# PhD in Mathematics and Statistics - Multiscale modelling of liquid crystal-filled porous media

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Dr Raimondo Penta, Prof Nigel Mottram  Applications accepted all year round  Competition Funded PhD Project (Students Worldwide)

Liquid crystals are scientifically fascinating and visually beautiful liquids that are all around us, forming an integral part of the liquid crystal display (LCD) used in almost every smart phone and computer display, and contained in both the cell wall and internal cytoplasm of all biological cells. The theory of liquid crystal materials that has been developed over the last fifty years has helped to bring about a revolution in display technology and increase the fundamental understanding of this phase of matter. The delicate nature of this phase, which can be disturbed by piconewton forces (about a trillionth of the force I am using to type these words on my keyboard) means that, to be made useful, they often need to be contained between rigid boundaries. In an LCD this is achieved by sandwiching the liquid crystal between to flat plates. However, more complicated structures to contain the liquid crystal have been proposed in recent years, including a polymer matrix or porous solids. By tailoring the porous medium in which the liquid crystal is contained, the optical and electrical properties and the flow of the liquid crystal can be controlled.

This PhD project will be focussed on developing a completely new multiscale continuum model of these liquid crystal-solid composites in order to understand and predict the microscopic behaviour of the liquid crystal within the pores, as well as the macroscopic properties of the whole composite system. The new modelling framework, which will be obtained by applying suitable homogenisation techniques, will provide a connection between the composite’s response at the micro- and macro-scale. It is the feedback between the effects at different scales which we aim to understand using this new theory.

Applicants should have an undergraduate degree in mathematics/applied mathematics and experience in one or more of the following is desirable: continuum mechanics and elasticity; numerical methods for solving differential equations; scientific programming in Matlab; excellent writing and presentation skills.

During the project the student will benefit from training through the Scottish Mathematical Sciences Training Centre and develop expertise in multiscale continuum models, liquid crystal theory, partial differential equations, and finite element software to perform multi-dimensional numerical simulations related to the implementation of the modelling framework.

The project will be supervised by Dr Raimondo Penta and Prof. Nigel Mottram, experts in homogenisation theory of porous media and liquid crystals respectively, and the student will join a research group of around fifteen postgraduate and postdoctoral researchers working on liquid crystals and/or porous media and will join the group of over one hundred postgraduate students, in the School of Mathematics and Statistics at Glasgow.

Competitive scholarships, for UK and International student, are available and further information can be obtained by contacting Dr Penta ([Email Address Removed]) and Prof. Mottram ([Email Address Removed]).

How to Apply: Please refer to the following website for details on how to apply: http://www.gla.ac.uk/research/opportunities/howtoapplyforaresearchdegree/

## Funding Notes

Funding is available to cover tuition fees for UK/INTL applicants for 3.5 years, as well as paying a stipend at the Research Council rate (estimated £15,690 for Session 2022/23).
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