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You searched for +publisher:"University of Colorado" +contributor:("Zachary Kilpatrick"). Showing records 1 – 3 of 3 total matches.

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University of Colorado

1. Krishnan, Nikhil. Foraging in Stochastic Environments.

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

For many organisms, foraging for food and resources is integral to survival. Mathematical models of foraging can provide insight into the benefits and drawbacks of different foraging strategies. We begin by considering the movement of a memoryless starving forager on a one-dimensional periodic lattice, where each location contains one unit of food. As the forager lands on sites with food, it consumes the food leaving the sites empty. If the forager lands consecutively on a certain number of empty sites, then it starves. The forager has two modes of movement: it can either diffuse by moving with equal probability to adjacent lattice sites, or it can jump uniformly randomly amongst the lattice sites. The lifetime of the forager can be approximated in either paradigm by the sum of the cover time plus the number of empty sites it can visit before starving. The lifetime of the forager varies nonmontonically according to the probability of jumping. The tradeoff between jumps and diffusion is explored using simpler systems as well as numerical simulation, and we demonstrate that the best strategy is one that incorporates both jumps and diffusion. When long range jumps are time-penalized, counterintuitively, this shifts the optimal strategy to pure jumping. We next consider optimal strategies for a group of foragers to search for a target (such as food in an environment where it is sparsely located). There is a single target in one of several patches, with a greater penalty if the foragers decide to switch their positions among the patches. Both in the case of a single searcher, and in the case of a group of searchers, efficient deterministic strategies can be found to locate the target. Advisors/Committee Members: Zachary Kilpatrick, Nancy Rodriguez, Juan Restrepo.

Subjects/Keywords: Foraging; Dynamic Systems

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APA (6th Edition):

Krishnan, N. (2019). Foraging in Stochastic Environments. (Masters Thesis). University of Colorado. Retrieved from https://scholar.colorado.edu/appm_gradetds/145

Chicago Manual of Style (16th Edition):

Krishnan, Nikhil. “Foraging in Stochastic Environments.” 2019. Masters Thesis, University of Colorado. Accessed January 26, 2021. https://scholar.colorado.edu/appm_gradetds/145.

MLA Handbook (7th Edition):

Krishnan, Nikhil. “Foraging in Stochastic Environments.” 2019. Web. 26 Jan 2021.

Vancouver:

Krishnan N. Foraging in Stochastic Environments. [Internet] [Masters thesis]. University of Colorado; 2019. [cited 2021 Jan 26]. Available from: https://scholar.colorado.edu/appm_gradetds/145.

Council of Science Editors:

Krishnan N. Foraging in Stochastic Environments. [Masters Thesis]. University of Colorado; 2019. Available from: https://scholar.colorado.edu/appm_gradetds/145


University of Colorado

2. Stotsky, Jay Alexander. Mathematical and Computational Studies of the Biomechanics of Biofilms.

Degree: PhD, 2018, University of Colorado

Bacterial biofilms are communities of bacteria growing on a surface to which they have adhered, typically in an aqueous environment. The motivation to understand biofilm behavior arises from a variety of applications including the development of strategies to mitigate corrosion in industrial machinery, the treatment of bacterial infections, and process control in bioreactors. The focus in this thesis is on fluid-structure interaction and biomechanical properties of biofilms. Detailed studies of a mathematical biofilm model that includes the heterogeneous rheology observed in biofilms, a statistical model of biofilm microstructure, and an application of techniques from <i>a posteriori</i> numerical analysis to the Method of Regularized Stokeslets are explored. Key findings include the validation of a biofilm model with experimental data, an exploration of the effect that biofilm microstructure has on macroscopic properties, and an elucidation of how error propagates in a numerical method for biofilm simulation. Advisors/Committee Members: David M. Bortz, Vanja Dukic, Keith Julien, Zachary Kilpatrick, Michael Solomon.

Subjects/Keywords: a posteriori error analysis; biofilms; immersed boundary method; mathematical biology; point processes; Applied Mathematics; Biomechanics

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

APA (6th Edition):

Stotsky, J. A. (2018). Mathematical and Computational Studies of the Biomechanics of Biofilms. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/appm_gradetds/107

Chicago Manual of Style (16th Edition):

Stotsky, Jay Alexander. “Mathematical and Computational Studies of the Biomechanics of Biofilms.” 2018. Doctoral Dissertation, University of Colorado. Accessed January 26, 2021. https://scholar.colorado.edu/appm_gradetds/107.

MLA Handbook (7th Edition):

Stotsky, Jay Alexander. “Mathematical and Computational Studies of the Biomechanics of Biofilms.” 2018. Web. 26 Jan 2021.

Vancouver:

Stotsky JA. Mathematical and Computational Studies of the Biomechanics of Biofilms. [Internet] [Doctoral dissertation]. University of Colorado; 2018. [cited 2021 Jan 26]. Available from: https://scholar.colorado.edu/appm_gradetds/107.

Council of Science Editors:

Stotsky JA. Mathematical and Computational Studies of the Biomechanics of Biofilms. [Doctoral Dissertation]. University of Colorado; 2018. Available from: https://scholar.colorado.edu/appm_gradetds/107


University of Colorado

3. Nardini, John Thomas. Partial Differential Equation Models of Collective Migration During Wound Healing.

Degree: PhD, 2018, University of Colorado

This dissertation is concerned with the derivation, analysis, and parameter inference of mathematical models of the collective migration of epithelial cells. During the wound healing process, epidermal keratinocytes collectively migrate from the wound edge into the wound area as a means to re-establish the outermost layer of skin. This migration into the wound is stimulated by the presence of epidermal growth factor. Accordingly, this dissertation focuses on the migratory response of epidermal keratinocytes in response to this growth factor. Such studies will suggest suitable clinical treatments to consider for chronic wounds and invasive cancers. We begin with a study into the role of cell-cell adhesions on keratinocyte migration during wound healing. We use an inverse problem methodology in combination with model validation to show that cells use these connections to promote migration by pulling on their follower cells as they migrate into the wound. We next derive a biochemically-structured version of Fisher's Equation that provides a framework to study how patterns of biochemical activation influence migration into the wound. We prove the existence of a self-similar traveling wave solution. In considering a more complicated scenario where cell migration depends on biochemical activity levels, we show numerically that the threshold parameter where all cells in the population become activated yields the simulations that migrate farthest into the wound. Lastly, we consider the role of numerical error on an inverse problem methodology. The numerical approximation of a cost function is dominated by either numerical or experimental error in computations, which leads to different rates of convergence as numerical resolution increases. We use residual analysis to derive an autocorrelative statistical model for cases where numerical error is the main source of error for first order schemes. This autocorrelative statistical model can correct confidence interval computation for these methods and hence improve uncertainty quantification. Advisors/Committee Members: David M. Bortz, Vanja Dukic, Zachary Kilpatrick, Xuedong Liu, Fatemeh Pourahmadian.

Subjects/Keywords: collective migration; inverse problems; partial differential equations; traveling waves; wound healing; Mathematics; Partial Differential Equations

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

APA (6th Edition):

Nardini, J. T. (2018). Partial Differential Equation Models of Collective Migration During Wound Healing. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/appm_gradetds/117

Chicago Manual of Style (16th Edition):

Nardini, John Thomas. “Partial Differential Equation Models of Collective Migration During Wound Healing.” 2018. Doctoral Dissertation, University of Colorado. Accessed January 26, 2021. https://scholar.colorado.edu/appm_gradetds/117.

MLA Handbook (7th Edition):

Nardini, John Thomas. “Partial Differential Equation Models of Collective Migration During Wound Healing.” 2018. Web. 26 Jan 2021.

Vancouver:

Nardini JT. Partial Differential Equation Models of Collective Migration During Wound Healing. [Internet] [Doctoral dissertation]. University of Colorado; 2018. [cited 2021 Jan 26]. Available from: https://scholar.colorado.edu/appm_gradetds/117.

Council of Science Editors:

Nardini JT. Partial Differential Equation Models of Collective Migration During Wound Healing. [Doctoral Dissertation]. University of Colorado; 2018. Available from: https://scholar.colorado.edu/appm_gradetds/117

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