Diffusional instabilities on curved manifolds
Name
1082855515-MIT.pdf
Description
Full printable version
Size
5.12 MB
Format
Adobe PDF
Checksum (MD5)
6a33947b00832689d0e6eea31ea75aa9
Author(s)
Shackleton, Henry (Henry J.)
Advisor(s)
Mehran Kardar.
Date Issued
2018
Publisher
Massachusetts Institute of Technology
Abstract
Diffusionally-driven instabilities provide a versatile mechanism for pattern formation, and have found applications in modeling a variety of biological and chemical systems. Although pattern formation has been observed in systems with a variety of geometries, the theoretical study of diffusional instabilities has primarily been restricted to systems of uniform curvature, such as flat planes, spheres, and cylinders. In this thesis, I study a method of analyzing pattern formation on more generally deformed surfaces, with a focus on perturbatively calculating effects due to small deformations from geometries of uniform curvature. Analytical predictions, ranging from pattern modifications to pinning of pattern development, are obtained on deformed drums, cylinders, and spheres. These predicted effects are compared to numerical studies, and additional cases where our analytical methods break down are studied numerically. Finally, the interplay between advection and non-uniform curvature is studied numerically.
Description
Thesis: S.B., Massachusetts Institute of Technology, Department of Physics, 2018.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 61-64).
Subjects
Physics.
MIT Department
Massachusetts Institute of Technology. Department of Physics
Terms of Use
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