Diffusional instabilities on curved manifolds

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.

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Physics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2018

Author dc:creator

• Shackleton, Henry (Henry J.)

Advisor dc:contributor.advisor

• Mehran Kardar.

• Physics.

Statement dc:rights

• MIT theses are protected by copyright. They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/120212

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/120212