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NEWS in the Department of Mathematics
Graduate Announcements


Melissa Adkins - PhD defense
Date: Tuesday, March 31, 2015
Place: Weber, 201
Time: 3:00 p.m.

Title: Modeling Local Pattern Formation on Membrane Surfaces using Non-local Interactions

Advisor: Dr. Yongcheng Zhou

Committee:
Dr. James Liu
Dr. Jennifer Mueller
Dr. Diego Krapf

Abstract: The cell membrane is of utmost importance in the transportation of nutrients and signals to the cell which are needed for survival.  The magnitude of this is the inspiration for our study of the lipid bilayer which forms the cell membrane.  It's been recently accepted that the lipid bilayer consists of lipid microdomains (lipid rafts), as opposed to freely moving lipids.  We present two lipid raft models using the Ginzburg-Landau energy with addition of the electrostatic energy and the geodesic curvature energy to describe the local pattern formation of these lipid rafts.  The development and implementation of a $C^0$ interior penalty surface finite element method along with an implicit time iteration scheme will also be discussed as the optimal solution technique.

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