Solution Landscapes in the Landau-de Gennes theory for Nematic Liquid Crystals: Analysis, Computations and Applications

Professor Apala Majumdar, University of Strathclyde

Abstract: Nematic liquid crystals are classical examples of partially ordered materials that combine fluidity with the order of crystalline solids. They are the working material of a range of electro-optic devices i.e. in the liquid crystal display industry and more recently, they are used in sensors, actuators, elastomers, security applications and pathological studies.

We review the celebrated Landau-de Gennes theory for nematic liquid crystals and focus on the modelling of nematics confined to thin quasi-2D systems, with reference to 2D polygons. We perform asymptotic analysis in certain distinguished limits, encoded in terms of geometrical, material and temperature-dependent parameters, accompanied by exhaustive numerical studies of solution landscapes that include stable and unstable solution branches for these systems. There are several numerical challenges associated with the numerical computation of the unstable solution branches and their unstable directions, for which we use the powerful High-Index Shrinking Optimisation Dimer Method. In the last leg of the talk, we discuss the mathematical modelling of some recent experiments on nematic shells and doped bent-core liquid crystals, to illustrate the synergistic links between theory, experiment and novel applications.

All collaborations will be acknowledged throughout the talk.

Brief Bio: Apala Majumdar is an internationally known expert in the mathematics and modelling of liquid crystals and their applications. She is Full Professor of Applied Mathematics at the University of Strathclyde. She received her PhD in applied mathematics from the University of Bristol in 2006, where she was also a CASE student with Hewlett Packard laboratories. She worked in Oxford as a research fellow, was appointed as a faculty member at the University of Bath in 2012 and moved to Strathclyde in 2019. Apala's research programme is strongly interdisciplinary and her scientific achievements and service to the community have been recognised by several national prizes - a London Mathematical Society Anne Bennett Prize in 2015, two prizes from the British Liquid Crystal Society in 2012 and 2020 respectively, an Academic Leader award from the FDM Everywoman in Technology awards and a Suffrage Science Award for inspirational women in STEM in 2020, and an international Humboldt Foundation Friedrich Wilhelm Bessel Award in 2022. Apala has worked extensively with researchers around the world - UK, Europe, Asia, North and South America, and is also the Associate Dean for International Research for the Faculty of Science at the University of Strathclyde. More details about her research and activities can be found at https://www.strath.ac.uk/staff/majumdarapalaprofessorLink opens in a new window

To join online: Click here to join the meetingLink opens in a new window