Friday, December 02 2016, 2:15pm
Approximation of large bending problems
Sören Bartels (Universität Freiburg)
The development of polymer structures suggests various new applications in the area of nanotechnology. The controlled fabrication of related devices and nanotools leads however to many difficulties. Numerical simulations can contribute to improving this. In the talk we discuss the mathematical modeling and reliable computation of large bilayer bending effects. Deformations are described via a nonlinear bending energy subject to a pointwise isometry constraint. We devise finite element discretizations using discrete Kirchhoff triangles and show accuracy of
approximations via Gamma-convergence of the discretized functionals. The practical energy minimization is based on a semiimplicit discretization of a related gradient flow. Self-avoidance of deformations is not included in the model and appears to be relevant only in some situations. We present first results concerning the convergent computation of self-avoiding inextensible curves using a tangent-point functional.
Location: Raum 008/SeMath, Pontdriesch 14-16, 52062 Aachen