Dissertation
Numerical methods and uniquness for the Canham-Helfrich model of biomembranes
Doctor of Philosophy (Ph.D.), Drexel University
01 May 2015
DOI:
https://doi.org/10.17918/etd-6330
Abstract
The classical Canham-Helfrich models of biomembranes consist of a family of geometric constrained variational problems. Their physical importance and mathematical challenge attract the attention of both biophysicists and geometric analysts. In this PhD thesis, we develop a numerical method for these models. Our method uses a high-order approximation of surfaces with arbitrary topology based on subdivision methods. We also develop multiscale and parallel versions of our method which substantially speed up computations. An implementation based on Matlab and CUDA is provided along with this thesis. We use our solver to explore a phenomenon known as conformal diusion in the biophysical literature, which is also connected to the open uniqueness question for the Canham and Helfrich variation problems. We establish the uniqueness of solution of the Canham problem in a special case related to the Willmore conjecture (now the Marques-Neves theorem).
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Details
- Title
- Numerical methods and uniquness for the Canham-Helfrich model of biomembranes
- Creators
- Jingmin Chen - DU
- Contributors
- Thomas Yu (Advisor) - Drexel University (1970-)
- Awarding Institution
- Drexel University
- Degree Awarded
- Doctor of Philosophy (Ph.D.)
- Publisher
- Drexel University; Philadelphia, Pennsylvania
- Resource Type
- Dissertation
- Language
- English
- Academic Unit
- College of Arts and Sciences; Drexel University; Mathematics
- Other Identifier
- 6330; 991014632944904721