자료유형  

 학위논문

Control Number  

0015490284

International Standard Book Number  

9781088325483

Dewey Decimal Classification Number  

574

Main Entry-Personal Name  

Brooks, Heather.

Publication, Distribution, etc. (Imprint  

[Sl] : The University of Utah, 2018

Publication, Distribution, etc. (Imprint  

Ann Arbor : ProQuest Dissertations & Theses, 2018

Physical Description  

94 p

General Note  

Source: Dissertations Abstracts International, Volume: 81-04, Section: B.

General Note  

Advisor: Bressloff, Paul.

Dissertation Note  

Thesis (Ph.D.)--The University of Utah, 2018.

Restrictions on Access Note  

This item must not be sold to any third party vendors.

Summary, Etc.  

요약The interplay of dynamics and structure is a common theme in both mathematics and biology. In this thesis, the author develops and analyzes mathematical models that give insight into the dynamics and structure of a variety of biological applications. The author presents a variety of contributions in applications of mathematics to explore biological systems across several scales. First, she analyzes pattern formation in a partial differential equation model based on two interacting proteins that are undergoing passive and active transport, respectively. This work is inspired by a longstanding problem in identifying a biophysical mechanism for the control of synaptic density in C. elegans and leads to a novel mathematical formulation of Turing-type patterns in intracellular transport. The author also demonstrates the persistence of these patterns on growing domains, and discusses extensions for a two-dimensional model. She then presents two models that explore how stochastic processes affect intracellular dynamics. First, the author and her collaborators derive effective stochastic differential equations that describe intermittent virus trafficking. Next, she shows how ion channel fluctuations lead to subthreshold oscillations in neuron models. In the final chapter, she discusses two projects for ongoing and future work: one on modeling parasite infection on dynamic social networks, and another on the bifurcation structure of localized patterns on lattices. All of these projects, presented together, chronicle the journey of the author through her mathematical development and attempts to identify, discover, create, and communicate mathematics that inspires and excites.

Subject Added Entry-Topical Term  

Applied mathematics

Subject Added Entry-Topical Term  

Differential equations

Subject Added Entry-Topical Term  

Mathematical models

Subject Added Entry-Topical Term  

Biophysics

Added Entry-Corporate Name  

The University of Utah Mathematics

Host Item Entry  

Dissertations Abstracts International. 81-04B.

Host Item Entry  

Dissertation Abstract International

Electronic Location and Access  

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Control Number  

joongbu:567463