Thin Elastic Materials Under Confinement

Series
Applied and Computational Mathematics Seminar
Time
Monday, September 29, 2008 - 1:00pm for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Silas Alben – School of Mathematics, Georgia Tech
Organizer
Haomin Zhou
We discuss two problems. First: When a piece of paper is crumpled, sharp folds and creases form. These are distributed over the sheet in a complex yet fascinating pattern. We study experimentally a two-dimensional version of this problem using thin strips of paper confined within rings of shrinking radius. We find a distribution of curvatures which can be fit by a power law. We provide a physical argument for the power law using simple elasticity and geometry. The second problem considers confinement of charged polymers to the surface of a sphere. This is a generalization of the classical Thompson model of the atom and has applications in the confinement of RNA and DNA in viral shells. Using computational results and asymptotics we describe the sequence of configurations of a simple class of charged polymers.