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Colorado School of Mines
1.
Charlesworth, Alexander E.
Class of staggered grid algorithms and analysis for time-domain Maxwell systems, A.
Degree: MS(M.S.), Applied Mathematics and Statistics, 2016, Colorado School of Mines
URL: http://hdl.handle.net/11124/170015 
► We describe, implement, and analyze a class of staggered grid algorithms for efficient simulation and analysis of time-domain Maxwell systems in the case of heterogeneous,…
(more)
▼ We describe, implement, and analyze a class of staggered grid algorithms for efficient simulation and analysis of time-domain Maxwell systems in the case of heterogeneous, conductive, and nondispersive, isotropic, linear media. We provide the derivation of a continuous mathematical model from the Maxwell equations in vacuum; however, the complexity of this system necessitates the use of computational methods for approximately solving for the physical unknowns. The finite difference approximation has been used for partial differential equations and the Maxwell Equations in particular for many years. We develop staggered grid based finite difference discrete operators as a class of approximations to continuous operators based on second order in time and various order approximations to the electric and magnetic field at staggered grid locations. A generalized parameterized operator which can be specified to any of this class of discrete operators is then applied to the Maxwell system and hence we develop discrete approximations through various choices of parameters in the approximation. We describe analysis of the resulting discrete system as an approximation to the continuous system. Using the comparison of dispersion analysis for the discrete and continuous systems, we derive a third difference approximation, in addition to the known (2, 2) and (2, 4) schemes. We conclude by providing the comparison of these three methods by simulating the Maxwell system for several choices of parameters in the system
Advisors/Committee Members: Ganesh, Mahadevan (advisor), Pankavich, Stephen (committee member), Tenorio, Luis (committee member).
Subjects/Keywords: computational electrodynamics; finite difference time domain
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APA (6th Edition):
Charlesworth, A. E. (2016). Class of staggered grid algorithms and analysis for time-domain Maxwell systems, A. (Masters Thesis). Colorado School of Mines. Retrieved from http://hdl.handle.net/11124/170015
Chicago Manual of Style (16th Edition):
Charlesworth, Alexander E. “Class of staggered grid algorithms and analysis for time-domain Maxwell systems, A.” 2016. Masters Thesis, Colorado School of Mines. Accessed March 06, 2021.
http://hdl.handle.net/11124/170015.
MLA Handbook (7th Edition):
Charlesworth, Alexander E. “Class of staggered grid algorithms and analysis for time-domain Maxwell systems, A.” 2016. Web. 06 Mar 2021.
Vancouver:
Charlesworth AE. Class of staggered grid algorithms and analysis for time-domain Maxwell systems, A. [Internet] [Masters thesis]. Colorado School of Mines; 2016. [cited 2021 Mar 06].
Available from: http://hdl.handle.net/11124/170015.
Council of Science Editors:
Charlesworth AE. Class of staggered grid algorithms and analysis for time-domain Maxwell systems, A. [Masters Thesis]. Colorado School of Mines; 2016. Available from: http://hdl.handle.net/11124/170015
Colorado School of Mines
2.
Quintero, Lucas E.
Solving the Laplace equation across a screen by radial basis functions.
Degree: MS(M.S.), Applied Mathematics and Statistics, 2016, Colorado School of Mines
URL: http://hdl.handle.net/11124/170412
► We consider the problem of solving for a function that satisfies the Laplace equation everywhere with the normal derivative of the unknown function given on…
(more)
▼ We consider the problem of solving for a function that satisfies the Laplace equation everywhere with the normal derivative of the unknown function given on a screen centered about the origin. This problem is found in fracture analysis, seismology, and electromagnetic wave scattering. We will use the Green function of the Laplacian to develop a relation for how the unknown function changes across the origin. By use of Fourier transforms, we develop an integral equation from the partial differential equation. Introducing radial basis functions on a square-grid to approximate our solution creates a matrix problem which can be solved numerically. We find that the matrix has a block symmetric-Toeplitz structure which can be solved with quick and efficient solvers, like LQ-decomposition. We use Gaussian radial basis functions to create a spline approximation. We use Chebyshev polynomials to find an exact solution for a certain screen shape, giving values with which we may compare to the approximation. After, we modify the problem to have a radial-symmetric grid we compare the errors produced and investigate the behavior of the solution.
Advisors/Committee Members: Martin, P. A. (advisor), Pankavich, Stephen (committee member), Nicholas, Michael (committee member).
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APA (6th Edition):
Quintero, L. E. (2016). Solving the Laplace equation across a screen by radial basis functions. (Masters Thesis). Colorado School of Mines. Retrieved from http://hdl.handle.net/11124/170412
Chicago Manual of Style (16th Edition):
Quintero, Lucas E. “Solving the Laplace equation across a screen by radial basis functions.” 2016. Masters Thesis, Colorado School of Mines. Accessed March 06, 2021.
http://hdl.handle.net/11124/170412.
MLA Handbook (7th Edition):
Quintero, Lucas E. “Solving the Laplace equation across a screen by radial basis functions.” 2016. Web. 06 Mar 2021.
Vancouver:
Quintero LE. Solving the Laplace equation across a screen by radial basis functions. [Internet] [Masters thesis]. Colorado School of Mines; 2016. [cited 2021 Mar 06].
Available from: http://hdl.handle.net/11124/170412.
Council of Science Editors:
Quintero LE. Solving the Laplace equation across a screen by radial basis functions. [Masters Thesis]. Colorado School of Mines; 2016. Available from: http://hdl.handle.net/11124/170412
Colorado School of Mines
3.
Stack, Nora E. H.
Applying mathematical models of human circadian rhythms for experimental design and data analysis.
Degree: PhD, Applied Mathematics and Statistics, 2019, Colorado School of Mines
URL: http://hdl.handle.net/11124/173059
► The adult human circadian pacemaker has an intrinsic period just over 24 h that entrains to a 24 h day by environmental cues such as…
(more)
▼ The adult human circadian pacemaker has an intrinsic period just over 24 h that entrains to a 24 h day by environmental cues such as light, eating, and exercise. Dynamic phenomenological mathematical models of the human circadian pacemaker have been developed to simulate the pacemaker's response to light. These models have been widely used for applications such as minimizing jet lag and optimizing experimental protocol design. This thesis is focused on applying mathematical models to account for the interindividual differences that are inherently present in humans and therefore also in circadian data. We optimized an experimental protocol to ensure robust performance across individuals with varying intrinsic circadian periods. Next, we developed novel MCMC-based methodology to use phase shift data to determine the mean intrinsic circadian period of a group of study participants. Finally, we investigated parameter sensitivity of a circadian pacemaker model and applied this knowledge to an adolescent data set where distinct behavior within the cohort was observed. This thesis highlights the utility of human circadian pacemaker models in a variety of contexts and establishes new insights into properties of these models and their influence on behavior.
Advisors/Committee Members: Diniz Behn, Cecilia (advisor), Pankavich, Stephen (committee member), Leiderman, Karin (committee member), Norrgran, Cynthia (committee member).
Subjects/Keywords: data analysis; human circadian rhythms; circadian pacemaker; mathematical modeling; experimental protocol design
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APA (6th Edition):
Stack, N. E. H. (2019). Applying mathematical models of human circadian rhythms for experimental design and data analysis. (Doctoral Dissertation). Colorado School of Mines. Retrieved from http://hdl.handle.net/11124/173059
Chicago Manual of Style (16th Edition):
Stack, Nora E H. “Applying mathematical models of human circadian rhythms for experimental design and data analysis.” 2019. Doctoral Dissertation, Colorado School of Mines. Accessed March 06, 2021.
http://hdl.handle.net/11124/173059.
MLA Handbook (7th Edition):
Stack, Nora E H. “Applying mathematical models of human circadian rhythms for experimental design and data analysis.” 2019. Web. 06 Mar 2021.
Vancouver:
Stack NEH. Applying mathematical models of human circadian rhythms for experimental design and data analysis. [Internet] [Doctoral dissertation]. Colorado School of Mines; 2019. [cited 2021 Mar 06].
Available from: http://hdl.handle.net/11124/173059.
Council of Science Editors:
Stack NEH. Applying mathematical models of human circadian rhythms for experimental design and data analysis. [Doctoral Dissertation]. Colorado School of Mines; 2019. Available from: http://hdl.handle.net/11124/173059
Colorado School of Mines
4.
Johnson, Gregory J.
Two-dimensional internal gravity waves generated by an oscillating circle in a density stratified fluid.
Degree: MS(M.S.), Applied Mathematics and Statistics, 2014, Colorado School of Mines
URL: http://hdl.handle.net/11124/423
► Two-dimensional time-harmonic internal gravity waves are generated by an oscillating body in a density stratified, inviscid, and incompressible fluid. The waves are found in columns…
(more)
▼ Two-dimensional time-harmonic internal gravity waves are generated by an oscillating body in a density stratified, inviscid, and incompressible fluid. The waves are found in columns that form a St. Andrew's Cross. We will solve a hyperbolic partial differential equation for the pressure p in two dimensions using a reciprocal theorem. We obtain an explicit integral representation for the pressure, in terms of single-layer and double-layer potentials. A method is used for calculating the far-field of these potentials of an oscillating circle. Our solution is verified by comparing the results with a known solution.
Advisors/Committee Members: Martin, P. A. (advisor), Collis, Jon M. (committee member), Pankavich, Stephen (committee member).
Subjects/Keywords: Differential equations, Partial; Gravity waves – Mathematical models; Internal waves – Mathematical models; Reciprocity theorems; Oscillations; Pressure
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APA (6th Edition):
Johnson, G. J. (2014). Two-dimensional internal gravity waves generated by an oscillating circle in a density stratified fluid. (Masters Thesis). Colorado School of Mines. Retrieved from http://hdl.handle.net/11124/423
Chicago Manual of Style (16th Edition):
Johnson, Gregory J. “Two-dimensional internal gravity waves generated by an oscillating circle in a density stratified fluid.” 2014. Masters Thesis, Colorado School of Mines. Accessed March 06, 2021.
http://hdl.handle.net/11124/423.
MLA Handbook (7th Edition):
Johnson, Gregory J. “Two-dimensional internal gravity waves generated by an oscillating circle in a density stratified fluid.” 2014. Web. 06 Mar 2021.
Vancouver:
Johnson GJ. Two-dimensional internal gravity waves generated by an oscillating circle in a density stratified fluid. [Internet] [Masters thesis]. Colorado School of Mines; 2014. [cited 2021 Mar 06].
Available from: http://hdl.handle.net/11124/423.
Council of Science Editors:
Johnson GJ. Two-dimensional internal gravity waves generated by an oscillating circle in a density stratified fluid. [Masters Thesis]. Colorado School of Mines; 2014. Available from: http://hdl.handle.net/11124/423
Colorado School of Mines
5.
Loudon, Tyson S.
Analysis and dynamic active subspaces for a long term model of HIV.
Degree: MS(M.S.), Applied Mathematics and Statistics, 2015, Colorado School of Mines
URL: http://hdl.handle.net/11124/20117
► The Human Immunodeficiency Virus (HIV) disables many components of the body's immune system and, without antiretroviral treatment, leads to the onset of Acquired Immune Deficiency…
(more)
▼ The Human Immunodeficiency Virus (HIV) disables many components of the body's immune system and, without antiretroviral treatment, leads to the onset of Acquired Immune Deficiency Syndrome (AIDS) and subsequently death. The infection progresses through three stages: initial or acute infection, an asymptomatic or latent period, and finally AIDS. Modeling the entire time course of HIV within the body can be difficult as many models have oversimplified its biological dynamics in the effort to gain mathematical insight but fail to capture the three stages of infection. Only one HIV model has been able to describe the entire time course of the infection, but this model is large and is expensive to simulate. In this paper, we'll show there are two viral free steady states and conduct a stability analysis of one of the steady states. Then, we'll present a reduced order model for the T-cell count 1700 days after initial infection using active subspace methods. Building on the previous results, we'll create a global in time approximation of the T-cell count at any time using dynamic active subspaces.
Advisors/Committee Members: Pankavich, Stephen (advisor), Collis, Jon M. (committee member), Constantine, Paul G. (committee member).
Subjects/Keywords: HIV; sensitivity analysis; math modeling; active subspaces
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APA (6th Edition):
Loudon, T. S. (2015). Analysis and dynamic active subspaces for a long term model of HIV. (Masters Thesis). Colorado School of Mines. Retrieved from http://hdl.handle.net/11124/20117
Chicago Manual of Style (16th Edition):
Loudon, Tyson S. “Analysis and dynamic active subspaces for a long term model of HIV.” 2015. Masters Thesis, Colorado School of Mines. Accessed March 06, 2021.
http://hdl.handle.net/11124/20117.
MLA Handbook (7th Edition):
Loudon, Tyson S. “Analysis and dynamic active subspaces for a long term model of HIV.” 2015. Web. 06 Mar 2021.
Vancouver:
Loudon TS. Analysis and dynamic active subspaces for a long term model of HIV. [Internet] [Masters thesis]. Colorado School of Mines; 2015. [cited 2021 Mar 06].
Available from: http://hdl.handle.net/11124/20117.
Council of Science Editors:
Loudon TS. Analysis and dynamic active subspaces for a long term model of HIV. [Masters Thesis]. Colorado School of Mines; 2015. Available from: http://hdl.handle.net/11124/20117
Colorado School of Mines
6.
Tran, Nhat Thanh Van.
Entropic criteria for computational models of advection-diffusion equations.
Degree: MS(M.S.), Applied Mathematics and Statistics, 2020, Colorado School of Mines
URL: http://hdl.handle.net/11124/174130
► Traditional probabilistic methods for the estimation of parameters within advection-diffusion equations (ADEs) often overlook the entropic contribution of the discretization, i.e.number of particles, within associated…
(more)
▼ Traditional probabilistic methods for the estimation of parameters within advection-diffusion equations (ADEs) often overlook the entropic contribution of the discretization, i.e.number of particles, within associated numerical methods. Many times, the gain in accuracyof a highly discretized numerical model is outweighed by its associated computational costs.The research project herein seeks to answer the question of how many particles one should usein a numerical simulation to best approximate and estimate parameters in one-dimensionaladvective-diffusive transport with constant coefficients. To answer this question, we use thewell-known Akaike Information Criteria (AIC) and a recently-developed correction calledthe Computational Information Criteria (COMIC) to guide the model selection process.Two Lagrangian numerical methods - the random-walk particle tracking (RWPT) and mass-transfer particle tracking (MTPT) methods - are employed to solve the ADE at variouslevels of discretization. The numerical results demonstrate that the newly developed COMICprovides an optimal number of particles that can describe a more efficient model in termsof parameter estimation and model prediction compared to the model selected by the AIC.These results demonstrate the need for future modelers and scientific researchers to utilizecomputationally-driven selection criteria in order to best select numerical models.
Advisors/Committee Members: Pankavich, Stephen (advisor), Benson, David A. (advisor), Leiderman, Karin (committee member), Tenorio, Luis (committee member).
Subjects/Keywords: computational criteria; particles methods; entropy; COMIC
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APA ·
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APA (6th Edition):
Tran, N. T. V. (2020). Entropic criteria for computational models of advection-diffusion equations. (Masters Thesis). Colorado School of Mines. Retrieved from http://hdl.handle.net/11124/174130
Chicago Manual of Style (16th Edition):
Tran, Nhat Thanh Van. “Entropic criteria for computational models of advection-diffusion equations.” 2020. Masters Thesis, Colorado School of Mines. Accessed March 06, 2021.
http://hdl.handle.net/11124/174130.
MLA Handbook (7th Edition):
Tran, Nhat Thanh Van. “Entropic criteria for computational models of advection-diffusion equations.” 2020. Web. 06 Mar 2021.
Vancouver:
Tran NTV. Entropic criteria for computational models of advection-diffusion equations. [Internet] [Masters thesis]. Colorado School of Mines; 2020. [cited 2021 Mar 06].
Available from: http://hdl.handle.net/11124/174130.
Council of Science Editors:
Tran NTV. Entropic criteria for computational models of advection-diffusion equations. [Masters Thesis]. Colorado School of Mines; 2020. Available from: http://hdl.handle.net/11124/174130
Colorado School of Mines
7.
Schmidt, Michael J.
Kernel-based Lagrangian method for imperfectly-mixed chemical reactions, A.
Degree: MS(M.S.), Applied Mathematics and Statistics, 2018, Colorado School of Mines
URL: http://hdl.handle.net/11124/172365
► Current Lagrangian (particle-tracking) algorithms used to simulate diffusion-reaction equations must employ a certain number of particles to properly emulate the system dynamics – particularly for imperfectly-mixed…
(more)
▼ Current Lagrangian (particle-tracking) algorithms used to simulate diffusion-reaction equations must employ a certain number of particles to properly emulate the system dynamics – particularly for imperfectly-mixed systems. The number of particles is tied to the statistics of the initial concentration fields of the system at hand. Systems with shorter-range correlation and/or smaller concentration variance require more particles, potentially limiting the computational feasibility of the method. For the well-known problem of bimolecular reaction, we show that using kernel-based, rather than Dirac delta, particles can significantly reduce the required number of particles. We derive the fixed half-width of a Gaussian kernel for a given reduced number of particles that analytically eliminates the error between kernel and Dirac solutions at any specified time. We also show how to solve for the fixed kernel size by minimizing the squared differences between solutions over any given time interval. Numerical results show that the half-width of the kernel should be kept below about 12% of the domain size, and that the analytic equations used to derive kernel size suffer significantly from the neglect of higher-order moments. The simulations with a kernel half-width given by least squares minimization perform better than those made to match at one specific time. A heuristic time-variable kernel size, based on the previous results, performs on par with the least squares fixed kernel size.
Advisors/Committee Members: Pankavich, Stephen (advisor), Benson, David A. (advisor), Tenorio, Luis (committee member), Leiderman, Karin (committee member).
Subjects/Keywords: imperfect mixing; diffusion-reaction equation; particle methods
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APA (6th Edition):
Schmidt, M. J. (2018). Kernel-based Lagrangian method for imperfectly-mixed chemical reactions, A. (Masters Thesis). Colorado School of Mines. Retrieved from http://hdl.handle.net/11124/172365
Chicago Manual of Style (16th Edition):
Schmidt, Michael J. “Kernel-based Lagrangian method for imperfectly-mixed chemical reactions, A.” 2018. Masters Thesis, Colorado School of Mines. Accessed March 06, 2021.
http://hdl.handle.net/11124/172365.
MLA Handbook (7th Edition):
Schmidt, Michael J. “Kernel-based Lagrangian method for imperfectly-mixed chemical reactions, A.” 2018. Web. 06 Mar 2021.
Vancouver:
Schmidt MJ. Kernel-based Lagrangian method for imperfectly-mixed chemical reactions, A. [Internet] [Masters thesis]. Colorado School of Mines; 2018. [cited 2021 Mar 06].
Available from: http://hdl.handle.net/11124/172365.
Council of Science Editors:
Schmidt MJ. Kernel-based Lagrangian method for imperfectly-mixed chemical reactions, A. [Masters Thesis]. Colorado School of Mines; 2018. Available from: http://hdl.handle.net/11124/172365
Colorado School of Mines
8.
Parkinson, Christian.
In-host modeling of the spatial dynamics of HIV.
Degree: MS(M.S.), Applied Mathematics and Statistics, 2015, Colorado School of Mines
URL: http://hdl.handle.net/11124/17136
► The well-known three-compartment model which describes the spatially homogeneous dynamics of HIV in-vivo is adapted to account for spatial heterogeneity by considering diffusion of populations…
(more)
▼ The well-known three-compartment model which describes the spatially homogeneous dynamics of HIV in-vivo is adapted to account for spatial heterogeneity by considering diffusion of populations and spatially varying parameters. The new system of nonlinear parabolic PDEs is analyzed in detail. Specifically, local and global existence, uniqueness and high-order regularity of solutions is proven. We also determine the global asymptotic behavior of the model in certain biologically relevant regimes and compare our findings with the analogous results for the spatially homogeneous model. In doing so, we diss existence and stability of viral extinction and viral persistence steady states in different cases. Finally, the system is simulated using a semi-implicit finite difference method with the goal of verifying the analysiscus.
Advisors/Committee Members: Pankavich, Stephen (advisor), Diniz Behn, Cecilia (committee member), Ahrens, Cory (committee member).
Subjects/Keywords: math modeling; diffusion; math biology; HIV; PDEs; HIV infections – Mathematical models; Finite differences; Differential equations, Partial; Differential equations, Parabolic; Diffusion; Computer simulation
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APA (6th Edition):
Parkinson, C. (2015). In-host modeling of the spatial dynamics of HIV. (Masters Thesis). Colorado School of Mines. Retrieved from http://hdl.handle.net/11124/17136
Chicago Manual of Style (16th Edition):
Parkinson, Christian. “In-host modeling of the spatial dynamics of HIV.” 2015. Masters Thesis, Colorado School of Mines. Accessed March 06, 2021.
http://hdl.handle.net/11124/17136.
MLA Handbook (7th Edition):
Parkinson, Christian. “In-host modeling of the spatial dynamics of HIV.” 2015. Web. 06 Mar 2021.
Vancouver:
Parkinson C. In-host modeling of the spatial dynamics of HIV. [Internet] [Masters thesis]. Colorado School of Mines; 2015. [cited 2021 Mar 06].
Available from: http://hdl.handle.net/11124/17136.
Council of Science Editors:
Parkinson C. In-host modeling of the spatial dynamics of HIV. [Masters Thesis]. Colorado School of Mines; 2015. Available from: http://hdl.handle.net/11124/17136
Colorado School of Mines
9.
Simens, Jacqueline.
Mathematical modeling of hepatic and adipose insulin resistance in girls with polycystic ovarian syndrome.
Degree: MS(M.S.), Applied Mathematics and Statistics, 2015, Colorado School of Mines
URL: http://hdl.handle.net/11124/20154
► Polycystic Ovarian Syndrome (PCOS) affects 6-10% of women in the United States and is one of the leading causes of infertility. The metabolic phenotype for…
(more)
▼ Polycystic Ovarian Syndrome (PCOS) affects 6-10% of women in the United States and is one of the leading causes of infertility. The metabolic phenotype for PCOS includes insulin resistance (IR), and IR may vary with tissue type. The goal of this project is to determine the contributions of hepatic (liver) tissue and adipose (fat) tissue to increased IR in a cohort of adolescent females. For hepatic IR, we use the Labeled Oral Minimal Model (OMM*), originally developed by Dalla Man and colleagues. This differential equations based mathematical model describes the dynamics of glucose and insulin during an oral glucose tolerance test (OGTT) with stable isotope tracers for glucose and glycerol. Parameters for OMM* are used to quantify hepatic IR. We investigate the identifiability of this system and estimate model parameters in 6 subjects. For adipose IR, we propose a novel approach to modeling glycerol dynamics during an OGTT. We investigate the identifiability of this system and develop a numerical approach for estimating model parameters in the same cohort of 6 subjects. We propose the use of model parameters and metrics involving the numerical solution to quantify adipose IR. This work contributes to an improved understanding of tissue-specific IR, which may lead to targeted therapeutics.
Advisors/Committee Members: Diniz Behn, Cecilia (advisor), Pankavich, Stephen (committee member), Constantine, Paul G. (committee member).
Subjects/Keywords: mathematical modeling; model identifiability; PCOS; metabolism; glucose-insulin dynamics; parameter estimation
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APA (6th Edition):
Simens, J. (2015). Mathematical modeling of hepatic and adipose insulin resistance in girls with polycystic ovarian syndrome. (Masters Thesis). Colorado School of Mines. Retrieved from http://hdl.handle.net/11124/20154
Chicago Manual of Style (16th Edition):
Simens, Jacqueline. “Mathematical modeling of hepatic and adipose insulin resistance in girls with polycystic ovarian syndrome.” 2015. Masters Thesis, Colorado School of Mines. Accessed March 06, 2021.
http://hdl.handle.net/11124/20154.
MLA Handbook (7th Edition):
Simens, Jacqueline. “Mathematical modeling of hepatic and adipose insulin resistance in girls with polycystic ovarian syndrome.” 2015. Web. 06 Mar 2021.
Vancouver:
Simens J. Mathematical modeling of hepatic and adipose insulin resistance in girls with polycystic ovarian syndrome. [Internet] [Masters thesis]. Colorado School of Mines; 2015. [cited 2021 Mar 06].
Available from: http://hdl.handle.net/11124/20154.
Council of Science Editors:
Simens J. Mathematical modeling of hepatic and adipose insulin resistance in girls with polycystic ovarian syndrome. [Masters Thesis]. Colorado School of Mines; 2015. Available from: http://hdl.handle.net/11124/20154
Colorado School of Mines
10.
Bartlette, Kai.
Comparison of methods for calculating the rate of appearance of exogenous glucose.
Degree: MS(M.S.), Applied Mathematics and Statistics, 2018, Colorado School of Mines
URL: http://hdl.handle.net/11124/172356
► Insulin resistance (IR) is a crucial element of the pathology of the metabolic syndrome, which now affects more than a third of the population in…
(more)
▼ Insulin resistance (IR) is a crucial element of the pathology of the metabolic syndrome, which now affects more than a third of the population in the United States. Understanding the role of hepatic glucose release following a meal in contributing to hyperglycemia is crucial for the assessment of potential new medications. Using an oral glucose tolerance test (OGTT) protocol with two stable isotope tracers, both the rate of appearance of exogenous glucose (Ra_exo) coming from the drink and the suppression of endogenous glucose in response to the drink may be computed. In previous work, investigators have proposed several different methods for computing Ra_exo. The aim of this project was to compare the implementation and results of these methods applied to OGTT data from a cohort of obese adolescent girls. Methods were compared based on inter-method variability and known physiology. Obtaining a reliable estimate of the rate of appearance of exogenous glucose from the drink is necessary to assess hepatic IR. In addition, such an estimate represents a key input to differential equations-based models of whole body glucose-insulin dynamics that are used to quantify hepatic IR, and the method-dependence of the resulting estimates of insulin sensitivity has not been assessed. Improved understanding of interactions between exogenous and endogenous hepatic glucose dynamics will facilitate the characterization of IR in individual patients and different disease conditions and may support the development of targeted therapeutic approaches.
Advisors/Committee Members: Diniz Behn, Cecilia (advisor), Pankavich, Stephen (committee member), Leiderman, Karin (committee member).
Subjects/Keywords: insulin sensitivity index; oral minimal model; stable isotope glucose tracers; oral glucose tolerance test; insulin resistance; rate of appearance of exogenous glucose
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APA (6th Edition):
Bartlette, K. (2018). Comparison of methods for calculating the rate of appearance of exogenous glucose. (Masters Thesis). Colorado School of Mines. Retrieved from http://hdl.handle.net/11124/172356
Chicago Manual of Style (16th Edition):
Bartlette, Kai. “Comparison of methods for calculating the rate of appearance of exogenous glucose.” 2018. Masters Thesis, Colorado School of Mines. Accessed March 06, 2021.
http://hdl.handle.net/11124/172356.
MLA Handbook (7th Edition):
Bartlette, Kai. “Comparison of methods for calculating the rate of appearance of exogenous glucose.” 2018. Web. 06 Mar 2021.
Vancouver:
Bartlette K. Comparison of methods for calculating the rate of appearance of exogenous glucose. [Internet] [Masters thesis]. Colorado School of Mines; 2018. [cited 2021 Mar 06].
Available from: http://hdl.handle.net/11124/172356.
Council of Science Editors:
Bartlette K. Comparison of methods for calculating the rate of appearance of exogenous glucose. [Masters Thesis]. Colorado School of Mines; 2018. Available from: http://hdl.handle.net/11124/172356
Colorado School of Mines
11.
Li, Qiuwei.
Convex and nonconvex optimization geometries.
Degree: PhD, Electrical Engineering, 2019, Colorado School of Mines
URL: http://hdl.handle.net/11124/173275
► Many machine learning and signal processing problems are fundamentally nonconvex. One way to solve them is to transform them into convex optimization problems (a.k.a. convex…
(more)
▼ Many machine learning and signal processing problems are fundamentally nonconvex. One way to solve them is to transform them into convex optimization problems (a.k.a. convex relaxation), which constitutes a major part of my research. Although the convex relaxation approach is elegant in some ways that it can give information-theoretical sample convexity and minimax denoising rate, but this approach is not efficient in dealing with high-dimensional problems. Therefore, as my second major part of the research, I will directly focus on the fundamentally nonconvex formulations of these nonconvex problems, with a particular interest in understanding the nonconvex optimization landscapes of their fundamental formulations. Then in the third part of my research, I will develop optimization algorithms with provable guarantees that can efficiently navigate these nonconvex landscapes and achieve the global optimality. Finally, in the final part, I will apply the alternating minimization algorithms to general tensor recovery problems and clustering problems. Part 1: Convex Optimization. In this part, we apply convex relaxations to several popular nonconvex problems in signal processing and machine learning (e.g. line spectral estimation problem and tensor decomposition problem) and prove that the solving the new convex relaxation problems can return the globally optimal solutions of their original nonconvex formulations. Part 2: Nonconvex Optimization. In this part, we focus on the fundamentally nonconvex optimization landscapes for several low-rank matrix optimization problems with general objective functions, which covers a massive number of popular problems in signal processing and machine learning. In particular, we develop mild conditions for these general low-rank matrix optimization problems to have a benign landscape: all second-order stationary points are global optimal solutions and all saddle points are strict saddles (i.e. Hessian matrix has a negative eigenvalue). Part 3: Algorithms. In this part, we will develop optimization algorithms with provable second-order optimal convergence for general nonconvex and non-Lipschitz problems. Further, in this part, we also solve an open problem for the second-order convergence of alternating minimization algorithms that have been widely used in practice to solve large-scale nonconvex problems due to their simple implementation, fast convergence, and superb empirical performance. Then the second-order convergence guarantees, along with the knowledge (see Part 2) that a massive number of nonconvex optimization problems have been shown to have a benign landscape (all second-order stationary points are global minima), ensure that the proposed algorithms can find global minima for a class of nonconvex problems. Part 4: Applications. In this part, we apply the alternating minimization algorithms to several popular applications in signal processing and machine learning, e.g., the low-rank tensor recovery problem and the spherical Principal Component Analysis (PCA).
Advisors/Committee Members: Tang, Gongguo (advisor), Wakin, Michael B. (committee member), Pankavich, Stephen (committee member), Vincent, Tyrone (committee member).
Subjects/Keywords: convex optimization; nonconvex optimization; tensor decomposition; landscape analysis; atomic norm; strict saddles
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APA (6th Edition):
Li, Q. (2019). Convex and nonconvex optimization geometries. (Doctoral Dissertation). Colorado School of Mines. Retrieved from http://hdl.handle.net/11124/173275
Chicago Manual of Style (16th Edition):
Li, Qiuwei. “Convex and nonconvex optimization geometries.” 2019. Doctoral Dissertation, Colorado School of Mines. Accessed March 06, 2021.
http://hdl.handle.net/11124/173275.
MLA Handbook (7th Edition):
Li, Qiuwei. “Convex and nonconvex optimization geometries.” 2019. Web. 06 Mar 2021.
Vancouver:
Li Q. Convex and nonconvex optimization geometries. [Internet] [Doctoral dissertation]. Colorado School of Mines; 2019. [cited 2021 Mar 06].
Available from: http://hdl.handle.net/11124/173275.
Council of Science Editors:
Li Q. Convex and nonconvex optimization geometries. [Doctoral Dissertation]. Colorado School of Mines; 2019. Available from: http://hdl.handle.net/11124/173275
Colorado School of Mines
12.
Kalmbach, Kelsey R.
Map-based approaches for investigating sleep/wake dynamics.
Degree: MS(M.S.), Applied Mathematics and Statistics, 2016, Colorado School of Mines
URL: http://hdl.handle.net/11124/170650
► A homeostatic need for sleep increases with time awake and decreases during sleep. When the build up and recovery of sleepiness occurs sufficiently quickly, a…
(more)
▼ A homeostatic need for sleep increases with time awake and decreases during sleep. When the build up and recovery of sleepiness occurs sufficiently quickly, a person experiences two sleep cycles, a nap as well as nighttime sleep, each day. To investigate the transition between one and two sleep cycles per day, we consider the bifurcations of a previously developed model for human sleep/wake dynamics. As the time constants related to the build up and recovery of sleepiness are decreased, the system exhibits an incremental increase in the number of sleep cycles per day. Using a one-dimensional map to represent the dynamics of the system, we relate this map to a normal form for a piecewise continuous system which undergoes a border collision bifurcation, and provide numerical evidence for period-adding behavior. This analysis has implications for understanding the dynamics of the transition from napping to non-napping behavior in early childhood.
Advisors/Committee Members: Diniz Behn, Cecilia (advisor), Leiderman, Karin (committee member), Pankavich, Stephen (committee member).
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APA (6th Edition):
Kalmbach, K. R. (2016). Map-based approaches for investigating sleep/wake dynamics. (Masters Thesis). Colorado School of Mines. Retrieved from http://hdl.handle.net/11124/170650
Chicago Manual of Style (16th Edition):
Kalmbach, Kelsey R. “Map-based approaches for investigating sleep/wake dynamics.” 2016. Masters Thesis, Colorado School of Mines. Accessed March 06, 2021.
http://hdl.handle.net/11124/170650.
MLA Handbook (7th Edition):
Kalmbach, Kelsey R. “Map-based approaches for investigating sleep/wake dynamics.” 2016. Web. 06 Mar 2021.
Vancouver:
Kalmbach KR. Map-based approaches for investigating sleep/wake dynamics. [Internet] [Masters thesis]. Colorado School of Mines; 2016. [cited 2021 Mar 06].
Available from: http://hdl.handle.net/11124/170650.
Council of Science Editors:
Kalmbach KR. Map-based approaches for investigating sleep/wake dynamics. [Masters Thesis]. Colorado School of Mines; 2016. Available from: http://hdl.handle.net/11124/170650
Colorado School of Mines
13.
Sattelberg, Ben.
Global sensitivity analysis for a collisionless plasma using a particle-in-cell method, A.
Degree: MS(M.S.), Applied Mathematics and Statistics, 2016, Colorado School of Mines
URL: http://hdl.handle.net/11124/170652
► Knowing the effects of physical parameters underlying the behavior of plasmas is useful when designing or investigating associated high velocity systems. We use a kinetic…
(more)
▼ Knowing the effects of physical parameters underlying the behavior of plasmas is useful when designing or investigating associated high velocity systems. We use a kinetic model given by the Vlasov-Poisson equations to consider global linear and gradient-based active subspace models that calculate sensitivity metrics related to the phenomena of Landau damping and the two-stream instability. Since analytic results are difficult or impossible to obtain for this system, we use a particle-in-cell method to numerically compute quantities of interest for which the sensitivity metrics can be calculated. In particular, we consider three equilibrium distributions that include Maxwellian and Lorentzian velocity distributions to demonstrate the usefulness of this method in understanding and quantifying parameter effects.
Advisors/Committee Members: Pankavich, Stephen (advisor), Constantine, Paul G. (committee member), Bialecki, Bernard (committee member).
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APA (6th Edition):
Sattelberg, B. (2016). Global sensitivity analysis for a collisionless plasma using a particle-in-cell method, A. (Masters Thesis). Colorado School of Mines. Retrieved from http://hdl.handle.net/11124/170652
Chicago Manual of Style (16th Edition):
Sattelberg, Ben. “Global sensitivity analysis for a collisionless plasma using a particle-in-cell method, A.” 2016. Masters Thesis, Colorado School of Mines. Accessed March 06, 2021.
http://hdl.handle.net/11124/170652.
MLA Handbook (7th Edition):
Sattelberg, Ben. “Global sensitivity analysis for a collisionless plasma using a particle-in-cell method, A.” 2016. Web. 06 Mar 2021.
Vancouver:
Sattelberg B. Global sensitivity analysis for a collisionless plasma using a particle-in-cell method, A. [Internet] [Masters thesis]. Colorado School of Mines; 2016. [cited 2021 Mar 06].
Available from: http://hdl.handle.net/11124/170652.
Council of Science Editors:
Sattelberg B. Global sensitivity analysis for a collisionless plasma using a particle-in-cell method, A. [Masters Thesis]. Colorado School of Mines; 2016. Available from: http://hdl.handle.net/11124/170652
Colorado School of Mines
14.
McCollom, William A.
Laplace's equation on perturbed domains.
Degree: MS(M.S.), Applied Mathematics and Statistics, 2014, Colorado School of Mines
URL: http://hdl.handle.net/11124/17033
► Laplace's equation is a prototypical elliptic PDE that appears in many electromagnetic and fluid dynamics problems. We develop two methods for solving Laplace's equation on…
(more)
▼ Laplace's equation is a prototypical elliptic PDE that appears in many electromagnetic and fluid dynamics problems. We develop two methods for solving Laplace's equation on domains that are perturbations of a circle. These methods are derived from governing equations and applied to several test cases. Both Dirichlet and Neumann boundary conditions are considered. We verify our methods by constructing exact solutions for the perturbed geometries.
Advisors/Committee Members: Martin, P. A. (advisor), Collis, Jon M. (committee member), Pankavich, Stephen (committee member).
Subjects/Keywords: perturbation; Laplacian; boundary-variation; Harmonic functions; Perturbation (Mathematics); Dirichlet problem; Neumann problem; Differential equations, Partial
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APA (6th Edition):
McCollom, W. A. (2014). Laplace's equation on perturbed domains. (Masters Thesis). Colorado School of Mines. Retrieved from http://hdl.handle.net/11124/17033
Chicago Manual of Style (16th Edition):
McCollom, William A. “Laplace's equation on perturbed domains.” 2014. Masters Thesis, Colorado School of Mines. Accessed March 06, 2021.
http://hdl.handle.net/11124/17033.
MLA Handbook (7th Edition):
McCollom, William A. “Laplace's equation on perturbed domains.” 2014. Web. 06 Mar 2021.
Vancouver:
McCollom WA. Laplace's equation on perturbed domains. [Internet] [Masters thesis]. Colorado School of Mines; 2014. [cited 2021 Mar 06].
Available from: http://hdl.handle.net/11124/17033.
Council of Science Editors:
McCollom WA. Laplace's equation on perturbed domains. [Masters Thesis]. Colorado School of Mines; 2014. Available from: http://hdl.handle.net/11124/17033
Colorado School of Mines
15.
Stack, Nora.
Adolescent sleep and the circadian pacemaker.
Degree: MS(M.S.), Applied Mathematics and Statistics, 2016, Colorado School of Mines
URL: http://hdl.handle.net/11124/170654
► Adolescence is a critical time of social, physical, and mental development. Adolescents often exhibit a circadian phase delay in which they tend to go to…
(more)
▼ Adolescence is a critical time of social, physical, and mental development. Adolescents often exhibit a circadian phase delay in which they tend to go to bed later and wake up later compared to adults. This thesis seeks to understand the adolescent phase delay and its relationship to the circadian pacemaker, the body’s master clock. Using a dynamic circadian pacemaker model, we identify parameters that affect features of the circadian system that may contribute to the phase delay. Specifically, we focus on the effect of light on the phase and amplitude of the circadian pacemaker as model parameters are varied. We compare simulation results with data characterizing the adolescent clock under different weekend sleep protocols. This work has implications for understanding the mechanisms associated with the adolescent phase delay and may inform efforts to create schedules for adolescents that mitigate sleep loss and the resulting impacts on physical and cognitive performance.
Advisors/Committee Members: Diniz Behn, Cecilia (advisor), Pankavich, Stephen (committee member), Leiderman, Karin (committee member).
Subjects/Keywords: circadian pacemaker; phase delay; mathematical model; adolescent sleep
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APA ·
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APA (6th Edition):
Stack, N. (2016). Adolescent sleep and the circadian pacemaker. (Masters Thesis). Colorado School of Mines. Retrieved from http://hdl.handle.net/11124/170654
Chicago Manual of Style (16th Edition):
Stack, Nora. “Adolescent sleep and the circadian pacemaker.” 2016. Masters Thesis, Colorado School of Mines. Accessed March 06, 2021.
http://hdl.handle.net/11124/170654.
MLA Handbook (7th Edition):
Stack, Nora. “Adolescent sleep and the circadian pacemaker.” 2016. Web. 06 Mar 2021.
Vancouver:
Stack N. Adolescent sleep and the circadian pacemaker. [Internet] [Masters thesis]. Colorado School of Mines; 2016. [cited 2021 Mar 06].
Available from: http://hdl.handle.net/11124/170654.
Council of Science Editors:
Stack N. Adolescent sleep and the circadian pacemaker. [Masters Thesis]. Colorado School of Mines; 2016. Available from: http://hdl.handle.net/11124/170654
Colorado School of Mines
16.
Neri, Nathan J.
Model for acute stage HIV infection, A.
Degree: MS(M.S.), Applied Mathematics and Statistics, 2016, Colorado School of Mines
URL: http://hdl.handle.net/11124/170646
► This document lays out a new within-host model of acute stage HIV infection. The acute stage of HIV infection is characterized by a sudden spike…
(more)
▼ This document lays out a new within-host model of acute stage HIV infection. The acute stage of HIV infection is characterized by a sudden spike of viral load, followed by either complete clearance of the disease or a low level but persistent chronic infection. Clinical data suggests that the initial concentration of healthy T-cells and virions is vital to the dynamics of this early stage, but this is not well modeled by the standard three component model. More nuanced models have had better success at representing the spread of HIV at all stages, but include many awkward biological components and are infeasible to fit to actual data. The model in this document incorporates the homeostatic nature of the immune system to provide a model for the acute stage of the disease which represents interesting nonlinear dynamics. Chief among these are bistable equilibria and a Hopf bifurcation within biologically relevant parameter regimes and dependent on initial conditions of infection. Local stability analysis of T-cell and virus populations to variation of parameters is also conducted, which leads to additional complexity in comparison to previous models.
Advisors/Committee Members: Pankavich, Stephen (advisor), Diniz Behn, Cecilia (committee member), Nicholas, Michael (committee member).
Subjects/Keywords: HIV; acute stage; ODE
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APA (6th Edition):
Neri, N. J. (2016). Model for acute stage HIV infection, A. (Masters Thesis). Colorado School of Mines. Retrieved from http://hdl.handle.net/11124/170646
Chicago Manual of Style (16th Edition):
Neri, Nathan J. “Model for acute stage HIV infection, A.” 2016. Masters Thesis, Colorado School of Mines. Accessed March 06, 2021.
http://hdl.handle.net/11124/170646.
MLA Handbook (7th Edition):
Neri, Nathan J. “Model for acute stage HIV infection, A.” 2016. Web. 06 Mar 2021.
Vancouver:
Neri NJ. Model for acute stage HIV infection, A. [Internet] [Masters thesis]. Colorado School of Mines; 2016. [cited 2021 Mar 06].
Available from: http://hdl.handle.net/11124/170646.
Council of Science Editors:
Neri NJ. Model for acute stage HIV infection, A. [Masters Thesis]. Colorado School of Mines; 2016. Available from: http://hdl.handle.net/11124/170646
Colorado School of Mines
17.
Hickman, David A.
Particle swarm optimization for energy minimization of molecular systems.
Degree: MS(M.S.), Applied Mathematics and Statistics, 2014, Colorado School of Mines
URL: http://hdl.handle.net/11124/10612
► The minimization of a potential energy function can be used to provide insight into the ground state configuration of a wide range of molecular systems.…
(more)
▼ The minimization of a potential energy function can be used to provide insight into the ground state configuration of a wide range of molecular systems. Optimization problems of this type can be challenging for deterministic (e.g. line search) optimization algorithms due to the size of the search space and the large number of local minima that are inherent within molecular configuration problems. We describe how Particle Swarm Optimization, a stochastic optimization algorithm inspired by flocking behavior, can be used to accurately and efficiently solve energy minimization problems associated with molecular systems.
Advisors/Committee Members: Pankavich, Stephen (advisor), Constantine, Paul G. (committee member), Collis, Jon M. (committee member).
Subjects/Keywords: Mathematical optimization; Molecular structure; Algorithms; Swarm intelligence; Potential theory (Mathematics)
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APA (6th Edition):
Hickman, D. A. (2014). Particle swarm optimization for energy minimization of molecular systems. (Masters Thesis). Colorado School of Mines. Retrieved from http://hdl.handle.net/11124/10612
Chicago Manual of Style (16th Edition):
Hickman, David A. “Particle swarm optimization for energy minimization of molecular systems.” 2014. Masters Thesis, Colorado School of Mines. Accessed March 06, 2021.
http://hdl.handle.net/11124/10612.
MLA Handbook (7th Edition):
Hickman, David A. “Particle swarm optimization for energy minimization of molecular systems.” 2014. Web. 06 Mar 2021.
Vancouver:
Hickman DA. Particle swarm optimization for energy minimization of molecular systems. [Internet] [Masters thesis]. Colorado School of Mines; 2014. [cited 2021 Mar 06].
Available from: http://hdl.handle.net/11124/10612.
Council of Science Editors:
Hickman DA. Particle swarm optimization for energy minimization of molecular systems. [Masters Thesis]. Colorado School of Mines; 2014. Available from: http://hdl.handle.net/11124/10612
Colorado School of Mines
18.
Alcala, Diego A.
Macroscopic quantum tunneling and quantum many-body dynamics in Bose-Einstein condensates.
Degree: PhD, Physics, 2020, Colorado School of Mines
URL: http://hdl.handle.net/11124/174203
► Quantum mechanics revolutionized the previous century, not only in technology with lasers and semiconductors but also our fundamental view of the world with Bell's inequality…
(more)
▼ Quantum mechanics revolutionized the previous century, not only in technology with lasers and semiconductors but also our fundamental view of the world with Bell's inequality and entanglement. Quantum tunneling was the first experimental verification of quantum mechanics, by solving the mystery of radioactive decay, that a particle can escape the nucleus without sufficient energy to overcome the classical energy barrier. In this century, many-body quantum mechanics is bringing about a second revolution, with the possibility of quantum simulators, quantum computers, and a deeper understanding the nature. However, in order to fully harness the power of these systems, a detailed understanding of many-body effects is required, such as fluctuations, correlations, and entanglement. In this thesis, we seek to understand these observables in the context of macroscopic quantum tunneling. We quantify the macroscopic quantum tunneling dynamics, showing how interactions alter tunneling and quantum phase transitions modify non-equilibrium dynamics, providing a road maps of future experiments. The first experimental realization of mean-field interactions producing non-exponential decay of a tunneling Bose-Einstein condensate has been achieved. We develop an effective semi-classical model which accounts for the repulsive atom-atom interactions via an additional mean-field potential. This captures the 3D quantum tunneling via classical oscillations in an effective 1D trap and tunneling through a barrier with time-dependent height due to mean-field interactions. Mean-field treatments work well for Bose-Einstein condensates with negligible many-body effects, such as fragmentation, depletion, and fluctuations away from the mean. We show how a Bose-Einstein condensate with non-negligible fragmentation and depletion can be described with a renormalized mean-field. This suggest mean-field models are more widely applicable than previously thought, and that many-body physics may be hiding in such experiments and systems. Next, we explicitly look at the dynamics of many-body tunneling from a meta-stable trap, described by the Bose-Hubbard Hamiltonian in the superfluid quantum phase. The many-body physics are simulated using matrix product state methods, which allow exploration of lowly-entangled dynamics via data compression methods, and can calculate a wide range of quantum observables, like number fluctuations, correlations, and entanglement entropy. We compare many-body and mean-field dynamics, explicitly showing many-body tunneling times converge to mean-field tunneling times with increasing number of atoms in the system. We find rich dynamics with different time scales for the escape time, fluctuations, and quantum entropy in the system. With a firm grasp on the superfluid dynamics in the Bose-Hubbard Hamiltonian, we turn our attention to the superfluid to Mott insulating quantum phase transition, and understanding how the initial quantum phase alters macroscopic quantum tunneling. We examine this for both the double-well and quantum…
Advisors/Committee Members: Carr, Lincoln D. (advisor), Wu, Mingzhong (advisor), Tenorio, Luis (committee member), Pankavich, Stephen (committee member), Flammer, P. David (committee member).
Subjects/Keywords: many-body dynamics; quantum tunneling; Bose-Hubbard model; ultracold atoms; quantum phase transition
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APA (6th Edition):
Alcala, D. A. (2020). Macroscopic quantum tunneling and quantum many-body dynamics in Bose-Einstein condensates. (Doctoral Dissertation). Colorado School of Mines. Retrieved from http://hdl.handle.net/11124/174203
Chicago Manual of Style (16th Edition):
Alcala, Diego A. “Macroscopic quantum tunneling and quantum many-body dynamics in Bose-Einstein condensates.” 2020. Doctoral Dissertation, Colorado School of Mines. Accessed March 06, 2021.
http://hdl.handle.net/11124/174203.
MLA Handbook (7th Edition):
Alcala, Diego A. “Macroscopic quantum tunneling and quantum many-body dynamics in Bose-Einstein condensates.” 2020. Web. 06 Mar 2021.
Vancouver:
Alcala DA. Macroscopic quantum tunneling and quantum many-body dynamics in Bose-Einstein condensates. [Internet] [Doctoral dissertation]. Colorado School of Mines; 2020. [cited 2021 Mar 06].
Available from: http://hdl.handle.net/11124/174203.
Council of Science Editors:
Alcala DA. Macroscopic quantum tunneling and quantum many-body dynamics in Bose-Einstein condensates. [Doctoral Dissertation]. Colorado School of Mines; 2020. Available from: http://hdl.handle.net/11124/174203
Colorado School of Mines
19.
Shutt, Deborah A.
Modeling, analysis, and simulation of complex disease dynamics for HIV, Ebola, and Zika virus.
Degree: PhD, Applied Mathematics and Statistics, 2017, Colorado School of Mines
URL: http://hdl.handle.net/11124/170996
► The contributions made by mathematical approaches to biological problems has become widely recognized in recent decades. The focus of this thesis is to develop and…
(more)
▼ The contributions made by mathematical approaches to biological problems has become widely recognized in recent decades. The focus of this thesis is to develop and analyze novel mathematical models for various aspects of three infectious diseases: Human Immunodeficiency Virus (HIV), Ebola virus disease (EVD) and Zika virus. HIV is examined at the in-host level by two models capturing two stages of the disease process within the blood. The first HIV model considered here incorporates the effects of latent infection and mutation of the virus. This research is meant to provide applicable information when considering various vaccine developments and combination strategies to maintain viral suppression. The second HIV model in this dissertation examines early stage viral development and the contribution of the homeostatic proliferation of CD4+ T cells on the dynamics of the disease process; in particular the dependence of long term outcomes on the initial viral load and healthy T cell count. Both EVD and Zika are analyzed at the epidemiological level with compartmental model structures. A branching SEIR Ebola model is embedded into a stochastic process by means of a novel multinomial distribution derivation. This model is used to determine the most prominent forces of infection causing the 2014 Ebola outbreak in West Africa based on data as recorded by the World Health Organization. Finally, the spread of Zika within Central and South American countries is modeled by way of a modified (SEIR)/SEI vector compartmental structure to estimate basic reproductive numbers, total outbreak size, and reporting rates for Colombia, El Salvador and Suriname. This study highlights the need for research and data collection that will better constrain parameter ranges.
Advisors/Committee Members: Pankavich, Stephen (advisor), Porter, Aaron T. (advisor), Martin, P. A. (committee member), Diniz Behn, Cecilia (committee member), Maupin, C. Mark (committee member).
Subjects/Keywords: epidemiology; modeling; Zika; infectious diseases; Ebola; parameter estimation
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APA (6th Edition):
Shutt, D. A. (2017). Modeling, analysis, and simulation of complex disease dynamics for HIV, Ebola, and Zika virus. (Doctoral Dissertation). Colorado School of Mines. Retrieved from http://hdl.handle.net/11124/170996
Chicago Manual of Style (16th Edition):
Shutt, Deborah A. “Modeling, analysis, and simulation of complex disease dynamics for HIV, Ebola, and Zika virus.” 2017. Doctoral Dissertation, Colorado School of Mines. Accessed March 06, 2021.
http://hdl.handle.net/11124/170996.
MLA Handbook (7th Edition):
Shutt, Deborah A. “Modeling, analysis, and simulation of complex disease dynamics for HIV, Ebola, and Zika virus.” 2017. Web. 06 Mar 2021.
Vancouver:
Shutt DA. Modeling, analysis, and simulation of complex disease dynamics for HIV, Ebola, and Zika virus. [Internet] [Doctoral dissertation]. Colorado School of Mines; 2017. [cited 2021 Mar 06].
Available from: http://hdl.handle.net/11124/170996.
Council of Science Editors:
Shutt DA. Modeling, analysis, and simulation of complex disease dynamics for HIV, Ebola, and Zika virus. [Doctoral Dissertation]. Colorado School of Mines; 2017. Available from: http://hdl.handle.net/11124/170996
Colorado School of Mines
20.
Nealy, Jennifer L.
Study of normal mode solutions for seismo-acoustic propagation scenarios, A: a generalized range-independent case, earthquake modeling using seismic moment tensors, and an improved moment tensor inversion method.
Degree: PhD, Applied Mathematics and Statistics, 2015, Colorado School of Mines
URL: http://hdl.handle.net/11124/17111
► This work presents improvements to the study of tsunamigenic offshore earthquakes and complex earthquakes, i.e., earthquakes that are better represented as multiple events, through the…
(more)
▼ This work presents improvements to the study of tsunamigenic offshore earthquakes and complex earthquakes, i.e., earthquakes that are better represented as multiple events, through the use of underwater acoustic normal mode solutions and updated inversion techniques. When considering offshore earthquakes, normal mode solutions, i.e., analytic solutions that can be expressed as an infinite sum of residues, are used to model the acoustic field generated by an event. The environment under consideration, an ocean environment where water is overlying the seafloor, is approximated as a fluid layer overlying an elastic bottom. A source, such as an explosion or earthquake, is represented as a point source that is located in either the water column or the sediment layer. Using a generalized Green's function formulation for normal mode solutions, accurate solutions are obtained for various source cases and are benchmarked against elastic parabolic equation solutions that have been previously benchmarked against wavenumber integration solutions. Normal mode solutions for seismo-acoustic propagation problems using generalized Green's functions can then be used to study tsunamigenic earthquakes. Moment tensor representations of earthquake sources are used to find forcing terms that represent earthquakes of varying shear-to-compressional composition. The extension of this technique to a range-dependent environment where a coupling integral technique is used to ensure mode coupling across range segments is then explored. When considering complex events that do not necessarily occur offshore, the environment being considered is now the earth rather than the ocean. In this case it is beneficial to find characteristics of the earthquake instead of studying pressure fields generated by events. Using normal mode solutions of this new system, a matrix-vector equation may be found which, through least-squares inversion techniques, can characterize a complex earthquake as two near-simultaneous events rather than a single event. This allows for a more accurate characterization of the earthquake being modeled. A statistical test is used to compare results from a single source inversion to results obtained with a double source inversion and select the most appropriate number of sources for any given earthquake.
Advisors/Committee Members: Collis, Jon M. (advisor), Callan, Kristine E. (committee member), Carney, Debra (committee member), Constantine, Paul G. (committee member), Pankavich, Stephen (committee member).
Subjects/Keywords: Earthquakes; Tsunamis; Seismology – Statistical methods; Matrix inversion; Wave guides; Underwater acoustics
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APA ·
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APA (6th Edition):
Nealy, J. L. (2015). Study of normal mode solutions for seismo-acoustic propagation scenarios, A: a generalized range-independent case, earthquake modeling using seismic moment tensors, and an improved moment tensor inversion method. (Doctoral Dissertation). Colorado School of Mines. Retrieved from http://hdl.handle.net/11124/17111
Chicago Manual of Style (16th Edition):
Nealy, Jennifer L. “Study of normal mode solutions for seismo-acoustic propagation scenarios, A: a generalized range-independent case, earthquake modeling using seismic moment tensors, and an improved moment tensor inversion method.” 2015. Doctoral Dissertation, Colorado School of Mines. Accessed March 06, 2021.
http://hdl.handle.net/11124/17111.
MLA Handbook (7th Edition):
Nealy, Jennifer L. “Study of normal mode solutions for seismo-acoustic propagation scenarios, A: a generalized range-independent case, earthquake modeling using seismic moment tensors, and an improved moment tensor inversion method.” 2015. Web. 06 Mar 2021.
Vancouver:
Nealy JL. Study of normal mode solutions for seismo-acoustic propagation scenarios, A: a generalized range-independent case, earthquake modeling using seismic moment tensors, and an improved moment tensor inversion method. [Internet] [Doctoral dissertation]. Colorado School of Mines; 2015. [cited 2021 Mar 06].
Available from: http://hdl.handle.net/11124/17111.
Council of Science Editors:
Nealy JL. Study of normal mode solutions for seismo-acoustic propagation scenarios, A: a generalized range-independent case, earthquake modeling using seismic moment tensors, and an improved moment tensor inversion method. [Doctoral Dissertation]. Colorado School of Mines; 2015. Available from: http://hdl.handle.net/11124/17111
Colorado School of Mines
21.
Eker, Ilkay.
Mass transport within the fracture-matrix systems of unconventional shale reservoirs: application to primary production and EOR in Eagle Ford.
Degree: PhD, Petroleum Engineering, 2018, Colorado School of Mines
URL: http://hdl.handle.net/11124/172839
► The average primary oil recovery factor of Eagle Ford shale is around six percent; thus, a considerable amount of oil will be left behind after…
(more)
▼ The average primary oil recovery factor of Eagle Ford shale is around six percent; thus, a considerable amount of oil will be left behind after primary production. A major technique to enhance oil production in Eagle Ford could be gas injection because waterflooding does not seem plausible. This thesis evaluates the potential of gas injection enhanced oil recovery (EOR) using dual-porosity compositional modeling. The modeling effort focuses on three areas: transport mechanism at the matrix fracture interface, rock deformation effect on the phase behavior in the matrix pores, and multi-phase rate transient analysis (RTA). The complex nature of the fluid system and its transport in unconventional shale reservoirs requires robust computation codes that clearly reflect the physics of mass transport and thermodynamic phase behavior calculations. In this thesis, I have addressed this issue and have developed a new implicit method which relies on partial molar volume to decouple the transport equations into a pressure-composition solution, followed by a straight forward flash calculation that provides unambiguous crossing of phase boundaries, quantification of phase saturations, and phase compositions. Specifically, this formulation maintains a strong connection to the underlying physics. The pressure-composition code is an implicit numerical solution technique and is formulated for the dual-porosity reservoirs and for application in stimulated shale reservoirs. The model also includes diffusion mass transport for studying diffusion of components across the fracture-matrix interface in conjunction of with wet-gas EOR in shale reservoirs. The conclusion is that diffusion mass transport across fracture-matrix interface is a major gas-EOR mechanism even when advective flow via Darcy velocity is inactive (i.e., zero pressure gradient) or is at a very low level (i.e., very low permeability and low-pressure gradient). The new model includes a geomechanical component to study the effect of the pore pressure change and associated rock deformation on shale reservoir performance, and a pore-confinement, thermodynamic component to account for the shift in the phase envelop in nano-scale shale reservoir pores. Here, the model results indicate that fracture pore deformation during production provides additional driving force for hydrocarbon recovery. Finally, the new model was used to evaluate the rate transient analysis (RTA) in shale reservoirs where is reservoir production characteristics is highly composition-dependent. The results indicate that RTA is also applicable in stimulated shale reservoirs (i.e., dual-porosity) and RTA results provides an accurate value for the effective stimulated reservoir rock.
Advisors/Committee Members: Kazemi, Hossein (advisor), Tutuncu, Azra (committee member), Sonnenberg, Stephen A. (committee member), Abass, Hazim H. (committee member), Pankavich, Stephen (committee member).
Subjects/Keywords: dual porosity; EOR; unconventional shale reservoir; Eagle Ford; compositional modeling; gas injection
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APA (6th Edition):
Eker, I. (2018). Mass transport within the fracture-matrix systems of unconventional shale reservoirs: application to primary production and EOR in Eagle Ford. (Doctoral Dissertation). Colorado School of Mines. Retrieved from http://hdl.handle.net/11124/172839
Chicago Manual of Style (16th Edition):
Eker, Ilkay. “Mass transport within the fracture-matrix systems of unconventional shale reservoirs: application to primary production and EOR in Eagle Ford.” 2018. Doctoral Dissertation, Colorado School of Mines. Accessed March 06, 2021.
http://hdl.handle.net/11124/172839.
MLA Handbook (7th Edition):
Eker, Ilkay. “Mass transport within the fracture-matrix systems of unconventional shale reservoirs: application to primary production and EOR in Eagle Ford.” 2018. Web. 06 Mar 2021.
Vancouver:
Eker I. Mass transport within the fracture-matrix systems of unconventional shale reservoirs: application to primary production and EOR in Eagle Ford. [Internet] [Doctoral dissertation]. Colorado School of Mines; 2018. [cited 2021 Mar 06].
Available from: http://hdl.handle.net/11124/172839.
Council of Science Editors:
Eker I. Mass transport within the fracture-matrix systems of unconventional shale reservoirs: application to primary production and EOR in Eagle Ford. [Doctoral Dissertation]. Colorado School of Mines; 2018. Available from: http://hdl.handle.net/11124/172839
Colorado School of Mines
22.
Anderson, Justin Quinn.
Chaos and complexity of magnetic spin-wave solitary wave dynamics in the complex cubic quintic Ginzburg-Landau equation.
Degree: PhD, Physics, 2020, Colorado School of Mines
URL: http://hdl.handle.net/11124/174201
► We report the development, implementation and complete experimental vindication of a model for complex dynamical behaviors in spin wave envelopes propagating in nonlinear, dissipative driven,…
(more)
▼ We report the development, implementation and complete experimental vindication of a model for complex dynamical behaviors in spin wave envelopes propagating in nonlinear, dissipative driven, damped systems. These backward volume spin waves evolve under attractive nonlinearity in active magnetic thin film-based feedback rings where the major loss mechanisms present in the film are directly compensated by periodic linear amplification. Such a quasi-conservative evolution allows for the self-generation of spin waves and the observation of long-time behaviors 𝓞({ms}) which persist for hundreds to tens of thousands of the fundamental round trip time 𝓞(100~{ns}). The cubic-quintic complex Ginzburg-Landau equation is developed as a predictive, descriptive model for the evolution of spin wave envelopes. Over 180000 nodes hours of computation are used to execute more than 10000 simulations in order characterize the model's six dimensional parameter space. This exploration of parameter space was conducted in full generality, spanning a minimum of eight orders of magnitude for each of three loss terms and five orders of magnitude for higher order nonlinearities. Nine distinct classes of behavior were identified, including four categories of dynamical pattern formation. This work contains the first predicted long time dynamical behaviors for spin waves and analogous physical systems. All four categories of dynamical pattern formation that were identified numerically were then cleanly realized experimentally. Additionally we observed the first known examples of dynamical behaviors for dark solitary waves self-generated under attractive nonlinearity. Our experimental verification of these dynamical regimes show that such ideas are not simply theoretical but in fact occur in the real physical world and are observable in an approachable, tunable spin-wave system which matches the conditions of many other real-world physical systems. It further established that the relatively simple cubic-quintic complex Ginzburg-Landau equation provides a highly accurate, effective, and predictive description of complex spin wave dynamics and should replace the commonly used nonlinear Schrödinger equation for these systems. Finally, simulations which model the ring dynamics on the scale round trips were conducted using 130000 node hours over 3000 unique numerical simulations. This yielded a robust general solution for stable bright solitary wave trains evolving under periodic amplification which is the numerical equivalent to the bright solitary wave train initial condition perturbed experimentally to generate soliton fractals and chaotic solitons. Using this novel dynamical equilibrium as an initial condition we developed a mechanism for the generation of bright soliton fractals. Our experimental and numerical works on complex spin wave envelopes in magnetic thin films suggest these systems provide for an approachable, table top, experiment for the study of fundamental nonlinear wave physics. The…
Advisors/Committee Members: Carr, Lincoln D. (advisor), Wu, Mingzhong (advisor), Callan, Kristine (committee member), Benson, David A. (committee member), Pankavich, Stephen (committee member).
Subjects/Keywords: complexity; pattern formation; chaos; soliton; nonlinear dynamics
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APA (6th Edition):
Anderson, J. Q. (2020). Chaos and complexity of magnetic spin-wave solitary wave dynamics in the complex cubic quintic Ginzburg-Landau equation. (Doctoral Dissertation). Colorado School of Mines. Retrieved from http://hdl.handle.net/11124/174201
Chicago Manual of Style (16th Edition):
Anderson, Justin Quinn. “Chaos and complexity of magnetic spin-wave solitary wave dynamics in the complex cubic quintic Ginzburg-Landau equation.” 2020. Doctoral Dissertation, Colorado School of Mines. Accessed March 06, 2021.
http://hdl.handle.net/11124/174201.
MLA Handbook (7th Edition):
Anderson, Justin Quinn. “Chaos and complexity of magnetic spin-wave solitary wave dynamics in the complex cubic quintic Ginzburg-Landau equation.” 2020. Web. 06 Mar 2021.
Vancouver:
Anderson JQ. Chaos and complexity of magnetic spin-wave solitary wave dynamics in the complex cubic quintic Ginzburg-Landau equation. [Internet] [Doctoral dissertation]. Colorado School of Mines; 2020. [cited 2021 Mar 06].
Available from: http://hdl.handle.net/11124/174201.
Council of Science Editors:
Anderson JQ. Chaos and complexity of magnetic spin-wave solitary wave dynamics in the complex cubic quintic Ginzburg-Landau equation. [Doctoral Dissertation]. Colorado School of Mines; 2020. Available from: http://hdl.handle.net/11124/174201
Colorado School of Mines
23.
Denning, Dylan.
Reflections of internal gravity waves off bumpy surfaces.
Degree: MS(M.S.), Applied Mathematics and Statistics, 2015, Colorado School of Mines
URL: http://hdl.handle.net/11124/17141
► Waves in a density stratified fluid, termed internal gravity waves, reflected by a sloping plane make an angle with the horizontal equal to the angle…
(more)
▼ Waves in a density stratified fluid, termed internal gravity waves, reflected by a sloping plane make an angle with the horizontal equal to the angle between the incident wave and the horizontal. We add a perturbation to the plane small in size when compared to the amplitude of the wave motion. An asymptotic expansion is used and problems are derived up to two orders O(1) and O(ε). The leading order problem is the same as the reflection problem by a flat plane. The problem on O(ε) is a radiation problem that we solve using Fourier transforms.
Advisors/Committee Members: Martin, P. A. (advisor), Collis, Jon M. (advisor), Pankavich, Stephen (committee member), Strong, Scott A. (committee member).
Subjects/Keywords: reflections; internal gravity waves; bumpy; Gravity waves; Wave equation; Asymptotic expansions; Differential equations, Partial; Fourier transformations; Perturbation (Mathematics)
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APA (6th Edition):
Denning, D. (2015). Reflections of internal gravity waves off bumpy surfaces. (Masters Thesis). Colorado School of Mines. Retrieved from http://hdl.handle.net/11124/17141
Chicago Manual of Style (16th Edition):
Denning, Dylan. “Reflections of internal gravity waves off bumpy surfaces.” 2015. Masters Thesis, Colorado School of Mines. Accessed March 06, 2021.
http://hdl.handle.net/11124/17141.
MLA Handbook (7th Edition):
Denning, Dylan. “Reflections of internal gravity waves off bumpy surfaces.” 2015. Web. 06 Mar 2021.
Vancouver:
Denning D. Reflections of internal gravity waves off bumpy surfaces. [Internet] [Masters thesis]. Colorado School of Mines; 2015. [cited 2021 Mar 06].
Available from: http://hdl.handle.net/11124/17141.
Council of Science Editors:
Denning D. Reflections of internal gravity waves off bumpy surfaces. [Masters Thesis]. Colorado School of Mines; 2015. Available from: http://hdl.handle.net/11124/17141
Colorado School of Mines
24.
Forrester, Mary Michael.
Understanding water fluxes through land, vegetation and air with coupled atmospheric and hydrologic modeling at extreme scales.
Degree: PhD, Geology and Geological Engineering, 2020, Colorado School of Mines
URL: http://hdl.handle.net/11124/174215
► The processes that govern the quality, quantity, and movement of water resources are a multifaceted and nonlinear system of interactions between the earth, the land…
(more)
▼ The processes that govern the quality, quantity, and movement of water resources are a multifaceted and nonlinear system of interactions between the earth, the land surface, vegetation, and the lower atmosphere. Recent advancements in computational efficiency and earth system modeling have awarded hydrologists with increasingly high resolution models of terrestrial hydrology, which are paramount to understanding and predicting these complex fluxes of moisture and energy. Extreme-scale (continental scale and above) hydrologic simulations are, in particular, of interest to the hydrologic community for numerous societal and operational applications. However, computational demand has traditionally necessitated some type of relaxed physical assumptions, usually by focusing physical realism on isolated components of the water cycle; for instance, land surface models as the lower boundary to meteorological models often simplify surface and subsurface hydrology, concentrating on the balance of radiation and surface turbulent fluxes but neglecting deep and lateral redistribution of soil moisture. Given the growing body of literature detailing the benefits of capturing coupled system exchange of moisture and energy, there is increasing demand for large-scale, high resolution models which simulate the hydrologic cycle as an integrated whole, from bedrock to land surface to atmosphere. This dissertation presents work towards fully-coupled, high-resolution hydrologic simulations at extreme scales. In these chapters, the importance of representing dynamic groundwater and lateral subsurface moisture redistribution is shown with regard to regional atmospheric modeling. Also discussed is the fidelity, uncertainty, and application of high-resolution, coupled-system hydrologic simulations at the continental scale. This work focuses on the connection between groundwater and atmosphere, demonstrates the importance of hydrologic representation in meteorological and remote sensing applications, and implicates the use of continental-scale hydrologic models to better understand the processes that govern our invaluable water resources.
Advisors/Committee Members: Maxwell, Reed M. (advisor), Navarre-Sitchler, Alexis K. (committee member), Pankavich, Stephen (committee member), Kroepsch, Adrianne (committee member).
Subjects/Keywords: computational; land surface; atmosphere; modeling; groundwater
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APA (6th Edition):
Forrester, M. M. (2020). Understanding water fluxes through land, vegetation and air with coupled atmospheric and hydrologic modeling at extreme scales. (Doctoral Dissertation). Colorado School of Mines. Retrieved from http://hdl.handle.net/11124/174215
Chicago Manual of Style (16th Edition):
Forrester, Mary Michael. “Understanding water fluxes through land, vegetation and air with coupled atmospheric and hydrologic modeling at extreme scales.” 2020. Doctoral Dissertation, Colorado School of Mines. Accessed March 06, 2021.
http://hdl.handle.net/11124/174215.
MLA Handbook (7th Edition):
Forrester, Mary Michael. “Understanding water fluxes through land, vegetation and air with coupled atmospheric and hydrologic modeling at extreme scales.” 2020. Web. 06 Mar 2021.
Vancouver:
Forrester MM. Understanding water fluxes through land, vegetation and air with coupled atmospheric and hydrologic modeling at extreme scales. [Internet] [Doctoral dissertation]. Colorado School of Mines; 2020. [cited 2021 Mar 06].
Available from: http://hdl.handle.net/11124/174215.
Council of Science Editors:
Forrester MM. Understanding water fluxes through land, vegetation and air with coupled atmospheric and hydrologic modeling at extreme scales. [Doctoral Dissertation]. Colorado School of Mines; 2020. Available from: http://hdl.handle.net/11124/174215
Colorado School of Mines
25.
Schmidt, Michael J.
Lagrangian methods for modeling transport, mixing, and geochemical reactions.
Degree: PhD, Applied Mathematics and Statistics, 2019, Colorado School of Mines
URL: http://hdl.handle.net/11124/173042
► This dissertation is concerned with methods for enhancing the current capabilities of Lagrangian (particle-tracking) methods for modeling transport, mixing, and geochemical reactions. We address the…
(more)
▼ This dissertation is concerned with methods for enhancing the current capabilities of Lagrangian (particle-tracking) methods for modeling transport, mixing, and geochemical reactions. We address the problem of fixed minimum particle numbers (previously dictated only by initial concentration statistics) by developing a method that employs Gaussian spatial kernels to reduce the required number of particles without introducing excess error. We demonstrate that the recently developed mass-transfer particle-tracking (MTPT) algorithm solves the diffusion equation with O(∆t) accuracy and can be used in conjunction with random walks to jointly simulate the distinct process of mixing and spreading. We extend the MTPT method to enable it to simulate chemical reactions involving aqueous and solid species via mobile and immobile particle interactions. We show that this mobile-immobile reactive particle-tracking (miRPT) algorithm can simulate an arbitrarily small amount of diffusion, and we apply it, with favorable results, to a calcite-dolomite reactive transport system that includes dissolution and precipitation reactions. We establish the numerical equivalence, under certain conditions, between smoothed-particle hydrodynamics (SPH) and MTPT methods, and we thus unify methods that were previously treated as distinct. As a result, these particle-tracking methods inherit a large body of theoretical underpinning. Finally, we apply the miRPT algorithm to a chemically-complex system involving the cycling of heavy metals in lake sediments, and we consider the effects of perturbing the spatial representation of solid species using immobile particles. In this analysis, we see that irregular distributions of solid species leads to increased variability in model results, and we see that this effect is greatest in areas where reactants are not in chemical equilibrium.
Advisors/Committee Members: Pankavich, Stephen (advisor), Benson, David A. (advisor), Leiderman, Karin (committee member), Tenorio, Luis (committee member), Navarre-Sitchler, Alexis K. (committee member).
Subjects/Keywords: computational methods; imperfect mixing; particle tracking; geochemical modeling; advection-diffusion-reaction equation; Lagrangian methods
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APA (6th Edition):
Schmidt, M. J. (2019). Lagrangian methods for modeling transport, mixing, and geochemical reactions. (Doctoral Dissertation). Colorado School of Mines. Retrieved from http://hdl.handle.net/11124/173042
Chicago Manual of Style (16th Edition):
Schmidt, Michael J. “Lagrangian methods for modeling transport, mixing, and geochemical reactions.” 2019. Doctoral Dissertation, Colorado School of Mines. Accessed March 06, 2021.
http://hdl.handle.net/11124/173042.
MLA Handbook (7th Edition):
Schmidt, Michael J. “Lagrangian methods for modeling transport, mixing, and geochemical reactions.” 2019. Web. 06 Mar 2021.
Vancouver:
Schmidt MJ. Lagrangian methods for modeling transport, mixing, and geochemical reactions. [Internet] [Doctoral dissertation]. Colorado School of Mines; 2019. [cited 2021 Mar 06].
Available from: http://hdl.handle.net/11124/173042.
Council of Science Editors:
Schmidt MJ. Lagrangian methods for modeling transport, mixing, and geochemical reactions. [Doctoral Dissertation]. Colorado School of Mines; 2019. Available from: http://hdl.handle.net/11124/173042
Colorado School of Mines
26.
Danes, Nicholas Archimedes.
Computational modeling of extravascular platelet aggregation under flow.
Degree: PhD, Applied Mathematics and Statistics, 2019, Colorado School of Mines
URL: http://hdl.handle.net/11124/173293
► Platelets in blood aggregate as part of the normal physiologic response to a blood vessel injury. Extravascular injuries, those that occur outside the blood vessel,…
(more)
▼ Platelets in blood aggregate as part of the normal physiologic response to a blood vessel injury. Extravascular injuries, those that occur outside the blood vessel, are not well understood and lack numerical tools to study them. In this research, we develop and validate numerical tools to study extravascular platelet aggregation based on the design of a microfluidic "bleeding chip'' device via the finite element method. Key model developments are for the fluid dynamics and platelet transport. For the platelet transport model, we also develop and benchmark the underlying flux-corrected transport algorithm to run in parallel using the FEniCS software suite. We use the numerical tools developed to calibrate and validate an ODE model of extravascular aggregation. With this model, we also benchmark and test the disparity of the fluid and reaction timescales to improve simulation time. These numerical tools provide a framework for future studies in extravascular platelet aggregation and other blood clotting phenomena.
Advisors/Committee Members: Leiderman, Karin (advisor), Sitaraman, Hariswaran (advisor), Neeves, Keith B. (committee member), Ganesh, Mahadevan (committee member), Pankavich, Stephen (committee member).
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APA (6th Edition):
Danes, N. A. (2019). Computational modeling of extravascular platelet aggregation under flow. (Doctoral Dissertation). Colorado School of Mines. Retrieved from http://hdl.handle.net/11124/173293
Chicago Manual of Style (16th Edition):
Danes, Nicholas Archimedes. “Computational modeling of extravascular platelet aggregation under flow.” 2019. Doctoral Dissertation, Colorado School of Mines. Accessed March 06, 2021.
http://hdl.handle.net/11124/173293.
MLA Handbook (7th Edition):
Danes, Nicholas Archimedes. “Computational modeling of extravascular platelet aggregation under flow.” 2019. Web. 06 Mar 2021.
Vancouver:
Danes NA. Computational modeling of extravascular platelet aggregation under flow. [Internet] [Doctoral dissertation]. Colorado School of Mines; 2019. [cited 2021 Mar 06].
Available from: http://hdl.handle.net/11124/173293.
Council of Science Editors:
Danes NA. Computational modeling of extravascular platelet aggregation under flow. [Doctoral Dissertation]. Colorado School of Mines; 2019. Available from: http://hdl.handle.net/11124/173293
Colorado School of Mines
27.
Meier, Amanda K.
Application of space-time structured light to controlled high-intensity laser matter interactions in point and line target geometries.
Degree: PhD, Physics, 2015, Colorado School of Mines
URL: http://hdl.handle.net/11124/20177
► With ultrashort laser pulses, nonlinear effects can be observed with low energy in each pulse. The broad bandwidth that makes it possible to produce a…
(more)
▼ With ultrashort laser pulses, nonlinear effects can be observed with low energy in each pulse. The broad bandwidth that makes it possible to produce a short pulse also introduces new degrees of freedom for manipulating the beam. The different frequency components that make up the bandwidth can be thought of as individual Gaussian beamlets that travel at different directions through optical elements due to dispersion or spatial chirp. These distortions are usually minimized in laser alignments yet manipulation of the of the Gaussian beamlets can be useful in axial localization and pulse front tilt (PFT), which is called simultaneous spatial and temporal focusing (SSTF) and is useful in many applications. In order to use SSTF, we need to characterize the pulse in both the spatial and spectral domains. We have developed a novel Sagnac shearing interferometer which combines spatial and spectral interference. The combination of divergence and spatial shear results in a local angle between the beams which can be extracted from the interference pattern using spatially resolved spectral interferometry by Fourier analysis. A spatial inversion allows our design to be extended to characterize a coupled spatio-temporal distortion, spatial chirp. We have developed techniques to control relative PFT for focused beams. We use a single pass grating compressor as a passively stable pump-probe experiment stemming from diffractive optics, where the +/-1 diffracted orders from a transmission grating pair are focused by an off-axis parabola which crosses the pump beams to form an index grating at the focus that is probed by the zero order. The experiment can be aligned for overlap of the pulse front tilt across the entire focal spot. This PF overlap can be applied in nonlinear mixing processes, such as harmonic generation or four wave mixing, to characterize semiconductor samples or ionization dynamics. We have also extended SSTF to a cylindrical geometry in Bessel-Gauss and vortex beams. Our novel setup for producing radial SSTF double passes a Gaussian beam through an axicon to produce a collimated ring beam that is then focused to a Bessel zone. Including a vortex mask in the beam gives a phase singularity on axis which creates a higher order Bessel-Gauss, corresponding to the vortex mode order. Circular gratings were also designed to extend SSTF to a cylindrical geometry as well as utilize the pulse front matching technique mentioned above. The Bessel zone with vortex singularity allows for high intensity walls that ionize causing the index of refraction to be higher in the core than the cladding, therefore allowing beam guiding. We modeled the waveguide geometry to optimize mode coupling. Radial SSTF could be used to guide high intensity beams with application to guide high harmonics.
Advisors/Committee Members: Durfee, Charles G. (advisor), Squier, Jeff A. (committee member), Ruskell, Todd G., 1969- (committee member), Scales, John Alan (committee member), Pankavich, Stephen (committee member).
Subjects/Keywords: circular grating; pulse front matching; spatial chirp; noncollinear mixing; Bessel-Gauss (B-G) beam; pulse front tilt (PFT)
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APA ·
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Export
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APA (6th Edition):
Meier, A. K. (2015). Application of space-time structured light to controlled high-intensity laser matter interactions in point and line target geometries. (Doctoral Dissertation). Colorado School of Mines. Retrieved from http://hdl.handle.net/11124/20177
Chicago Manual of Style (16th Edition):
Meier, Amanda K. “Application of space-time structured light to controlled high-intensity laser matter interactions in point and line target geometries.” 2015. Doctoral Dissertation, Colorado School of Mines. Accessed March 06, 2021.
http://hdl.handle.net/11124/20177.
MLA Handbook (7th Edition):
Meier, Amanda K. “Application of space-time structured light to controlled high-intensity laser matter interactions in point and line target geometries.” 2015. Web. 06 Mar 2021.
Vancouver:
Meier AK. Application of space-time structured light to controlled high-intensity laser matter interactions in point and line target geometries. [Internet] [Doctoral dissertation]. Colorado School of Mines; 2015. [cited 2021 Mar 06].
Available from: http://hdl.handle.net/11124/20177.
Council of Science Editors:
Meier AK. Application of space-time structured light to controlled high-intensity laser matter interactions in point and line target geometries. [Doctoral Dissertation]. Colorado School of Mines; 2015. Available from: http://hdl.handle.net/11124/20177
28.
Diaz, Paul Marcus.
Global sensitivity metrics from active subspaces with applications.
Degree: MS(M.S.), Applied Mathematics and Statistics, 2016, Colorado School of Mines
URL: http://hdl.handle.net/11124/170244
► Predictions from science and engineering models depend on input parameters. Global sensitivity metrics quantify the importance of input parameters, which can lead to model insight…
(more)
▼ Predictions from science and engineering models depend on input parameters. Global sensitivity metrics quantify the importance of input parameters, which can lead to model insight and reduced computational cost. Active subspaces are an emerging set of tools for identifying important directions in a model's input parameter space; these directions can be exploited to reduce the model's dimension enabling otherwise infeasible parameter studies. We develop global sensitivity metrics called activity scores from the estimated active subspace and analytically compare the active subspace-based metrics to established sensitivity metrics. These commonly used metrics include Sobol' indices derived from a variance-based decomposition and derivative-based metrics. Additionally, we outline practical computational methods to estimate the activity scores. We then consider three numerical examples with algebraic scalar valued functions from engineering and biological models. In each case, the models admit reduced dimensional active subspaces. For each of the models, a variety of sensitivity metrics are compared to the activity scores.
Advisors/Committee Members: Constantine, Paul G. (advisor), Pankavich, Stephen (committee member), Doostan, Alireza (committee member).
Subjects/Keywords: active subspaces; activity scores; Ebola; global sensitivity metrics; sensitivity analysis; Sobol
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APA (6th Edition):
Diaz, P. M. (2016). Global sensitivity metrics from active subspaces with applications. (Masters Thesis). Colorado School of Mines. Retrieved from http://hdl.handle.net/11124/170244
Chicago Manual of Style (16th Edition):
Diaz, Paul Marcus. “Global sensitivity metrics from active subspaces with applications.” 2016. Masters Thesis, Colorado School of Mines. Accessed March 06, 2021.
http://hdl.handle.net/11124/170244.
MLA Handbook (7th Edition):
Diaz, Paul Marcus. “Global sensitivity metrics from active subspaces with applications.” 2016. Web. 06 Mar 2021.
Vancouver:
Diaz PM. Global sensitivity metrics from active subspaces with applications. [Internet] [Masters thesis]. Colorado School of Mines; 2016. [cited 2021 Mar 06].
Available from: http://hdl.handle.net/11124/170244.
Council of Science Editors:
Diaz PM. Global sensitivity metrics from active subspaces with applications. [Masters Thesis]. Colorado School of Mines; 2016. Available from: http://hdl.handle.net/11124/170244
. 
Open Access Theses and Dissertations
