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Dept: Applied Mathematics ^{❌}

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1. Hadzic, Mahir. Stability and instability in the Stefan problem with surface tension.

Degree: PhD, Applied Mathematics, 2010, Brown University

URL: https://repository.library.brown.edu/studio/item/bdr:11068/

► We develop a high-order nonlinear energy method to study the stability of steady states of the Stefan problem with surface tension. There are two prominent…
(more)

Subjects/Keywords: partial differential equations

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APA (6^{th} Edition):

Hadzic, M. (2010). Stability and instability in the Stefan problem with surface tension. (Doctoral Dissertation). Brown University. Retrieved from https://repository.library.brown.edu/studio/item/bdr:11068/

Chicago Manual of Style (16^{th} Edition):

Hadzic, Mahir. “Stability and instability in the Stefan problem with surface tension.” 2010. Doctoral Dissertation, Brown University. Accessed August 18, 2019. https://repository.library.brown.edu/studio/item/bdr:11068/.

MLA Handbook (7^{th} Edition):

Hadzic, Mahir. “Stability and instability in the Stefan problem with surface tension.” 2010. Web. 18 Aug 2019.

Vancouver:

Hadzic M. Stability and instability in the Stefan problem with surface tension. [Internet] [Doctoral dissertation]. Brown University; 2010. [cited 2019 Aug 18]. Available from: https://repository.library.brown.edu/studio/item/bdr:11068/.

Council of Science Editors:

Hadzic M. Stability and instability in the Stefan problem with surface tension. [Doctoral Dissertation]. Brown University; 2010. Available from: https://repository.library.brown.edu/studio/item/bdr:11068/

2. Walsh, Samuel Peter. Stratified and steady periodic water waves.

Degree: PhD, Applied Mathematics, 2010, Brown University

URL: https://repository.library.brown.edu/studio/item/bdr:11084/

► This thesis considers two-dimensional stratified water waves propagating under the force of gravity over an impermeable flat bed and with a free surface. In the…
(more)

Subjects/Keywords: partial differential equations

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APA (6^{th} Edition):

Walsh, S. P. (2010). Stratified and steady periodic water waves. (Doctoral Dissertation). Brown University. Retrieved from https://repository.library.brown.edu/studio/item/bdr:11084/

Chicago Manual of Style (16^{th} Edition):

Walsh, Samuel Peter. “Stratified and steady periodic water waves.” 2010. Doctoral Dissertation, Brown University. Accessed August 18, 2019. https://repository.library.brown.edu/studio/item/bdr:11084/.

MLA Handbook (7^{th} Edition):

Walsh, Samuel Peter. “Stratified and steady periodic water waves.” 2010. Web. 18 Aug 2019.

Vancouver:

Walsh SP. Stratified and steady periodic water waves. [Internet] [Doctoral dissertation]. Brown University; 2010. [cited 2019 Aug 18]. Available from: https://repository.library.brown.edu/studio/item/bdr:11084/.

Council of Science Editors:

Walsh SP. Stratified and steady periodic water waves. [Doctoral Dissertation]. Brown University; 2010. Available from: https://repository.library.brown.edu/studio/item/bdr:11084/

University of Colorado

3. Maiden, Michelle. Dispersive hydrodynamics in viscous fluid conduits.

Degree: PhD, Applied Mathematics, 2019, University of Colorado

URL: https://scholar.colorado.edu/appm_gradetds/141

► Viscous fluid conduits provide an ideal system for the study of dissipationless, dispersive hydrodynamics. A dense, viscous fluid serves as the background medium through…
(more)

Subjects/Keywords: Fluid Dynamics; Partial Differential Equations

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APA (6^{th} Edition):

Maiden, M. (2019). Dispersive hydrodynamics in viscous fluid conduits. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/appm_gradetds/141

Chicago Manual of Style (16^{th} Edition):

Maiden, Michelle. “Dispersive hydrodynamics in viscous fluid conduits.” 2019. Doctoral Dissertation, University of Colorado. Accessed August 18, 2019. https://scholar.colorado.edu/appm_gradetds/141.

MLA Handbook (7^{th} Edition):

Maiden, Michelle. “Dispersive hydrodynamics in viscous fluid conduits.” 2019. Web. 18 Aug 2019.

Vancouver:

Maiden M. Dispersive hydrodynamics in viscous fluid conduits. [Internet] [Doctoral dissertation]. University of Colorado; 2019. [cited 2019 Aug 18]. Available from: https://scholar.colorado.edu/appm_gradetds/141.

Council of Science Editors:

Maiden M. Dispersive hydrodynamics in viscous fluid conduits. [Doctoral Dissertation]. University of Colorado; 2019. Available from: https://scholar.colorado.edu/appm_gradetds/141

North Carolina State University

4. Taylor, Monique Richardson. Dafermos Regularization of a Modified KdV-Burgers Equation.

Degree: PhD, Applied Mathematics, 2010, North Carolina State University

URL: http://www.lib.ncsu.edu/resolver/1840.16/4034

► This project involves Dafermos regularization of a *partial* *differential* equation of order higher than 2. The modified Korteweg de Vries-Burgers equation is u_{T} + f(u)_{X}…
(more)

Subjects/Keywords: Geometric singular perturbation theory; Partial differential equations

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APA (6^{th} Edition):

Taylor, M. R. (2010). Dafermos Regularization of a Modified KdV-Burgers Equation. (Doctoral Dissertation). North Carolina State University. Retrieved from http://www.lib.ncsu.edu/resolver/1840.16/4034

Chicago Manual of Style (16^{th} Edition):

Taylor, Monique Richardson. “Dafermos Regularization of a Modified KdV-Burgers Equation.” 2010. Doctoral Dissertation, North Carolina State University. Accessed August 18, 2019. http://www.lib.ncsu.edu/resolver/1840.16/4034.

MLA Handbook (7^{th} Edition):

Taylor, Monique Richardson. “Dafermos Regularization of a Modified KdV-Burgers Equation.” 2010. Web. 18 Aug 2019.

Vancouver:

Taylor MR. Dafermos Regularization of a Modified KdV-Burgers Equation. [Internet] [Doctoral dissertation]. North Carolina State University; 2010. [cited 2019 Aug 18]. Available from: http://www.lib.ncsu.edu/resolver/1840.16/4034.

Council of Science Editors:

Taylor MR. Dafermos Regularization of a Modified KdV-Burgers Equation. [Doctoral Dissertation]. North Carolina State University; 2010. Available from: http://www.lib.ncsu.edu/resolver/1840.16/4034

University of Colorado

5.
Gillman, Adrianna.
Fast Direct Solvers for Elliptic *Partial* *Differential* * Equations*.

Degree: PhD, Applied Mathematics, 2011, University of Colorado

URL: http://scholar.colorado.edu/appm_gradetds/20

► The dissertation describes fast, robust, and highly accurate numerical methods for solving boundary value problems associated with elliptic PDEs such as Laplace's and Helmholtz'…
(more)

Subjects/Keywords: Fast methods; Linear algebra; Numerical Analysis; Partial Differential Equations; Applied Mathematics

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APA (6^{th} Edition):

Gillman, A. (2011). Fast Direct Solvers for Elliptic Partial Differential Equations. (Doctoral Dissertation). University of Colorado. Retrieved from http://scholar.colorado.edu/appm_gradetds/20

Chicago Manual of Style (16^{th} Edition):

Gillman, Adrianna. “Fast Direct Solvers for Elliptic Partial Differential Equations.” 2011. Doctoral Dissertation, University of Colorado. Accessed August 18, 2019. http://scholar.colorado.edu/appm_gradetds/20.

MLA Handbook (7^{th} Edition):

Gillman, Adrianna. “Fast Direct Solvers for Elliptic Partial Differential Equations.” 2011. Web. 18 Aug 2019.

Vancouver:

Gillman A. Fast Direct Solvers for Elliptic Partial Differential Equations. [Internet] [Doctoral dissertation]. University of Colorado; 2011. [cited 2019 Aug 18]. Available from: http://scholar.colorado.edu/appm_gradetds/20.

Council of Science Editors:

Gillman A. Fast Direct Solvers for Elliptic Partial Differential Equations. [Doctoral Dissertation]. University of Colorado; 2011. Available from: http://scholar.colorado.edu/appm_gradetds/20

University of Colorado

6. Barnett, Gregory Allen. A Robust RBF-FD Formulation based on Polyharmonic Splines and Polynomials.

Degree: PhD, Applied Mathematics, 2015, University of Colorado

URL: http://scholar.colorado.edu/appm_gradetds/66

► We introduce a local method based on radial basis function-generated finite differences (RBFFD) for interpolation and the numerical solution of *partial* *differential* *equations* (PDEs).…
(more)

Subjects/Keywords: partial differential equations; radial basis functions; Applied Mathematics

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APA (6^{th} Edition):

Barnett, G. A. (2015). A Robust RBF-FD Formulation based on Polyharmonic Splines and Polynomials. (Doctoral Dissertation). University of Colorado. Retrieved from http://scholar.colorado.edu/appm_gradetds/66

Chicago Manual of Style (16^{th} Edition):

Barnett, Gregory Allen. “A Robust RBF-FD Formulation based on Polyharmonic Splines and Polynomials.” 2015. Doctoral Dissertation, University of Colorado. Accessed August 18, 2019. http://scholar.colorado.edu/appm_gradetds/66.

MLA Handbook (7^{th} Edition):

Barnett, Gregory Allen. “A Robust RBF-FD Formulation based on Polyharmonic Splines and Polynomials.” 2015. Web. 18 Aug 2019.

Vancouver:

Barnett GA. A Robust RBF-FD Formulation based on Polyharmonic Splines and Polynomials. [Internet] [Doctoral dissertation]. University of Colorado; 2015. [cited 2019 Aug 18]. Available from: http://scholar.colorado.edu/appm_gradetds/66.

Council of Science Editors:

Barnett GA. A Robust RBF-FD Formulation based on Polyharmonic Splines and Polynomials. [Doctoral Dissertation]. University of Colorado; 2015. Available from: http://scholar.colorado.edu/appm_gradetds/66

Georgia Tech

7. Lee, Philip Francis. The form of a solution to the inhomogeneous heat equation.

Degree: MS, Applied Mathematics, 1967, Georgia Tech

URL: http://hdl.handle.net/1853/32946

Subjects/Keywords: Differential equations, Partial; Heat

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APA (6^{th} Edition):

Lee, P. F. (1967). The form of a solution to the inhomogeneous heat equation. (Masters Thesis). Georgia Tech. Retrieved from http://hdl.handle.net/1853/32946

Chicago Manual of Style (16^{th} Edition):

Lee, Philip Francis. “The form of a solution to the inhomogeneous heat equation.” 1967. Masters Thesis, Georgia Tech. Accessed August 18, 2019. http://hdl.handle.net/1853/32946.

MLA Handbook (7^{th} Edition):

Lee, Philip Francis. “The form of a solution to the inhomogeneous heat equation.” 1967. Web. 18 Aug 2019.

Vancouver:

Lee PF. The form of a solution to the inhomogeneous heat equation. [Internet] [Masters thesis]. Georgia Tech; 1967. [cited 2019 Aug 18]. Available from: http://hdl.handle.net/1853/32946.

Council of Science Editors:

Lee PF. The form of a solution to the inhomogeneous heat equation. [Masters Thesis]. Georgia Tech; 1967. Available from: http://hdl.handle.net/1853/32946

Louisiana State University

8. Viator Jr, Robert Paul. Spectral Properties of Photonic Crystals: Bloch Waves and Band Gaps.

Degree: PhD, Applied Mathematics, 2016, Louisiana State University

URL: etd-07072016-223744 ; https://digitalcommons.lsu.edu/gradschool_dissertations/2462

► The author of this dissertation studies the spectral properties of high-contrast photonic crystals, i.e. periodic electromagnetic waveguides made of two materials (a connected phase and…
(more)

Subjects/Keywords: Perturbation Theory; Layer Potentials; Partial Differential Equations; Spectral Theory

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APA (6^{th} Edition):

Viator Jr, R. P. (2016). Spectral Properties of Photonic Crystals: Bloch Waves and Band Gaps. (Doctoral Dissertation). Louisiana State University. Retrieved from etd-07072016-223744 ; https://digitalcommons.lsu.edu/gradschool_dissertations/2462

Chicago Manual of Style (16^{th} Edition):

Viator Jr, Robert Paul. “Spectral Properties of Photonic Crystals: Bloch Waves and Band Gaps.” 2016. Doctoral Dissertation, Louisiana State University. Accessed August 18, 2019. etd-07072016-223744 ; https://digitalcommons.lsu.edu/gradschool_dissertations/2462.

MLA Handbook (7^{th} Edition):

Viator Jr, Robert Paul. “Spectral Properties of Photonic Crystals: Bloch Waves and Band Gaps.” 2016. Web. 18 Aug 2019.

Vancouver:

Viator Jr RP. Spectral Properties of Photonic Crystals: Bloch Waves and Band Gaps. [Internet] [Doctoral dissertation]. Louisiana State University; 2016. [cited 2019 Aug 18]. Available from: etd-07072016-223744 ; https://digitalcommons.lsu.edu/gradschool_dissertations/2462.

Council of Science Editors:

Viator Jr RP. Spectral Properties of Photonic Crystals: Bloch Waves and Band Gaps. [Doctoral Dissertation]. Louisiana State University; 2016. Available from: etd-07072016-223744 ; https://digitalcommons.lsu.edu/gradschool_dissertations/2462

University of Southern California

9.
Liu, Haoyuan.
On spectral approximations of stochastic *partial*
*differential* *equations* driven by Poisson noise.

Degree: PhD, Applied Mathematics, 2007, University of Southern California

URL: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/498604/rec/4526

► In this dissertation, we will recall some basic settings and definitions for nonlinear filtering theory and based on the important optimal filtering estimator provided by…
(more)

Subjects/Keywords: stochastic partial differential equations

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APA (6^{th} Edition):

Liu, H. (2007). On spectral approximations of stochastic partial differential equations driven by Poisson noise. (Doctoral Dissertation). University of Southern California. Retrieved from http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/498604/rec/4526

Chicago Manual of Style (16^{th} Edition):

Liu, Haoyuan. “On spectral approximations of stochastic partial differential equations driven by Poisson noise.” 2007. Doctoral Dissertation, University of Southern California. Accessed August 18, 2019. http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/498604/rec/4526.

MLA Handbook (7^{th} Edition):

Liu, Haoyuan. “On spectral approximations of stochastic partial differential equations driven by Poisson noise.” 2007. Web. 18 Aug 2019.

Vancouver:

Liu H. On spectral approximations of stochastic partial differential equations driven by Poisson noise. [Internet] [Doctoral dissertation]. University of Southern California; 2007. [cited 2019 Aug 18]. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/498604/rec/4526.

Council of Science Editors:

Liu H. On spectral approximations of stochastic partial differential equations driven by Poisson noise. [Doctoral Dissertation]. University of Southern California; 2007. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/498604/rec/4526

Texas State University – San Marcos

10. Clancy, Richard J. Numerical Solutions to Poisson's Equation Over Non-Uniform Discretizations with Associated Fast Solvers.

Degree: MS, Applied Mathematics, 2017, Texas State University – San Marcos

URL: https://digital.library.txstate.edu/handle/10877/6613

► *Partial* *differential* *equations* (PDE's) lay the foundation for the physical sciences and many engineering disciplines. Unfortunately, most PDE's can't be solved analytically. This limitation necessitates…
(more)

Subjects/Keywords: Numerical PDE; Shortley-Weller; Differential equations, Partial; Numerical analysis

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APA (6^{th} Edition):

Clancy, R. J. (2017). Numerical Solutions to Poisson's Equation Over Non-Uniform Discretizations with Associated Fast Solvers. (Masters Thesis). Texas State University – San Marcos. Retrieved from https://digital.library.txstate.edu/handle/10877/6613

Chicago Manual of Style (16^{th} Edition):

Clancy, Richard J. “Numerical Solutions to Poisson's Equation Over Non-Uniform Discretizations with Associated Fast Solvers.” 2017. Masters Thesis, Texas State University – San Marcos. Accessed August 18, 2019. https://digital.library.txstate.edu/handle/10877/6613.

MLA Handbook (7^{th} Edition):

Clancy, Richard J. “Numerical Solutions to Poisson's Equation Over Non-Uniform Discretizations with Associated Fast Solvers.” 2017. Web. 18 Aug 2019.

Vancouver:

Clancy RJ. Numerical Solutions to Poisson's Equation Over Non-Uniform Discretizations with Associated Fast Solvers. [Internet] [Masters thesis]. Texas State University – San Marcos; 2017. [cited 2019 Aug 18]. Available from: https://digital.library.txstate.edu/handle/10877/6613.

Council of Science Editors:

Clancy RJ. Numerical Solutions to Poisson's Equation Over Non-Uniform Discretizations with Associated Fast Solvers. [Masters Thesis]. Texas State University – San Marcos; 2017. Available from: https://digital.library.txstate.edu/handle/10877/6613

Louisiana State University

11.
Grey, Jacob.
Analysis of Nonlinear Dispersive Model * Equations*.

Degree: PhD, Applied Mathematics, 2015, Louisiana State University

URL: etd-07132015-161603 ; https://digitalcommons.lsu.edu/gradschool_dissertations/1587

► In this work we begin with a brief survey of the classical fluid dynamics problem of water waves, and then proceed to derive well known…
(more)

Subjects/Keywords: nonlinear dispersive; PDE; nonlinear partial differential equations; evolution equations; BBM; BBM-KP; KdV; water wave

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APA (6^{th} Edition):

Grey, J. (2015). Analysis of Nonlinear Dispersive Model Equations. (Doctoral Dissertation). Louisiana State University. Retrieved from etd-07132015-161603 ; https://digitalcommons.lsu.edu/gradschool_dissertations/1587

Chicago Manual of Style (16^{th} Edition):

Grey, Jacob. “Analysis of Nonlinear Dispersive Model Equations.” 2015. Doctoral Dissertation, Louisiana State University. Accessed August 18, 2019. etd-07132015-161603 ; https://digitalcommons.lsu.edu/gradschool_dissertations/1587.

MLA Handbook (7^{th} Edition):

Grey, Jacob. “Analysis of Nonlinear Dispersive Model Equations.” 2015. Web. 18 Aug 2019.

Vancouver:

Grey J. Analysis of Nonlinear Dispersive Model Equations. [Internet] [Doctoral dissertation]. Louisiana State University; 2015. [cited 2019 Aug 18]. Available from: etd-07132015-161603 ; https://digitalcommons.lsu.edu/gradschool_dissertations/1587.

Council of Science Editors:

Grey J. Analysis of Nonlinear Dispersive Model Equations. [Doctoral Dissertation]. Louisiana State University; 2015. Available from: etd-07132015-161603 ; https://digitalcommons.lsu.edu/gradschool_dissertations/1587

North Carolina State University

12. Zager, Michael Gary. Modeling the Distribution and Metabolism of the Phytoestrogen Genistein in Rats.

Degree: PhD, Applied Mathematics, 2003, North Carolina State University

URL: http://www.lib.ncsu.edu/resolver/1840.16/3843

► Genistein is an endocrine-active compound found naturally in soy products. It has been linked to various health effects, both beneficial and adverse. The liver is…
(more)

Subjects/Keywords: PBPK model; genistein; metabolism; partial differential equations; delay differential equations; biliary excretion

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APA (6^{th} Edition):

Zager, M. G. (2003). Modeling the Distribution and Metabolism of the Phytoestrogen Genistein in Rats. (Doctoral Dissertation). North Carolina State University. Retrieved from http://www.lib.ncsu.edu/resolver/1840.16/3843

Chicago Manual of Style (16^{th} Edition):

Zager, Michael Gary. “Modeling the Distribution and Metabolism of the Phytoestrogen Genistein in Rats.” 2003. Doctoral Dissertation, North Carolina State University. Accessed August 18, 2019. http://www.lib.ncsu.edu/resolver/1840.16/3843.

MLA Handbook (7^{th} Edition):

Zager, Michael Gary. “Modeling the Distribution and Metabolism of the Phytoestrogen Genistein in Rats.” 2003. Web. 18 Aug 2019.

Vancouver:

Zager MG. Modeling the Distribution and Metabolism of the Phytoestrogen Genistein in Rats. [Internet] [Doctoral dissertation]. North Carolina State University; 2003. [cited 2019 Aug 18]. Available from: http://www.lib.ncsu.edu/resolver/1840.16/3843.

Council of Science Editors:

Zager MG. Modeling the Distribution and Metabolism of the Phytoestrogen Genistein in Rats. [Doctoral Dissertation]. North Carolina State University; 2003. Available from: http://www.lib.ncsu.edu/resolver/1840.16/3843

University of Colorado

13. Yang, Xinshuo. Reduction of Multivariate Mixtures and Its Applications.

Degree: PhD, Applied Mathematics, 2018, University of Colorado

URL: https://scholar.colorado.edu/appm_gradetds/139

► We consider a fast deterministic algorithm to identify the "best" linearly independent terms in multivariate mixtures and use them to compute an equivalent representation…
(more)

Subjects/Keywords: multivariate mixtures; reduction algorithms; Hartree-Fock equations; integral equations; far-field summation in high dimensions; kernel density estimation; Numerical Analysis and Computation; Partial Differential Equations

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APA (6^{th} Edition):

Yang, X. (2018). Reduction of Multivariate Mixtures and Its Applications. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/appm_gradetds/139

Chicago Manual of Style (16^{th} Edition):

Yang, Xinshuo. “Reduction of Multivariate Mixtures and Its Applications.” 2018. Doctoral Dissertation, University of Colorado. Accessed August 18, 2019. https://scholar.colorado.edu/appm_gradetds/139.

MLA Handbook (7^{th} Edition):

Yang, Xinshuo. “Reduction of Multivariate Mixtures and Its Applications.” 2018. Web. 18 Aug 2019.

Vancouver:

Yang X. Reduction of Multivariate Mixtures and Its Applications. [Internet] [Doctoral dissertation]. University of Colorado; 2018. [cited 2019 Aug 18]. Available from: https://scholar.colorado.edu/appm_gradetds/139.

Council of Science Editors:

Yang X. Reduction of Multivariate Mixtures and Its Applications. [Doctoral Dissertation]. University of Colorado; 2018. Available from: https://scholar.colorado.edu/appm_gradetds/139

University of Colorado

14. Biagioni, David Joseph. Numerical construction of Greenâ€™s functions in high dimensional elliptic problems with variable coefficients and analysis of renewable energy data via sparse and separable approximations.

Degree: PhD, Applied Mathematics, 2012, University of Colorado

URL: http://scholar.colorado.edu/appm_gradetds/29

► This thesis consists of two parts. In Part I, we describe an algorithm for approximating the Green's function for elliptic problems with variable coefficients…
(more)

Subjects/Keywords: Curse of dimensionality; Direct Poisson solver; High dimensional partial differential equations; Numerical analysis; Randomized canonical tensor decomposition; Separated representations; Applied Mathematics

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APA (6^{th} Edition):

Biagioni, D. J. (2012). Numerical construction of Greenâ€™s functions in high dimensional elliptic problems with variable coefficients and analysis of renewable energy data via sparse and separable approximations. (Doctoral Dissertation). University of Colorado. Retrieved from http://scholar.colorado.edu/appm_gradetds/29

Chicago Manual of Style (16^{th} Edition):

Biagioni, David Joseph. “Numerical construction of Greenâ€™s functions in high dimensional elliptic problems with variable coefficients and analysis of renewable energy data via sparse and separable approximations.” 2012. Doctoral Dissertation, University of Colorado. Accessed August 18, 2019. http://scholar.colorado.edu/appm_gradetds/29.

MLA Handbook (7^{th} Edition):

Biagioni, David Joseph. “Numerical construction of Greenâ€™s functions in high dimensional elliptic problems with variable coefficients and analysis of renewable energy data via sparse and separable approximations.” 2012. Web. 18 Aug 2019.

Vancouver:

Biagioni DJ. Numerical construction of Greenâ€™s functions in high dimensional elliptic problems with variable coefficients and analysis of renewable energy data via sparse and separable approximations. [Internet] [Doctoral dissertation]. University of Colorado; 2012. [cited 2019 Aug 18]. Available from: http://scholar.colorado.edu/appm_gradetds/29.

Council of Science Editors:

Biagioni DJ. Numerical construction of Greenâ€™s functions in high dimensional elliptic problems with variable coefficients and analysis of renewable energy data via sparse and separable approximations. [Doctoral Dissertation]. University of Colorado; 2012. Available from: http://scholar.colorado.edu/appm_gradetds/29

University of Colorado

15.
Hammond, Jason Frank.
Analysis and Simulation of *Partial* *Differential* *Equations* in Mathematical Biology: Applications to Bacterial Biofilms and Fisher's Equation.

Degree: PhD, Applied Mathematics, 2012, University of Colorado

URL: http://scholar.colorado.edu/appm_gradetds/31

► In this dissertation, we investigate two important problems in mathematical biology that are best modeled using *partial* *differential* *equations*. We first consider the question…
(more)

Subjects/Keywords: biofilm; fisher's equation; fluid mechanics; immersed boundary method; painleve; partial differential equations; Applied Mathematics; Biomechanics and Biotransport

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APA (6^{th} Edition):

Hammond, J. F. (2012). Analysis and Simulation of Partial Differential Equations in Mathematical Biology: Applications to Bacterial Biofilms and Fisher's Equation. (Doctoral Dissertation). University of Colorado. Retrieved from http://scholar.colorado.edu/appm_gradetds/31

Chicago Manual of Style (16^{th} Edition):

Hammond, Jason Frank. “Analysis and Simulation of Partial Differential Equations in Mathematical Biology: Applications to Bacterial Biofilms and Fisher's Equation.” 2012. Doctoral Dissertation, University of Colorado. Accessed August 18, 2019. http://scholar.colorado.edu/appm_gradetds/31.

MLA Handbook (7^{th} Edition):

Hammond, Jason Frank. “Analysis and Simulation of Partial Differential Equations in Mathematical Biology: Applications to Bacterial Biofilms and Fisher's Equation.” 2012. Web. 18 Aug 2019.

Vancouver:

Hammond JF. Analysis and Simulation of Partial Differential Equations in Mathematical Biology: Applications to Bacterial Biofilms and Fisher's Equation. [Internet] [Doctoral dissertation]. University of Colorado; 2012. [cited 2019 Aug 18]. Available from: http://scholar.colorado.edu/appm_gradetds/31.

Council of Science Editors:

Hammond JF. Analysis and Simulation of Partial Differential Equations in Mathematical Biology: Applications to Bacterial Biofilms and Fisher's Equation. [Doctoral Dissertation]. University of Colorado; 2012. Available from: http://scholar.colorado.edu/appm_gradetds/31

University of Colorado

16.
Mitchell, Wayne Bradford.
Low-Communication, Parallel Multigrid Algorithms for Elliptic *Partial* *Differential* * Equations*.

Degree: PhD, Applied Mathematics, 2017, University of Colorado

URL: https://scholar.colorado.edu/appm_gradetds/90

► When solving elliptic *partial* *differential* *equations* (PDE's) multigrid algorithms often provide optimal solvers and preconditioners capable of providing solutions with O(N) computational cost, where…
(more)

Subjects/Keywords: adaptive mesh refinement; algebraic multigrid; domain decomposition; first-order system least-squares; nested iteration; range decomposition; Applied Mathematics; Partial Differential Equations

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APA (6^{th} Edition):

Mitchell, W. B. (2017). Low-Communication, Parallel Multigrid Algorithms for Elliptic Partial Differential Equations. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/appm_gradetds/90

Chicago Manual of Style (16^{th} Edition):

Mitchell, Wayne Bradford. “Low-Communication, Parallel Multigrid Algorithms for Elliptic Partial Differential Equations.” 2017. Doctoral Dissertation, University of Colorado. Accessed August 18, 2019. https://scholar.colorado.edu/appm_gradetds/90.

MLA Handbook (7^{th} Edition):

Mitchell, Wayne Bradford. “Low-Communication, Parallel Multigrid Algorithms for Elliptic Partial Differential Equations.” 2017. Web. 18 Aug 2019.

Vancouver:

Mitchell WB. Low-Communication, Parallel Multigrid Algorithms for Elliptic Partial Differential Equations. [Internet] [Doctoral dissertation]. University of Colorado; 2017. [cited 2019 Aug 18]. Available from: https://scholar.colorado.edu/appm_gradetds/90.

Council of Science Editors:

Mitchell WB. Low-Communication, Parallel Multigrid Algorithms for Elliptic Partial Differential Equations. [Doctoral Dissertation]. University of Colorado; 2017. Available from: https://scholar.colorado.edu/appm_gradetds/90

University of Akron

17. Johnston, Joshua D. Analytically and Numerically Modeling Reservoir-Extended Porous Slider and Journal Bearings Incorporating Cavitation Effects.

Degree: PhD, Applied Mathematics, 2011, University of Akron

URL: http://rave.ohiolink.edu/etdc/view?acc_num=akron1303563391

► The technology of porous bearings is well-known in industry. In classical cases, the porous medium acts as an external reservoir making their use ideal…
(more)

Subjects/Keywords: Mathematics; Mechanical Engineering; bearing; cavitation; numerical analysis; partial differential equations; slider; journal; porous medium; heat transfer

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APA (6^{th} Edition):

Johnston, J. D. (2011). Analytically and Numerically Modeling Reservoir-Extended Porous Slider and Journal Bearings Incorporating Cavitation Effects. (Doctoral Dissertation). University of Akron. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=akron1303563391

Chicago Manual of Style (16^{th} Edition):

Johnston, Joshua D. “Analytically and Numerically Modeling Reservoir-Extended Porous Slider and Journal Bearings Incorporating Cavitation Effects.” 2011. Doctoral Dissertation, University of Akron. Accessed August 18, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=akron1303563391.

MLA Handbook (7^{th} Edition):

Johnston, Joshua D. “Analytically and Numerically Modeling Reservoir-Extended Porous Slider and Journal Bearings Incorporating Cavitation Effects.” 2011. Web. 18 Aug 2019.

Vancouver:

Johnston JD. Analytically and Numerically Modeling Reservoir-Extended Porous Slider and Journal Bearings Incorporating Cavitation Effects. [Internet] [Doctoral dissertation]. University of Akron; 2011. [cited 2019 Aug 18]. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=akron1303563391.

Council of Science Editors:

Johnston JD. Analytically and Numerically Modeling Reservoir-Extended Porous Slider and Journal Bearings Incorporating Cavitation Effects. [Doctoral Dissertation]. University of Akron; 2011. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=akron1303563391

North Carolina State University

18. DeVault, Kristen Jean. Numerical Study of Two Problems in Fluid Flow: Cavitation and Cerebral Circulation.

Degree: PhD, Applied Mathematics, 2008, North Carolina State University

URL: http://www.lib.ncsu.edu/resolver/1840.16/5960

► Two different computational models of fluid flow are considered. First, the possibility of cavitation is investigated numerically in two and three dimensions for the spherically…
(more)

Subjects/Keywords: Mathematical Modeling; Numerical Methods; Partial Differential Equations; Computational Mathematics

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APA (6^{th} Edition):

DeVault, K. J. (2008). Numerical Study of Two Problems in Fluid Flow: Cavitation and Cerebral Circulation. (Doctoral Dissertation). North Carolina State University. Retrieved from http://www.lib.ncsu.edu/resolver/1840.16/5960

Chicago Manual of Style (16^{th} Edition):

DeVault, Kristen Jean. “Numerical Study of Two Problems in Fluid Flow: Cavitation and Cerebral Circulation.” 2008. Doctoral Dissertation, North Carolina State University. Accessed August 18, 2019. http://www.lib.ncsu.edu/resolver/1840.16/5960.

MLA Handbook (7^{th} Edition):

DeVault, Kristen Jean. “Numerical Study of Two Problems in Fluid Flow: Cavitation and Cerebral Circulation.” 2008. Web. 18 Aug 2019.

Vancouver:

DeVault KJ. Numerical Study of Two Problems in Fluid Flow: Cavitation and Cerebral Circulation. [Internet] [Doctoral dissertation]. North Carolina State University; 2008. [cited 2019 Aug 18]. Available from: http://www.lib.ncsu.edu/resolver/1840.16/5960.

Council of Science Editors:

DeVault KJ. Numerical Study of Two Problems in Fluid Flow: Cavitation and Cerebral Circulation. [Doctoral Dissertation]. North Carolina State University; 2008. Available from: http://www.lib.ncsu.edu/resolver/1840.16/5960

University of Colorado

19.
Mitchell, Wayne.
Low-Communication, Parallel Multigrid Algorithms for Elliptic *Partial* *Differential* * Equations*.

Degree: PhD, Applied Mathematics, 2017, University of Colorado

URL: http://scholar.colorado.edu/appm_gradetds/80

► When solving elliptic *partial* *differential* *equations* (PDE's) multigrid algorithms often provide optimal solvers and preconditioners capable of providing solutions with O(N) computational cost, where…
(more)

Subjects/Keywords: nested iteration; first-order system least-squares; algebraic multigrid; domain decomposition; range decomposition; adaptive mesh refinement; Applied Mathematics; Numerical Analysis and Computation; Partial Differential Equations

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

APA (6^{th} Edition):

Mitchell, W. (2017). Low-Communication, Parallel Multigrid Algorithms for Elliptic Partial Differential Equations. (Doctoral Dissertation). University of Colorado. Retrieved from http://scholar.colorado.edu/appm_gradetds/80

Chicago Manual of Style (16^{th} Edition):

Mitchell, Wayne. “Low-Communication, Parallel Multigrid Algorithms for Elliptic Partial Differential Equations.” 2017. Doctoral Dissertation, University of Colorado. Accessed August 18, 2019. http://scholar.colorado.edu/appm_gradetds/80.

MLA Handbook (7^{th} Edition):

Mitchell, Wayne. “Low-Communication, Parallel Multigrid Algorithms for Elliptic Partial Differential Equations.” 2017. Web. 18 Aug 2019.

Vancouver:

Mitchell W. Low-Communication, Parallel Multigrid Algorithms for Elliptic Partial Differential Equations. [Internet] [Doctoral dissertation]. University of Colorado; 2017. [cited 2019 Aug 18]. Available from: http://scholar.colorado.edu/appm_gradetds/80.

Council of Science Editors:

Mitchell W. Low-Communication, Parallel Multigrid Algorithms for Elliptic Partial Differential Equations. [Doctoral Dissertation]. University of Colorado; 2017. Available from: http://scholar.colorado.edu/appm_gradetds/80

University of Colorado

20. Kalchev, Delyan Zhelev. Dual-Norm Least-Squares Finite Element Methods for Hyperbolic Problems.

Degree: PhD, Applied Mathematics, 2018, University of Colorado

URL: https://scholar.colorado.edu/appm_gradetds/138

► Least-squares finite element discretizations of first-order hyperbolic *partial* *differential* *equations* (PDEs) are proposed and studied. Hyperbolic problems are notorious for possessing solutions with jump…
(more)

Subjects/Keywords: first-order hyperbolic problems; balance laws; conservation laws; space-time discretization; least-squares methods; finite element methods; Numerical Analysis and Computation; Partial Differential Equations

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

APA (6^{th} Edition):

Kalchev, D. Z. (2018). Dual-Norm Least-Squares Finite Element Methods for Hyperbolic Problems. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/appm_gradetds/138

Chicago Manual of Style (16^{th} Edition):

Kalchev, Delyan Zhelev. “Dual-Norm Least-Squares Finite Element Methods for Hyperbolic Problems.” 2018. Doctoral Dissertation, University of Colorado. Accessed August 18, 2019. https://scholar.colorado.edu/appm_gradetds/138.

MLA Handbook (7^{th} Edition):

Kalchev, Delyan Zhelev. “Dual-Norm Least-Squares Finite Element Methods for Hyperbolic Problems.” 2018. Web. 18 Aug 2019.

Vancouver:

Kalchev DZ. Dual-Norm Least-Squares Finite Element Methods for Hyperbolic Problems. [Internet] [Doctoral dissertation]. University of Colorado; 2018. [cited 2019 Aug 18]. Available from: https://scholar.colorado.edu/appm_gradetds/138.

Council of Science Editors:

Kalchev DZ. Dual-Norm Least-Squares Finite Element Methods for Hyperbolic Problems. [Doctoral Dissertation]. University of Colorado; 2018. Available from: https://scholar.colorado.edu/appm_gradetds/138

North Carolina State University

21.
Levy, Rachel.
*Partial**Differential* *Equations* of Thin Liquid Films: Analysis and Numerical Simulation.

Degree: PhD, Applied Mathematics, 2005, North Carolina State University

URL: http://www.lib.ncsu.edu/resolver/1840.16/3917

► We consider four problems related to Marangoni-driven thin liquid films. The first compares two models for the motion of a contact line: the precursor model…
(more)

Subjects/Keywords: thin liquid films; partial differential equations; shock; contact line; nucleation; surfactant

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APA (6^{th} Edition):

Levy, R. (2005). Partial Differential Equations of Thin Liquid Films: Analysis and Numerical Simulation. (Doctoral Dissertation). North Carolina State University. Retrieved from http://www.lib.ncsu.edu/resolver/1840.16/3917

Chicago Manual of Style (16^{th} Edition):

Levy, Rachel. “Partial Differential Equations of Thin Liquid Films: Analysis and Numerical Simulation.” 2005. Doctoral Dissertation, North Carolina State University. Accessed August 18, 2019. http://www.lib.ncsu.edu/resolver/1840.16/3917.

MLA Handbook (7^{th} Edition):

Levy, Rachel. “Partial Differential Equations of Thin Liquid Films: Analysis and Numerical Simulation.” 2005. Web. 18 Aug 2019.

Vancouver:

Levy R. Partial Differential Equations of Thin Liquid Films: Analysis and Numerical Simulation. [Internet] [Doctoral dissertation]. North Carolina State University; 2005. [cited 2019 Aug 18]. Available from: http://www.lib.ncsu.edu/resolver/1840.16/3917.

Council of Science Editors:

Levy R. Partial Differential Equations of Thin Liquid Films: Analysis and Numerical Simulation. [Doctoral Dissertation]. North Carolina State University; 2005. Available from: http://www.lib.ncsu.edu/resolver/1840.16/3917

University of Southern California

22.
Glatt-Holtz, Nathan Edward.
Well posedness and asymptotic analysis for the stochastic
*equations* of geophysical fluid dynamics.

Degree: PhD, Applied Mathematics, 2008, University of Southern California

URL: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/82250/rec/7877

► This work collects three interrelated projects that develop rigorous mathematical tools for the study of the stochastically forced *equations* of geophysical fluid dynamics and turbulence.…
(more)

Subjects/Keywords: stochastic partial differential equations; Navier-Stokes equations; primitive equations; geophysical fluid dynamics; asymptotic analysis

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APA (6^{th} Edition):

Glatt-Holtz, N. E. (2008). Well posedness and asymptotic analysis for the stochastic equations of geophysical fluid dynamics. (Doctoral Dissertation). University of Southern California. Retrieved from http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/82250/rec/7877

Chicago Manual of Style (16^{th} Edition):

Glatt-Holtz, Nathan Edward. “Well posedness and asymptotic analysis for the stochastic equations of geophysical fluid dynamics.” 2008. Doctoral Dissertation, University of Southern California. Accessed August 18, 2019. http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/82250/rec/7877.

MLA Handbook (7^{th} Edition):

Glatt-Holtz, Nathan Edward. “Well posedness and asymptotic analysis for the stochastic equations of geophysical fluid dynamics.” 2008. Web. 18 Aug 2019.

Vancouver:

Glatt-Holtz NE. Well posedness and asymptotic analysis for the stochastic equations of geophysical fluid dynamics. [Internet] [Doctoral dissertation]. University of Southern California; 2008. [cited 2019 Aug 18]. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/82250/rec/7877.

Council of Science Editors:

Glatt-Holtz NE. Well posedness and asymptotic analysis for the stochastic equations of geophysical fluid dynamics. [Doctoral Dissertation]. University of Southern California; 2008. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/82250/rec/7877

Arizona State University

23.
Caldwell, Wendy K.
* Differential* Equation Models for Understanding Phenomena
beyond Experimental Capabilities.

Degree: Applied Mathematics, 2019, Arizona State University

URL: http://repository.asu.edu/items/53687

Subjects/Keywords: Applied mathematics; Applied physics; Asteroid 16 Psyche; hydrocode; ordinary differential equations; partial differential equaitons; verification and validation; Vicodin abuse

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

APA (6^{th} Edition):

Caldwell, W. K. (2019). Differential Equation Models for Understanding Phenomena beyond Experimental Capabilities. (Doctoral Dissertation). Arizona State University. Retrieved from http://repository.asu.edu/items/53687

Chicago Manual of Style (16^{th} Edition):

Caldwell, Wendy K. “Differential Equation Models for Understanding Phenomena beyond Experimental Capabilities.” 2019. Doctoral Dissertation, Arizona State University. Accessed August 18, 2019. http://repository.asu.edu/items/53687.

MLA Handbook (7^{th} Edition):

Caldwell, Wendy K. “Differential Equation Models for Understanding Phenomena beyond Experimental Capabilities.” 2019. Web. 18 Aug 2019.

Vancouver:

Caldwell WK. Differential Equation Models for Understanding Phenomena beyond Experimental Capabilities. [Internet] [Doctoral dissertation]. Arizona State University; 2019. [cited 2019 Aug 18]. Available from: http://repository.asu.edu/items/53687.

Council of Science Editors:

Caldwell WK. Differential Equation Models for Understanding Phenomena beyond Experimental Capabilities. [Doctoral Dissertation]. Arizona State University; 2019. Available from: http://repository.asu.edu/items/53687

University of Akron

24. Brubaker, Lauren P. Completely Residual Based Code Verification.

Degree: MS, Applied Mathematics, 2006, University of Akron

URL: http://rave.ohiolink.edu/etdc/view?acc_num=akron1132592325

► Mathematical models of physical processes often include *partial* *differential* *equations* (PDEs). Oftentimes solving PDEs analytically is not feasible and a numerical method is implemented to…
(more)

Subjects/Keywords: Mathematics; Code verification; Partial Differential Equations; Numerical Methods; Method of Manufactured Exact Solutions; Frontal Polymerization; Heat Equation; Residual

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

APA (6^{th} Edition):

Brubaker, L. P. (2006). Completely Residual Based Code Verification. (Masters Thesis). University of Akron. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=akron1132592325

Chicago Manual of Style (16^{th} Edition):

Brubaker, Lauren P. “Completely Residual Based Code Verification.” 2006. Masters Thesis, University of Akron. Accessed August 18, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=akron1132592325.

MLA Handbook (7^{th} Edition):

Brubaker, Lauren P. “Completely Residual Based Code Verification.” 2006. Web. 18 Aug 2019.

Vancouver:

Brubaker LP. Completely Residual Based Code Verification. [Internet] [Masters thesis]. University of Akron; 2006. [cited 2019 Aug 18]. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=akron1132592325.

Council of Science Editors:

Brubaker LP. Completely Residual Based Code Verification. [Masters Thesis]. University of Akron; 2006. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=akron1132592325

University of Akron

25. Evans, Oliver Graham, Evans. Modeling the Light Field in Macroalgae Aquaculture.

Degree: MS, Applied Mathematics, 2018, University of Akron

URL: http://rave.ohiolink.edu/etdc/view?acc_num=akron1542810712432336

► A mathematical model is developed to describe the light field in vertical line seaweed cultivation to determine the degree to which the seaweed shades itself…
(more)

Subjects/Keywords: Applied Mathematics; Aquaculture; Aquatic Sciences; Ocean Engineering; Optics; Numerical Methods, Partial Differential Equations, PDE, Math Modeling, Mathematical Modeling, Seaweed, Kelp, Light, Radiative Transfer, Aquaculture, Asymptotics, Finite Difference, Error Estimation, Fortran, Verification, Validation, WWTP, IMTA

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

APA (6^{th} Edition):

Evans, Oliver Graham, E. (2018). Modeling the Light Field in Macroalgae Aquaculture. (Masters Thesis). University of Akron. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=akron1542810712432336

Chicago Manual of Style (16^{th} Edition):

Evans, Oliver Graham, Evans. “Modeling the Light Field in Macroalgae Aquaculture.” 2018. Masters Thesis, University of Akron. Accessed August 18, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=akron1542810712432336.

MLA Handbook (7^{th} Edition):

Evans, Oliver Graham, Evans. “Modeling the Light Field in Macroalgae Aquaculture.” 2018. Web. 18 Aug 2019.

Vancouver:

Evans, Oliver Graham E. Modeling the Light Field in Macroalgae Aquaculture. [Internet] [Masters thesis]. University of Akron; 2018. [cited 2019 Aug 18]. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=akron1542810712432336.

Council of Science Editors:

Evans, Oliver Graham E. Modeling the Light Field in Macroalgae Aquaculture. [Masters Thesis]. University of Akron; 2018. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=akron1542810712432336

26. Wood, Gabriel. A Fast Marching Level Set Method for the Stefan Problem.

Degree: MS, Applied Mathematics, 2015, Texas State University – San Marcos

URL: https://digital.library.txstate.edu/handle/10877/5568

► The Stefan problem describes the change in temperature distribution with respect to time in a medium undergoing phase change. In this thesis we provide a…
(more)

Subjects/Keywords: Stefan, Level Set Method; Differential equations, Partial; Algorithms; Chemistry, Physical and theoretical

…*differential* *equations* and
were known by Euler in 1768 when he published Institutionum calculi… …convergence of
the numerical approximation to the solution of a *partial* *differential* equation to the… …normal velocity at the front . The governing *equations* for our
formulation of the problem are… …approximating the solution to a
*differential* equation defined on a discrete grid. The finite… …arbitrarily spaced grid
All of the proceeding *equations* assume that the function is defined on a…

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

APA (6^{th} Edition):

Wood, G. (2015). A Fast Marching Level Set Method for the Stefan Problem. (Masters Thesis). Texas State University – San Marcos. Retrieved from https://digital.library.txstate.edu/handle/10877/5568

Chicago Manual of Style (16^{th} Edition):

Wood, Gabriel. “A Fast Marching Level Set Method for the Stefan Problem.” 2015. Masters Thesis, Texas State University – San Marcos. Accessed August 18, 2019. https://digital.library.txstate.edu/handle/10877/5568.

MLA Handbook (7^{th} Edition):

Wood, Gabriel. “A Fast Marching Level Set Method for the Stefan Problem.” 2015. Web. 18 Aug 2019.

Vancouver:

Wood G. A Fast Marching Level Set Method for the Stefan Problem. [Internet] [Masters thesis]. Texas State University – San Marcos; 2015. [cited 2019 Aug 18]. Available from: https://digital.library.txstate.edu/handle/10877/5568.

Council of Science Editors:

Wood G. A Fast Marching Level Set Method for the Stefan Problem. [Masters Thesis]. Texas State University – San Marcos; 2015. Available from: https://digital.library.txstate.edu/handle/10877/5568