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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 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
2.
Wang, Yao.
Efficient Tunnel Detection with Waveform Inversion of Back-scattered Surface Waves.
Degree: MA, Mathematics, 2019, University of Kansas
URL: http://hdl.handle.net/1808/30104
► An efficient subsurface imaging method employing back-scattered surface waves is developed to detect near-surface underground elastic-wave velocity anomalies, such as tunnels, sinkholes, fractures, faults, and…
(more)
▼ An efficient subsurface imaging method employing back-scattered surface waves is developed to detect near-surface underground elastic-wave velocity anomalies, such as tunnels, sinkholes, fractures, faults, and abandoned manmade infrastructures. The back-scattered surface waves are generated by seismic waves impinging on the velocity anomalies and diffracting back toward the source. These wave events contain plentiful information of the subsurface velocity anomalies including spatial location, shape, size, and velocity of the interior medium. Studies have demonstrated that the back-scattered surface waves can be easily distinguished in the frequency-wavenumber (F-k) domain and have less interference by other wave modes. Based on these features, a near-surface velocity anomaly detection method by using waveform inversion of the back-scattered surface waves (BSWI) is proposed. The main objective of this thesis is to review the theoretical background and study the feasibility of the proposed BSWI method. The proposed BSWI method is tested with numerical and real-world examples. First, the numerical example uses the conventional full-waveform inversion (FWI) method as a benchmark to demonstrate the efficiency of BSWI method in detecting shallow velocity anomalies. Then, the BSWI method is tested with field data. In this study, 2D seismic data were acquired over a manmade concrete tunnel located on the main campus of the
University of
Kansas (KU). Different workflows including FWI method and BSWI method are applied to the acquired data and tested for imaging the known tunnel. The field example demonstrates that BSWI can accurately image the tunnel. Compared with FWI, BSWI is less demanding in data processing. Finally, this thesis concludes that the proposed BSWI method is capable of efficiently detecting a near-surface tunnel with the minimum amount of data processing which lends it as a method suitable for application in the field.
Advisors/Committee Members: Tu, Xuemin (advisor), Xu, Hongguo (cmtemember), Tsoflias, Georgios P (cmtemember).
Subjects/Keywords: Mathematics; Geophysical engineering; back-scatter; surface waves; waveform inversion
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APA (6th Edition):
Wang, Y. (2019). Efficient Tunnel Detection with Waveform Inversion of Back-scattered Surface Waves. (Masters Thesis). University of Kansas. Retrieved from http://hdl.handle.net/1808/30104
Chicago Manual of Style (16th Edition):
Wang, Yao. “Efficient Tunnel Detection with Waveform Inversion of Back-scattered Surface Waves.” 2019. Masters Thesis, University of Kansas. Accessed February 27, 2021.
http://hdl.handle.net/1808/30104.
MLA Handbook (7th Edition):
Wang, Yao. “Efficient Tunnel Detection with Waveform Inversion of Back-scattered Surface Waves.” 2019. Web. 27 Feb 2021.
Vancouver:
Wang Y. Efficient Tunnel Detection with Waveform Inversion of Back-scattered Surface Waves. [Internet] [Masters thesis]. University of Kansas; 2019. [cited 2021 Feb 27].
Available from: http://hdl.handle.net/1808/30104.
Council of Science Editors:
Wang Y. Efficient Tunnel Detection with Waveform Inversion of Back-scattered Surface Waves. [Masters Thesis]. University of Kansas; 2019. Available from: http://hdl.handle.net/1808/30104
University of Kansas
3.
Fei, Hongliang.
Learning from Structured Data with High Dimensional Structured Input and Output Domain.
Degree: PhD, Electrical Engineering & Computer Science, 2012, University of Kansas
URL: http://hdl.handle.net/1808/10466
► Structured data is accumulated rapidly in many applications, e.g. Bioinformatics, Cheminformatics, social network analysis, natural language processing and text mining. Designing and analyzing algorithms for…
(more)
▼ Structured data is accumulated rapidly in many applications, e.g. Bioinformatics, Cheminformatics, social network analysis, natural language processing and text mining. Designing and analyzing algorithms for handling these large collections of structured data has received significant interests in data mining and machine learning communities, both in the input and output domain. However, it is nontrivial to adopt traditional machine learning algorithms, e.g. SVM, linear regression to structured data. For one thing, the structural information in the input domain and output domain is ignored if applying the normal algorithms to structured data. For another, the major challenge in learning from many high-dimensional structured data is that input/output domain can contain tens of thousands even larger number of features and labels. With the high dimensional structured input space and/or structured output space, learning a low dimensional and consistent structured predictive function is important for both robustness and interpretability of the model. In this dissertation, we will present a few machine learning models that learn from the data with structured input features and structured output tasks. For learning from the data with structured input features, I have developed structured sparse boosting for graph classification, structured joint sparse PCA for anomaly detection and localization. Besides learning from structured input, I also investigated the interplay between structured input and output under the context of multi-task learning. In particular, I designed a multi-task learning algorithms that performs structured feature selection & task relationship Inference. We will demonstrate the applications of these structured models on subgraph based graph classification, networked data stream anomaly detection/localization, multiple cancer type prediction, neuron activity prediction and social behavior prediction. Finally, through my intern work at IBM T.J. Watson Research, I will demonstrate how to leverage structural information from mobile data (e.g. call detail record and GPS data) to derive important places from people's daily life for transit optimization and urban planning.
Advisors/Committee Members: Huan, Jun (advisor), Luo, Bo (cmtemember), Potetz, Brian (cmtemember), Agah, Arvin (cmtemember), Xu, Hongguo (cmtemember).
Subjects/Keywords: Computer science; Information science; Anomaly detection; Classification; Data mining; Machine learning; Structrual sparsity; Structured data
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APA (6th Edition):
Fei, H. (2012). Learning from Structured Data with High Dimensional Structured Input and Output Domain. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/10466
Chicago Manual of Style (16th Edition):
Fei, Hongliang. “Learning from Structured Data with High Dimensional Structured Input and Output Domain.” 2012. Doctoral Dissertation, University of Kansas. Accessed February 27, 2021.
http://hdl.handle.net/1808/10466.
MLA Handbook (7th Edition):
Fei, Hongliang. “Learning from Structured Data with High Dimensional Structured Input and Output Domain.” 2012. Web. 27 Feb 2021.
Vancouver:
Fei H. Learning from Structured Data with High Dimensional Structured Input and Output Domain. [Internet] [Doctoral dissertation]. University of Kansas; 2012. [cited 2021 Feb 27].
Available from: http://hdl.handle.net/1808/10466.
Council of Science Editors:
Fei H. Learning from Structured Data with High Dimensional Structured Input and Output Domain. [Doctoral Dissertation]. University of Kansas; 2012. Available from: http://hdl.handle.net/1808/10466
University of Kansas
4.
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 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
5.
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
6.
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 27, 2021.
http://hdl.handle.net/1808/12977.
MLA Handbook (7th Edition):
Gu, Peidi. “Finding Eigenvalues of Unitary Matrices.” 2013. Web. 27 Feb 2021.
Vancouver:
Gu P. Finding Eigenvalues of Unitary Matrices. [Internet] [Masters thesis]. University of Kansas; 2013. [cited 2021 Feb 27].
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
7.
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
8.
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 ·
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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
9.
Sun, Xiaohui.
Resilient behavior and permanent deformations of triaxial geogrid stabilized bases over weak subgrade.
Degree: D.Eng., Civil, Environmental & Architectural Engineering, 2015, University of Kansas
URL: http://hdl.handle.net/1808/19407
► Geogrid has been playing an important role in solving geotechnical problems such as paved/unpaved roads constructed on weak subgrade. Geogrid provides lateral confinement to resist…
(more)
▼ Geogrid has been playing an important role in solving geotechnical problems such as paved/unpaved roads constructed on weak subgrade. Geogrid provides lateral confinement to resist the lateral movement of aggregates by the interlocking action that occurs between geogrid apertures and surrounding aggregates. The inclusion of geogrid influences the resilient behavior of stabilized bases and benefits the stabilized bases by reducing permanent deformations (i.e. rutting). However, the resilient behavior and the accumulation mechanism of permanent deformations have not been well understood. In this study, cyclic and static plate loading tests were conducted on test sections of geogrid stabilized bases over subgrade under various loading intensities. The test sections were constructed in a geotechnical box with dimensions of 2 m (W) × 2.2 m (L) × 2 m (H) at the
University of
Kansas. The vertical and horizontal pressures along the interface were monitored by earth pressure cells with varying distances away from the centerline of test sections. Permanent and resilient deformations were monitored by LVDTs installed at 0, 0.25, 0.5, and 0.75 m away from the center. The results show that both the vertical and horizontal stresses were redistributed due to the inclusion of geogrids. Vertical stresses were distributed to a wider area, while horizontal stresses were confined to a smaller area close to the loading plate. The presence of geogrids reduced permanent deformations but increased resilient deformations. An analytical solution of the geogrid-stabilized layered elastic system was derived to evaluate the change of earth pressures induced by the inclusion of geogrids. Confinement effect and tensioned membrane effect were treated as external stresses applied at the interface. The base course was treated as transversely-isotropic to capture the modulus degradation at the horizontal direction. Results show that vertical stresses at the interface decreased and horizontal stresses along the centerline increased due to the inclusion of geogrids. The geogrid stabilized sections had higher lateral earth pressure coefficients along the centerline. A simple hypoplastic model was adopted to simulate the resilient behavior of stabilized soils (i.e. with higher lateral earth pressure coefficients). The results show that the soil sample under a stabilized condition had a higher resilient deformation under unloading n as compared with that under an unstabilized condition. The confinement and tensioned membrane effect due to the inclusion of geogrids reduced the permanent deformations not only at the loading stage, but also at the unloading stage.
Advisors/Committee Members: Han, Jie (advisor), Parsons, Robert L (cmtemember), Misra, Anil (cmtemember), Darabi, Masoud (cmtemember), Xu, Hongguo (cmtemember).
Subjects/Keywords: Civil engineering; Base course; Hypoplastic model; Permanent deformation; Resilient behavior; Triaxial geogrid; Weak subgrade
…53
Figure 3.15 The geotechnical box at the University of Kansas…
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APA (6th Edition):
Sun, X. (2015). Resilient behavior and permanent deformations of triaxial geogrid stabilized bases over weak subgrade. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/19407
Chicago Manual of Style (16th Edition):
Sun, Xiaohui. “Resilient behavior and permanent deformations of triaxial geogrid stabilized bases over weak subgrade.” 2015. Doctoral Dissertation, University of Kansas. Accessed February 27, 2021.
http://hdl.handle.net/1808/19407.
MLA Handbook (7th Edition):
Sun, Xiaohui. “Resilient behavior and permanent deformations of triaxial geogrid stabilized bases over weak subgrade.” 2015. Web. 27 Feb 2021.
Vancouver:
Sun X. Resilient behavior and permanent deformations of triaxial geogrid stabilized bases over weak subgrade. [Internet] [Doctoral dissertation]. University of Kansas; 2015. [cited 2021 Feb 27].
Available from: http://hdl.handle.net/1808/19407.
Council of Science Editors:
Sun X. Resilient behavior and permanent deformations of triaxial geogrid stabilized bases over weak subgrade. [Doctoral Dissertation]. University of Kansas; 2015. Available from: http://hdl.handle.net/1808/19407
University of Kansas
10.
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…
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▼ 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
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