Alison Ramage
Department of Mathematics
University of Strathclyde
Glasgow, Scotland
Although the mathematical theory of liquid crystals has been extensively studied for over
75 years, to date there has been much less work done on the numerous interesting and
important numerical analysis issues which the study of such materials raises. Often,
the underlying physical problems involve characteristic length and time scales which
vary by many orders of magnitude, or complex combinations of fluid flow and changes
in orientational order within a liquid crystal cell. Such features provide difficult
numerical challenges to those trying to simulate the real-life dynamic situations
which are of interest in an industrial setting.
In addition to the defect core structure, the dynamics of defect movement is also
a crucial issue for liquid crystal cells. One obvious approach is to use an adaptive
grid technique, ensuring that there is no waste of computational effort in areas where
there is no need for a fine grid. Adaptive grid methods have been successfully used to
solve PDEs in many branches of computational mathematics such as computational fluid
dynamics, mathematical biology, semiconductor modelling and aerospace engineering. In
this talk we will present an introductory study of the use of adaptive grid methods for
solving partial differential equation (PDE) problems in Q-tensor theory of liquid crystals.
This work is in collaboration with Dr Christopher J. Newton of Hewlett-Packard Laboratories in Bristol, UK.