| EPSRC Reference: |
EP/C53154X/1 |
| Title: |
Adaptive Methods for Liquid Crystal Device Modelling |
| Principal Investigator: |
Ramage, Dr A |
| Other Investigators: |
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| Researcher Co-Investigators: |
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| Project Partners: |
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| Department: |
Mathematics and Statistics |
| Organisation: |
University of Strathclyde |
| Scheme: |
Springboards Scheme (Pre-FEC) |
| Starts: |
26 September 2005 |
Ends: |
25 September 2006 |
Value (£): |
51,758
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| EPSRC Research Topic Classifications: |
| Non-linear Systems Mathematics |
Numerical Analysis |
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| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
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| Panel History: |
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Summary on Grant Application Form |
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Items containing a liquid crystal display (LCD), for example, laptop computers, mobile phones, digital watches, CD players and many more, are in common use every day. Developing new liquid crystal devices with better quality and more versatility of display properties is therefore of great interest to industrial manufacturers, due to the enormous commercial potential of such improvements. This project involves the development of new computational techniques which will help in the efficient mathematical modelling and computer simulation of liquid crystal devices.Everyone is familiar with the three common states of matter: solid, liquid and gas. Liquid crystals are substances which occur between the crystalline solid state and the isotropic liquid state and display some of the properties of both. A simple liquid crystal can be thought of as consisting of elongated rod-like molecules which have a preferred local average direction (unlike, for example, in an isotropic liquid where the orientation of molecules is random). Different liquid crystal phases may be classified by the amount and type of orientational and positional order of molecules within the material. Competition between the influences of bounding surfaces and an applied electric field can cause the material to switch between different orientational states. The resulting change in optical characteristics allows the material to be used in a LCD.The mathematical theory of liquid crystals has been extensively studied for over 75 years and the underlying theoretical ideas are well established. However, to date there has been much less work done on the numerous interesting and important computational 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. As an example, consider the nematic liquid crystal phase, which exhibits orientational ordering but no positional ordering: the molecules tend to align, on average, in one direction but their centres of mass are randomly distributed. In some liquid crystal cells, there are regions of high elastic distortion (defects) where the orientation varies over small length scales (between 10-100nm) and the molecular order is significantly altered. The effect of these defects on the switching properties of the liquid crystal system is of key importance, but such features provide difficult numerical challenges to those trying to simulate the real-life dynamic situations which are of interest in an industrial setting. The aim of this proposed Fellowship is to enable the applicant to develop her research in this new and exciting area at the interface between liquid crystal theory and computational mathematics,The specific project proposed here will involve numerical modelling of a simple model problem with two defects moving in a two-dimensional planar cell. The key idea is to model the movement of the defects in time with an adaptive moving mesh, that is, a mesh where existing grid points move to regions of high errors while maintaining the same grid connectivity. This ensures that there is no waste of computational effort in areas where there is no need for a fine computational grid. Adaptive grid methods are a hot topic in current numerical analysis research and advances in this area would have important implications for solving partial differential equations in many other areas of science and engineering.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
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| Date Materialised |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.strath.ac.uk |