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University of Kansas
1.
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 (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 27, 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. 27 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 27].
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
2.
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…
(more)
▼ 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 27, 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. 27 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 27].
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
3.
Hwang, Seung-Jae.
Numerical Simulation of Enhanced Mixing in Scramjet Combustor Using Ramp, Tabs and Suction Collar.
Degree: PhD, Aerospace Engineering, 2011, University of Kansas
URL: http://hdl.handle.net/1808/8080
► Numerical simulations of the scramjet combustor by using the commercial CFD code Fluent with the coupled implicit method with second-order accurate discretization have been obtained…
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▼ Numerical simulations of the scramjet combustor by using the commercial CFD code Fluent with the coupled implicit method with second-order accurate discretization have been obtained for the reacting flows with the parallel fuel injection (ramp injection) and normal fuel injection (wall injection) schemes. Incorporated in the scramjet combustors are delta tabs and suction collars of two types as means of mixing enhancement. The main mechanism of the tabs and suction collars for mixing enhancement is the generation of streamwise vorticity and providing outstanding flameholding capability along with the induced global instability of the shear layer. The idea has been previously recommended for mixing enhancement of the scramjet combustor, but no experimental or computational data on the combustor performance has been reported, yet. The finite rate reaction model is used for the species transport model that only considers four species, H2, O2, H2O and N2. Vitiated air (mass fraction of O2, H2O, and N2 being 0.198, 0.139, and 0.663, respectively) enters the combustor at Mach number of 2.5 at a stagnation temperature and pressure of 1500 K and 101,325 Pa, respectively. The equivalence ratio is fixed at 0.45 in the present study. An optimization study of the combinations of the tabs and suction collars has been performed. Uninstalled thrust force for the optimal combination which was composed of the relieved ramp, 4 delta tabs, suction collar type I and 4 delta tabs in the fuel inlet scheme produced an additional 73% increase in thrust with only an additional 3.37% loss of the total pressure compared to the ramp injection alone, i.e., the baseline case. The numerical results clearly indicate that the fuel injection schemes investigated in the present study are more efficient than a strut or multi-staged strut and wall injection scheme.
Advisors/Committee Members: Farokhi, Saeed (advisor), Taghavi, Ray (cmtemember), Barrett-Gonzalez, Ron (cmtemember), Keshmiri, Shahriar (cmtemember), Huang, Weizhang (cmtemember).
Subjects/Keywords: Aerospace engineering; Combustor; Enhanced; Mixing; Scramjet; Suction collar; Tabs
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APA (6th Edition):
Hwang, S. (2011). Numerical Simulation of Enhanced Mixing in Scramjet Combustor Using Ramp, Tabs and Suction Collar. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/8080
Chicago Manual of Style (16th Edition):
Hwang, Seung-Jae. “Numerical Simulation of Enhanced Mixing in Scramjet Combustor Using Ramp, Tabs and Suction Collar.” 2011. Doctoral Dissertation, University of Kansas. Accessed February 27, 2021.
http://hdl.handle.net/1808/8080.
MLA Handbook (7th Edition):
Hwang, Seung-Jae. “Numerical Simulation of Enhanced Mixing in Scramjet Combustor Using Ramp, Tabs and Suction Collar.” 2011. Web. 27 Feb 2021.
Vancouver:
Hwang S. Numerical Simulation of Enhanced Mixing in Scramjet Combustor Using Ramp, Tabs and Suction Collar. [Internet] [Doctoral dissertation]. University of Kansas; 2011. [cited 2021 Feb 27].
Available from: http://hdl.handle.net/1808/8080.
Council of Science Editors:
Hwang S. Numerical Simulation of Enhanced Mixing in Scramjet Combustor Using Ramp, Tabs and Suction Collar. [Doctoral Dissertation]. University of Kansas; 2011. Available from: http://hdl.handle.net/1808/8080
University of Kansas
4.
Wei, Zhenglun.
Numerical and theoretical study of flapping airfoil aerodynamics using a parallelized immersed-boundary method.
Degree: PhD, Aerospace Engineering, 2014, University of Kansas
URL: http://hdl.handle.net/1808/19600
► Flight has fascinated humans for centuries. Human inventions such as missiles, aircraft , unmanned aerial vehicles (UAV), and micro air vehicle (MAV) are inspired by…
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▼ Flight has fascinated humans for centuries. Human inventions such as missiles, aircraft , unmanned aerial vehicles (UAV), and micro air vehicle (MAV) are inspired by natural flying expertise. As natural flyers usually operate in a vortex-dominated environment, interactions between their wings and the vortices have significant influences on force generation and flying efficiency. Some interesting phenomena induced from such vortex-body interactions have gotten a lot of attention in the past few decades. A good example is that birds and insects are credited with extracting energy from ambient vortices. In a simpler form, bio-inspired airfoils with either passive or active flapping motions are found to have the potential to harvest energy from incoming vortices generated from an upstream object, i.e. a cylinder. The current study identified the interaction modes of the leading edge vortex (LEV) and trailing edge vortex (TEV) between the active flapping airfoil and the incoming vortices. The relation between the interaction modes and the energy extraction capacity of an active harvester is investigated guided by a potential theory. The interaction modes induced by a passive energy harvester always benefit the energy extraction efficiency. However, the dynamic response of the passive harvester was found to vary corresponding to the properties of the incoming vortical wake. A profound appreciation of energy extracting mechanisms can provide a solution for the energy consumption issue of MAV and UAV. However, difficulties are encountered in practical applications of energy harvesting on how to detect the locations of generated vortices and what the trajectory of the vortex downstream of the moving body is. Some observations are realized and the fluid dynamics of the phenomena is beyond the fundamentals described in the textbook. One well-known instance is the asymmetric wake formed downstream of a symmetric sinusoidal heaving airfoil. In this study, factors that influence the formation of the asymmetric wakes on both the near wake and far wake regions are demonstrated. Novel vortex models are developed to explore the vortex dynamic mechanisms of the asymmetric wake and its development from the near wake region to the far wake region. In order to analyze the flow fields for the bio-inspired problems, Computational Fluid Dynamics (CFD) provides powerful and convenient tools. The shape of bio-inspired wings/airfoils and their maneuvers are usually very complicated. In CFD, the immersed-boundary (IB) method is an advantageous approach to simulate such problems. In this study, an immersed-boundary method is implemented in a parallel fashion in order to speed up the computational rate.. A variety of numerical schemes have been applied to the IB method, including different spatial schemes and temporal schemes; their performances are investigated. In addition, the IB method has been successfully implemented with the fluid-structure interaction models for studying passive mobile objectives, i.e. the energy harvester. The possibility…
Advisors/Committee Members: Zheng, Zhongquan (advisor), Farokhi, Saeed (cmtemember), Huang, Weizhang (cmtemember), Keshmiri, Shawn (cmtemember), Taghavi, Ray (cmtemember).
Subjects/Keywords: Aerospace engineering; Mechanical engineering
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APA ·
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APA (6th Edition):
Wei, Z. (2014). Numerical and theoretical study of flapping airfoil aerodynamics using a parallelized immersed-boundary method. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/19600
Chicago Manual of Style (16th Edition):
Wei, Zhenglun. “Numerical and theoretical study of flapping airfoil aerodynamics using a parallelized immersed-boundary method.” 2014. Doctoral Dissertation, University of Kansas. Accessed February 27, 2021.
http://hdl.handle.net/1808/19600.
MLA Handbook (7th Edition):
Wei, Zhenglun. “Numerical and theoretical study of flapping airfoil aerodynamics using a parallelized immersed-boundary method.” 2014. Web. 27 Feb 2021.
Vancouver:
Wei Z. Numerical and theoretical study of flapping airfoil aerodynamics using a parallelized immersed-boundary method. [Internet] [Doctoral dissertation]. University of Kansas; 2014. [cited 2021 Feb 27].
Available from: http://hdl.handle.net/1808/19600.
Council of Science Editors:
Wei Z. Numerical and theoretical study of flapping airfoil aerodynamics using a parallelized immersed-boundary method. [Doctoral Dissertation]. University of Kansas; 2014. Available from: http://hdl.handle.net/1808/19600
University of Kansas
5.
Jiang, Yan.
Evaluating Performance of Hybrid Geosynthetic-Reinforced Retaining Walls.
Degree: PhD, Civil, Environmental & Architectural Engineering, 2016, University of Kansas
URL: http://hdl.handle.net/1808/21982
► Geosynthetic-Reinforced Retaining (GRR) walls have been extensively used in highway projects. A novel GRR wall was proposed to mitigate the problems (e.g. high connection stress)…
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▼ Geosynthetic-Reinforced Retaining (GRR) walls have been extensively used in highway projects. A novel GRR wall was proposed to mitigate the problems (e.g. high connection stress) resulting from the relatively large spacing of primary reinforcement. This new GRR wall has secondary reinforcement installed between primary reinforcement layers. This new GRR wall has a similarity in the structure of the GMSE wall and the GRS wall in terms of the vertical reinforcement spacing (i.e., it has the same vertical primary reinforcement spacing as the GMSE wall and the same vertical secondary reinforcement spacing as the GRS wall). In this study, it is named as a hybrid GRR wall. Since the hybrid GRR wall is an innovative retaining structure, few studies have been carried out on it and then its performance has not been well understood. Therefore, it is necessary to evaluate the performance of the hybrid GRR wall. Three GRR wall sections were constructed and monitored in the field: (1) a hybrid GRR wall section with uniaxial geogrid layers as primary and secondary reinforcement, (2) a hybrid GRR wall section with uniaxial geogrid layers as primary reinforcement and with biaxial geogrid layers as secondary reinforcement, and (3) a GRR wall section with uniaxial geogrid layers as primary reinforcement only (i.e., the control section). Earth pressure cells, inclinometer casings and probes, and foil-type strain gauges were used in these three test wall sections to measure vertical and lateral earth pressures, accumulated lateral wall facing deflections, and strains of primary and secondary geogrid layers during construction, respectively. The results from monitoring of these three GRR wall sections were analyzed. The test results demonstrated the effects of secondary reinforcement on the improved performance of GRR walls, including reduced accumulated wall facing deflections, a more uniform lateral earth pressure distribution, and reduced tensile strains in primary geogrid layers. In addition to the field tests, the numerical study was performed to evaluate the performance of the instrumented GRR walls in the field tests. The wall facing and the foundation soil were modelled as a linearly elastic material and the retained soil was modelled as a linearly elastic perfectly plastic material with the Mohr Coulomb (MC) failure criterion. The behavior of the backfill soil in the reinforced soil zone was modelled using the Cap Yield (CY) model and the MC model. The behavior of the reinforcement was described by a strip element with a linearly elastic perfectly plastic behavior. An 8-kPa compaction stress was considered in the numerical model. The vertical and lateral earth pressures, wall facing deflections, and strains in primary and secondary geogrid layers during construction were calculated by the numerical simulation and also compared with the measured ones in the field tests. The calculated results from the numerical simulation agreed well with the measured one in the field tests. The calculated results from the numerical simulation…
Advisors/Committee Members: Han, Jie (advisor), Parsons, Robert Lee (cmtemember), Cai, Hongyi (cmtemember), Misra, Anil (cmtemember), Huang, Weizhang (cmtemember).
Subjects/Keywords: Civil engineering; Geotechnology; Field test; Geosynthetic reinforced retaining wall; Geosynthetic reinforced soil (GRS) wall; Mechanically stabilized earth (MSE) wall; Numerical modelling; Secondary reinforcement
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APA (6th Edition):
Jiang, Y. (2016). Evaluating Performance of Hybrid Geosynthetic-Reinforced Retaining Walls. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/21982
Chicago Manual of Style (16th Edition):
Jiang, Yan. “Evaluating Performance of Hybrid Geosynthetic-Reinforced Retaining Walls.” 2016. Doctoral Dissertation, University of Kansas. Accessed February 27, 2021.
http://hdl.handle.net/1808/21982.
MLA Handbook (7th Edition):
Jiang, Yan. “Evaluating Performance of Hybrid Geosynthetic-Reinforced Retaining Walls.” 2016. Web. 27 Feb 2021.
Vancouver:
Jiang Y. Evaluating Performance of Hybrid Geosynthetic-Reinforced Retaining Walls. [Internet] [Doctoral dissertation]. University of Kansas; 2016. [cited 2021 Feb 27].
Available from: http://hdl.handle.net/1808/21982.
Council of Science Editors:
Jiang Y. Evaluating Performance of Hybrid Geosynthetic-Reinforced Retaining Walls. [Doctoral Dissertation]. University of Kansas; 2016. Available from: http://hdl.handle.net/1808/21982
University of Kansas
6.
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 27, 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. 27 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 27].
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
7.
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 ·
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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 27, 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. 27 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 27].
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
8.
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 27, 2021.
http://hdl.handle.net/1808/18632.
MLA Handbook (7th Edition):
Brucal-Hallare, Maila. “Solutions of Lattice Differential Equations over Inhomogeneous Media.” 2012. Web. 27 Feb 2021.
Vancouver:
Brucal-Hallare M. Solutions of Lattice Differential Equations over Inhomogeneous Media. [Internet] [Doctoral dissertation]. University of Kansas; 2012. [cited 2021 Feb 27].
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
9.
Shi, Lei.
Adaptive High-Order Differential Formulation for the Compressible Navier-Stokes Equations.
Degree: PhD, Aerospace Engineering, 2014, University of Kansas
URL: http://hdl.handle.net/1808/27533
► High-order methods have the potential to achieve higher accuracy at lower cost than lower order methods. This potential has been demonstrated conclusively for smooth problems…
(more)
▼ High-order methods have the potential to achieve higher accuracy at lower cost than lower order methods. This potential has been demonstrated conclusively for smooth problems in the 1st International Workshop on High-Order Methods. For non-smooth problems, solution based hp-adaptations offer the best promise. Adjoint-based adaptive methods have the capability of dynamically distributing computing resources to areas which are important for predicting engineering performance parameters, such as lift or drag. This thesis presents a robust and efficient adjoint-based adaptive high-order differential formulation for the compressible Navier-Stokes equations, which can rapidly determine an accurate estimate of an engineering output within a prescribed error threshold. The flux reconstruction (FR) or the correction procedure via reconstruction (CPR) method used in this work is a high-order differential formulation. We develop a parallel adjoint-based adaptive CPR solver which can work with any element-based error estimate and handle arbitrary discretization orders for mixed elements. First, a dual-consistent discrete form of the CPR method is derived. Then, an efficient and accurate adjoint-based error estimation method for the CPR method is developed and its accuracy and effectiveness are verified for the linear and non-linear partial differential equations (PDE). For anisotropic h-adaptations, we use a local output error sampling procedure to find the optimal refinement option. The current method has been applied to aerodynamic problems. Numerical tests show that significant savings in the number of DOFs can be achieved through the adjoint-based adaptation.
Advisors/Committee Members: Wang, Z.J. (advisor), Farokhi, Saeed (cmtemember), Huang, Weizhang (cmtemember), Taghavi, Ray (cmtemember), Tu, Xuemin (cmtemember), Zheng, Zhongquan (cmtemember).
Subjects/Keywords: Aerospace engineering; Adaptive Method; Adjoint-based Adaptation; Computational Fluid Dynamics; High-order Method; Navier-Stokes Equations
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APA (6th Edition):
Shi, L. (2014). Adaptive High-Order Differential Formulation for the Compressible Navier-Stokes Equations. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/27533
Chicago Manual of Style (16th Edition):
Shi, Lei. “Adaptive High-Order Differential Formulation for the Compressible Navier-Stokes Equations.” 2014. Doctoral Dissertation, University of Kansas. Accessed February 27, 2021.
http://hdl.handle.net/1808/27533.
MLA Handbook (7th Edition):
Shi, Lei. “Adaptive High-Order Differential Formulation for the Compressible Navier-Stokes Equations.” 2014. Web. 27 Feb 2021.
Vancouver:
Shi L. Adaptive High-Order Differential Formulation for the Compressible Navier-Stokes Equations. [Internet] [Doctoral dissertation]. University of Kansas; 2014. [cited 2021 Feb 27].
Available from: http://hdl.handle.net/1808/27533.
Council of Science Editors:
Shi L. Adaptive High-Order Differential Formulation for the Compressible Navier-Stokes Equations. [Doctoral Dissertation]. University of Kansas; 2014. Available from: http://hdl.handle.net/1808/27533
University of Kansas
10.
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 27, 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. 27 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 27].
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
University of Kansas
11.
Zeng, Chong.
Wavefield Analysis of Rayleigh Waves for Near-Surface Shear-Wave Velocity.
Degree: PhD, Geology, 2011, University of Kansas
URL: http://hdl.handle.net/1808/8407
► Shear (S)-wave velocity is a key property of near-surface materials and is the fundamental parameter for many environmental and engineering geophysical studies. Directly acquiring accurate…
(more)
▼ Shear (S)-wave velocity is a key property of near-surface materials and is the fundamental parameter for many environmental and engineering geophysical studies. Directly acquiring accurate S-wave velocities from a seismic shot gather is usually difficult due to the poor signal-to-noise ratio. The relationship between Rayleigh-wave phase velocity and frequency has been widely utilized to estimate the S-wave velocities in shallow layers using the multichannel analysis of surface waves (MASW) technique. Hence, Rayleigh wave is a main focus of most near-surface seismic studies. Conventional dispersion analysis of Rayleigh waves assumes that the earth is laterally homogeneous and the free surface is horizontally flat, which limits the application of surface-wave methods to only 1D earth models or very smooth 2D models. In this study I extend the analysis of Rayleigh waves to a 2D domain by employing the 2D full elastic wave equation so as to address the lateral heterogeneity problem. I first discuss the accurate simulation of Rayleigh waves through finite-difference method and the boundary absorbing problems in the numerical modeling with a high Poisson's ratio ( 0.4), which is a unique near-surface problem. Then I develop an improved vacuum formulation to generate accurate synthetic seismograms focusing on Rayleigh waves in presence of surface topography and internal discontinuities. With these solutions to forward modeling of Rayleigh waves, I evaluate the influence of surface topography to conventional dispersion analysis in 2D and 3D domains by numerical investigations. At last I examine the feasibility of inverting waveforms of Rayleigh waves for shallow S-wave velocities using a genetic algorithm. Results of the study show that Rayleigh waves can be accurately simulated in near surface using the improved vacuum formulation. Spurious reflections during the numerical modeling can be efficiently suppressed by the simplified multiaxial perfectly matched layers. The conventional MASW method can tolerate gentle topography changes with insignificant errors. Finally, many near-surface features with strong lateral heterogeneity such as dipping interfaces, faults, and tunnels can be imaged by the waveform inversion of Rayleigh waves for shallow S-wave velocities. This thesis consists of four papers that are either published (chapter 1) or in review (chapter 2, 3, and 4) for consideration of publication to peer-refereed journals. Each chapter represents a paper, and therefore inadvertently there will be a certain degree of overlap between chapters (particularly for the introduction parts, where references to many common papers occur).
Advisors/Committee Members: Xia, Jianghai (advisor), Tsoflias, George (advisor), Tsoflias, Georgios P. (cmtemember), Xia, Jianghai (cmtemember), Walker, J. Douglas (cmtemember), Roberts, Jennifer A. (cmtemember), Huang, Weizhang (cmtemember).
Subjects/Keywords: Geology; Geophysics; Near surface; Rayleigh wave; Shear waves; Wavefield
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APA (6th Edition):
Zeng, C. (2011). Wavefield Analysis of Rayleigh Waves for Near-Surface Shear-Wave Velocity. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/8407
Chicago Manual of Style (16th Edition):
Zeng, Chong. “Wavefield Analysis of Rayleigh Waves for Near-Surface Shear-Wave Velocity.” 2011. Doctoral Dissertation, University of Kansas. Accessed February 27, 2021.
http://hdl.handle.net/1808/8407.
MLA Handbook (7th Edition):
Zeng, Chong. “Wavefield Analysis of Rayleigh Waves for Near-Surface Shear-Wave Velocity.” 2011. Web. 27 Feb 2021.
Vancouver:
Zeng C. Wavefield Analysis of Rayleigh Waves for Near-Surface Shear-Wave Velocity. [Internet] [Doctoral dissertation]. University of Kansas; 2011. [cited 2021 Feb 27].
Available from: http://hdl.handle.net/1808/8407.
Council of Science Editors:
Zeng C. Wavefield Analysis of Rayleigh Waves for Near-Surface Shear-Wave Velocity. [Doctoral Dissertation]. University of Kansas; 2011. Available from: http://hdl.handle.net/1808/8407
12.
Benyamen, Hady.
Stability and Control Derivatives Identification for an Unmanned Aerial Vehicle with Low Cost Sensors Using an Extended Kalman Filter Algorithm.
Degree: MS, Aerospace Engineering, 2019, University of Kansas
URL: http://hdl.handle.net/1808/29631
► Unmanned aerial systems (UASs) tend to be autonomous vehicles. Thus, they require control algorithms. More advanced control algorithms can be developed when high quality UAS…
(more)
▼ Unmanned aerial systems (UASs) tend to be autonomous vehicles. Thus, they require control algorithms. More advanced control algorithms can be developed when high quality UAS dynamic models are available. It is common to develop dynamic models for UAS using low fidelity theoretical methods. In this thesis, a higher fidelity approach which has been used for manned aircraft over the past 40-50 years is applied to the SkyHunter UAS. That approach is system identification. In this approach, the aircraft dynamic model is developed based on flight data. This thesis focuses particularly on identifying the longitudinal stability and control derivatives of the UAS. Such derivatives are important in developing UAS dynamic models. An extended Kalman filter (EKF) algorithm was used to identify the derivatives. The algorithm is appealing since it can potentially allow online system identification. The SkyHunter analyzed in this thesis weighs about 10 lb. (4.5 kg) and its wing span is about 82 in (2 m.) Like many UASs, the SkyHunter uses relatively low-cost sensors. Therefore, the data contains high noise levels. Several flight portions from three different flights were analyzed and the results are presented. These flight portions were selected carefully based on criteria that make the flight data more suitable for system identification. The identified derivatives showed reasonable results in several instances. However, a large degree of variation was observed when comparing derivatives identified from the different flight portions. The inconsistency is caused by unsteady aerodynamics, sensor noise, inability of the EKF to capture aircraft dynamics due to the use of simplified equations of motion, along with other reasons discussed in the thesis. The unsteady aerodynamics were investigated through: (A) Calculation of reduced frequency and (B) Measuring the effect of the propeller on empennage aerodynamics. This is relevant since the propeller is directly in front of the empennage.
Advisors/Committee Members: Keshmiri, Shawn (advisor), Taghavi, Ray (cmtemember), Huang, Weizhang (cmtemember).
Subjects/Keywords: Aerospace engineering; Mechanical engineering; Aircraft System Identification; Extended Kalman Filter; Flight Dynamics; Stability and Control Derivatives; UAV; Unmanned Aerial Vehicle
…CFD results obtained from another UAS at the University of Kansas [18]. This… …of Kansas Flight
Systems Team owns several SkyHunter aircraft that it uses for research… …the SkyHunter
UAS. An image of the UAS is presented in the following figure. The University…
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APA ·
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APA (6th Edition):
Benyamen, H. (2019). Stability and Control Derivatives Identification for an Unmanned Aerial Vehicle with Low Cost Sensors Using an Extended Kalman Filter Algorithm. (Masters Thesis). University of Kansas. Retrieved from http://hdl.handle.net/1808/29631
Chicago Manual of Style (16th Edition):
Benyamen, Hady. “Stability and Control Derivatives Identification for an Unmanned Aerial Vehicle with Low Cost Sensors Using an Extended Kalman Filter Algorithm.” 2019. Masters Thesis, University of Kansas. Accessed February 27, 2021.
http://hdl.handle.net/1808/29631.
MLA Handbook (7th Edition):
Benyamen, Hady. “Stability and Control Derivatives Identification for an Unmanned Aerial Vehicle with Low Cost Sensors Using an Extended Kalman Filter Algorithm.” 2019. Web. 27 Feb 2021.
Vancouver:
Benyamen H. Stability and Control Derivatives Identification for an Unmanned Aerial Vehicle with Low Cost Sensors Using an Extended Kalman Filter Algorithm. [Internet] [Masters thesis]. University of Kansas; 2019. [cited 2021 Feb 27].
Available from: http://hdl.handle.net/1808/29631.
Council of Science Editors:
Benyamen H. Stability and Control Derivatives Identification for an Unmanned Aerial Vehicle with Low Cost Sensors Using an Extended Kalman Filter Algorithm. [Masters Thesis]. University of Kansas; 2019. Available from: http://hdl.handle.net/1808/29631
13.
Saraswat, Jyoti.
A Study of Vandermonde-like Matrix Systems With Emphasis on Preconditioning and Krylov Matrix Connection.
Degree: MA, Mathematics, 2009, University of Kansas
URL: http://hdl.handle.net/1808/5528
► The study focuses primarily on Vandermonde-like matrix systems. The idea is to express Vandermonde and Vandermonde-like matrix systems as the problems related to Krylov Matrices.…
(more)
▼ The study focuses primarily on Vandermonde-like matrix systems. The idea is to express Vandermonde and Vandermonde-like matrix systems as the problems related to Krylov Matrices. The connection provides a different angle to view the Vandermonde-like systems. Krylov subspace methods are strongly related to polynomial spaces, hence a nice connection can be established using LU factorization as proposed by Bjorck and Pereyra and QR factorization by Reichel. Further an algorithm to generate a preconditioner is incorporated in GR algorithm given by Reichel . This generates a preconditioner for Vandermonde-like matrices consisting of polynomials which obey a three term recurrence relation. This general preconditioner works effectively for Vandermonde matrices as well. The preconditioner is then tested on various distinct nodes. Based on results obtained, it is established that the condition number of Vandermonde -like matrices can be lowered significantly by application of the preconditioner, for some cases.
Advisors/Committee Members: Xu, Dr. Hongguo (advisor), Huang, Weizhang (cmtemember), Vleck, Dr. Erik Van (cmtemember).
Subjects/Keywords: Mathematics; Krylov matrix; Preconditioner; Vandermonde matrix
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APA (6th Edition):
Saraswat, J. (2009). A Study of Vandermonde-like Matrix Systems With Emphasis on Preconditioning and Krylov Matrix Connection. (Masters Thesis). University of Kansas. Retrieved from http://hdl.handle.net/1808/5528
Chicago Manual of Style (16th Edition):
Saraswat, Jyoti. “A Study of Vandermonde-like Matrix Systems With Emphasis on Preconditioning and Krylov Matrix Connection.” 2009. Masters Thesis, University of Kansas. Accessed February 27, 2021.
http://hdl.handle.net/1808/5528.
MLA Handbook (7th Edition):
Saraswat, Jyoti. “A Study of Vandermonde-like Matrix Systems With Emphasis on Preconditioning and Krylov Matrix Connection.” 2009. Web. 27 Feb 2021.
Vancouver:
Saraswat J. A Study of Vandermonde-like Matrix Systems With Emphasis on Preconditioning and Krylov Matrix Connection. [Internet] [Masters thesis]. University of Kansas; 2009. [cited 2021 Feb 27].
Available from: http://hdl.handle.net/1808/5528.
Council of Science Editors:
Saraswat J. A Study of Vandermonde-like Matrix Systems With Emphasis on Preconditioning and Krylov Matrix Connection. [Masters Thesis]. University of Kansas; 2009. Available from: http://hdl.handle.net/1808/5528
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 27, 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. 27 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 27].
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.
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 27, 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. 27 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 27].
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
16.
Smith, Nathan Allen.
Optimal Lateral Guidance for Automatic Landing of a High Altitude Long Endurance Unmanned Aerial System with Crosswind Rejection.
Degree: MS, Aerospace Engineering, 2016, University of Kansas
URL: http://hdl.handle.net/1808/22354
► Unmanned aerial systems will be the dominant force in the aviation industry. Among these aircraft the use of high altitude long endurance unmanned aerial systems…
(more)
▼ Unmanned aerial systems will be the dominant force in the aviation industry. Among these aircraft the use of high altitude long endurance unmanned aerial systems has increased dramatically. Based on the geometry of these types of aircraft the possible changing weather conditions during long flights poses many problems. These difficulties are compounded by the push towards fully autonomous systems. Large wingspan and, typically, small in-line landing gear make a landing in crosswind exceedingly difficult. This study uses a modified gain scheduling technique for optimizing the landing attitude for a generic vehicle based on geometry and crosswind speed. This is performed by directly utilizing the crosswind estimation to calculate a desired crab and roll angle that gives the lowest risk attitude for landing. An extended Kalman filter is developed that estimates the aircraft states as well as the 3D wind component acting on the aircraft. The aircraft used in this analysis is the DG808S, a large wingspan lightweight electric glider. The aircraft is modelled using Advanced Aircraft Analysis software and a six degree of freedom nonlinear simulation is implemented for testing. The controller used is a nonlinear model predictive controller. The simulations show that the extended Kalman filter is capable of estimating the crosswind and can therefore be used in the full aircraft simulation. Different crosswind settings are used which include both constant crosswind and gust conditions. Crosswind landing capabilities are increased by 35%. Deviation from the desired path in the cruise phase is reduced by up to 68% and time to path convergence is reduced by up to 53%.
Advisors/Committee Members: Keshmiri, Shawn (advisor), Keshmiri, Shawn (cmtemember), Ewing, Mark (cmtemember), Huang, Weizhang (cmtemember).
Subjects/Keywords: Aerospace engineering; Crosswind; Guidance; High Altitude Long Endurance; Unmanned Aerial System
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APA (6th Edition):
Smith, N. A. (2016). Optimal Lateral Guidance for Automatic Landing of a High Altitude Long Endurance Unmanned Aerial System with Crosswind Rejection. (Masters Thesis). University of Kansas. Retrieved from http://hdl.handle.net/1808/22354
Chicago Manual of Style (16th Edition):
Smith, Nathan Allen. “Optimal Lateral Guidance for Automatic Landing of a High Altitude Long Endurance Unmanned Aerial System with Crosswind Rejection.” 2016. Masters Thesis, University of Kansas. Accessed February 27, 2021.
http://hdl.handle.net/1808/22354.
MLA Handbook (7th Edition):
Smith, Nathan Allen. “Optimal Lateral Guidance for Automatic Landing of a High Altitude Long Endurance Unmanned Aerial System with Crosswind Rejection.” 2016. Web. 27 Feb 2021.
Vancouver:
Smith NA. Optimal Lateral Guidance for Automatic Landing of a High Altitude Long Endurance Unmanned Aerial System with Crosswind Rejection. [Internet] [Masters thesis]. University of Kansas; 2016. [cited 2021 Feb 27].
Available from: http://hdl.handle.net/1808/22354.
Council of Science Editors:
Smith NA. Optimal Lateral Guidance for Automatic Landing of a High Altitude Long Endurance Unmanned Aerial System with Crosswind Rejection. [Masters Thesis]. University of Kansas; 2016. Available from: http://hdl.handle.net/1808/22354
17.
Heslar, John.
EFFECTS OF MULTI-ELECTRON CORRELATION ON MULTIPHOTON IONIZATION AND HIGH-ORDER HARMONIC GENERATION OF ATOMIC AND MOLECULAR SYSTEMS IN INTENSE ULTRASHORT LASER FIELDS.
Degree: PhD, Chemistry, 2009, University of Kansas
URL: http://hdl.handle.net/1808/5939
► The study of the electron correlation and quantum dynamics of many-electron atoms and molecules in the presence of intense external fields is a subject of…
(more)
▼ The study of the electron correlation and quantum dynamics of many-electron atoms and molecules in the presence of intense external fields is a subject of much current importance in science and technology. While experimental breakthroughs constantly challenge theorists, the reverse is also true, with theorists suggesting new experimental paths and novel ways to reach exciting regimes where new physics can be explored. For example, we have recently developed ab initio methods and applications to study time dependent quantum dynamics of atoms and molecules which cannot be understood by traditional perturbation theories. Moreover, currently there exist no adequate methods capable of studying the dynamical role of the individual valence electron to the high-order harmonic generation (HHG) and multiphoton ionization (MPI) processes in strong fields. Such a study can provide insights regarding the detailed quantum dynamics and HHG mechanisms, as well as the optimal control of strong-field processes. To advance this strong-field atomic and molecular physics, this dissertation aims at the developing new theoretical formalisms and accurate computational methods for ab initio non-perturbative studies of atomic and molecular processes in intense laser fields. The new methods developed allow in-depth and precision studies of strong-field phenomena for multielectron systems. In this dissertation we investigate the role of electron correlation in dynamics of multielectron systems subject to strong fields. We present a time-dependent density functional theory (TDDFT), with proper asymptotic long-range potential, for nonperturbative treatment of multiphoton processes of homonuclear and heteronuclear diatomic molecules in intense ultrashort laser fields. A time-dependent two-center generalized pseudospectral method is presented for accurate and efficient treatment of the TDDFT equations in space and time. The procedure allows nonuniform and optimal spatial grid discretization of the Hamiltonian in prolate spheroidal coordinates and a split-operator scheme in the energy representation is extended for the time propagation of the individual molecular spin-orbital. The theory is applied to a detailed all-electron study of multiphoton ionization (MPI) and high-order harmonic generation (HHG) processes of N2 and CO molecules in intense laser pulses. The results reveal intriguing and substantially different nonlinear optical response behaviors for N2 and CO, despite the fact that CO has only a very small permanent dipole moment. In particular, we found that the MPI rate for CO is higher than that of N2. Furthermore, while laser excitation of the homonuclear N2 molecule can generate only odd harmonics, both even and odd harmonics can be produced from the heteronuclear CO molecule. Next, we present a complex-scaling (CS)-generalized pseudospectral (GPS) method in hyperspherical coordinates (HSC) for an accurate ab initio and accurate treatment of the electron structure and quantum dynamics of two-electron systems. The six-dimensional coupled…
Advisors/Committee Members: Chu, Shih-I (advisor), Cravens, Thomas E. (cmtemember), Hierl, Peter M. (cmtemember), Kuczera, Krzysztof (cmtemember), Huang, Weizhang (cmtemember).
Subjects/Keywords: Physical chemistry; Physics; Theory; Atomic physics; Complex-scaling generalized; Density functional theory; Generalized pseudospectral method; High-harmonic generation; Hyperspherical coordinates
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APA (6th Edition):
Heslar, J. (2009). EFFECTS OF MULTI-ELECTRON CORRELATION ON MULTIPHOTON IONIZATION AND HIGH-ORDER HARMONIC GENERATION OF ATOMIC AND MOLECULAR SYSTEMS IN INTENSE ULTRASHORT LASER FIELDS. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/5939
Chicago Manual of Style (16th Edition):
Heslar, John. “EFFECTS OF MULTI-ELECTRON CORRELATION ON MULTIPHOTON IONIZATION AND HIGH-ORDER HARMONIC GENERATION OF ATOMIC AND MOLECULAR SYSTEMS IN INTENSE ULTRASHORT LASER FIELDS.” 2009. Doctoral Dissertation, University of Kansas. Accessed February 27, 2021.
http://hdl.handle.net/1808/5939.
MLA Handbook (7th Edition):
Heslar, John. “EFFECTS OF MULTI-ELECTRON CORRELATION ON MULTIPHOTON IONIZATION AND HIGH-ORDER HARMONIC GENERATION OF ATOMIC AND MOLECULAR SYSTEMS IN INTENSE ULTRASHORT LASER FIELDS.” 2009. Web. 27 Feb 2021.
Vancouver:
Heslar J. EFFECTS OF MULTI-ELECTRON CORRELATION ON MULTIPHOTON IONIZATION AND HIGH-ORDER HARMONIC GENERATION OF ATOMIC AND MOLECULAR SYSTEMS IN INTENSE ULTRASHORT LASER FIELDS. [Internet] [Doctoral dissertation]. University of Kansas; 2009. [cited 2021 Feb 27].
Available from: http://hdl.handle.net/1808/5939.
Council of Science Editors:
Heslar J. EFFECTS OF MULTI-ELECTRON CORRELATION ON MULTIPHOTON IONIZATION AND HIGH-ORDER HARMONIC GENERATION OF ATOMIC AND MOLECULAR SYSTEMS IN INTENSE ULTRASHORT LASER FIELDS. [Doctoral Dissertation]. University of Kansas; 2009. Available from: http://hdl.handle.net/1808/5939
18.
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 27, 2021.
http://hdl.handle.net/1808/10819.
MLA Handbook (7th Edition):
Lamb, Charles. “Neutral Equations of Mixed Type.” 2012. Web. 27 Feb 2021.
Vancouver:
Lamb C. Neutral Equations of Mixed Type. [Internet] [Doctoral dissertation]. University of Kansas; 2012. [cited 2021 Feb 27].
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
19.
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 27, 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. 27 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 27].
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
20.
Yang, Xiaoming.
Numerical Analyses of Geocell-Reinforced Granular Soils under Static and Repeated Loads.
Degree: PhD, Civil, Environmental, & Architectural Engineering, 2010, University of Kansas
URL: http://hdl.handle.net/1808/6782
► Geocell is one of the geosynthetic products used primarily for soil reinforcement. It was originally developed by US Army Corps of Engineers in 1970s for…
(more)
▼ Geocell is one of the geosynthetic products used primarily for soil reinforcement. It was originally developed by US Army Corps of Engineers in 1970s for quick reinforcement of cohesionless soil in the military field. Due to its unique three-dimensional geometry, geocell can provide great lateral confinement to the infill soil without relying on the interlocking or friction with the infill soil. Despite the successful applications in various types of civil engineering projects, the mechanism of geocell reinforcement has not been well understood, especially for load-supporting applications. In this study, laboratory model tests (including static load tests and moving wheel load tests) were performed to characterize the performance of the geocell-reinforced soil. A total of four types of geocell (manufactured by PRS Mediterranean, Inc.) were tested in this study. One was made from conventional high density polyethylene (HDPE) and the other three were made from novel polymer alloy (NPA). NPA is a new material characterized by flexibility at low temperatures similar to HDPE with elastic behavior similar to engineering thermoplastic. Test result showed that geocell products tested in this study can improve the modulus and strength of the granular soil under static load, as well as reduce the permanent deformation of the unpaved road under moving wheel loads. Three-dimensional numerical models were developed in this study to simulate the behavior of geocell-reinforced soil under static and repeated loads. In the model for static loading, the infill soil is modeled using a non-linear elastoplastic model (also known as the Duncan-Chang model), and the geocell was modeled using linear elastic plate model. A mechanistic-empirical model was developed for NPA geocell-reinforced soil under repeated loads. This model was developed based on the stress-dependent response model in the current mechanistic-empirical pavement design guide (MEPDG). Some modifications were made to consider (a) the three-dimensional constitutive equation of tangent resilient modulus, (b) the compaction-induced initial horizontal stress in the soil, and (c) the residual stress increase due to the accumulated permanent deformation of geocell with the number of load passes. Analyses showed that the numerical models created in this study can well simulate the experimental result from the geocell-reinforced soils. Based on the calibrated numerical models, a parametric study was performed to investigate the effects from various factors, i.e., (a) thickness of the geocell-reinforced layer, (b) geocell modulus, (c) subgrade stiffness and strength, (d) interface shear modulus, and (e) infill material modulus. The mechanistic-empirical design methods for paved and unpaved roads with geocell-reinforced bases were also discussed.
Advisors/Committee Members: Han, Jie (advisor), Huang, Weizhang (cmtemember), Misra, Anil (cmtemember), Parsons, Robert L. (cmtemember), Schrock, Steven (cmtemember).
Subjects/Keywords: Civil engineering
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Export
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APA (6th Edition):
Yang, X. (2010). Numerical Analyses of Geocell-Reinforced Granular Soils under Static and Repeated Loads. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/6782
Chicago Manual of Style (16th Edition):
Yang, Xiaoming. “Numerical Analyses of Geocell-Reinforced Granular Soils under Static and Repeated Loads.” 2010. Doctoral Dissertation, University of Kansas. Accessed February 27, 2021.
http://hdl.handle.net/1808/6782.
MLA Handbook (7th Edition):
Yang, Xiaoming. “Numerical Analyses of Geocell-Reinforced Granular Soils under Static and Repeated Loads.” 2010. Web. 27 Feb 2021.
Vancouver:
Yang X. Numerical Analyses of Geocell-Reinforced Granular Soils under Static and Repeated Loads. [Internet] [Doctoral dissertation]. University of Kansas; 2010. [cited 2021 Feb 27].
Available from: http://hdl.handle.net/1808/6782.
Council of Science Editors:
Yang X. Numerical Analyses of Geocell-Reinforced Granular Soils under Static and Repeated Loads. [Doctoral Dissertation]. University of Kansas; 2010. Available from: http://hdl.handle.net/1808/6782
University of Kansas
21.
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 27, 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. 27 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 27].
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
22.
Huang, Jie.
COUPLED MECHANICAL AND HYDRAULIC MODELING OF GEOSYNTHETIC-REINFORCED COLUMN-SUPPORTED EMBANKMENTS.
Degree: PH.D., Civil, Environmental, & Architectural Engineering, 2007, University of Kansas
URL: http://hdl.handle.net/1808/1980
► Geosynthetic-reinforced column-supported (GRCS) embankments have been increasingly used worldwide in the past few years. Even though a number of research investigations have been completed on…
(more)
▼ Geosynthetic-reinforced column-supported (GRCS) embankments have been increasingly used worldwide in the past few years. Even though a number of research investigations have been completed on this topic, the behavior of GRCS embankments is not well understood. To improve the understanding of this technology, coupled mechanical and hydraulic numerical analyses were conducted in this study under both two-dimensional (2D) and three-dimensional (3D) conditions to investigate influence of various factors on the performance of GRCS embankments. The selected parameters and their ranges in this study were based on deep-mixed (DM) columns; however, a similar study can be conducted for other types of columns. 2D and 3D models were developed based on elasto-plastic constitutive relationships with Mohr-Coulomb failure criteria for DM walls or columns, soft soil, firm soil, and embankment fill. Cable and geogrid elements were selected to simulate geosynthetic reinforcement in 2D and 3D models, respectively. Staged construction was modeled by building the embankment in lifts. The ground water table was assumed at the ground surface. The mechanical model was coupled with the hydraulic model to simulate the generation and dissipation of excess pore water pressure during and after the construction. The 2D and 3D models were calibrated using a well documented case history with long-term field measurement data and fairly detailed material information to ensure their reasonableness and adequacy. Upon completion of the model calibrations, a 2D baseline case based on a typical configuration of GRCS embankment was analyzed. A 2D parametric study was conducted by changing the parameters individually from the baseline case to investigate the influence of that factor on the performance of the embankment including post-construction settlement, post-construction differential settlement, distortion, tension in geosynthetic, effective stress, stress concentration ratio, excess pore water pressure, and degree of consolidation. The investigated factors include soft soil modulus, soft soil friction angle, soft soil permeability, DM column modulus, DM column spacing, geosynthetic tensile stiffness, and average construction rate. After the 2D study was completed, the 2D baseline case was converted into a 3D baseline case based on an area-weighted average approach assuming a square pattern of DM columns. The 3D parametric study was preformed by changing parameters individually from the 3D baseline case to investigate the influence of that specific factor on the performance of the embankment. The factors investigated are the same as those in the 2D parametric study. On the basis of the numerical results from the 2D and 3D studies, the influence of factors on the performance of the embankment system was rated to provide guidance for practical use.
Advisors/Committee Members: Han, Jie (advisor), Bennett, Caroline (cmtemember), Huang, Weizhang (cmtemember), Parsons, Robert L. (cmtemember), Thomas, Francis (cmtemember).
Subjects/Keywords: Civil engineering
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APA ·
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Export
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APA (6th Edition):
Huang, J. (2007). COUPLED MECHANICAL AND HYDRAULIC MODELING OF GEOSYNTHETIC-REINFORCED COLUMN-SUPPORTED EMBANKMENTS. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/1980
Chicago Manual of Style (16th Edition):
Huang, Jie. “COUPLED MECHANICAL AND HYDRAULIC MODELING OF GEOSYNTHETIC-REINFORCED COLUMN-SUPPORTED EMBANKMENTS.” 2007. Doctoral Dissertation, University of Kansas. Accessed February 27, 2021.
http://hdl.handle.net/1808/1980.
MLA Handbook (7th Edition):
Huang, Jie. “COUPLED MECHANICAL AND HYDRAULIC MODELING OF GEOSYNTHETIC-REINFORCED COLUMN-SUPPORTED EMBANKMENTS.” 2007. Web. 27 Feb 2021.
Vancouver:
Huang J. COUPLED MECHANICAL AND HYDRAULIC MODELING OF GEOSYNTHETIC-REINFORCED COLUMN-SUPPORTED EMBANKMENTS. [Internet] [Doctoral dissertation]. University of Kansas; 2007. [cited 2021 Feb 27].
Available from: http://hdl.handle.net/1808/1980.
Council of Science Editors:
Huang J. COUPLED MECHANICAL AND HYDRAULIC MODELING OF GEOSYNTHETIC-REINFORCED COLUMN-SUPPORTED EMBANKMENTS. [Doctoral Dissertation]. University of Kansas; 2007. Available from: http://hdl.handle.net/1808/1980
University of Kansas
23.
Jin, Yasong.
Maximum Queue Length of a Fluid Model with a Gaussian Input.
Degree: PH.D., Mathematics, 2007, University of Kansas
URL: http://hdl.handle.net/1808/3993
► A fractional Brownian queueing model, that is, a fluid model with an input of a fractional Brownian motion, was proposed in the 1990s to capture…
(more)
▼ A fractional Brownian queueing model, that is, a fluid model with an input of a fractional Brownian motion, was proposed in the 1990s to capture the self-similarity and long-range dependence observed in Internet traffic. Since then, a Gaussian queueing model, which is a queueing model with an input of a continuous Gaussian process, has received much attention. In this dissertation, a Gaussian queueing model is discussed and the maximum queue length over a time interval [0, t] is analyzed. Under some mild assumptions, it is shown that a limit of the maximum queue length suitably normalized is determined by a suitable function of the asymptotic variance of the Gaussian input. Some Gaussian queueing models, such as a queue with an input of several independent fractional Brownian motions and a queue with an input of an integrated Ornstein-Uhlenbeck process, are discussed as examples. For a fractional Brownian queueing model, the main results extend some related known results in the literature. The results on the maximum queue length provide insights for the occurrence of large excursions, which are also called congestion events, in a queueing process. In the context of a fractional Brownian queueing model the temporal properties of congestion events, such as the duration and the inter-congestion event time, are analyzed. A new method based on a Poisson clumping approximation is proposed to evaluate these properties. By comparing with simulation results, it is illustrated that the proposed methodology produces satisfying results for estimating the temporal properties of congestion events in a fractional Brownian queueing model.
Advisors/Committee Members: Duncan, Tyrone E. (advisor), Hu, Yaozhong (cmtemember), Huang, Weizhang (cmtemember), Pasik-Duncan, Bozenna (cmtemember), Frost, Victor S. (cmtemember).
Subjects/Keywords: Mathematics; Queue; Fractional brownian motion; Maximum queue length; Network modeling
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APA (6th Edition):
Jin, Y. (2007). Maximum Queue Length of a Fluid Model with a Gaussian Input. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/3993
Chicago Manual of Style (16th Edition):
Jin, Yasong. “Maximum Queue Length of a Fluid Model with a Gaussian Input.” 2007. Doctoral Dissertation, University of Kansas. Accessed February 27, 2021.
http://hdl.handle.net/1808/3993.
MLA Handbook (7th Edition):
Jin, Yasong. “Maximum Queue Length of a Fluid Model with a Gaussian Input.” 2007. Web. 27 Feb 2021.
Vancouver:
Jin Y. Maximum Queue Length of a Fluid Model with a Gaussian Input. [Internet] [Doctoral dissertation]. University of Kansas; 2007. [cited 2021 Feb 27].
Available from: http://hdl.handle.net/1808/3993.
Council of Science Editors:
Jin Y. Maximum Queue Length of a Fluid Model with a Gaussian Input. [Doctoral Dissertation]. University of Kansas; 2007. Available from: http://hdl.handle.net/1808/3993
University of Kansas
24.
Son, Sang-Kil.
New Development of Theoretical and Computational Methods for Probing Strong-Field Multiphoton Processes.
Degree: PhD, Chemistry, 2009, University of Kansas
URL: http://hdl.handle.net/1808/5986
► The study of the strong-field multiphoton processes is a subject of much current significance in physics and chemistry. Recent progress of laser technology has triggered…
(more)
▼ The study of the strong-field multiphoton processes is a subject of much current significance in physics and chemistry. Recent progress of laser technology has triggered a burst of attosecond science where the electron dynamics plays a vital role in underlying physics. The nonlinear strong-field phenomena, such as multiphoton ionization, multiphoton resonance, high-order harmonic generation, etc, are beyond the perturbative regime and demand novel theoretical approaches for better understanding. This dissertation aims at developing new theoretical and computational methods with innovative spatial and temporal treatments, and delivering comprehensive studies of strong-field multiphoton processes explored by the proposed methods. The time-dependent Voronoi-cell finite difference method is a new grid-based method for electronic structure and dynamics calculations of polyatomic molecules. The spatial part is accurately treated by the Voronoi-cell finite difference method on multicenter molecular grids, featuring high adaptivity and simplicity. The temporal part is solved by the split-operator time propagation technique, allowing accurate and efficient non-perturbative treatment of electronic dynamics in strong fields. The method is applied to self-interaction-free time-dependent density-functional calculations to probe multiphoton processes of polyatomic molecules in intense ultrashort laser fields with arbitrary field-molecule orientation, highlighting the importance of multielectron effects. The generalized Floquet theory is extended for the investigations of an atom in intense frequency-comb laser fields and a qubit system driven by intense oscillating fields. For the frequency-comb laser generated by a temporal train of pulses, the many-mode Floquet theory is extended to treat the interaction of an atom and a series of comb frequencies, demonstrating coherent control of simultaneous multiphoton resonance processes. For the strongly driven qubit, the Floquet theory is extended and its analytic solution is derived to explore multiphoton quantum interference in the superconducting flux qubit.
Advisors/Committee Members: Chu, Shih-I (advisor), Cravens, Thomas E. (cmtemember), Han, Siyuan (cmtemember), Hierl, Peter M. (cmtemember), Huang, Weizhang (cmtemember), Kuczera, Krzysztof (cmtemember).
Subjects/Keywords: Physical chemistry; Molecular physics; Physics; Optics; Attosecond electronic dynamics in polyatomic molecules; Frequency-comb laser; Generalized floquet theory; Strong-field multiphoton processes; Superconducting flux qubit; Time-dependent voronoi-cell finite difference method
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APA ·
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MLA ·
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Export
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Manager
APA (6th Edition):
Son, S. (2009). New Development of Theoretical and Computational Methods for Probing Strong-Field Multiphoton Processes. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/5986
Chicago Manual of Style (16th Edition):
Son, Sang-Kil. “New Development of Theoretical and Computational Methods for Probing Strong-Field Multiphoton Processes.” 2009. Doctoral Dissertation, University of Kansas. Accessed February 27, 2021.
http://hdl.handle.net/1808/5986.
MLA Handbook (7th Edition):
Son, Sang-Kil. “New Development of Theoretical and Computational Methods for Probing Strong-Field Multiphoton Processes.” 2009. Web. 27 Feb 2021.
Vancouver:
Son S. New Development of Theoretical and Computational Methods for Probing Strong-Field Multiphoton Processes. [Internet] [Doctoral dissertation]. University of Kansas; 2009. [cited 2021 Feb 27].
Available from: http://hdl.handle.net/1808/5986.
Council of Science Editors:
Son S. New Development of Theoretical and Computational Methods for Probing Strong-Field Multiphoton Processes. [Doctoral Dissertation]. University of Kansas; 2009. Available from: http://hdl.handle.net/1808/5986
. 
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