Geometrical evolution problems at low Reynolds numbers: reduced models

Wednesday, March 25, 2009 - 2:30pm - 3:15pm
EE/CS 3-180
Darren Crowdy (Imperial College London)
In this talk we report on some mathematical techniques
for modelling evolving geometries at low Reynolds
numbers. Two problems will be discussed, both involving
free capillary surfaces. The first
is a study of organisms swimming in Stokes flows
in the presence of free surfaces. An idealized mathematical
model is presented whereby the swimmer's interaction with a free capillary
surface is captured.
The second problem is of industrial importance
involving the optimal design of thin optic fibres with microstructure.
There is much interest in reducing transmission loss in
optic fibres by careful design of the microstucture imparted to a
fibre during the drawing process in which molten glass is pulled
through a casting die. During this process, geometrical changes in
the microstucture take place owing to capillary effects resulting in
the need to understand a highly nonlinear inverse problem.
New ideas for modelling this process will be described.
MSC Code: