As part of the European Framework 5 project, monlcd,
we have developed a 3D finite element program to calculate the dynamics
of LC reorientation. Since completion of the project further refinements
and optimisations have been made. A three-elastic constant formulation
is used, and the user can select a vector or tensor representation
of the LC orientation.
Device geometries entered using a CAD interface, allowing a wide
range of complex geometric shapes. Program is very flexible and
is capable of modelling large pixel sizes, using a fine discretisation,
with meager memory requirements.
When disclinations are present, the LC ordering
becomes biaxial near the core and the order parameter drops (as
represented by the background colour of the figure to the right).
We have developed Finite Element discretisations of the Qian and
Sheng Equations in both 2D and 3D. The Qian and Sheng equations
are a generalisation of Ericksen-Leslie theory for LC hydrodynamics
to include changes in the order parameter. The Finite Element Method
is well suited to resolve the rapid variations in order parameter
about disclination whilst still being able to model large container
sizes.
- Three elastic constants
- Adaptive meshing scheme based on an empirical error estimate
- Crank-Nicholson time integration using a variable time step
- Weak anchoring
Flow of the liquid crystal is calculated by solving the Navier-Stokes
equations with a stress tensor that takes into account the anisotropy
of the LC. Mixed interpolation (P2-P1 shape functions) are used
to avoid oscillatory pressure solutions.
This implicit scheme leads to a larger memory use than the constant
order program. However, the rapid spatial variations in the order
parameter near disclinations severely limits the time step for explicit
methods (<1ns!). We prefer the implicit method in this case to
achieve reasonable simulation times.
This program visualises director fields on both irregular
and regular 2D and 3D meshes. Director plots can be made across
slices, or sampled regularly in 3D space. Iso-surface plots of potential,
twist and tilt can be made.
Built in Extended Jones optics code, for image plots or viewing
angle plots. Free energy calculation, surface and contour plots.
Provides a means to rapidly convert results from irregular to regular
meshes, as required for most optical calculations
This page last modified
2 June, 2006
by r.james
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