Description
The main objective of mathematical modeling is to connect mathematics with other scientific fields. Developing predictable models help to understand the behavior of biological systems. By testing models, one can relate mathematics and real-world experiments. To validate predictions numerically, one has to compare them with experimental data sets. Mathematical modeling can be split into two groups: microscopic and macroscopic models. Microscopic models described the motion of so-called agents (e.g. cells, ants) that interact with their surrounding neighbors. The interactions among these agents form at a large scale some special structures such as flocking and swarming. One of the key questions is to relate the particular interactions among agents with the overall emerging structures. Macroscopic models are precisely designed to describe the evolution of such large structures. They are usually given as partial differential equations describing the time evolution of a density distribution (instead of tracking each individual agent). For instance, reaction-diffusion equations are used to model glioma cells and are being used to predict tumor growth. This dissertation aims at developing such a framework to better understand the complex behavior of foraging ants and glioma cells.
Details
Title
- Modeling collective motion of complex systems using agent-based models & macroscopic models
Contributors
- Jamous, Sara Sami (Author)
- Motsch, Sebastien (Thesis advisor)
- Armbruster, Dieter (Committee member)
- Camacho, Erika (Committee member)
- Moustaoui, Mohamed (Committee member)
- Platte, Rodrigo (Committee member)
- Arizona State University (Publisher)
Date Created
The date the item was original created (prior to any relationship with the ASU Digital Repositories.)
2019
Subjects
Resource Type
Collections this item is in
Note
- thesisPartial requirement for: Ph.D., Arizona State University, 2019
- bibliographyIncludes bibliographical references (pages 82-86)
- Field of study: Applied mathematics
Citation and reuse
Statement of Responsibility
by Sara Sami Jamous