subject:(Partial differential equation)

1. Kim, Chanwoo. Initial Boundary Value Problem of the Boltzmann Equation.

Degree: PhD, Mathematics, 2011, Brown University

URL: https://repository.library.brown.edu/studio/item/bdr:11308/

► In this thesis, we study some boundary problems of the Boltzmann equation and the Boltzmann equation with the large external potential.If the gas is contained… (more)

Subjects/Keywords: partial differential equation

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APA (6^th Edition):

Kim, C. (2011). Initial Boundary Value Problem of the Boltzmann Equation. (Doctoral Dissertation). Brown University. Retrieved from https://repository.library.brown.edu/studio/item/bdr:11308/

Chicago Manual of Style (16^th Edition):

Kim, Chanwoo. “Initial Boundary Value Problem of the Boltzmann Equation.” 2011. Doctoral Dissertation, Brown University. Accessed March 05, 2021. https://repository.library.brown.edu/studio/item/bdr:11308/.

MLA Handbook (7^th Edition):

Kim, Chanwoo. “Initial Boundary Value Problem of the Boltzmann Equation.” 2011. Web. 05 Mar 2021.

Vancouver:

Kim C. Initial Boundary Value Problem of the Boltzmann Equation. [Internet] [Doctoral dissertation]. Brown University; 2011. [cited 2021 Mar 05]. Available from: https://repository.library.brown.edu/studio/item/bdr:11308/.

Council of Science Editors:

Kim C. Initial Boundary Value Problem of the Boltzmann Equation. [Doctoral Dissertation]. Brown University; 2011. Available from: https://repository.library.brown.edu/studio/item/bdr:11308/

Delft University of Technology

2. Van Leeuwen, J.P.H. (author). A nonlinear Schrödinger equation in L² with multiplicative white noise.

Degree: 2011, Delft University of Technology

URL: http://resolver.tudelft.nl/uuid:33bc6c32-bf78-4a99-82a4-f315b21781be

In this thesis existence and uniqueness of the solution of a nonlinear Schrödinger equation in L² with multiplicative white noise is proven under some assumptions. Furthermore, pathwise L²-norm conservation of the solution is studied.

Analysis

Applied mathematics

Electrical Engineering, Mathematics and Computer Science

Advisors/Committee Members: Veraar, M.C. (mentor).

Subjects/Keywords: stochastic partial differential equation; nonlinear Schrödinger equation

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APA (6^th Edition):

Van Leeuwen, J. P. H. (. (2011). A nonlinear Schrödinger equation in L² with multiplicative white noise. (Masters Thesis). Delft University of Technology. Retrieved from http://resolver.tudelft.nl/uuid:33bc6c32-bf78-4a99-82a4-f315b21781be

Chicago Manual of Style (16^th Edition):

Van Leeuwen, J P H (author). “A nonlinear Schrödinger equation in L² with multiplicative white noise.” 2011. Masters Thesis, Delft University of Technology. Accessed March 05, 2021. http://resolver.tudelft.nl/uuid:33bc6c32-bf78-4a99-82a4-f315b21781be.

MLA Handbook (7^th Edition):

Van Leeuwen, J P H (author). “A nonlinear Schrödinger equation in L² with multiplicative white noise.” 2011. Web. 05 Mar 2021.

Vancouver:

Van Leeuwen JPH(. A nonlinear Schrödinger equation in L² with multiplicative white noise. [Internet] [Masters thesis]. Delft University of Technology; 2011. [cited 2021 Mar 05]. Available from: http://resolver.tudelft.nl/uuid:33bc6c32-bf78-4a99-82a4-f315b21781be.

Council of Science Editors:

Van Leeuwen JPH(. A nonlinear Schrödinger equation in L² with multiplicative white noise. [Masters Thesis]. Delft University of Technology; 2011. Available from: http://resolver.tudelft.nl/uuid:33bc6c32-bf78-4a99-82a4-f315b21781be

University of Notre Dame

3. Melissa Davidson. Continuity Properties of the Solution Map for the Generalized Reduced Ostrovsky Equation</h1>.

Degree: Mathematics, 2013, University of Notre Dame

URL: https://curate.nd.edu/show/9p29086334c

► It is shown that the data-to-solution map for the generalized reduced Ostrovsky (gRO) equation is not uniformly continuous on bounded sets in Sobolev spaces… (more)

Subjects/Keywords: soliton; wave equation; partial differential equation

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APA (6^th Edition):

Davidson, M. (2013). Continuity Properties of the Solution Map for the Generalized Reduced Ostrovsky Equation</h1>. (Thesis). University of Notre Dame. Retrieved from https://curate.nd.edu/show/9p29086334c

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Davidson, Melissa. “Continuity Properties of the Solution Map for the Generalized Reduced Ostrovsky Equation</h1>.” 2013. Thesis, University of Notre Dame. Accessed March 05, 2021. https://curate.nd.edu/show/9p29086334c.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Davidson, Melissa. “Continuity Properties of the Solution Map for the Generalized Reduced Ostrovsky Equation</h1>.” 2013. Web. 05 Mar 2021.

Vancouver:

Davidson M. Continuity Properties of the Solution Map for the Generalized Reduced Ostrovsky Equation</h1>. [Internet] [Thesis]. University of Notre Dame; 2013. [cited 2021 Mar 05]. Available from: https://curate.nd.edu/show/9p29086334c.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Davidson M. Continuity Properties of the Solution Map for the Generalized Reduced Ostrovsky Equation</h1>. [Thesis]. University of Notre Dame; 2013. Available from: https://curate.nd.edu/show/9p29086334c

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Louisville

4. Hapuarachchi, Sujeewa Indika. Regularized solutions for terminal problems of parabolic equations.

Degree: PhD, 2017, University of Louisville

URL: 10.18297/etd/2776 ; https://ir.library.louisville.edu/etd/2776

► The heat equation with a terminal condition problem is not well-posed in the sense of Hadamard so regularization is needed. In general, partial differential… (more)

Subjects/Keywords: partial differential equation; sobolev space; regularization; Partial Differential Equations

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APA (6^th Edition):

Hapuarachchi, S. I. (2017). Regularized solutions for terminal problems of parabolic equations. (Doctoral Dissertation). University of Louisville. Retrieved from 10.18297/etd/2776 ; https://ir.library.louisville.edu/etd/2776

Chicago Manual of Style (16^th Edition):

Hapuarachchi, Sujeewa Indika. “Regularized solutions for terminal problems of parabolic equations.” 2017. Doctoral Dissertation, University of Louisville. Accessed March 05, 2021. 10.18297/etd/2776 ; https://ir.library.louisville.edu/etd/2776.

MLA Handbook (7^th Edition):

Hapuarachchi, Sujeewa Indika. “Regularized solutions for terminal problems of parabolic equations.” 2017. Web. 05 Mar 2021.

Vancouver:

Hapuarachchi SI. Regularized solutions for terminal problems of parabolic equations. [Internet] [Doctoral dissertation]. University of Louisville; 2017. [cited 2021 Mar 05]. Available from: 10.18297/etd/2776 ; https://ir.library.louisville.edu/etd/2776.

Council of Science Editors:

Hapuarachchi SI. Regularized solutions for terminal problems of parabolic equations. [Doctoral Dissertation]. University of Louisville; 2017. Available from: 10.18297/etd/2776 ; https://ir.library.louisville.edu/etd/2776

University of Alberta

5. Huang, Hanlin. Optimal Portfolio-Consumption with Habit Formation under Partial Observations.

Degree: MS, Department of Mathematical and Statistical Sciences, 2016, University of Alberta

URL: https://era.library.ualberta.ca/files/cmc87pq439

► The aim of my thesis consists of characterizing explicitly the optimal consumption and investment strategy for an investor, when her habit level process is incorporated… (more)

Subjects/Keywords: Habit formation; partial observation; stochastic differential equation

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APA (6^th Edition):

Huang, H. (2016). Optimal Portfolio-Consumption with Habit Formation under Partial Observations. (Masters Thesis). University of Alberta. Retrieved from https://era.library.ualberta.ca/files/cmc87pq439

Chicago Manual of Style (16^th Edition):

Huang, Hanlin. “Optimal Portfolio-Consumption with Habit Formation under Partial Observations.” 2016. Masters Thesis, University of Alberta. Accessed March 05, 2021. https://era.library.ualberta.ca/files/cmc87pq439.

MLA Handbook (7^th Edition):

Huang, Hanlin. “Optimal Portfolio-Consumption with Habit Formation under Partial Observations.” 2016. Web. 05 Mar 2021.

Vancouver:

Huang H. Optimal Portfolio-Consumption with Habit Formation under Partial Observations. [Internet] [Masters thesis]. University of Alberta; 2016. [cited 2021 Mar 05]. Available from: https://era.library.ualberta.ca/files/cmc87pq439.

Council of Science Editors:

Huang H. Optimal Portfolio-Consumption with Habit Formation under Partial Observations. [Masters Thesis]. University of Alberta; 2016. Available from: https://era.library.ualberta.ca/files/cmc87pq439

Cornell University

6. Chen, Peng. Novel Uncertainty Quantification Techniques For Problems Described By Stochastic Partial Differential Equations.

Degree: PhD, Mechanical Engineering, 2014, Cornell University

URL: http://hdl.handle.net/1813/38898

► Uncertainty propagation (UP) in physical systems governed by PDEs is a challenging problem. This thesis addresses the development of a number of innovative techniques that… (more)

▼ Uncertainty propagation (UP) in physical systems governed by PDEs is a challenging problem. This thesis addresses the development of a number of innovative techniques that emphasize the need for high-dimensionality modeling, resolving discontinuities in the stochastic space and considering the computational expense of forward solvers. Both Bayesian and non-Bayesian approaches are considered. Applications demonstrating the developed techniques are investigated in the context of flow in porous media and reservoir engineering applications. An adaptive locally weighted projection method (ALWPR) is firstly developed. It adaptively selects the needed runs of the forward solver (data collection) to maximize the predictive capability of the method. The methodology effectively learns the local features and accurately quantifies the uncertainty in the prediction of the statistics. It could provide predictions and confidence intervals at any query input and can deal with multi-output responses. A probabilistic graphical model framework for uncertainty quantification is next introduced. The high dimensionality issue of the input is addressed by a local model reduction framework. Then the conditional distribution of the multi-output responses on the low dimensional representation of the input field is factorized into a product of local potential functions that are represented non-parametrically. A nonparametric loopy belief propagation algorithm is developed for studying uncertainty quantification directly on the graph. The nonparametric nature of the model is able to efficiently capture non-Gaussian features of the response. Finally an infinite mixture of Multi-output Gaussian Process (MGP) models is presented to effectively deal with many of the difficulties of current UQ methods. This model involves an infinite mixture of MGP's using Dirichlet process priors and is trained using Variational Bayesian Inference. The Bayesian nature of the model allows for the quantification of the uncertainties due to the limited number of simulations. The automatic detection of the mixture components by the Variational Inference algorithm is able to capture discontinuities and localized features without adhering to ad hoc constructions. Finally, correlations between the components of multi-variate responses are captured by the underlying MGP model in a natural way. A summary of suggestions for future research in the area of uncertainty quantification field are given at the end of the thesis. Advisors/Committee Members: Zabaras, Nicholas John (chair), Samorodnitsky, Gennady (committee member), Warner, Derek H. (committee member).

Subjects/Keywords: Uncertainty quantification; stochastic partial differential equation

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APA (6^th Edition):

Chen, P. (2014). Novel Uncertainty Quantification Techniques For Problems Described By Stochastic Partial Differential Equations. (Doctoral Dissertation). Cornell University. Retrieved from http://hdl.handle.net/1813/38898

Chicago Manual of Style (16^th Edition):

Chen, Peng. “Novel Uncertainty Quantification Techniques For Problems Described By Stochastic Partial Differential Equations.” 2014. Doctoral Dissertation, Cornell University. Accessed March 05, 2021. http://hdl.handle.net/1813/38898.

MLA Handbook (7^th Edition):

Chen, Peng. “Novel Uncertainty Quantification Techniques For Problems Described By Stochastic Partial Differential Equations.” 2014. Web. 05 Mar 2021.

Vancouver:

Chen P. Novel Uncertainty Quantification Techniques For Problems Described By Stochastic Partial Differential Equations. [Internet] [Doctoral dissertation]. Cornell University; 2014. [cited 2021 Mar 05]. Available from: http://hdl.handle.net/1813/38898.

Council of Science Editors:

Chen P. Novel Uncertainty Quantification Techniques For Problems Described By Stochastic Partial Differential Equations. [Doctoral Dissertation]. Cornell University; 2014. Available from: http://hdl.handle.net/1813/38898

University of Wollongong

7. Mofarreh, Fatemah. Fully nonlinear curvature flow of axially symmetric hypersurfaces.

Degree: PhD, 2015, University of Wollongong

URL: 010102 Algebraic and Differential Geometry, 010110 Partial Differential Equations ; https://ro.uow.edu.au/theses/4699

► In this thesis we consider axially symmetric evolving hypersurfaces mostly with boundary conditions between two parallel planes. The speed function is a fully nonlinear… (more)

Subjects/Keywords: hypersurface; curvature flow; parabolic partial differential equation

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APA (6^th Edition):

Mofarreh, F. (2015). Fully nonlinear curvature flow of axially symmetric hypersurfaces. (Doctoral Dissertation). University of Wollongong. Retrieved from 010102 Algebraic and Differential Geometry, 010110 Partial Differential Equations ; https://ro.uow.edu.au/theses/4699

Chicago Manual of Style (16^th Edition):

Mofarreh, Fatemah. “Fully nonlinear curvature flow of axially symmetric hypersurfaces.” 2015. Doctoral Dissertation, University of Wollongong. Accessed March 05, 2021. 010102 Algebraic and Differential Geometry, 010110 Partial Differential Equations ; https://ro.uow.edu.au/theses/4699.

MLA Handbook (7^th Edition):

Mofarreh, Fatemah. “Fully nonlinear curvature flow of axially symmetric hypersurfaces.” 2015. Web. 05 Mar 2021.

Vancouver:

Mofarreh F. Fully nonlinear curvature flow of axially symmetric hypersurfaces. [Internet] [Doctoral dissertation]. University of Wollongong; 2015. [cited 2021 Mar 05]. Available from: 010102 Algebraic and Differential Geometry, 010110 Partial Differential Equations ; https://ro.uow.edu.au/theses/4699.

Council of Science Editors:

Mofarreh F. Fully nonlinear curvature flow of axially symmetric hypersurfaces. [Doctoral Dissertation]. University of Wollongong; 2015. Available from: 010102 Algebraic and Differential Geometry, 010110 Partial Differential Equations ; https://ro.uow.edu.au/theses/4699

University of Georgia

8. Slavov, George Petrov. Bivariate spline solution to a class of reaction-diffusion equations.

Degree: 2017, University of Georgia

URL: http://hdl.handle.net/10724/36897

► This work presents a method of solving a time dependent partial differential equation, which arises from classic models in ecology concerned with a species’ population… (more)

Subjects/Keywords: bivariate splines; partial differential equation; nonlinear; diffusion

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APA (6^th Edition):

Slavov, G. P. (2017). Bivariate spline solution to a class of reaction-diffusion equations. (Thesis). University of Georgia. Retrieved from http://hdl.handle.net/10724/36897

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Slavov, George Petrov. “Bivariate spline solution to a class of reaction-diffusion equations.” 2017. Thesis, University of Georgia. Accessed March 05, 2021. http://hdl.handle.net/10724/36897.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Slavov, George Petrov. “Bivariate spline solution to a class of reaction-diffusion equations.” 2017. Web. 05 Mar 2021.

Vancouver:

Slavov GP. Bivariate spline solution to a class of reaction-diffusion equations. [Internet] [Thesis]. University of Georgia; 2017. [cited 2021 Mar 05]. Available from: http://hdl.handle.net/10724/36897.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Slavov GP. Bivariate spline solution to a class of reaction-diffusion equations. [Thesis]. University of Georgia; 2017. Available from: http://hdl.handle.net/10724/36897

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Waterloo

9. Tang, Herbert Hoi Chi. The Effects of Extrinsic and Intrinsic Noise on a Tumour and a Proposed Metastasis Model.

Degree: 2015, University of Waterloo

URL: http://hdl.handle.net/10012/10023

► Cancer is a ubiquitous disease that afflicts millions of people worldwide and we will undoubtedly encounter it at some point in our lives, whether it… (more)

▼ Cancer is a ubiquitous disease that afflicts millions of people worldwide and we will undoubtedly encounter it at some point in our lives, whether it be random strangers on the news, or someone much closer. As such, research into cancer (and cures for cancer) has been an intense area of focus. Malignant tumours show three main characteristics: 1) aggressive and uncontrolled growth, 2) invasion into surrounding tissue, and 3) the ability to leave the primary tumour site and invade another organ (metastasis). Mathematical models of these three aspects began in earnest about half a century ago, for example with Laird in 1964 proposing that tumour growth was gompertzian. With the advent of the modern computer, complex partial differential equation (PDE) models of tumour growth which incorporate the other two features of malignant tumours have become accessible to the average researcher. Utilizing a mixture of both analytical and numerical methods, this thesis aims to add to the schema of cancer research by examining the effects of noise on a well established model of tumour growth, and a promising model for mitosis that we hope to eventually adapt to describe metastasis. The tumour model that we will examine is a single species reaction-diffusion model that captures the first two aspects of tumour growth. The reaction part determines how fast the tumour grows and the diffusion part describes how quickly the cancer cells spread within the domain. Adding noise to the model is a method of describing the disorder that is in a typical tumour, and allows us to determine error bounds on the tumour size and survival time, which gives us a sense of how accurate the estimates of those two quantities are. This method of estimating the uncertainty in survival time also allows us to further determine how modifications to the model (such as changing the diffusivity or adding chemotherapy) affects the error in the system. Our model of mitosis is an excitable system that admits a traveling wave as a possible solution. Mitosis is a process that occurs in a very spatially specific manner within the embryo and this model describes how a signal propagates from the centre of the embryo outwards. When we allow noise to perturb the system we will see that the model allows noise induced traveling waves in what would normally be a stable system in a deterministic setting. This means that the parameter range under which signalling can occur is relaxed and traveling waves occur more readily than expected. In terms of metastasis, where the tumour microenvironment is especially noisy and chaotic, that might explain why metastasis is so prevalent in malignant tumours. Adding noise to well established PDE models gives it an extra layer of fidelity that allows us to extract additional information from the model not available in the traditional deterministic setting. Using both a numerical and an analytical approach, this thesis develops and demonstrates general methods for estimating the uncertainty in the model outputs and also…

Subjects/Keywords: Stochastic Differential Equation; Partial Differential Equation; Stochastic Processes; Master Equation; Mathematical Biology

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APA (6^th Edition):

Tang, H. H. C. (2015). The Effects of Extrinsic and Intrinsic Noise on a Tumour and a Proposed Metastasis Model. (Thesis). University of Waterloo. Retrieved from http://hdl.handle.net/10012/10023

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Tang, Herbert Hoi Chi. “The Effects of Extrinsic and Intrinsic Noise on a Tumour and a Proposed Metastasis Model.” 2015. Thesis, University of Waterloo. Accessed March 05, 2021. http://hdl.handle.net/10012/10023.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Tang, Herbert Hoi Chi. “The Effects of Extrinsic and Intrinsic Noise on a Tumour and a Proposed Metastasis Model.” 2015. Web. 05 Mar 2021.

Vancouver:

Tang HHC. The Effects of Extrinsic and Intrinsic Noise on a Tumour and a Proposed Metastasis Model. [Internet] [Thesis]. University of Waterloo; 2015. [cited 2021 Mar 05]. Available from: http://hdl.handle.net/10012/10023.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Tang HHC. The Effects of Extrinsic and Intrinsic Noise on a Tumour and a Proposed Metastasis Model. [Thesis]. University of Waterloo; 2015. Available from: http://hdl.handle.net/10012/10023

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

East Carolina University

10. Tran, Kevin K. Mathematical Techniques for the Analysis of Partial Differential Equations.

Degree: MA, MA-Mathematics, 2018, East Carolina University

URL: http://hdl.handle.net/10342/6745

► This thesis explores various solution methods for partial differential equations. The heat equation, wave equation and Laplace equation are analyzed using techniques from functional analysis,… (more)

Subjects/Keywords: Differential equations, Partial; Heat equation – Numerical solutions; Wave equation – Numerical solutions

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APA (6^th Edition):

Tran, K. K. (2018). Mathematical Techniques for the Analysis of Partial Differential Equations. (Masters Thesis). East Carolina University. Retrieved from http://hdl.handle.net/10342/6745

Chicago Manual of Style (16^th Edition):

Tran, Kevin K. “Mathematical Techniques for the Analysis of Partial Differential Equations.” 2018. Masters Thesis, East Carolina University. Accessed March 05, 2021. http://hdl.handle.net/10342/6745.

MLA Handbook (7^th Edition):

Tran, Kevin K. “Mathematical Techniques for the Analysis of Partial Differential Equations.” 2018. Web. 05 Mar 2021.

Vancouver:

Tran KK. Mathematical Techniques for the Analysis of Partial Differential Equations. [Internet] [Masters thesis]. East Carolina University; 2018. [cited 2021 Mar 05]. Available from: http://hdl.handle.net/10342/6745.

Council of Science Editors:

Tran KK. Mathematical Techniques for the Analysis of Partial Differential Equations. [Masters Thesis]. East Carolina University; 2018. Available from: http://hdl.handle.net/10342/6745

University of Georgia

11. Yan, Yi Heng. Multi-Omic and multi-scale data integration for the characterization of malaria infection in non-human primates.

Degree: 2018, University of Georgia

URL: http://hdl.handle.net/10724/37577

► Plasmodium parasites were identified as the cause of malaria more than 200 years ago. However, malaria remains a public health burden responsible for approximately 400,000… (more)

Subjects/Keywords: Malaria,; Plasmodium cynomolgi; Bioinformatics; Partial Differential Equation Model; Differential Network Analysis

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APA (6^th Edition):

Yan, Y. H. (2018). Multi-Omic and multi-scale data integration for the characterization of malaria infection in non-human primates. (Thesis). University of Georgia. Retrieved from http://hdl.handle.net/10724/37577

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Yan, Yi Heng. “Multi-Omic and multi-scale data integration for the characterization of malaria infection in non-human primates.” 2018. Thesis, University of Georgia. Accessed March 05, 2021. http://hdl.handle.net/10724/37577.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Yan, Yi Heng. “Multi-Omic and multi-scale data integration for the characterization of malaria infection in non-human primates.” 2018. Web. 05 Mar 2021.

Vancouver:

Yan YH. Multi-Omic and multi-scale data integration for the characterization of malaria infection in non-human primates. [Internet] [Thesis]. University of Georgia; 2018. [cited 2021 Mar 05]. Available from: http://hdl.handle.net/10724/37577.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Yan YH. Multi-Omic and multi-scale data integration for the characterization of malaria infection in non-human primates. [Thesis]. University of Georgia; 2018. Available from: http://hdl.handle.net/10724/37577

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Southern Mississippi

12. Walker, Carley. Rapid Implicit Diagonalization of Variable-Coefficient Differential Operators Using the Uncertainty Principle.

Degree: MS, 2020, University of Southern Mississippi

URL: https://aquila.usm.edu/masters_theses/778

► We propose to create a new numerical method for a class of time-dependent PDEs (second-order, one space dimension, Dirichlet boundary conditions) that can be… (more)

Subjects/Keywords: partial; differential; equation; smoothly-varying; second-order; one-dimensional; Partial Differential Equations

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APA (6^th Edition):

Walker, C. (2020). Rapid Implicit Diagonalization of Variable-Coefficient Differential Operators Using the Uncertainty Principle. (Masters Thesis). University of Southern Mississippi. Retrieved from https://aquila.usm.edu/masters_theses/778

Chicago Manual of Style (16^th Edition):

Walker, Carley. “Rapid Implicit Diagonalization of Variable-Coefficient Differential Operators Using the Uncertainty Principle.” 2020. Masters Thesis, University of Southern Mississippi. Accessed March 05, 2021. https://aquila.usm.edu/masters_theses/778.

MLA Handbook (7^th Edition):

Walker, Carley. “Rapid Implicit Diagonalization of Variable-Coefficient Differential Operators Using the Uncertainty Principle.” 2020. Web. 05 Mar 2021.

Vancouver:

Walker C. Rapid Implicit Diagonalization of Variable-Coefficient Differential Operators Using the Uncertainty Principle. [Internet] [Masters thesis]. University of Southern Mississippi; 2020. [cited 2021 Mar 05]. Available from: https://aquila.usm.edu/masters_theses/778.

Council of Science Editors:

Walker C. Rapid Implicit Diagonalization of Variable-Coefficient Differential Operators Using the Uncertainty Principle. [Masters Thesis]. University of Southern Mississippi; 2020. Available from: https://aquila.usm.edu/masters_theses/778

13. Hunter, Ellen R. Energy Calculations and Wave Equations.

Degree: MSin Mathematics, Mathematics, 2018, Missouri State University

URL: https://bearworks.missouristate.edu/theses/3232

► The focus of this thesis is to show how methods of Fourier analysis, in particular Parseval’s equality, can be used to provide explicit energy… (more)

Subjects/Keywords: wave equation; energy; Fourier series; Fourier coeﬃcients; partial diﬀerential equations; Partial Differential Equations

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APA (6^th Edition):

Hunter, E. R. (2018). Energy Calculations and Wave Equations. (Masters Thesis). Missouri State University. Retrieved from https://bearworks.missouristate.edu/theses/3232

Chicago Manual of Style (16^th Edition):

Hunter, Ellen R. “Energy Calculations and Wave Equations.” 2018. Masters Thesis, Missouri State University. Accessed March 05, 2021. https://bearworks.missouristate.edu/theses/3232.

MLA Handbook (7^th Edition):

Hunter, Ellen R. “Energy Calculations and Wave Equations.” 2018. Web. 05 Mar 2021.

Vancouver:

Hunter ER. Energy Calculations and Wave Equations. [Internet] [Masters thesis]. Missouri State University; 2018. [cited 2021 Mar 05]. Available from: https://bearworks.missouristate.edu/theses/3232.

Council of Science Editors:

Hunter ER. Energy Calculations and Wave Equations. [Masters Thesis]. Missouri State University; 2018. Available from: https://bearworks.missouristate.edu/theses/3232

University of Alberta

14. Alavi Shoushtari, Navid. Modern Control Methods for First Order Hyperbolic Partial Differential Equations.

Degree: MS, Department of Chemical and Materials Engineering, 2016, University of Alberta

URL: https://era.library.ualberta.ca/files/cr207tp57n

► This work is focused on two control methods for first order hyperbolic partial differential equations (PDE). The first method investigated is output regulation by employing… (more)

Subjects/Keywords: Backstepping; Output Regulation; First Order Hyperbolic; Partial Differential Equation

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APA (6^th Edition):

Alavi Shoushtari, N. (2016). Modern Control Methods for First Order Hyperbolic Partial Differential Equations. (Masters Thesis). University of Alberta. Retrieved from https://era.library.ualberta.ca/files/cr207tp57n

Chicago Manual of Style (16^th Edition):

Alavi Shoushtari, Navid. “Modern Control Methods for First Order Hyperbolic Partial Differential Equations.” 2016. Masters Thesis, University of Alberta. Accessed March 05, 2021. https://era.library.ualberta.ca/files/cr207tp57n.

MLA Handbook (7^th Edition):

Alavi Shoushtari, Navid. “Modern Control Methods for First Order Hyperbolic Partial Differential Equations.” 2016. Web. 05 Mar 2021.

Vancouver:

Alavi Shoushtari N. Modern Control Methods for First Order Hyperbolic Partial Differential Equations. [Internet] [Masters thesis]. University of Alberta; 2016. [cited 2021 Mar 05]. Available from: https://era.library.ualberta.ca/files/cr207tp57n.

Council of Science Editors:

Alavi Shoushtari N. Modern Control Methods for First Order Hyperbolic Partial Differential Equations. [Masters Thesis]. University of Alberta; 2016. Available from: https://era.library.ualberta.ca/files/cr207tp57n

Vanderbilt University

15. Gao, Min. Age-structured Population Models with Applications.

Degree: PhD, Mathematics, 2015, Vanderbilt University

URL: http://hdl.handle.net/1803/13547

► A general model of age-structured population dynamics of early humans is developed and the fundamental properties of its solutions are analyzed. The model is a… (more)

Subjects/Keywords: semilinear partial differential equation; steady states; stability; Lyapunov functional; population dynamics

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APA (6^th Edition):

Gao, M. (2015). Age-structured Population Models with Applications. (Doctoral Dissertation). Vanderbilt University. Retrieved from http://hdl.handle.net/1803/13547

Chicago Manual of Style (16^th Edition):

Gao, Min. “Age-structured Population Models with Applications.” 2015. Doctoral Dissertation, Vanderbilt University. Accessed March 05, 2021. http://hdl.handle.net/1803/13547.

MLA Handbook (7^th Edition):

Gao, Min. “Age-structured Population Models with Applications.” 2015. Web. 05 Mar 2021.

Vancouver:

Gao M. Age-structured Population Models with Applications. [Internet] [Doctoral dissertation]. Vanderbilt University; 2015. [cited 2021 Mar 05]. Available from: http://hdl.handle.net/1803/13547.

Council of Science Editors:

Gao M. Age-structured Population Models with Applications. [Doctoral Dissertation]. Vanderbilt University; 2015. Available from: http://hdl.handle.net/1803/13547

Boston University

16. Wyman, Jeffries. The Dirichlet problem.

Degree: MA, Mathematics, 1960, Boston University

URL: http://hdl.handle.net/2144/26084

► The problem of finding the solution to a general eliptic type partial differential equation, when the boundary values are given, is generally referred to as… (more)

Subjects/Keywords: Dirichlet problem; Partial differential equation

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APA (6^th Edition):

Wyman, J. (1960). The Dirichlet problem. (Masters Thesis). Boston University. Retrieved from http://hdl.handle.net/2144/26084

Chicago Manual of Style (16^th Edition):

Wyman, Jeffries. “The Dirichlet problem.” 1960. Masters Thesis, Boston University. Accessed March 05, 2021. http://hdl.handle.net/2144/26084.

MLA Handbook (7^th Edition):

Wyman, Jeffries. “The Dirichlet problem.” 1960. Web. 05 Mar 2021.

Vancouver:

Wyman J. The Dirichlet problem. [Internet] [Masters thesis]. Boston University; 1960. [cited 2021 Mar 05]. Available from: http://hdl.handle.net/2144/26084.

Council of Science Editors:

Wyman J. The Dirichlet problem. [Masters Thesis]. Boston University; 1960. Available from: http://hdl.handle.net/2144/26084

Université Catholique de Louvain

17. Di Cosmo, Jonathan. Nonlinear Schrödinger equation and Schrödinger-Poisson system in the semiclassical limit.

Degree: 2011, Université Catholique de Louvain

URL: http://hdl.handle.net/2078.1/93557

►

The nonlinear Schrödinger equation appears in different fields of physics, for example in the theory of Bose-Einstein condensates or in wave propagation models. From a… (more)

▼

The nonlinear Schrödinger equation appears in different fields of physics, for example in the theory of Bose-Einstein condensates or in wave propagation models. From a mathematical point of view, the study of this equation is interesting and delicate, notably because it can have a very rich set of solutions with various behaviours. In this thesis, we have been interested in standing waves, which satisfy an elliptic partial differential equation. When this equation is seen as a singularly perturbed problem, its solutions concentrate, in the sense that they converge uniformly to zero outside some concentration set, while they remain positive on this set. We have obtained three kind of new results. Firstly, under symmetry assumptions, we have found solutions concentrating on a sphere. Secondly, we have obtained the same type of solutions for the Schrödinger-Poisson system. The method consists in applying the mountain pass theorem to a penalized problem. Thirdly, we have proved the existence of solutions of the nonlinear Schrödinger equation concentrating at a local maximum of the potential. These solutions are found by a more general minimax principle. Our results are characterized by very weak assumptions on the potential.

L'équation de Schrödinger non-linéaire apparaît dans différents domaines de la physique, par exemple dans la théorie des condensats de Bose-Einstein ou dans des modèles de propagation d'ondes. D'un point de vue mathématique, l'étude de cette équation est intéressante et délicate, notamment parce qu'elle peut posséder un ensemble très riche de solutions avec des comportements variés. Dans cette thèse , nous nous sommes intéressés aux ondes stationnaires, qui satisfont une équation aux dérivées partielles elliptique. Lorsque cette équation est vue comme un problème de perturbations singulières, ses solutions se concentrent, dans le sens où elles tendent uniformément vers zéro en dehors d'un certain ensemble de concentration, tout en restant positives sur cet ensemble. Nous avons obtenu trois types de résultats nouveaux. Premièrement, sous des hypothèses de symétrie, nous avons trouvé des solutions qui se concentrent sur une sphère. Deuxièmement, nous avons obtenu le même type de solutions pour le système de Schrödinger-Poisson. La méthode consiste à appliquer le théorème du col à un problème pénalisé. Troisièmement, nous avons démontré l'existence de solutions de l'équation de Schrödinger non-linéaire qui se concentrent en un maximum local du potentiel. Ces solutions sont obtenues par un principe de minimax plus général. Nos résultats se caractérisent par des hypothèses très faibles sur le potentiel.

(MATH 3) – UCL, 2011

Advisors/Committee Members: UCL - SST/IRMP/IRMP - Institut de recherche en mathématique et physique, Bonheure, Denis, Van Schaftingen, Jean, Félix, Yves, Gossez, Jean-Pierre, Jeanjean, Louis, Lami Dozo, Enrique, Ponce, Augusto, Willem, Michel.

Subjects/Keywords: Partial differential equations; Nonlinear Schrödinger equation; Variational methods

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APA (6^th Edition):

Di Cosmo, J. (2011). Nonlinear Schrödinger equation and Schrödinger-Poisson system in the semiclassical limit. (Thesis). Université Catholique de Louvain. Retrieved from http://hdl.handle.net/2078.1/93557

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Di Cosmo, Jonathan. “Nonlinear Schrödinger equation and Schrödinger-Poisson system in the semiclassical limit.” 2011. Thesis, Université Catholique de Louvain. Accessed March 05, 2021. http://hdl.handle.net/2078.1/93557.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Di Cosmo, Jonathan. “Nonlinear Schrödinger equation and Schrödinger-Poisson system in the semiclassical limit.” 2011. Web. 05 Mar 2021.

Vancouver:

Di Cosmo J. Nonlinear Schrödinger equation and Schrödinger-Poisson system in the semiclassical limit. [Internet] [Thesis]. Université Catholique de Louvain; 2011. [cited 2021 Mar 05]. Available from: http://hdl.handle.net/2078.1/93557.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Di Cosmo J. Nonlinear Schrödinger equation and Schrödinger-Poisson system in the semiclassical limit. [Thesis]. Université Catholique de Louvain; 2011. Available from: http://hdl.handle.net/2078.1/93557

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Notre Dame

18. Sujin Khomrutai. Regularity of Singular Solutions to Sigma_k-Yamabe Problems</h1>.

Degree: Mathematics, 2009, University of Notre Dame

URL: https://curate.nd.edu/show/wd375t37b4z

► We prove some regularity results for singular solutions of σ_k-Yamabe problem, where the singular set is a compact hypersurface in a Riemannian manifold. This… (more)

Subjects/Keywords: singular solutions; partial differential equation

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APA (6^th Edition):

Khomrutai, S. (2009). Regularity of Singular Solutions to Sigma_k-Yamabe Problems</h1>. (Thesis). University of Notre Dame. Retrieved from https://curate.nd.edu/show/wd375t37b4z

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Khomrutai, Sujin. “Regularity of Singular Solutions to Sigma_k-Yamabe Problems</h1>.” 2009. Thesis, University of Notre Dame. Accessed March 05, 2021. https://curate.nd.edu/show/wd375t37b4z.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Khomrutai, Sujin. “Regularity of Singular Solutions to Sigma_k-Yamabe Problems</h1>.” 2009. Web. 05 Mar 2021.

Vancouver:

Khomrutai S. Regularity of Singular Solutions to Sigma_k-Yamabe Problems</h1>. [Internet] [Thesis]. University of Notre Dame; 2009. [cited 2021 Mar 05]. Available from: https://curate.nd.edu/show/wd375t37b4z.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Khomrutai S. Regularity of Singular Solutions to Sigma_k-Yamabe Problems</h1>. [Thesis]. University of Notre Dame; 2009. Available from: https://curate.nd.edu/show/wd375t37b4z

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Illinois – Urbana-Champaign

19. Skulkhu, Ruth. Asymptotic stability and completeness in 2D nonlinear Schrodinger equation.

Degree: PhD, 0439, 2012, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/32082

► In this thesis we obtained new results on the asymptotic stability of ground states of the nonlinear Schrödinger equation in space dimension two. Under our… (more)

Subjects/Keywords: Mathematics; Partial Differential Equations; Schrödinger Equation; Nonlinear; Completeness; Asymptotic Stability

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APA (6^th Edition):

Skulkhu, R. (2012). Asymptotic stability and completeness in 2D nonlinear Schrodinger equation. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/32082

Chicago Manual of Style (16^th Edition):

Skulkhu, Ruth. “Asymptotic stability and completeness in 2D nonlinear Schrodinger equation.” 2012. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed March 05, 2021. http://hdl.handle.net/2142/32082.

MLA Handbook (7^th Edition):

Skulkhu, Ruth. “Asymptotic stability and completeness in 2D nonlinear Schrodinger equation.” 2012. Web. 05 Mar 2021.

Vancouver:

Skulkhu R. Asymptotic stability and completeness in 2D nonlinear Schrodinger equation. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2012. [cited 2021 Mar 05]. Available from: http://hdl.handle.net/2142/32082.

Council of Science Editors:

Skulkhu R. Asymptotic stability and completeness in 2D nonlinear Schrodinger equation. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2012. Available from: http://hdl.handle.net/2142/32082

University of Illinois – Urbana-Champaign

20. Paranjape, Aditya. Dynamics and control of robotic aircraft with articulated wings.

Degree: PhD, 4048, 2012, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/29818

► There is a considerable interest in developing robotic aircraft, inspired by birds, for a variety of missions covering reconnaissance and surveillance. Flapping wing aircraft concepts… (more)

▼ There is a considerable interest in developing robotic aircraft, inspired by birds, for a variety of missions covering reconnaissance and surveillance. Flapping wing aircraft concepts have been put forth in light of the efficiency of flapping flight at small scales. These aircraft are naturally equipped with the ability to rotate their wings about the root, a form of wing articulation. This thesis covers some problems concerning the performance, stability and control of robotic aircraft with articulated wings in gliding flight. Speci cally, we are interested in aircraft without a vertical tail, which would then use wing articulation for longitudinal as well as lateral-directional control. Although the dynamics and control of articulated wing aircraft share several common features with conventional fi xed wing aircraft, the presence of wing articulation presents several unique benefi ts as well as limitations from the perspective of performance and control. One of the objectives of this thesis is to understand these features using a combination of theoretical and numerical tools. The aircraft concept envisioned in this thesis uses the wing dihedral angles for longitudinal and lateral-directional control. Aircraft with flexible articulated wings are also investigated. We derive a complete nonlinear model of the flight dynamics incorporating dynamic CG location and the changing moment of inertia. We show that symmetric dihedral con guration, along with a conventional horizontal tail, can be used to control flight speed and flight path angle independently of each other. This characteristic is very useful for initiating an efficient perching maneuver. It is shown that wing dihedral angles alone can e ffectively regulate sideslip during rapid turns and generate a wide range of equilibrium turn rates while maintaining a constant flight speed and regulating sideslip. We compute the turning performance limitations that arise due to the use of wing dihedral for yaw control, and compare the steady state performance of rigid and flexible winged aircraft. We present an intuitive but very useful notion, called the e ffective dihedral, which allows us to extend some of the stability and performance results derived for rigid aircraft to flexible aircraft. In the process, we identify the extent of flexibility needed to induce substantial performance bene fits, and conversely the extent to which results derived for rigid aircraft apply to a flexible aircraft. We demonstrate, interestingly enough, that wing flexibility actually causes a deterioration in the maximum achievable turn rate when the sideslip is regulated. We also present experimental results which help demonstrate the capability of wing dihedral for control and for executing maneuvers such as slow, rapid descent and perching. Open loop as well as closed loop experiments are performed to demonstrate (a) the e ffectiveness of symmetric dihedral for flight path angle control, (b) yaw control using asymmetric dihedral, and (c) the elements of perching. … Advisors/Committee Members: Chung, Soon-Jo (advisor), Bergman, Lawrence A. (committee member), Hilton, Harry H. (committee member), Mehta, Prashant G. (committee member), Selig, Michael S. (committee member).

Subjects/Keywords: Flight control; flight mechanics; PDE control; partial differential equation (PDE)

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Paranjape, A. (2012). Dynamics and control of robotic aircraft with articulated wings. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/29818

Chicago Manual of Style (16^th Edition):

Paranjape, Aditya. “Dynamics and control of robotic aircraft with articulated wings.” 2012. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed March 05, 2021. http://hdl.handle.net/2142/29818.

MLA Handbook (7^th Edition):

Paranjape, Aditya. “Dynamics and control of robotic aircraft with articulated wings.” 2012. Web. 05 Mar 2021.

Vancouver:

Paranjape A. Dynamics and control of robotic aircraft with articulated wings. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2012. [cited 2021 Mar 05]. Available from: http://hdl.handle.net/2142/29818.

Council of Science Editors:

Paranjape A. Dynamics and control of robotic aircraft with articulated wings. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2012. Available from: http://hdl.handle.net/2142/29818

University of Waterloo

21. Wang, Heming. A Novel Diffusion-based Empirical Mode Decomposition Algorithm for Signal and Image Analysis.

Degree: 2018, University of Waterloo

URL: http://hdl.handle.net/10012/13559

► In the area of signal analysis and processing, the Fourier transform and wavelet transform are widely applied. Empirical Mode Decomposition(EMD) was proposed as an alternative… (more)

Subjects/Keywords: Empirical Mode Decomposition; Spectral Analysis; Partial Differential Equation

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APA (6^th Edition):

Wang, H. (2018). A Novel Diffusion-based Empirical Mode Decomposition Algorithm for Signal and Image Analysis. (Thesis). University of Waterloo. Retrieved from http://hdl.handle.net/10012/13559

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Wang, Heming. “A Novel Diffusion-based Empirical Mode Decomposition Algorithm for Signal and Image Analysis.” 2018. Thesis, University of Waterloo. Accessed March 05, 2021. http://hdl.handle.net/10012/13559.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Wang, Heming. “A Novel Diffusion-based Empirical Mode Decomposition Algorithm for Signal and Image Analysis.” 2018. Web. 05 Mar 2021.

Vancouver:

Wang H. A Novel Diffusion-based Empirical Mode Decomposition Algorithm for Signal and Image Analysis. [Internet] [Thesis]. University of Waterloo; 2018. [cited 2021 Mar 05]. Available from: http://hdl.handle.net/10012/13559.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Wang H. A Novel Diffusion-based Empirical Mode Decomposition Algorithm for Signal and Image Analysis. [Thesis]. University of Waterloo; 2018. Available from: http://hdl.handle.net/10012/13559

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Georgia

22. Lanterman, James Maxwell. A generalization of bivariate splines over polygonal partitions and applications.

Degree: 2018, University of Georgia

URL: http://hdl.handle.net/10724/38433

► There has recently been interest in extending various finite element methods to more arbitrary partitions, particularly unstructured partitions of various polygons. Various methods aimed at… (more)

Subjects/Keywords: bivariate splines; partial differential equation; finite element methods; local basis

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APA (6^th Edition):

Lanterman, J. M. (2018). A generalization of bivariate splines over polygonal partitions and applications. (Thesis). University of Georgia. Retrieved from http://hdl.handle.net/10724/38433

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Lanterman, James Maxwell. “A generalization of bivariate splines over polygonal partitions and applications.” 2018. Thesis, University of Georgia. Accessed March 05, 2021. http://hdl.handle.net/10724/38433.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Lanterman, James Maxwell. “A generalization of bivariate splines over polygonal partitions and applications.” 2018. Web. 05 Mar 2021.

Vancouver:

Lanterman JM. A generalization of bivariate splines over polygonal partitions and applications. [Internet] [Thesis]. University of Georgia; 2018. [cited 2021 Mar 05]. Available from: http://hdl.handle.net/10724/38433.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Lanterman JM. A generalization of bivariate splines over polygonal partitions and applications. [Thesis]. University of Georgia; 2018. Available from: http://hdl.handle.net/10724/38433

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Oklahoma

23. Razi, Mani. ADAPTIVE GRID BASED FINITE DIFFERENCE METHODS FOR SOLUTION OF HYPERBOLIC PDES: APPLICATION TO COMPUTATIONAL MECHANICS AND UNCERTAINTY QUANTIFICATION.

Degree: PhD, 2015, University of Oklahoma

URL: http://hdl.handle.net/11244/14579

► Novel finite-difference based numerical methods for solution of linear and nonlinear hyperbolic partial differential equations (PDEs) using adaptive grids are proposed in this dissertation. The… (more)

▼ Novel finite-difference based numerical methods for solution of linear and nonlinear hyperbolic partial differential equations (PDEs) using adaptive grids are proposed in this dissertation. The overall goal of this research is to improve the accuracy and/or computational efficiency of numerical solutions via the use of adaptive grids and suitable modifications of a given low-order order finite-difference scheme. These methods can be grouped in two broad categories. The first category of adaptive FD methods proposed in the dissertation attempt to reduce the truncation error and/or enhance the accuracy of the underlying numerical schemes via grid distribution alone. Some approaches for grid distribution considered include those based on (i) a moving uniform mesh/domain, (ii) adaptive gradient based refinement (AGBR) and (iii) unit local Courant-Freidrich-Lewy (CFL) number. The improvement in the accuracy which is obtained using these adaptive methods is limited by the underlying scheme formal order of accuracy. In the second category, the CFL based approach proposed in the first category was extended further using defect correction in order to improve the formal order of accuracy and computational efficiency significantly (i.e. by at least one order or higher). The proposed methods in this category are constructed based upon the analysis of the leading order error terms in the modified differential equation associated with the underlying partial differential equation and finite difference scheme. The error terms corresponding to regular and irregular perturbations are identified and the leading order error terms associated with regular perturbations are eliminated using a non-iterative defect correction approach while the error terms associated with irregular perturbations are eliminated using grid adaptation. In the second category of methods involving defect correction (or reduction of leading order terms of truncation error), we explored two different approaches for selection of adaptive grids. These are based on (i) optimal grid dis- tribution and (ii) remapping with monotonicity preserving interpolation. While the first category of methods may be preferred in view of ease of implementation and lower computational complexity, the second category of methods may be preferred in view of greater accuracy and computational efficiency. The two broad categories of methods, which have been applied to problems involving both bounded and unbounded domains, were also extended to multidimensional cases using a dimensional splitting approaches. The performance of these methods was demonstrated using several example problems in computational uncertainty quantification (CUQ) and computational mechanics. The results of the application of the proposed approaches all indicate improvement in both the accuracy and computational efficiency (by about three orders of magnitude in some selected cases) of underlying schemes. In the context of CUQ, all three proposed adaptive finite different solvers are combined with the… Advisors/Committee Members: Attar, Peter J. (advisor), Vedula, Prakash (advisor), Altan, Cengiz (committee member), Parthasarathy, Ramkumar (committee member), Papavassiliou, Dimitrios (committee member).

Subjects/Keywords: Hyperbolic Partial Differential Equation; Uncertainty Qunatification; Grid Adaptation; Defect Correction

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Razi, M. (2015). ADAPTIVE GRID BASED FINITE DIFFERENCE METHODS FOR SOLUTION OF HYPERBOLIC PDES: APPLICATION TO COMPUTATIONAL MECHANICS AND UNCERTAINTY QUANTIFICATION. (Doctoral Dissertation). University of Oklahoma. Retrieved from http://hdl.handle.net/11244/14579

Chicago Manual of Style (16^th Edition):

Razi, Mani. “ADAPTIVE GRID BASED FINITE DIFFERENCE METHODS FOR SOLUTION OF HYPERBOLIC PDES: APPLICATION TO COMPUTATIONAL MECHANICS AND UNCERTAINTY QUANTIFICATION.” 2015. Doctoral Dissertation, University of Oklahoma. Accessed March 05, 2021. http://hdl.handle.net/11244/14579.

MLA Handbook (7^th Edition):

Razi, Mani. “ADAPTIVE GRID BASED FINITE DIFFERENCE METHODS FOR SOLUTION OF HYPERBOLIC PDES: APPLICATION TO COMPUTATIONAL MECHANICS AND UNCERTAINTY QUANTIFICATION.” 2015. Web. 05 Mar 2021.

Vancouver:

Razi M. ADAPTIVE GRID BASED FINITE DIFFERENCE METHODS FOR SOLUTION OF HYPERBOLIC PDES: APPLICATION TO COMPUTATIONAL MECHANICS AND UNCERTAINTY QUANTIFICATION. [Internet] [Doctoral dissertation]. University of Oklahoma; 2015. [cited 2021 Mar 05]. Available from: http://hdl.handle.net/11244/14579.

Council of Science Editors:

Razi M. ADAPTIVE GRID BASED FINITE DIFFERENCE METHODS FOR SOLUTION OF HYPERBOLIC PDES: APPLICATION TO COMPUTATIONAL MECHANICS AND UNCERTAINTY QUANTIFICATION. [Doctoral Dissertation]. University of Oklahoma; 2015. Available from: http://hdl.handle.net/11244/14579

North Carolina State University

24. May, Lindsay Bard Hilbert. Shear-Driven Particle Size Segregation: Models, Analysis, Numerical Solutions, and Experiments.

Degree: PhD, Applied Mathematics, 2009, North Carolina State University

URL: http://www.lib.ncsu.edu/resolver/1840.16/3398

► Granular materials segregate by particle size when subject to shear, as in avalanches. Particles roll and slide across one another, and other particles fall into… (more)

▼ Granular materials segregate by particle size when subject to shear, as in avalanches. Particles roll and slide across one another, and other particles fall into the voids that form, with smaller particles more likely to fit than larger particles. Small particles segregate to the bottom of the sample, and larger particles are levered upward. These processes are known as kinetic sieving and squeeze expulsion. The evolution of the volume fraction of small particles (ratio of the volume of small particles to the total volume of the system) corresponds to the evolution of segregation in a binary mixture of particles and can be modeled by a nonlinear first order partial differential equation, provided the velocity or shear is a known function of position. In an avalanche, shear is approximately uniform in depth, however, in boundary driven shear, the velocity is nonlinear and a shear band forms adjacent to the boundary. We explore size segregation with a laboratory experiment and by analyzing a model. We classify solutions to a fundamental initial boundary value problem for avalanche flow in two space dimensions akin to a two dimensional Riemann problem. We describe three solution types; the initial condition determines which solution occurs. We also modify the partial differential equation to model segregation in a system that experiencing nonuniform shear. We measure a velocity profile from the experimental data from a Couette experiment, which provides parameters used to visualize the solution to the initial boundary value problem. We experimentally investigate size segregation using an annular Couette cell, which is constructed of concentric cylinders and has a moving lower boundary that imparts shear to the system and an upper confining boundary that is free to move vertically to accommodate changes in the volume of the system. Initially, the Couette cell contains a layer of large particles below a layer of small particles. The system dilates as shear begins, then contracts as the sample mixes, and again expands as the sample resegregates; the height of the system is correlated to the amount of mixing or segregation. At the end of the experiment, we find a layer of small particles below a layer of large particles. The initial condition for the partial differential equation corresponds to the one dimensional initial configuration of the experiment. We solve two initial boundary value problems, one with a piecewise linear shear rate and one with an exponential shear rate, where the parameters for both cases are derived from the experimental data. In each case, we use the method of characteristics to solve the initial boundary value problem. In both cases, almost all pieces of the solution can be explicitly calculated, and those that cannot are calculated numerically. In the piecewise linear case, there is a material interface across which the characteristic speed jumps; in the exponential case, the characteristics are curved. We compare the model with the exponential shear rate to the experimental data. The… Advisors/Committee Members: Michael Shearer, Committee Chair (advisor), Karen E. Daniels, Committee Co-Chair (advisor), Pierre A. Gremaud, Committee Member (advisor), Mansoor A. Haider, Committee Member (advisor).

Subjects/Keywords: Couette cell experiment; granular materials; partial differential equation model; size segregrgation

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APA (6^th Edition):

May, L. B. H. (2009). Shear-Driven Particle Size Segregation: Models, Analysis, Numerical Solutions, and Experiments. (Doctoral Dissertation). North Carolina State University. Retrieved from http://www.lib.ncsu.edu/resolver/1840.16/3398

Chicago Manual of Style (16^th Edition):

May, Lindsay Bard Hilbert. “Shear-Driven Particle Size Segregation: Models, Analysis, Numerical Solutions, and Experiments.” 2009. Doctoral Dissertation, North Carolina State University. Accessed March 05, 2021. http://www.lib.ncsu.edu/resolver/1840.16/3398.

MLA Handbook (7^th Edition):

May, Lindsay Bard Hilbert. “Shear-Driven Particle Size Segregation: Models, Analysis, Numerical Solutions, and Experiments.” 2009. Web. 05 Mar 2021.

Vancouver:

May LBH. Shear-Driven Particle Size Segregation: Models, Analysis, Numerical Solutions, and Experiments. [Internet] [Doctoral dissertation]. North Carolina State University; 2009. [cited 2021 Mar 05]. Available from: http://www.lib.ncsu.edu/resolver/1840.16/3398.

Council of Science Editors:

May LBH. Shear-Driven Particle Size Segregation: Models, Analysis, Numerical Solutions, and Experiments. [Doctoral Dissertation]. North Carolina State University; 2009. Available from: http://www.lib.ncsu.edu/resolver/1840.16/3398

University of South Carolina

25. Yuan, Shuai. An Ensemble-Based Projection Method and Its Numerical Investigation.

Degree: PhD, Mathematics, 2020, University of South Carolina

URL: https://scholarcommons.sc.edu/etd/5777

► In many cases, partial differential equation (PDE) models involve a set of parameters whose values may vary over a wide range in application problems,… (more)

Subjects/Keywords: Mathematics; partial differential equation; numerical simulations; Navier-Stokes equations; Navier-Stokes

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APA (6^th Edition):

Yuan, S. (2020). An Ensemble-Based Projection Method and Its Numerical Investigation. (Doctoral Dissertation). University of South Carolina. Retrieved from https://scholarcommons.sc.edu/etd/5777

Chicago Manual of Style (16^th Edition):

Yuan, Shuai. “An Ensemble-Based Projection Method and Its Numerical Investigation.” 2020. Doctoral Dissertation, University of South Carolina. Accessed March 05, 2021. https://scholarcommons.sc.edu/etd/5777.

MLA Handbook (7^th Edition):

Yuan, Shuai. “An Ensemble-Based Projection Method and Its Numerical Investigation.” 2020. Web. 05 Mar 2021.

Vancouver:

Yuan S. An Ensemble-Based Projection Method and Its Numerical Investigation. [Internet] [Doctoral dissertation]. University of South Carolina; 2020. [cited 2021 Mar 05]. Available from: https://scholarcommons.sc.edu/etd/5777.

Council of Science Editors:

Yuan S. An Ensemble-Based Projection Method and Its Numerical Investigation. [Doctoral Dissertation]. University of South Carolina; 2020. Available from: https://scholarcommons.sc.edu/etd/5777

Iowa State University

26. Hwang, Sukjung. Holder regularity of solutions of generalized p-Laplacian type parabolic equations.

Degree: 2012, Iowa State University

URL: https://lib.dr.iastate.edu/etd/12667

► Using ideas from the theory of Orlicz spaces, we discuss the Holder regularity of a bounded weak solution of a p-Laplacian type parabolic partial differential… (more)

Subjects/Keywords: generalized Laplacian equation; Holder regularity; Laplacian equation; Orlicz space; Parabolic equation; Partial differential equation; Applied Mathematics

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Hwang, S. (2012). Holder regularity of solutions of generalized p-Laplacian type parabolic equations. (Thesis). Iowa State University. Retrieved from https://lib.dr.iastate.edu/etd/12667

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Hwang, Sukjung. “Holder regularity of solutions of generalized p-Laplacian type parabolic equations.” 2012. Thesis, Iowa State University. Accessed March 05, 2021. https://lib.dr.iastate.edu/etd/12667.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Hwang, Sukjung. “Holder regularity of solutions of generalized p-Laplacian type parabolic equations.” 2012. Web. 05 Mar 2021.

Vancouver:

Hwang S. Holder regularity of solutions of generalized p-Laplacian type parabolic equations. [Internet] [Thesis]. Iowa State University; 2012. [cited 2021 Mar 05]. Available from: https://lib.dr.iastate.edu/etd/12667.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Hwang S. Holder regularity of solutions of generalized p-Laplacian type parabolic equations. [Thesis]. Iowa State University; 2012. Available from: https://lib.dr.iastate.edu/etd/12667

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of South Africa

27. Masebe, Tshidiso Phanuel. A Lie symmetry analysis of the Black-scholes Merton finance model through modified local one-parameter transformations .

Degree: 2014, University of South Africa

URL: http://hdl.handle.net/10500/18410

► The thesis presents a new method of Symmetry Analysis of the Black-Scholes Merton Finance Model through modi ed Local one-parameter transformations. We determine the symmetries… (more)

Subjects/Keywords: Black-Scholes equation; Partial differential equation; Lie Point Symmetry; Lie equivalence transformation; Invariant solution

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Masebe, T. P. (2014). A Lie symmetry analysis of the Black-scholes Merton finance model through modified local one-parameter transformations . (Doctoral Dissertation). University of South Africa. Retrieved from http://hdl.handle.net/10500/18410

Chicago Manual of Style (16^th Edition):

Masebe, Tshidiso Phanuel. “A Lie symmetry analysis of the Black-scholes Merton finance model through modified local one-parameter transformations .” 2014. Doctoral Dissertation, University of South Africa. Accessed March 05, 2021. http://hdl.handle.net/10500/18410.

MLA Handbook (7^th Edition):

Masebe, Tshidiso Phanuel. “A Lie symmetry analysis of the Black-scholes Merton finance model through modified local one-parameter transformations .” 2014. Web. 05 Mar 2021.

Vancouver:

Masebe TP. A Lie symmetry analysis of the Black-scholes Merton finance model through modified local one-parameter transformations . [Internet] [Doctoral dissertation]. University of South Africa; 2014. [cited 2021 Mar 05]. Available from: http://hdl.handle.net/10500/18410.

Council of Science Editors:

Masebe TP. A Lie symmetry analysis of the Black-scholes Merton finance model through modified local one-parameter transformations . [Doctoral Dissertation]. University of South Africa; 2014. Available from: http://hdl.handle.net/10500/18410

University of South Africa

28. Adams, Conny Molatlhegi. A Lie symmetry analysis of the heat equation through modified one-parameter local point transformation .

Degree: 2014, University of South Africa

URL: http://hdl.handle.net/10500/18414

► Using a Lie symmetry group generator and a generalized form of Manale's formula for solving second order ordinary di erential equations, we determine new symmetries… (more)

Subjects/Keywords: Heat equation; Partial differential equation; Lie point symmetry; Lie equivalence transformation; Invariant solution

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Adams, C. M. (2014). A Lie symmetry analysis of the heat equation through modified one-parameter local point transformation . (Masters Thesis). University of South Africa. Retrieved from http://hdl.handle.net/10500/18414

Chicago Manual of Style (16^th Edition):

Adams, Conny Molatlhegi. “A Lie symmetry analysis of the heat equation through modified one-parameter local point transformation .” 2014. Masters Thesis, University of South Africa. Accessed March 05, 2021. http://hdl.handle.net/10500/18414.

MLA Handbook (7^th Edition):

Adams, Conny Molatlhegi. “A Lie symmetry analysis of the heat equation through modified one-parameter local point transformation .” 2014. Web. 05 Mar 2021.

Vancouver:

Adams CM. A Lie symmetry analysis of the heat equation through modified one-parameter local point transformation . [Internet] [Masters thesis]. University of South Africa; 2014. [cited 2021 Mar 05]. Available from: http://hdl.handle.net/10500/18414.

Council of Science Editors:

Adams CM. A Lie symmetry analysis of the heat equation through modified one-parameter local point transformation . [Masters Thesis]. University of South Africa; 2014. Available from: http://hdl.handle.net/10500/18414

Duke University

29. Rudd, Keith. Solving Partial Differential Equations Using Artificial Neural Networks .

Degree: 2013, Duke University

URL: http://hdl.handle.net/10161/8197

► This thesis presents a method for solving partial differential equations (PDEs) using articial neural networks. The method uses a constrained backpropagation (CPROP) approach for… (more)

▼ This thesis presents a method for solving partial differential equations (PDEs) using articial neural networks. The method uses a constrained backpropagation (CPROP) approach for preserving prior knowledge during incremental training for solving nonlinear elliptic and parabolic PDEs adaptively, in non-stationary environments. Compared to previous methods that use penalty functions or Lagrange multipliers, CPROP reduces the dimensionality of the optimization problem by using direct elimination, while satisfying the equality constraints associated with the boundary and initial conditions exactly, at every iteration of the algorithm. The effectiveness of this method is demonstrated through several examples, including nonlinear elliptic and parabolic PDEs with changing parameters and non-homogeneous terms. The computational complexity analysis shows that CPROP compares favorably to existing methods of solution, and that it leads to considerable computational savings when subject to non-stationary environments. The CPROP based approach is extended to a constrained integration (CINT) method for solving initial boundary value partial differential equations (PDEs). The CINT method combines classical Galerkin methods with CPROP in order to constrain the ANN to approximately satisfy the boundary condition at each stage of integration. The advantage of the CINT method is that it is readily applicable to PDEs in irregular domains and requires no special modification for domains with complex geometries. Furthermore, the CINT method provides a semi-analytical solution that is infinitely differentiable. The CINT method is demonstrated on two hyperbolic and one parabolic initial boundary value problems (IBVPs). These IBVPs are widely used and have known analytical solutions. When compared with Matlab's nite element (FE) method, the CINT method is shown to achieve significant improvements both in terms of computational time and accuracy. The CINT method is applied to a distributed optimal control (DOC) problem of computing optimal state and control trajectories for a multiscale dynamical system comprised of many interacting dynamical systems, or agents. A generalized reduced gradient (GRG) approach is presented in which the agent dynamics are described by a small system of stochastic dierential equations (SDEs). A set of optimality conditions is derived using calculus of variations, and used to compute the optimal macroscopic state and microscopic control laws. An indirect GRG approach is used to solve the optimality conditions numerically for large systems of agents. By assuming a parametric control law obtained from the superposition of linear basis functions, the agent control laws can be determined via set-point regulation, such that the macroscopic behavior of the agents is optimized over time, based on multiple, interactive navigation objectives. Lastly, the CINT method is used to identify optimal root profiles in water limited ecosystems. Knowledge of root depths and distributions is vital in… Advisors/Committee Members: Ferrari, Silvia (advisor).

Subjects/Keywords: Mathematics; Artificial Neural Network; Galerkin; Optimal Control; Partial Differential Equation; Richards' Equation

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Rudd, K. (2013). Solving Partial Differential Equations Using Artificial Neural Networks . (Thesis). Duke University. Retrieved from http://hdl.handle.net/10161/8197

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Rudd, Keith. “Solving Partial Differential Equations Using Artificial Neural Networks .” 2013. Thesis, Duke University. Accessed March 05, 2021. http://hdl.handle.net/10161/8197.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Rudd, Keith. “Solving Partial Differential Equations Using Artificial Neural Networks .” 2013. Web. 05 Mar 2021.

Vancouver:

Rudd K. Solving Partial Differential Equations Using Artificial Neural Networks . [Internet] [Thesis]. Duke University; 2013. [cited 2021 Mar 05]. Available from: http://hdl.handle.net/10161/8197.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Rudd K. Solving Partial Differential Equations Using Artificial Neural Networks . [Thesis]. Duke University; 2013. Available from: http://hdl.handle.net/10161/8197

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Kansas

30. Le, Khoa Nguyen. Nonlinear Integrals, Diffusion in Random Environments and Stochastic Partial Differential Equations.

Degree: PhD, Mathematics, 2015, University of Kansas

URL: http://hdl.handle.net/1808/19176

► In this dissertation, we investigate various problems in the analysis of stochastic (partial) differential equations. A part of the dissertation introduces several notions of nonlinear… (more)

Subjects/Keywords: Mathematics; Feynman-Kac formula; Garsia-Rodemich-Rumsey inequality; random environment; stochastic partial differential equation; transport differential equation; young integration

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Le, K. N. (2015). Nonlinear Integrals, Diffusion in Random Environments and Stochastic Partial Differential Equations. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/19176

Chicago Manual of Style (16^th Edition):

Le, Khoa Nguyen. “Nonlinear Integrals, Diffusion in Random Environments and Stochastic Partial Differential Equations.” 2015. Doctoral Dissertation, University of Kansas. Accessed March 05, 2021. http://hdl.handle.net/1808/19176.

MLA Handbook (7^th Edition):

Le, Khoa Nguyen. “Nonlinear Integrals, Diffusion in Random Environments and Stochastic Partial Differential Equations.” 2015. Web. 05 Mar 2021.

Vancouver:

Le KN. Nonlinear Integrals, Diffusion in Random Environments and Stochastic Partial Differential Equations. [Internet] [Doctoral dissertation]. University of Kansas; 2015. [cited 2021 Mar 05]. Available from: http://hdl.handle.net/1808/19176.

Council of Science Editors:

Le KN. Nonlinear Integrals, Diffusion in Random Environments and Stochastic Partial Differential Equations. [Doctoral Dissertation]. University of Kansas; 2015. Available from: http://hdl.handle.net/1808/19176

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