- Mathematical Modeling of Wrinkles in Thinly Curved Sheets
- Project Year:
2024
- REU Student (s):
Shreya Sinha | Princeton University NJ
- Student 1 Institution:
Princeton University
- Project Mentor:
Ian Tobasco
- Project Mentor Area:
Mathematics
- Project Abstract:
What rules dictate the wrinkle-patterns in general, simply-connected curved sheets? This project aimed to expand on results in the case of simply-connected sheets to non-simply connected sheets. The overall goal was to find a relation between the upper and lower convex envelopes of admissible convex functions (ones that satisfied certain requirements in order to successfully model wrinkle patterns), which we achieved and wish to further understand and simplify. We found concrete functions that solved the optimization problem in the case of an annulus, and found leads into the cases of a shifted annulus (where the hole is not centered on the disk) as well as have some idea as to how to solve the case of a disk with concentric regions of differently-signed curvature.
