Nematic liquid crystals are perhaps one of the most classical and widely-used examples of soft matter, materials that combine directionality with fluidity and have special material directions, referred to as "nematic directors". Consequently, nematics have a direction-dependent response to external light, temperature, mechanical stress, electric fields etc., resulting in directional physical, optical and mechanical properties. In fact, nematics are the working material of choice for the multibillion-dollar liquid crystal display industry. Contemporary research in nematics has shifted from conventional displays to altogether new areas such as sensors, actuators, photonics and generally information-rich technologies. Scientifically, these advanced applications require a well-defined framework connecting fundamental physics to programmable materials science in fields such as biology and nanoscience and finally to commercial applications. Mathematics is the crucial link between physics and applications, which has been underexploited to date.
In this project, we will study two-dimensional (2D) and three-dimensional (3D) nematic systems in terms of their complex solution landscapes, an umbrella term used to describe the plethora of admissible NLC configurations in different settings. We will model the experimentally observable nematic configurations, how to switch between different configurations, and crucially how to use geometrical properties to control and steer processes of importance. We will work with experimentalists to use the theory for the design and optimisation of 2D and 3D nematic systems and test their potential for different applications. This is an exciting project at the interface of mathematical modelling, analysis, and scientific computation in a broad interdisciplinary setting.