Dissertation
Theory and Applications of Multi-Scale Geometric Methods
Washington State University
Doctor of Philosophy (PhD), Washington State University
01/2021
DOI:
https://doi.org/10.7273/000002400
Handle:
https://hdl.handle.net/2376/119671
Abstract
This dissertation is about the application and theoretical investigation of two multi-scale geometric minimization problems from Geometric Measure Theory called the maximum distance problem (MDP) and the multi-scale flat norm (MFN). The investigation of approximation results for the MDP leads us to the construction of minimum spanning trees over points whose neighborhoods cover the given set, and to the study of the ways in which the geometry of a set can effect the ability for it to be covered by a random collection of balls with a high probability. For sets in n-dimensional Euclidean space, this random covering problem is investigated with techniques that are similar to Whitney decompositions. For sets in the plane, we show that we may use the MFN as a way to turn bad sets into sets that do admit coverings with high probability. In addition, we use the multi-scale flat norm in the simplicial complex setting to analyze the interfaces that form between immiscible chemical systems.
Metrics
40 File views/ downloads
22 Record Views
Details
- Title
- Theory and Applications of Multi-Scale Geometric Methods
- Creators
- Enrique Guadalupe Alvarado
- Contributors
- Kevin R Vixie (Advisor)Kevin R Vixie (Committee Member)Bala Krishnamoorthy (Advisor)Bala Krishnamoorthy (Committee Member)Aurora Clark (Committee Member)Matthew Sottile (Committee Member)
- Awarding Institution
- Washington State University
- Academic Unit
- Mathematics and Statistics, Department of
- Theses and Dissertations
- Doctor of Philosophy (PhD), Washington State University
- Publisher
- Washington State University
- Number of pages
- 157
- Identifiers
- 99900606653401842
- Language
- English
- Resource Type
- Dissertation