of phase transition for shape memory alloys. This thesis shows that the anti-diffusion lattice Nagumo equation has a period-2 traveling wavefront solution that is stable and unique. Utilizing the concrete expressions for the nonlinearities, we obtain criteria on the (d, a)-parameter plane that guarantee a display of bistable and monostable dynamics. Where there's bistable dynamics, we study the propagation failure phenomenon; where there's monostable dynamics, we compute a minimum wave speed for the traveling waves. (2) a lattice Nagumo equation that has a single diffusion-defect in the middle of Z, which may occur due to deviations in the diffusive property of the medium. This thesis shows that such an equation has a time-global solution which behaves as two fronts coming from the both sides of Z. A key idea for the existence proof is a characterization of the asymptotic behavior of the solutions for negative time in terms of an appropriate super-solution, sub-solution pair.
Advisors/Committee Members: Van Vleck, Erik S (advisor), Liu, Weishi (cmtemember), Stefanov, Atanas (cmtemember), Huang, Weizhang (cmtemember), Kieweg, Sarah (cmtemember).
Subjects/Keywords: Mathematics; inhomogeneous medium; lattice differential equations; Nagumo equations; negative diffusion
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APA (6th Edition):
Brucal-Hallare, M. (2012). Solutions of Lattice Differential Equations over Inhomogeneous Media. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/18632
Chicago Manual of Style (16th Edition):
Brucal-Hallare, Maila. “Solutions of Lattice Differential Equations over Inhomogeneous Media.” 2012. Doctoral Dissertation, University of Kansas. Accessed February 28, 2021.
http://hdl.handle.net/1808/18632.
MLA Handbook (7th Edition):
Brucal-Hallare, Maila. “Solutions of Lattice Differential Equations over Inhomogeneous Media.” 2012. Web. 28 Feb 2021.
Vancouver:
Brucal-Hallare M. Solutions of Lattice Differential Equations over Inhomogeneous Media. [Internet] [Doctoral dissertation]. University of Kansas; 2012. [cited 2021 Feb 28].
Available from: http://hdl.handle.net/1808/18632.
Council of Science Editors:
Brucal-Hallare M. Solutions of Lattice Differential Equations over Inhomogeneous Media. [Doctoral Dissertation]. University of Kansas; 2012. Available from: http://hdl.handle.net/1808/18632
University of Kansas
8.
Li, Xi.
Dynamics of A Degenerate Fokker-Planck Equation and Its Application.
Degree: PhD, Mathematics, 2015, University of Kansas
URL: http://hdl.handle.net/1808/21706
► In this project, a Fokker-Planck equation with two singular points is studied. The equation is derived from a stochastic evolution equation, LMM-SABR model, which is…
(more)
▼ In this project, a Fokker-Planck equation with two singular points is studied. The equation is derived from a stochastic evolution equation, LMM-SABR model, which is widely used in financial industry. It is difficult to directly study the original equation due to the singularity. As an alternative approach, we introduce appropriate modifications to certain terms of original Fokker-Planck equation at each singular point so that the modified equation has a stationary solution. With the stable stationary solution, the intermediate behavior of the modified Fokker-Planck equation can be captured and described to some extent. The non-modified solutions are compared to modified solutions within finite time and a relatively concrete estimation is given in terms of the modification parameter and the given finite time. We also study some possible modifications. For each modification, the properties of the stationary solution are given. Some numerical results of the time-evolution solutions for these modified equations are also included. As an attempt, we have initiated in this project the study of the difference between the modified and non-modified stochastic differential equations (SDEs). Although no complete analytical results are available, our initial work appears pointing in a promising direction, based on the numerical simulation results that we have observed. The further study of the SDEs will be carried out in the future work.
Advisors/Committee Members: Liu, Weishi (advisor), Liu, Weishi (cmtemember), Hu, Yaozhong (cmtemember), Stanislavova, Milena (cmtemember), Van Vleck, Erik (cmtemember), Zhang, Jianbo (cmtemember).
Subjects/Keywords: Mathematics; Applied mathematics; Degenerate; Dynamics; Fokker-Planck Equation; Stochastic Differential Equation
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APA ·
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APA (6th Edition):
Li, X. (2015). Dynamics of A Degenerate Fokker-Planck Equation and Its Application. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/21706
Chicago Manual of Style (16th Edition):
Li, Xi. “Dynamics of A Degenerate Fokker-Planck Equation and Its Application.” 2015. Doctoral Dissertation, University of Kansas. Accessed February 28, 2021.
http://hdl.handle.net/1808/21706.
MLA Handbook (7th Edition):
Li, Xi. “Dynamics of A Degenerate Fokker-Planck Equation and Its Application.” 2015. Web. 28 Feb 2021.
Vancouver:
Li X. Dynamics of A Degenerate Fokker-Planck Equation and Its Application. [Internet] [Doctoral dissertation]. University of Kansas; 2015. [cited 2021 Feb 28].
Available from: http://hdl.handle.net/1808/21706.
Council of Science Editors:
Li X. Dynamics of A Degenerate Fokker-Planck Equation and Its Application. [Doctoral Dissertation]. University of Kansas; 2015. Available from: http://hdl.handle.net/1808/21706
University of Kansas
9.
Hu, Bin.
EFFECTS OF SURFACE TENSION AND VISCOELASTIC BEHAVIOR ON THE THIN FILM COATING FLOW OF MICROBICIDE GELS.
Degree: PhD, Mechanical Engineering, 2016, University of Kansas
URL: http://hdl.handle.net/1808/22335
► Thin film coating flow is of importance in many fields, as well as for the design of polymeric drug delivery vehicles, such as anti-HIV topical…
(more)
▼ Thin film coating flow is of importance in many fields, as well as for the design of polymeric drug delivery vehicles, such as anti-HIV topical microbicides. This dissertation describes a few models to investigate the coating flow of a microbicidal gel. At the beginning of this dissertation, we studied the gravity-driven thin film flow model. In our 2D (i.e. 1D spreading) power-law model, we found that surface tension effect not only impacted the spreading speed of the microbicide gel, but also had an influence on the shape of the 2D spreading profile. We observed a capillary ridge at the front of the fluid bolus. We focused on the capillary ridge in 2D flow and performed a series of simulations and showed how the capillary ridge height varies with other parameters. As shown in our results, we found that capillary ridge height increased with higher surface tension, steeper inclination angle, larger initial thickness, and more Newtonian fluids. In the second study, a model of fingering instability at a moving contact line was developed. Previous literature showed that the emergence of a capillary ridge is strongly related to the contact line fingering instability in Newtonian fluids. Fingering instabilities during epithelial coating may change the microbicide gel distribution and therefore impact how well it can protect the epithelium. Results from our 2D model indicated more shear-thinning fluids should have suppressed finger growth and longer finger wavelength, and this should be evident in linear stability analysis (LSA) and 3D (i.e. 2D spreading) numerical simulations. In our 3D model studies, we developed a LSA model for the gravity-driven flow of shear-thinning films, and carried out a parametric study to investigate the impact of shear-thinning on the growth rate of the emerging fingering pattern. A fully 3D model was also developed to compare and verify the LSA results using single perturbations, and to explore the result of multiple-mode, randomly imposed perturbations. Both the LSA and 3D numerical results confirmed that the contact line fingers grow faster for Newtonian fluids than the shear-thinning fluids on both vertical and inclined planes. In addition, both the LSA and 3D model indicated that the Newtonian fluids form fingers with shorter wavelengths than the shear-thinning fluids when the plane is inclined; no difference in the most unstable (i.e. emerging) wavelength was observed at vertical. For the first time for shear-thinning fluids, these results connect trends in capillary ridge and contact line finger formation in 2D models, LSA, and 3D simulations. At the end of this dissertation, we used a more complicated constitutive model – the Phan-Thien-Tanner (PTT) rheological model – to describe the viscoelastic behavior on two different models for the vehicle delivery process: the gravity-driven spreading model, and epithelial squeezing flow model. We used ANSYS POLYFLOW software package to solve the resulting PDEs. Elastic viscous split stress (EVSS) approach was used to split the stress tensor of…
Advisors/Committee Members: Kieweg, Sarah L (advisor), Dougherty, Ronald L (cmtemember), Luchies, Carl W (cmtemember), Van Vleck, Erik (cmtemember), Wilson, Sara E (cmtemember).
Subjects/Keywords: Mechanical engineering; Biomechanics; Biomedical engineering; Microbicide gels; Non-Newtonian fluids; Numerical analysis; Surface tension; Thin film flow; Viscoelastic behavior
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APA (6th Edition):
Hu, B. (2016). EFFECTS OF SURFACE TENSION AND VISCOELASTIC BEHAVIOR ON THE THIN FILM COATING FLOW OF MICROBICIDE GELS. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/22335
Chicago Manual of Style (16th Edition):
Hu, Bin. “EFFECTS OF SURFACE TENSION AND VISCOELASTIC BEHAVIOR ON THE THIN FILM COATING FLOW OF MICROBICIDE GELS.” 2016. Doctoral Dissertation, University of Kansas. Accessed February 28, 2021.
http://hdl.handle.net/1808/22335.
MLA Handbook (7th Edition):
Hu, Bin. “EFFECTS OF SURFACE TENSION AND VISCOELASTIC BEHAVIOR ON THE THIN FILM COATING FLOW OF MICROBICIDE GELS.” 2016. Web. 28 Feb 2021.
Vancouver:
Hu B. EFFECTS OF SURFACE TENSION AND VISCOELASTIC BEHAVIOR ON THE THIN FILM COATING FLOW OF MICROBICIDE GELS. [Internet] [Doctoral dissertation]. University of Kansas; 2016. [cited 2021 Feb 28].
Available from: http://hdl.handle.net/1808/22335.
Council of Science Editors:
Hu B. EFFECTS OF SURFACE TENSION AND VISCOELASTIC BEHAVIOR ON THE THIN FILM COATING FLOW OF MICROBICIDE GELS. [Doctoral Dissertation]. University of Kansas; 2016. Available from: http://hdl.handle.net/1808/22335
University of Kansas
10.
Pacey, Mark D.
The Development and Characterization of a Novel Instrument for Measuring Vaginal Closing Force: EVE the Elevated-Surface Vaginal Elastometer.
Degree: D.Eng., Mechanical Engineering, 2016, University of Kansas
URL: http://hdl.handle.net/1808/25356
► In 2012 there were an estimated 35.3 million people living with HIV [1]. Microbicides address an important gap in HIV prevention for vulnerable groups unable…
(more)
▼ In 2012 there were an estimated 35.3 million people living with HIV [1]. Microbicides address an important gap in HIV prevention for vulnerable groups unable to implement other prevention strategies [2]. Models are being developed in our lab to optimize microbicide delivery vehicle properties so that the microbicide will coat the entire vaginal epithelial surface, stay in place for the duration of possible exposure, and coat thick enough to deliver sufficient active ingredient to prevent infection. A complete model should incorporate vaginal closing force to understand how a delivery vehicle will be distributed and retained in the vagina. However, the physiological magnitudes of vaginal closing forces are not known. Several previous methods have been utilized to determine an appropriate magnitude of one or several components, but they all neglect important features to measure the forces relevant to microbicide delivery vehicle spreading. An ideal measurement device to measure all aspects of vaginal closing force should: be controllable, operate in a variety of modes, have a constant contact area, be able to measure at different places along the vaginal axis and in different directions, be modular, be convenient and easy to operate in a clinical environment, and be safe to operate. This dissertation describes the design and testing of a new instrument to measure vaginal closing force, its calibration process, and the software to control it. Throughout this document the identified obstacles and the strategies used to mitigate them are discussed. Validation testing was performed on tissue phantoms and by bench testing using the calibration instrument. Validation testing shows that the instrument has the ability to differentiate between phantoms. Future testing on more tissue phantoms will allow further quantification of the instrument and a better determination of the precision of the measurements. Two alternate approaches have also been developed for the possible refinement of the EVE instrument. Utilizing force sensing within the probe body would violate the initial design constraints, but might be a relatively simple way to address the issues which have disrupted the instrument’s development. Alternatively a new probe which completely eliminates the hydraulic system in favor of mechanical linkages, although more drastic of a change, might allow for data generation without compromising the initial design requirements. The EVE instrument is a successful step forward in properly measuring vaginal tissue closing force. Many of the initial design challenges have been overcome, and a majority of the programming necessary has been completed. Measurements of phantom tissue elasticity are now possible. EVE is nearly ready for in vivo testing.
Advisors/Committee Members: Kieweg, Sarah L (advisor), Dougherty, Ronald L (cmtemember), Fischer, Kenneth J (cmtemember), Van Vleck, Erik S (cmtemember), Wilson, Sara E (cmtemember).
Subjects/Keywords: Engineering; Biomedical engineering; Mechanical engineering; Instrument; Microbicide; Tissue; Vaginal
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APA (6th Edition):
Pacey, M. D. (2016). The Development and Characterization of a Novel Instrument for Measuring Vaginal Closing Force: EVE the Elevated-Surface Vaginal Elastometer. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/25356
Chicago Manual of Style (16th Edition):
Pacey, Mark D. “The Development and Characterization of a Novel Instrument for Measuring Vaginal Closing Force: EVE the Elevated-Surface Vaginal Elastometer.” 2016. Doctoral Dissertation, University of Kansas. Accessed February 28, 2021.
http://hdl.handle.net/1808/25356.
MLA Handbook (7th Edition):
Pacey, Mark D. “The Development and Characterization of a Novel Instrument for Measuring Vaginal Closing Force: EVE the Elevated-Surface Vaginal Elastometer.” 2016. Web. 28 Feb 2021.
Vancouver:
Pacey MD. The Development and Characterization of a Novel Instrument for Measuring Vaginal Closing Force: EVE the Elevated-Surface Vaginal Elastometer. [Internet] [Doctoral dissertation]. University of Kansas; 2016. [cited 2021 Feb 28].
Available from: http://hdl.handle.net/1808/25356.
Council of Science Editors:
Pacey MD. The Development and Characterization of a Novel Instrument for Measuring Vaginal Closing Force: EVE the Elevated-Surface Vaginal Elastometer. [Doctoral Dissertation]. University of Kansas; 2016. Available from: http://hdl.handle.net/1808/25356
University of Kansas
11.
Steyer, Andrew Jacob.
A Lyapunov exponent based stability theory for ordinary differential equation initial value problem solvers.
Degree: PhD, Mathematics, 2016, University of Kansas
URL: http://hdl.handle.net/1808/24193
► In this dissertation we consider the stability of numerical methods approximating the solution of bounded, stable, and time-dependent solutions of ordinary differential equation initial value…
(more)
▼ In this dissertation we consider the stability of numerical methods approximating the solution of bounded, stable, and time-dependent solutions of ordinary differential equation initial value problems. We use Lyapunov exponent theory to determine conditions on the maximum allowable step-size that guarantees that a one-step method produces a decaying numerical solution to an asymptotically contracting, time-dependent, linear problem. This result is used to justify using a one-dimensional asymptotically contracting real-valued nonautonomous linear test problem to characterize the stability of a one-step method. The linear stability result is applied to prove a stability result for the numerical solution of a class of stable nonlinear problems. We use invariant manifold theory to show that we can obtain similar stability results for strictly stable linear multistep methods approximating asymptotically contracting, time-dependent, linear problems by relating their stability to the stability of an underlying one-step method. The stability theory for one-step methods is used to devise a procedure for stabilizing a solver that fails to produce a decaying solution to a linear problem when selecting step-size using standard error control techniques. Additionally, we develop an algorithm that selects step-size for the numerical solution of a decaying nonautonomous scalar test problem based on accuracy and the stability theory we developed.
Advisors/Committee Members: Van Vleck, Erik S (advisor), Huang, Weizhang (cmtemember), Liu, Weishi (cmtemember), Xu, Hongguo (cmtemember), Mechem, David (cmtemember).
Subjects/Keywords: Mathematics; differential equations; Lyapunov exponent; numerical analysis; ODE; Runge-Kutta
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APA (6th Edition):
Steyer, A. J. (2016). A Lyapunov exponent based stability theory for ordinary differential equation initial value problem solvers. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/24193
Chicago Manual of Style (16th Edition):
Steyer, Andrew Jacob. “A Lyapunov exponent based stability theory for ordinary differential equation initial value problem solvers.” 2016. Doctoral Dissertation, University of Kansas. Accessed February 28, 2021.
http://hdl.handle.net/1808/24193.
MLA Handbook (7th Edition):
Steyer, Andrew Jacob. “A Lyapunov exponent based stability theory for ordinary differential equation initial value problem solvers.” 2016. Web. 28 Feb 2021.
Vancouver:
Steyer AJ. A Lyapunov exponent based stability theory for ordinary differential equation initial value problem solvers. [Internet] [Doctoral dissertation]. University of Kansas; 2016. [cited 2021 Feb 28].
Available from: http://hdl.handle.net/1808/24193.
Council of Science Editors:
Steyer AJ. A Lyapunov exponent based stability theory for ordinary differential equation initial value problem solvers. [Doctoral Dissertation]. University of Kansas; 2016. Available from: http://hdl.handle.net/1808/24193
12.
Oderio, Nicholas.
A Comparison of Some Dimension Reduction Techniques with Varied Parameters.
Degree: MA, Mathematics, 2017, University of Kansas
URL: http://hdl.handle.net/1808/26902
► This paper presents and explains several methods of dimensionality reduction of data sets, beginning with the well known PCA and moving onto techniques that deal…
(more)
▼ This paper presents and explains several methods of dimensionality reduction of data sets, beginning with the well known PCA and moving onto techniques that deal with data on a nonlinear manifold. Methods for handling data whose underlying structure is a nonlinear manifold are separated by whether or not sparse matrices are involved in the computation. Additionally, the methods discussed are demonstrated and compared by running them on data sets whose underlying structure is known. Results from same methods with different values for input parameters are also examined. Finally, some results on a small set of Persyst EEG data collected as a part of the Epilepsy Bioinformatics Study for Antiepileptogenic Therapy from the Laboratory of Neuro Imaging at USC Stevens Institute of Neuroimaging and Informatics in the Keck School of Medicine of USC is analyzed using some of these methods.
Advisors/Committee Members: Pasik-Duncan, Bozenna (advisor), Duncan, Tyrone (cmtemember), Van Vleck, Erik (cmtemember).
Subjects/Keywords: Applied mathematics; Mathematics; application; Dimensionality reduction; principal component analysis
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APA (6th Edition):
Oderio, N. (2017). A Comparison of Some Dimension Reduction Techniques with Varied Parameters. (Masters Thesis). University of Kansas. Retrieved from http://hdl.handle.net/1808/26902
Chicago Manual of Style (16th Edition):
Oderio, Nicholas. “A Comparison of Some Dimension Reduction Techniques with Varied Parameters.” 2017. Masters Thesis, University of Kansas. Accessed February 28, 2021.
http://hdl.handle.net/1808/26902.
MLA Handbook (7th Edition):
Oderio, Nicholas. “A Comparison of Some Dimension Reduction Techniques with Varied Parameters.” 2017. Web. 28 Feb 2021.
Vancouver:
Oderio N. A Comparison of Some Dimension Reduction Techniques with Varied Parameters. [Internet] [Masters thesis]. University of Kansas; 2017. [cited 2021 Feb 28].
Available from: http://hdl.handle.net/1808/26902.
Council of Science Editors:
Oderio N. A Comparison of Some Dimension Reduction Techniques with Varied Parameters. [Masters Thesis]. University of Kansas; 2017. Available from: http://hdl.handle.net/1808/26902
13.
Demirkaya, Aslihan.
Long time behavior and stability of special solutions of nonlinear partial differential equations.
Degree: PhD, Mathematics, 2011, University of Kansas
URL: http://hdl.handle.net/1808/7695
► In this dissertation, in the first part, I study the long-time behavior of the solutions of the Kuramoto-Sivashinsky equation and the Burgers-Sivashinsky equation. First, I…
(more)
▼ In this dissertation, in the first part, I study the long-time behavior of the solutions of the Kuramoto-Sivashinsky equation and the Burgers-Sivashinsky equation. First, I work on a two-dimensional modified KS equation and prove the existence of a global attractor on a bounded domain. Next, I study the long-time behavior of the solutions of the one-dimensional BS equation for general initial data as opposed to the usually considered odd initial data. Third, I study the long-time behavior of radially symmetric solutions of the KS equation in a shell domain in three-dimensions. In the second part, we deal with the conditional stability of radial steady state solutions for the one-dimensional Klein-Gordon equation. I consider the one-dimensional case and construct the infinite-dimensional invariant manifolds explicitly. The result is a precise center-stable manifold theorem, which includes the co-dimension of the manifolds and the decay rates.
Advisors/Committee Members: Stanislavova, Milena (advisor), Stefanov, Atanas (cmtemember), Van Vleck, Erik (cmtemember), Liu, Weishi (cmtemember), Sabarwal, Tarun (cmtemember).
Subjects/Keywords: Mathematics; Applied mathematics; Klein-gordon equation; Kuramoto-sivashinsky equation; Long-time behavior; Partial differential equations; Special solutions; Stability
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APA (6th Edition):
Demirkaya, A. (2011). Long time behavior and stability of special solutions of nonlinear partial differential equations. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/7695
Chicago Manual of Style (16th Edition):
Demirkaya, Aslihan. “Long time behavior and stability of special solutions of nonlinear partial differential equations.” 2011. Doctoral Dissertation, University of Kansas. Accessed February 28, 2021.
http://hdl.handle.net/1808/7695.
MLA Handbook (7th Edition):
Demirkaya, Aslihan. “Long time behavior and stability of special solutions of nonlinear partial differential equations.” 2011. Web. 28 Feb 2021.
Vancouver:
Demirkaya A. Long time behavior and stability of special solutions of nonlinear partial differential equations. [Internet] [Doctoral dissertation]. University of Kansas; 2011. [cited 2021 Feb 28].
Available from: http://hdl.handle.net/1808/7695.
Council of Science Editors:
Demirkaya A. Long time behavior and stability of special solutions of nonlinear partial differential equations. [Doctoral Dissertation]. University of Kansas; 2011. Available from: http://hdl.handle.net/1808/7695
14.
Ngo, Cuong.
Moving mesh methods for numerical solution of porous medium equations.
Degree: PhD, Mathematics, 2017, University of Kansas
URL: http://hdl.handle.net/1808/26343
► Porous medium equation (PME) has been found in many applications of the physical sciences. The equation is nonlinear, degenerate, and in many situations has a…
(more)
▼ Porous medium equation (PME) has been found in many applications of the physical sciences. The equation is nonlinear, degenerate, and in many situations has a free boundary, which altogether pose great challenges for mathematical and numerical analyses. In contrast with the mathematical development of PME, which began in the 1950s and has since had much success, studies of numerical solution did not appear until the 1980s. Though a significant progress has been made since then for the 1D setting, only limited success has been observed for 2D cases. In this dissertation, we will propose several moving mesh methods which improve the accuracy and convergence order of the PME numerical solution.
Advisors/Committee Members: Huang, Weizhang (advisor), Van Vleck, Erik (cmtemember), Tu, Xuemin (cmtemember), Xu, Hongguo (cmtemember), Zheng, Charlie (cmtemember).
Subjects/Keywords: Mathematics; Adaptive moving mesh method; Finite element method; Free boundary; Hessian-based adaptivity; MMPDE method; Porous medium equation
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APA (6th Edition):
Ngo, C. (2017). Moving mesh methods for numerical solution of porous medium equations. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/26343
Chicago Manual of Style (16th Edition):
Ngo, Cuong. “Moving mesh methods for numerical solution of porous medium equations.” 2017. Doctoral Dissertation, University of Kansas. Accessed February 28, 2021.
http://hdl.handle.net/1808/26343.
MLA Handbook (7th Edition):
Ngo, Cuong. “Moving mesh methods for numerical solution of porous medium equations.” 2017. Web. 28 Feb 2021.
Vancouver:
Ngo C. Moving mesh methods for numerical solution of porous medium equations. [Internet] [Doctoral dissertation]. University of Kansas; 2017. [cited 2021 Feb 28].
Available from: http://hdl.handle.net/1808/26343.
Council of Science Editors:
Ngo C. Moving mesh methods for numerical solution of porous medium equations. [Doctoral Dissertation]. University of Kansas; 2017. Available from: http://hdl.handle.net/1808/26343
15.
Austin, Evan Christopher.
Theorem Provers as Libraries – An Approach to Formally Verifying Functional Programs.
Degree: PhD, Electrical Engineering & Computer Science, 2015, University of Kansas
URL: http://hdl.handle.net/1808/19419
► Property-directed verification of functional programs tends to take one of two paths. First, is the traditional testing approach, where properties are expressed in the original…
(more)
▼ Property-directed verification of functional programs tends to take one of two paths. First, is the traditional testing approach, where properties are expressed in the original programming language and checked with a collection of test data. Alternatively, for those desiring a more rigorous approach, properties can be written and checked with a formal tool; typically, an external proof system. This dissertation details a hybrid approach that captures the best of both worlds: the formality of a proof system paired with the native integration of an embedded, domain specific language (EDSL) for testing. At the heart of this hybridization is the titular concept – a theorem prover as a library. The verification capabilities of this prover, HaskHOL, are introduced to a Haskell development environment as a GHC compiler plugin. Operating at the compiler level provides for a comparatively simpler integration and allows verification to co-exist with the numerous other passes that stand between source code and program.
Advisors/Committee Members: Alexander, Perry (advisor), Gill, Andy (cmtemember), Kulkarni, Prasad (cmtemember), Agah, Arvin (cmtemember), Van Vleck, Erik (cmtemember).
Subjects/Keywords: Computer science; Formal Methods; Functional Programming; Haskell; HaskHOL; Higher-Order Logic; Theorem Proving
…University of Kansas. By the time I joined the research group, a fairly robust
tool suite had…
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APA (6th Edition):
Austin, E. C. (2015). Theorem Provers as Libraries – An Approach to Formally Verifying Functional Programs. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/19419
Chicago Manual of Style (16th Edition):
Austin, Evan Christopher. “Theorem Provers as Libraries – An Approach to Formally Verifying Functional Programs.” 2015. Doctoral Dissertation, University of Kansas. Accessed February 28, 2021.
http://hdl.handle.net/1808/19419.
MLA Handbook (7th Edition):
Austin, Evan Christopher. “Theorem Provers as Libraries – An Approach to Formally Verifying Functional Programs.” 2015. Web. 28 Feb 2021.
Vancouver:
Austin EC. Theorem Provers as Libraries – An Approach to Formally Verifying Functional Programs. [Internet] [Doctoral dissertation]. University of Kansas; 2015. [cited 2021 Feb 28].
Available from: http://hdl.handle.net/1808/19419.
Council of Science Editors:
Austin EC. Theorem Provers as Libraries – An Approach to Formally Verifying Functional Programs. [Doctoral Dissertation]. University of Kansas; 2015. Available from: http://hdl.handle.net/1808/19419
16.
Wang, Bin.
Balancing domain decomposition by constraints algorithms for incompressible Stokes equations with nonconforming finite element discretizations.
Degree: PhD, Mathematics, 2017, University of Kansas
URL: http://hdl.handle.net/1808/27005
► Hybridizable Discontinuous Galerkin (HDG) is an important family of methods, which combine the advantages of both Discontinuous Galerkin in terms of flexibility and standard finite…
(more)
▼ Hybridizable Discontinuous Galerkin (HDG) is an important family of methods, which combine the advantages of both Discontinuous Galerkin in terms of flexibility and standard finite elements in terms of accuracy and efficiency. The impact of this method is partly evidenced by the prolificacy of research work in this area. Weak Galerkin (WG) is a relatively newly proposed method by introducing weak functions and generalizing the differential operator for them. This method has also drawn remarkable interests from both numerical practitioners and analysts recently. HDG and WG are different but closely related. BDDC algorithms are developed for numerical solution of elliptic problems with both methods. We prove that the optimal condition number estimate for BDDC operators with standard finite element methods can be extended to the counterparts arising from the HDG and WG methods, which are nonconforming finite element methods. Numerical experiments are conducted to verify the theoretical analysis. Further, we propose BDDC algorithms for the saddle point system arising from the Stokes equations using both HDG and WG methods. By design of the preconditioner, the iterations are restricted to a benign subspace, which makes the BDDC operator effectively positive definite thus solvable by the conjugate gradient method. We prove that the algorithm is scalable in the number of subdomains with convergence rate only dependent on subdomain problem size. The condition number bound for the BDDC preconditioned Stokes system is the same as the optimal bound for the elliptic case. Numerical results confirm the theoretical analysis.
Advisors/Committee Members: Tu, Xuemin (advisor), Huang, Weizhang (cmtemember), Van Vleck, Erik (cmtemember), Xu, Hongguo (cmtemember), Wang, Z.J. (cmtemember).
Subjects/Keywords: Mathematics; BDDC; domain decomposition; hybridizable discontinuous Galerkin; saddle point problems; Stokes; weak Galerkin
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APA (6th Edition):
Wang, B. (2017). Balancing domain decomposition by constraints algorithms for incompressible Stokes equations with nonconforming finite element discretizations. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/27005
Chicago Manual of Style (16th Edition):
Wang, Bin. “Balancing domain decomposition by constraints algorithms for incompressible Stokes equations with nonconforming finite element discretizations.” 2017. Doctoral Dissertation, University of Kansas. Accessed February 28, 2021.
http://hdl.handle.net/1808/27005.
MLA Handbook (7th Edition):
Wang, Bin. “Balancing domain decomposition by constraints algorithms for incompressible Stokes equations with nonconforming finite element discretizations.” 2017. Web. 28 Feb 2021.
Vancouver:
Wang B. Balancing domain decomposition by constraints algorithms for incompressible Stokes equations with nonconforming finite element discretizations. [Internet] [Doctoral dissertation]. University of Kansas; 2017. [cited 2021 Feb 28].
Available from: http://hdl.handle.net/1808/27005.
Council of Science Editors:
Wang B. Balancing domain decomposition by constraints algorithms for incompressible Stokes equations with nonconforming finite element discretizations. [Doctoral Dissertation]. University of Kansas; 2017. Available from: http://hdl.handle.net/1808/27005
17.
Gu, Peidi.
Finding Eigenvalues of Unitary Matrices.
Degree: MA, Mathematics, 2013, University of Kansas
URL: http://hdl.handle.net/1808/12977
► The study introduces methods of finding eigenvalues for unitary matrices and pencils. Bunse-Gerstner and Elsner ([2]) proposed an algorithm of using the Schur parameter pencil…
(more)
▼ The study introduces methods of finding eigenvalues for unitary matrices and pencils. Bunse-Gerstner and Elsner ([2]) proposed an algorithm of using the Schur parameter pencil to solve eigenproblems for unitary matrices and pencils. This thesis reviews the Schur parameter pencil algorithm. The method is divided into two phases: Reducing a unitary pencil to a Schur parameter form and QR-type shifted iteration. The algorithm is proved to be backward stable and more efficient than the standard QR/QZ algorithm. However, during the process of reduction, norms of vectors are frequently compared for numerical stability, which causes a lot of extra work for computations. Based on the idea in [8], we introduce a modified Schur parameter algorithm to avoid such frequent comparison. The modified algorithm is still divided into two phases similar to the one in [2]. A detailed reduction process and shifted iteration are described in this thesis.
Advisors/Committee Members: Xu, Hongguo (advisor), Xu, Hongguo (cmtemember), Tu, Xuemin (cmtemember), Van Vleck, Erik (cmtemember).
Subjects/Keywords: Mathematics; Eigenvalue; Givens matrix; Householder reflector; Iteration; Schur parameter form; Unitary matrix
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APA (6th Edition):
Gu, P. (2013). Finding Eigenvalues of Unitary Matrices. (Masters Thesis). University of Kansas. Retrieved from http://hdl.handle.net/1808/12977
Chicago Manual of Style (16th Edition):
Gu, Peidi. “Finding Eigenvalues of Unitary Matrices.” 2013. Masters Thesis, University of Kansas. Accessed February 28, 2021.
http://hdl.handle.net/1808/12977.
MLA Handbook (7th Edition):
Gu, Peidi. “Finding Eigenvalues of Unitary Matrices.” 2013. Web. 28 Feb 2021.
Vancouver:
Gu P. Finding Eigenvalues of Unitary Matrices. [Internet] [Masters thesis]. University of Kansas; 2013. [cited 2021 Feb 28].
Available from: http://hdl.handle.net/1808/12977.
Council of Science Editors:
Gu P. Finding Eigenvalues of Unitary Matrices. [Masters Thesis]. University of Kansas; 2013. Available from: http://hdl.handle.net/1808/12977
18.
Zhang, Mingji.
Dynamics of Poisson-Nernst-Planck systems and applications to ionic channels.
Degree: PhD, Mathematics, 2013, University of Kansas
URL: http://hdl.handle.net/1808/12250
► Dynamics of Poisson-Nernst-Planck systems and its applications to ion channels are studied in this dissertation. The Poisson-Nernst-Planck systems serve as basic electro-diffusion equations modeling, for…
(more)
▼ Dynamics of Poisson-Nernst-Planck systems and its applications to ion channels are studied in this dissertation. The Poisson-Nernst-Planck systems serve as basic electro-diffusion equations modeling, for example, ion flow through membrane channels and transport of holes and electrons in semiconductors. The model can be derived from the more fundamental models of the Langevin-Poisson system and the Maxwell-Boltzmann equations, and from the energy variational analysis EnVarA. A brief description of the model is given in Chapter 2 including the physical meaning of each equation involved. Ion channels are cylindrical, hollow proteins that regulate the movement of ions ( mainly Na+, K+, Ca++ and Cl-;) through nearly all the membrane channels. When an initial potential is applied at one end of the channel, it will drive the ions through the channel, and the movement of these ions will produce the current which can be measured. Different initial potentials will result in different currents, and the collection of all those data will provide a relation, the so-called I-V (current-voltage) relation, which is an important characterization of two most relevant properties of a channel: permeation and selectivity. In Chapter 3, a classical Poisson-Nernst-Planck system is studied both analytically and numerically to investigate the cubic-like feature of the I-V relation. For the case of zero permanent charge, under electroneutrality boundary conditions at both ends of the channel, our result concerning the I-V relation for two oppositely charged ion speciesis that the third order correction is cubic in the potential V , and furthermore, up to the third order, the cubic I-V relation has three distinct real roots (except for a very degenerate case) which corresponds to the bi-stable structure in the FitzHugh-Nagumo simplification of the Hodgkin-Huxley model. Numerical simulations are performed and and they are consistent with our analytical results. In Chapter 4, we consider a one-dimensional steady-state Poisson-Nernst-Planck type model for ionic flow through membrane channels including ionic interaction modeled by a nonlocal hard-sphere potential from the Density Functional Theory. The resulting problem is a singularly perturbed boundary value problem of an integro-differential system. Ion size effect on the I-V relations is investigated numerically. Two numerical tasks are conducted. The first one is a numerical approach of solving the boundary value problem and obtaining I-V curves. This is accomplished through a numerical implement of the analytical strategy introduced in [46]. The second task is to numerically detect two critical potential values Vc and Vc. Our numerical detections are based on the defining properties of Vc and V c and are designed to use the numerical I-V curves directly. For the setting in the above mentioned reference, our numerical results agree well with the analytical predictions. In Chapter 5, a one-dimensional steady-state Poisson-Nernst-Planck type model for ionic flow through a membrane channel is…
Advisors/Committee Members: Liu, Weishi (advisor), Liu, Weishi (cmtemember), Stanislavova, Milena (cmtemember), Tu, Xuemin (cmtemember), Van Vleck, Erik (cmtemember), Shi, Jack (cmtemember).
Subjects/Keywords: Mathematics; Biochemistry
…China), Dr. Xuemin Tu ( from University
of Kansas), Dr. Yingfei Yi (from…
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APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
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APA (6th Edition):
Zhang, M. (2013). Dynamics of Poisson-Nernst-Planck systems and applications to ionic channels. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/12250
Chicago Manual of Style (16th Edition):
Zhang, Mingji. “Dynamics of Poisson-Nernst-Planck systems and applications to ionic channels.” 2013. Doctoral Dissertation, University of Kansas. Accessed February 28, 2021.
http://hdl.handle.net/1808/12250.
MLA Handbook (7th Edition):
Zhang, Mingji. “Dynamics of Poisson-Nernst-Planck systems and applications to ionic channels.” 2013. Web. 28 Feb 2021.
Vancouver:
Zhang M. Dynamics of Poisson-Nernst-Planck systems and applications to ionic channels. [Internet] [Doctoral dissertation]. University of Kansas; 2013. [cited 2021 Feb 28].
Available from: http://hdl.handle.net/1808/12250.
Council of Science Editors:
Zhang M. Dynamics of Poisson-Nernst-Planck systems and applications to ionic channels. [Doctoral Dissertation]. University of Kansas; 2013. Available from: http://hdl.handle.net/1808/12250
19.
Mannen, Erin Mychael.
Advancing Thoracic Spine Biomechanical Research.
Degree: PhD, Mechanical Engineering, 2014, University of Kansas
URL: http://hdl.handle.net/1808/18375
► The long term objective of this research was to elucidate issues with current thoracic spine testing methods and develop more accurate ways to quantify the…
(more)
▼ The long term objective of this research was to elucidate issues with current thoracic spine testing methods and develop more accurate ways to quantify the biomechanical impact of surgical procedures or medical devices. The ability to perform thoracic spine testing with a rib cage is limited by test machine variability and experimental design inconsistency, so surgeons are left with little reliable information on the biomechanical impacts of procedures and implants. This research sought to validate a novel spine test machine, provide biomechanical data to support the inclusion of an intact rib cage when testing the thoracic spine, and quantify the biomechanical impacts of sequential Ponte osteotomies. Specific Aim 1 validated the accuracy of the spine test machine for rigidity ranges that represent cadaveric specimen rigidities present in the spine. Cervical, thoracic, and lumbar spine specimens were modeled with synthetic rubber that represented the breadth of rigidities, and testing was conducted in bending and axial rotation. The maximum machine displacement error was less than 2° for lumbar and thoracic specimens, so it is suggested that researchers use an external motion-tracking system in conjunction with the test machine when high accuracy measurements are required. Specific Aim 2 quantified the biomechanical differences of testing full cadaveric thoracic spine specimens with and without an intact rib cage. While it was presumed that the rib cage provides structural stability to the thoracic spine, the extent to which the rib cage contributes to spinal motion had not been fully quantified. Testing quantified the motion and stiffness values of an intact thoracic spine specimen, and results showed that testing without a rib cage changes both motion and stiffness values. Specific Aim 3 quantified the biomechanical impact of sequential Ponte osteotomies in cadaveric thoracic spine specimens with intact rib cages. Overall and regional changes in motion due to Ponte osteotomies were analyzed, and results showed increased flexibility in the sagittal plane on both overall and regional levels. The results from this work could provide researchers and surgeons the tools they need to better understand and improve spine procedures and implants, which could ultimately improve the quality of life for patients.
Advisors/Committee Members: Friis, Elizabeth (advisor), Wilson, Sara (cmtemember), Luchies, Carl (cmtemember), Dougherty, Ronald (cmtemember), Van Vleck, Erik (cmtemember), Arnold, Paul (cmtemember).
Subjects/Keywords: Mechanical engineering; Biomechanics; Mechanics; Motion; Ponte Osteotomy; Rib Cage; Spine; Thoracic
…University of Kansas
L1-L5
lumbar spine levels 1 through 5
LB
lateral bending
MoB
mode of… …University of Kansas (KU) alumnus, Norm Carroll. This company provides
commercial test…
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APA (6th Edition):
Mannen, E. M. (2014). Advancing Thoracic Spine Biomechanical Research. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/18375
Chicago Manual of Style (16th Edition):
Mannen, Erin Mychael. “Advancing Thoracic Spine Biomechanical Research.” 2014. Doctoral Dissertation, University of Kansas. Accessed February 28, 2021.
http://hdl.handle.net/1808/18375.
MLA Handbook (7th Edition):
Mannen, Erin Mychael. “Advancing Thoracic Spine Biomechanical Research.” 2014. Web. 28 Feb 2021.
Vancouver:
Mannen EM. Advancing Thoracic Spine Biomechanical Research. [Internet] [Doctoral dissertation]. University of Kansas; 2014. [cited 2021 Feb 28].
Available from: http://hdl.handle.net/1808/18375.
Council of Science Editors:
Mannen EM. Advancing Thoracic Spine Biomechanical Research. [Doctoral Dissertation]. University of Kansas; 2014. Available from: http://hdl.handle.net/1808/18375
20.
Oh, Seungly.
Normal form approach for dispersive equations with low-regularity data.
Degree: PhD, Mathematics, 2012, University of Kansas
URL: http://hdl.handle.net/1808/10258
► In this dissertation, we examine applications of the normal form technique to nonlinear dispersive equations with rough initial data. Working within the framework of Bourgain…
(more)
▼ In this dissertation, we examine applications of the normal form technique to nonlinear dispersive equations with rough initial data. Working within the framework of Bourgain spaces, the normal form method often produces ample smoothing effects on the non-linearity. The extra gain in regularity is ideal for analysing solutions with low-regularity initial data, thus this approach can be used to overcome difficulties due to lack of smoothness in polynomial-type non-linearities. In particular, we will consider three canonical models in dispersive equations with quadratic and derivative quadratic non-linearities.
Advisors/Committee Members: Stefanov, Atanas (advisor), Johnson, Mat (cmtemember), Shao, Shuanglin (cmtemember), Sheu, Albert (cmtemember), Van Vleck, Erik (cmtemember), Perrins, Erik (cmtemember).
Subjects/Keywords: Mathematics
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APA (6th Edition):
Oh, S. (2012). Normal form approach for dispersive equations with low-regularity data. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/10258
Chicago Manual of Style (16th Edition):
Oh, Seungly. “Normal form approach for dispersive equations with low-regularity data.” 2012. Doctoral Dissertation, University of Kansas. Accessed February 28, 2021.
http://hdl.handle.net/1808/10258.
MLA Handbook (7th Edition):
Oh, Seungly. “Normal form approach for dispersive equations with low-regularity data.” 2012. Web. 28 Feb 2021.
Vancouver:
Oh S. Normal form approach for dispersive equations with low-regularity data. [Internet] [Doctoral dissertation]. University of Kansas; 2012. [cited 2021 Feb 28].
Available from: http://hdl.handle.net/1808/10258.
Council of Science Editors:
Oh S. Normal form approach for dispersive equations with low-regularity data. [Doctoral Dissertation]. University of Kansas; 2012. Available from: http://hdl.handle.net/1808/10258
21.
Maddux, Nathaniel R.
High throughput prediction of the long term stability of pharmaceutical macromolecules from short term multi-instrument spectroscopic data.
Degree: PhD, Physics & Astronomy, 2013, University of Kansas
URL: http://hdl.handle.net/1808/12312
► The field of pharmaceutical chemistry is currently struggling with the question of how to relate changes in the physical form of a macromolecular biopharmaceutical, such…
(more)
▼ The field of pharmaceutical chemistry is currently struggling with the question of how to relate changes in the physical form of a macromolecular biopharmaceutical, such as a therapeutic protein, to changes in the drug's efficacy, safety, and long term stability (ESS). A great number of experimental methods are typically utilized to investigate the differences between forms of a macromolecule, yet conclusions regarding changes in ESS are frequently tentative. An opportunity exists, however, to relate changes in form to changes in ESS. At least once during the development of a new drug, a study is undertaken (at great expense) of the ESS of the drug upon perturbation by multiple manufacturing, formulation, storage and transportation variables. The data acquired is then used to build a model that relates changes in ESS to manufacturing, formulation, storage and transportation variables. It is not common in the pharmaceutical industry, however, to relate changes in comprehensive ESS data sets to comprehensive measurements of changes in macromolecular form. We bridge the gap between physical measurements of a macromolecule's form and measurements of its long term stability, utilizing two data sets collected in a collaboration between our group at the
University of
Kansas and a group at the Ludwig Maximilians
University in Munich, Germany. The long term stability data, collected by the team in Germany, contains measurements of the chemical and conformation stability of Granulocyte Colony Stimulating Factor (GCSF) over a period of two years in 16 different liquid formulations. The short term physical data, collected in our lab, is comprised of spectroscopic characterization of the response of GCSF to thermal unfolding. The same 16 liquid formulations of GCSF were used in each study, allowing us to fit models predicting the long term stability of GCSF from short term measurements. We first apply a novel data reduction method to the short term data. This method selects data in the neighborhood of thermal unfolding transitions, and automates traditional comparative analyses. We then model the long term stability measurements using a linear technique, least squares fits, and a nonlinear one, radial basis function networks (RBFN). Using a Pearson correlation coefficient permutation test, we find that many of the fitted results have less than a 1 percent probability of occurring by chance.
Advisors/Committee Members: Ralston, John (advisor), Middaugh, Russ (advisor), Han, Siyuan (cmtemember), Fischer, Chris (cmtemember), Antonik, Matthew (cmtemember), Van Vleck, Erik (cmtemember).
Subjects/Keywords: Physics; Pharmaceutical sciences
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APA (6th Edition):
Maddux, N. R. (2013). High throughput prediction of the long term stability of pharmaceutical macromolecules from short term multi-instrument spectroscopic data. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/12312
Chicago Manual of Style (16th Edition):
Maddux, Nathaniel R. “High throughput prediction of the long term stability of pharmaceutical macromolecules from short term multi-instrument spectroscopic data.” 2013. Doctoral Dissertation, University of Kansas. Accessed February 28, 2021.
http://hdl.handle.net/1808/12312.
MLA Handbook (7th Edition):
Maddux, Nathaniel R. “High throughput prediction of the long term stability of pharmaceutical macromolecules from short term multi-instrument spectroscopic data.” 2013. Web. 28 Feb 2021.
Vancouver:
Maddux NR. High throughput prediction of the long term stability of pharmaceutical macromolecules from short term multi-instrument spectroscopic data. [Internet] [Doctoral dissertation]. University of Kansas; 2013. [cited 2021 Feb 28].
Available from: http://hdl.handle.net/1808/12312.
Council of Science Editors:
Maddux NR. High throughput prediction of the long term stability of pharmaceutical macromolecules from short term multi-instrument spectroscopic data. [Doctoral Dissertation]. University of Kansas; 2013. Available from: http://hdl.handle.net/1808/12312
22.
Ghosh, Taniya.
Bifurcation Analysis of Endogenous Growth Models.
Degree: PhD, Economics, 2013, University of Kansas
URL: http://hdl.handle.net/1808/12333
► It is important to recognize that bifurcation boundaries do not necessarily separate stable from unstable solution domains. Bifurcation boundaries can separate one kind of unstable…
(more)
▼ It is important to recognize that bifurcation boundaries do not necessarily separate stable from unstable solution domains. Bifurcation boundaries can separate one kind of unstable dynamics domain from another kind of unstable dynamics domain, or one kind of stable dynamics domain from another kind, such as monotonic stability from damped periodic stability or from damped multiperiodic stability. There are not only an infinite number of kinds of unstable dynamics, some very close to stability in appearance, but also an infinite number of kinds of stable dynamics. Hence subjective prior views on whether the economy is or is not stable provide little guidance without mathematical analysis of model dynamics. The thesis analyzes, within its feasible parameter space, the dynamics of the Uzawa-Lucas endogenous growth model. We examine the stability properties of both centralized and decentralized versions of the model and locate Hopf and transcritical bifurcation boundaries. In an extended analysis, we investigate the existence of Andronov-Hopf bifurcation, branch point bifurcation, limit point cycle bifurcation, and period doubling bifurcations. While these all are local bifurcations, the presence of global bifurcation is confirmed as well. We find evidence that the model could produce chaotic dynamics, but our analysis cannot confirm that conjecture. Further this thesis analyses the dynamics of a variant of Jones semi-endogenous growth model "Sources of US Economic growth in a World of Ideas" The American Economic Review, March 2002, Vol 92 No. 1, pp 220-239. A detailed bifurcation analysis is done within the feasible parameter space of the models. We showed the existence of codimension-1 bifurcations (Hopf, Branch Point, Limit Point of Cycles, and Period Doubling). In addition some codimension-2 (Bogdanov-Takens and Generalized Hopf) bifurcations are detected in the modified Jones model. While the aforementioned are all local bifurcations, the Uzawa-Lucas model also shows the presence of global bifurcation.
Advisors/Committee Members: Barnett, William A. (advisor), Keating, John (cmtemember), Liu, Weishi (cmtemember), Van Vleck, Erik (cmtemember), Wu, Shu (cmtemember).
Subjects/Keywords: Economics
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APA (6th Edition):
Ghosh, T. (2013). Bifurcation Analysis of Endogenous Growth Models. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/12333
Chicago Manual of Style (16th Edition):
Ghosh, Taniya. “Bifurcation Analysis of Endogenous Growth Models.” 2013. Doctoral Dissertation, University of Kansas. Accessed February 28, 2021.
http://hdl.handle.net/1808/12333.
MLA Handbook (7th Edition):
Ghosh, Taniya. “Bifurcation Analysis of Endogenous Growth Models.” 2013. Web. 28 Feb 2021.
Vancouver:
Ghosh T. Bifurcation Analysis of Endogenous Growth Models. [Internet] [Doctoral dissertation]. University of Kansas; 2013. [cited 2021 Feb 28].
Available from: http://hdl.handle.net/1808/12333.
Council of Science Editors:
Ghosh T. Bifurcation Analysis of Endogenous Growth Models. [Doctoral Dissertation]. University of Kansas; 2013. Available from: http://hdl.handle.net/1808/12333
23.
Lamb, Charles.
Neutral Equations of Mixed Type.
Degree: PhD, Mathematics, 2012, University of Kansas
URL: http://hdl.handle.net/1808/10819
► In this dissertation we consider neutral equations of mixed type. In particular, we con- sider the associated linear Fredholm theory and nerve fiber models that…
(more)
▼ In this dissertation we consider neutral equations of mixed type. In particular, we con- sider the associated linear Fredholm theory and nerve fiber models that are written as systems of neutral equations of mixed type. In Chapter 2, we extend the existing Fredholm theory for mixed type functional differential equations developed by Mallet-Paret to the case of implicitly defined mixed type functional differential equations. In Chapter 3, we apply the theory to an example arising from modeling signal prop- agation in nerve fibers. In this two-dimensional system, we rely on the Lyapunov- Schmidt method to demonstrate the existence of traveling wave solutions. With the aid of numerical computations, a saddle-node bifurcation was detected. In Chapter 4, we consider an extension of the parallel nerve fiber model examining in Chapter 3 and present the results of a numerical study. In this chapter, an additional form of coupling is examined not considered in the model from Chapter 3. This second type of coupling may be excitatory or inhibitory depending on the sign of the coupling parameter. Within a continuation framework, we employ a pseudo-spectral approach utilizing Chebyshev polynomials as basis functions. The chebfun package, consisting of Chebyshev tools, was utilized to manipulate the polynomials.
Advisors/Committee Members: Van Vleck, Erik S (advisor), Huang, Weizhang (cmtemember), Liu, Weishi (cmtemember), Stefanov, Atanas (cmtemember), Chertoff, Mark (cmtemember).
Subjects/Keywords: Mathematics; Functional differential equations; Lyapunov-schmidt; Neutral equations
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APA (6th Edition):
Lamb, C. (2012). Neutral Equations of Mixed Type. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/10819
Chicago Manual of Style (16th Edition):
Lamb, Charles. “Neutral Equations of Mixed Type.” 2012. Doctoral Dissertation, University of Kansas. Accessed February 28, 2021.
http://hdl.handle.net/1808/10819.
MLA Handbook (7th Edition):
Lamb, Charles. “Neutral Equations of Mixed Type.” 2012. Web. 28 Feb 2021.
Vancouver:
Lamb C. Neutral Equations of Mixed Type. [Internet] [Doctoral dissertation]. University of Kansas; 2012. [cited 2021 Feb 28].
Available from: http://hdl.handle.net/1808/10819.
Council of Science Editors:
Lamb C. Neutral Equations of Mixed Type. [Doctoral Dissertation]. University of Kansas; 2012. Available from: http://hdl.handle.net/1808/10819
University of Kansas
24.
Rush, Wade Drury.
A STRUCTURED METHOD FOR THE REAL QUADRATIC EIGENVALUE PROBLEM FOR SPECIFIC GYROSCOPIC SYSTEMS.
Degree: MA, Mathematics, 2008, University of Kansas
URL: http://hdl.handle.net/1808/5332
► This study examines a specific numerical approach that computes the eigenvalues (normal modes) of a Quadratic Eigenvalue Problem (QEP) of the form (&lambda2 & middotI…
(more)
▼ This study examines a specific numerical approach that computes the eigenvalues (normal modes) of a Quadratic Eigenvalue Problem (QEP) of the form (&lambda
2 & middotI + &lambda · B + C)· x = 0 where B is constrained to a real skew-symmetric matrix and C is constrained to a real symmetric positive definite matrix. A widely used linearization of this QEP is the companion matrix A which is an 2n-by-2n matrix such that (1,1) block is a n-by-n skew symmetric matrix, the (1,2) block is an n-by-n symmetric positive definite matrix, (2,1) block is the Identity matrix and finally the (2,2) zero block.. The goal is to find an algorithm method which diagonalizes matrix A without contaminating the (2,2) zero block. Once this algorithm is developed, the study measures the eigenvalue error bounds and compare its efficiency to the standard symmetric QR workhorse. Also, this approach preserves the structure of the error matrix in the same form as the QEP. In ensuring that the error matrix structure is a QEP, this algorithm provides fertile ground for future analysis in sensitivity and perturbation errors in the algorithm's eigenvalues. This study concludes that the algorithm appears to have a reasonable error bound; and it is more cost efficient in finding the eigenvalues then the symmetric QR algorithm.
Advisors/Committee Members: Xu, Hongguo (advisor), Van Vleck, Erik (cmtemember), Huang, Weizhang (cmtemember).
Subjects/Keywords: Mathematics; Cholesky; Eigenvalue; Givens; Gyroscopic; Quadratic; Skew-symmetric
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APA (6th Edition):
Rush, W. D. (2008). A STRUCTURED METHOD FOR THE REAL QUADRATIC EIGENVALUE PROBLEM FOR SPECIFIC GYROSCOPIC SYSTEMS. (Masters Thesis). University of Kansas. Retrieved from http://hdl.handle.net/1808/5332
Chicago Manual of Style (16th Edition):
Rush, Wade Drury. “A STRUCTURED METHOD FOR THE REAL QUADRATIC EIGENVALUE PROBLEM FOR SPECIFIC GYROSCOPIC SYSTEMS.” 2008. Masters Thesis, University of Kansas. Accessed February 28, 2021.
http://hdl.handle.net/1808/5332.
MLA Handbook (7th Edition):
Rush, Wade Drury. “A STRUCTURED METHOD FOR THE REAL QUADRATIC EIGENVALUE PROBLEM FOR SPECIFIC GYROSCOPIC SYSTEMS.” 2008. Web. 28 Feb 2021.
Vancouver:
Rush WD. A STRUCTURED METHOD FOR THE REAL QUADRATIC EIGENVALUE PROBLEM FOR SPECIFIC GYROSCOPIC SYSTEMS. [Internet] [Masters thesis]. University of Kansas; 2008. [cited 2021 Feb 28].
Available from: http://hdl.handle.net/1808/5332.
Council of Science Editors:
Rush WD. A STRUCTURED METHOD FOR THE REAL QUADRATIC EIGENVALUE PROBLEM FOR SPECIFIC GYROSCOPIC SYSTEMS. [Masters Thesis]. University of Kansas; 2008. Available from: http://hdl.handle.net/1808/5332
University of Kansas
25.
Abaid, Nicole Teresa.
Steady-State Poisson-Nernst-Planck Systems: Asymptotic expansions and applications to ion channels.
Degree: MA, Mathematics, 2008, University of Kansas
URL: http://hdl.handle.net/1808/4131
► Important properties of ion channels can be described by a steady state Poisson-Nernst-Plank system for electrodiffusion. The solution to the PNP system gives a relation…
(more)
▼ Important properties of ion channels can be described by a steady state Poisson-Nernst-Plank system for electrodiffusion. The solution to the PNP system gives a relation between the current and electric potential of the ions in the channel, called the I-V curve. In this thesis, we will discuss the matched asymptotic expansions method of solving a singularly perturbed system and apply this method to find an approximate solution to the steady-state Poisson-Nernst-Planck system. In general, for nonlinear systems, it is impossible to obtain any representations of solutions. Due to the presence of a singular parameter in the PNP system, we can treat the system as a singularly perturbed problem. This system with specific nonlinearity has special structures that are crucial for the explicit higher order asymptotic expansions of the solutions. Although the ion channel problem considers only one cell, the I-V relation obtained in this thesis is consistent with the cubic-like assumption of the I-V relation in the FitzHugh-Nagumo model for action potential involving a population of ion channels. However, applications of the results of this thesis to ion channels are limited, since we considered a simplified model with two species of ions and a zero permanent charge in the channel.
Advisors/Committee Members: Liu, Weishi (advisor), Van Vleck, Erik (cmtemember), Oh, Myunghyun (cmtemember).
Subjects/Keywords: Mathematics; Poisson-Nernst-Planck systems; Dynamical systems; Ion channels
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APA (6th Edition):
Abaid, N. T. (2008). Steady-State Poisson-Nernst-Planck Systems: Asymptotic expansions and applications to ion channels. (Masters Thesis). University of Kansas. Retrieved from http://hdl.handle.net/1808/4131
Chicago Manual of Style (16th Edition):
Abaid, Nicole Teresa. “Steady-State Poisson-Nernst-Planck Systems: Asymptotic expansions and applications to ion channels.” 2008. Masters Thesis, University of Kansas. Accessed February 28, 2021.
http://hdl.handle.net/1808/4131.
MLA Handbook (7th Edition):
Abaid, Nicole Teresa. “Steady-State Poisson-Nernst-Planck Systems: Asymptotic expansions and applications to ion channels.” 2008. Web. 28 Feb 2021.
Vancouver:
Abaid NT. Steady-State Poisson-Nernst-Planck Systems: Asymptotic expansions and applications to ion channels. [Internet] [Masters thesis]. University of Kansas; 2008. [cited 2021 Feb 28].
Available from: http://hdl.handle.net/1808/4131.
Council of Science Editors:
Abaid NT. Steady-State Poisson-Nernst-Planck Systems: Asymptotic expansions and applications to ion channels. [Masters Thesis]. University of Kansas; 2008. Available from: http://hdl.handle.net/1808/4131
University of Kansas
26.
He, Feng.
Analytical and Numerical Studies of One-Dimensional Poisson-Nernst-Planck Models for Ion Channels.
Degree: MA, Mathematics, 2008, University of Kansas
URL: http://hdl.handle.net/1808/4128
► We study the event of ion flow through ion channel proteins modeled with a one-dimensional Poisson-Nernst-Planck system in presence of two or three types of…
(more)
▼ We study the event of ion flow through ion channel proteins modeled with a one-dimensional Poisson-Nernst-Planck system in presence of two or three types of ions with permanently charges located inside the channel. A singular parameter ε, related to the Debye length, is presented in the PNP system. In the case of two ions, the boundary conditions for the charged region can be specifically solved by solving a scaled algebraic equation. These conditions are then used to solve the PNP system numerically. Multiple solutions emerge from the computation and are probably indicative of more complex functions of ion channels. The system can be solved using numerical approaches and examples of these results are presented in this paper. The PNP system contains information of the current-voltage (I-V) relations of ion channels when reaching steady-state. Analysis of the I-V property is shown and some representative results discussed.
Advisors/Committee Members: Liu, Weishi (advisor), Liu, Weishi (cmtemember), Huang, Weizhang (cmtemember), Van Vleck, Erik (cmtemember).
Subjects/Keywords: Mathematics; Poisson-Nernst-Planck systems; Ion channels
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APA (6th Edition):
He, F. (2008). Analytical and Numerical Studies of One-Dimensional Poisson-Nernst-Planck Models for Ion Channels. (Masters Thesis). University of Kansas. Retrieved from http://hdl.handle.net/1808/4128
Chicago Manual of Style (16th Edition):
He, Feng. “Analytical and Numerical Studies of One-Dimensional Poisson-Nernst-Planck Models for Ion Channels.” 2008. Masters Thesis, University of Kansas. Accessed February 28, 2021.
http://hdl.handle.net/1808/4128.
MLA Handbook (7th Edition):
He, Feng. “Analytical and Numerical Studies of One-Dimensional Poisson-Nernst-Planck Models for Ion Channels.” 2008. Web. 28 Feb 2021.
Vancouver:
He F. Analytical and Numerical Studies of One-Dimensional Poisson-Nernst-Planck Models for Ion Channels. [Internet] [Masters thesis]. University of Kansas; 2008. [cited 2021 Feb 28].
Available from: http://hdl.handle.net/1808/4128.
Council of Science Editors:
He F. Analytical and Numerical Studies of One-Dimensional Poisson-Nernst-Planck Models for Ion Channels. [Masters Thesis]. University of Kansas; 2008. Available from: http://hdl.handle.net/1808/4128
University of Kansas
27.
Kastens, Jude Heathcliff.
SOME NEW DEVELOPMENTS ON TWO SEPARATE TOPICS: STATISTICAL CROSS VALIDATION AND FLOODPLAIN MAPPING.
Degree: PH.D., Mathematics, 2008, University of Kansas
URL: http://hdl.handle.net/1808/5354
► This dissertation describes two unrelated threads of research. The first is a study of cross validation (CV), which is a data resampling method. CV is…
(more)
▼ This dissertation describes two unrelated threads of research. The first is a study of cross validation (CV), which is a data resampling method. CV is used for model ranking in model selection and for estimating expected prediction error of a model. A review of three resampling methods is provided in Chapter 1. Chapter 2 contains results from simulations that examine various properties of CV, in particular the use of CV for model selection in small sample settings as well as the expected value of the delete-d cross validation statistic. The second research thread is described in Chapter 3, where a new, physically-based computational model (called FLDPLN, or "Floodplain") for mapping potential inundation extents (floodplains) using gridded topographic data is introduced. Due to the parametric economy of FLDPLN, this model has significant advantages over existing methods such as hydrodynamic models. The model is validated using imagery from an actual flood event.
Advisors/Committee Members: Lerner, David (advisor), Church, James (cmtemember), Cobb, Ben (cmtemember), Egbert, Stephen (cmtemember), Huggins, Don (cmtemember), Van Vleck, Erik (cmtemember).
Subjects/Keywords: Mathematics
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APA (6th Edition):
Kastens, J. H. (2008). SOME NEW DEVELOPMENTS ON TWO SEPARATE TOPICS: STATISTICAL CROSS VALIDATION AND FLOODPLAIN MAPPING. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/5354
Chicago Manual of Style (16th Edition):
Kastens, Jude Heathcliff. “SOME NEW DEVELOPMENTS ON TWO SEPARATE TOPICS: STATISTICAL CROSS VALIDATION AND FLOODPLAIN MAPPING.” 2008. Doctoral Dissertation, University of Kansas. Accessed February 28, 2021.
http://hdl.handle.net/1808/5354.
MLA Handbook (7th Edition):
Kastens, Jude Heathcliff. “SOME NEW DEVELOPMENTS ON TWO SEPARATE TOPICS: STATISTICAL CROSS VALIDATION AND FLOODPLAIN MAPPING.” 2008. Web. 28 Feb 2021.
Vancouver:
Kastens JH. SOME NEW DEVELOPMENTS ON TWO SEPARATE TOPICS: STATISTICAL CROSS VALIDATION AND FLOODPLAIN MAPPING. [Internet] [Doctoral dissertation]. University of Kansas; 2008. [cited 2021 Feb 28].
Available from: http://hdl.handle.net/1808/5354.
Council of Science Editors:
Kastens JH. SOME NEW DEVELOPMENTS ON TWO SEPARATE TOPICS: STATISTICAL CROSS VALIDATION AND FLOODPLAIN MAPPING. [Doctoral Dissertation]. University of Kansas; 2008. Available from: http://hdl.handle.net/1808/5354
University of Kansas
28.
Mani, Pradeepkumar.
A Framework for Service Differentiation and Optimization in Multi-hop Wireless Networks.
Degree: PH.D., Electrical Engineering & Computer Science, 2008, University of Kansas
URL: http://hdl.handle.net/1808/4344
► In resource-constrained networks such as multi-hop wireless networks (MHWNs), service differentiation algorithms designed to address end users' interests (e.g. user satisfaction, QoS, etc.) should also…
(more)
▼ In resource-constrained networks such as multi-hop wireless networks (MHWNs), service differentiation algorithms designed to address end users' interests (e.g. user satisfaction, QoS, etc.) should also consider efficient utilization of the scarce network resources in order to maximize the network's interests (e.g. revenue). For this very reason, service differentiation in MHWNs is quite different from the wired network scenario. We propose a service differentiation tool called the ``Investment Function'', which essentially captures the network's cumulative resource investment in a given packet at a given time. This investment value can be used by the network algorithm to implement specific service differentiation principles. As proof-of-concept, we use the investment function to improve fairness among simultaneous flows that traverse varying number of hops in a MHWN (multihop flow fairness). However, to attain the optimal value of a specific service differentiation objective, optimal service differentiation and investment function parameters may need to be computed. The optimal parameters can be computed by casting the service differentiation problem as a network flow problem in MHWNs, with the goal of optimizing the service differentiation objective. The capacity constraints for these problems require knowledge of the adjacent-node interference values, and constructing these constraints could be very expensive based on the transmission scheduling scheme used. As a result, even formulating the optimization problem may take unacceptable computational effort or memory or both. Under optimal scheduling, the adjacent node interference values (and thus the capacity constraints) are not only very expensive to compute, but also cannot be expressed in polynomial form. Therefore, existing optimization techniques cannot be directly applied to solve optimization problems in MHWNs. To develop an efficient optimization framework, we first model the MHWN as a Unit Disk Graph (UDG). The optimal transmission schedule in the MHWN is related to the chromatic number of the UDG, which is very expensive to compute. However, the clique number, which is a lower bound on the chromatic number, can be computed in polynomial time in UDGs. Through an empirical study, we obtain tighter bounds on the ratio of the chromatic number to clique number in UDGs, which enables us to leverage existing polynomial time clique-discovery algorithms to compute very close approximations to the chromatic number value. This approximation not only allows us to quickly formulate the capacity constraints in polynomial form, but also allows us to significantly deviate from the traditional approach of discovering all or most of the constraints it{a priori}; instead, we can discover the constraints as needed. We have integrated this approach of constraint-discovery into an active-set optimization algorithm (Gradient Projection method) to solve network flow problems in multi-hop wireless networks. Our results show significant memory and computational savings when…
Advisors/Committee Members: Petr, David W (advisor), Frost, Victor (cmtemember), Evans, Joseph B. (cmtemember), Kong, Man (cmtemember), Van Vleck, Erik (cmtemember).
Subjects/Keywords: Electronics and electrical engineering; Computer science; Multi-hop wireless; Optimization; Investment function; Fairness; Interference
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APA (6th Edition):
Mani, P. (2008). A Framework for Service Differentiation and Optimization in Multi-hop Wireless Networks. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/4344
Chicago Manual of Style (16th Edition):
Mani, Pradeepkumar. “A Framework for Service Differentiation and Optimization in Multi-hop Wireless Networks.” 2008. Doctoral Dissertation, University of Kansas. Accessed February 28, 2021.
http://hdl.handle.net/1808/4344.
MLA Handbook (7th Edition):
Mani, Pradeepkumar. “A Framework for Service Differentiation and Optimization in Multi-hop Wireless Networks.” 2008. Web. 28 Feb 2021.
Vancouver:
Mani P. A Framework for Service Differentiation and Optimization in Multi-hop Wireless Networks. [Internet] [Doctoral dissertation]. University of Kansas; 2008. [cited 2021 Feb 28].
Available from: http://hdl.handle.net/1808/4344.
Council of Science Editors:
Mani P. A Framework for Service Differentiation and Optimization in Multi-hop Wireless Networks. [Doctoral Dissertation]. University of Kansas; 2008. Available from: http://hdl.handle.net/1808/4344
. 
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