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NGCM-0070: Multiscale modelling of defect and particles in liquid crystals

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  • Full or part time
    Dr Giampaolo D'Alessandro
    Dr KR Daly
  • Application Deadline
    Applications accepted all year round

Project Description

Liquid crystals form an intermediate state of matter that has the long-range orientational order of crystals, while maintaining the ability to flow and the plasticity of liquids. These properties make them ideal materials for devices whose configuration needs to be updated in real time, e.g. displays. Their properties can be enhanced by doping them with nanoparticles to make them, for example, respond to weaker external fields or to have better optical or thermal properties.

Modelling liquid crystals, either pure or doped, represents many challenges, due to the many spatial and temporal scales present in the problem. You can imagine liquid crystal molecules as cigar--shaped molecules that, in general, tend to align parallel to each other: their average orientation is called the “director field”. Occasionally the molecules get stuck at different angles so that it is not possible to define an average orientation. In liquid crystal parlance these points are called defects. Their size is of the order of ten nanometres, but they have to be tracked in a device that is ten thousand times larger. The equations that describe their dynamics are stiff, as the creation and annihilation of a defect happens on a much faster time scale that the reorientation dynamics of the liquid crystal. If nanoparticles are present, then we need to model the effects that millions of them have on the orientation of the liquid crystal and on its response to external fields.

This modelling project will develop new, computationally efficient and mathematically sophisticated multiscale algorithms to model defects in pure and doped liquid crystals. In this project we aim to use advanced mathematical methods, like homogenisation and multiple scale expansions, coupled to large scale computations to develop computationally intensive, but extremely efficient algorithms for large scale computation of the liquid crystal dynamics. This will allow the research community to optimise device design and liquid crystal properties to obtain faster dynamics for better displays or more sensitive response to external stimuli for sensing applications.

If you wish to discuss any details of the project informally, please contact Dr Giampaolo D’Alessandro, Computational Applied Mathematics research group, Email: [email protected], Tel: +44 (0) 2380 593650.

This project is run through participation in the EPSRC Centre for Doctoral Training in Next Generation Computational Modelling ( For details of our 4 Year PhD programme, please see

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