Diffusional instabilities on curved manifolds
Author(s)Shackleton, Henry (Henry J.)
Massachusetts Institute of Technology. Department of Physics.
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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.
Thesis: S.B., Massachusetts Institute of Technology, Department of Physics, 2018.Cataloged from PDF version of thesis.Includes bibliographical references (pages 61-64).
DepartmentMassachusetts Institute of Technology. Department of Physics.
Massachusetts Institute of Technology