Seminar Mathematik in den Naturwissenschaften: Minicourse - Nematic Liquid Crystals: A Playground for Mathematics and Applications, Prof. Dr. Apala Majumdar

Minicourse
Nematic Liquid Crystals: A Playground for Mathematics and Applications

Prof. Dr. Apala Majumdar, University of Strathclyde, UK

Place: Emil-Fischer-Str. 40, 40.03.003

Time:
Wednesday 14 June 2023, 10.00-11.00
Thursday 15 June 2023, 10.00-11.00
Wednesday 21 June 2023, 10.00-11.00
Thursday 22 June 2023, 10.00-11.00

Abstract:

Nematic liquid crystals are paradigm examples of soft materials and complex
fluids. Nematics combine the fluidity of liquids with the orientational order of conventional
solids i.e. they have distinguished special directions, referred to as “directors”.
Consequently, they have a direction-dependent response to external fields and light, making
them the working material of choice for the multi-billion liquid crystal display industry,
along with new applications in biosciences, artificial intelligence and nanotechnologies etc.
The mathematics of nematic liquid crystals is broad and rich, spanning multiple branches of
mathematics such as the calculus of variations, nonlinear partial differential equations,
numerical analysis, topology, stochastic analysis and scientific computation.
In the first lecture, we will survey the continuum Oseen-Frank and Nobel-Prize winning
Landau-de Gennes theory for nematic liquid crystals, the governing systems of nonlinear
coupled partial differential equations and the theory of isotropic-nematic phase transitions.
In the second lecture, we will focus on two case studies - the canonical radial-hedgehog
defect in the Landau-de Gennes theory for nematic liquid crystals and the reduced Landau-
de Gennes approach for planar or two-dimensional bistable liquid crystal devices. All
collaborations will be acknowledged during the lectures. Some references are given below.

References:
[1] A. Majumdar, Equilibrium order parameters of liquid crystals in the Landau-de Gennes
theory, European Journal of Applied Mathematics, 21 (2010), 181.
[2] A. Majumdar and A. Zarnescu, The Landau-de Gennes theory of nematic liquid crystals:
the Oseen-Frank limit and beyond, Archive of Rational Mechanics and Analysis, 196 (2010),
227.
[3] A. Majumdar, The radial-hedgehog solution in Landau – de Gennes’ theory for nematic
liquid crystals, European Journal of Applied Mathematics, 23 (2012), 61.
[4] C. Luo, A. Majumdar and R. Erban, Multistability in planar liquid crystal wells, Physical
Review E, 85 (2012), 061702.
[5] Y. Han, A. Majumdar and L. Zhang, A Reduced Study for Nematic Equilibria on Two-
Dimensional Polygons, SIAM Journal of Applied Mathematics, 80 (2020), 1678 - 1703.
Brief Bio: Apala Majumdar is an internationally acclaimed expert in the mathemati

You can find all information about the seminar and Prof. Apala Majumdar HERE.