# On numerical schemes for Nematic Liquid Crystals and their Applications

# On numerical schemes for Nematic Liquid Crystals and their Applications

ABSTRACT: Liquid crystals are important materials that are used in several technological applications. The most common usage is in the omnipresent liquid crystal displays which uses the birefringence property of the material to create images on a screen. However, liquid crystals also respond to other external stimuli, e.g. magnetic, mechanical, chemical, which can be used to induce complex shape changes in the material used for applications in biomedical devices, robotics, optics, textiles, and sensors.

Liquid crystals exhibit intermediate phases between solid and liquid. One such phase is the nematic phase which possess the microscopic orientational order of a crystalline solid, however, the molecules have no positional order but flow freely past each other and thus display macroscopic properties of a liquid. Models of liquid crystals usually represent molecules as rods or disks and use some parameter to describe the orientation of the molecules.

In this presentation I will discuss the main ideas of two of the most popular models to represent nematic liquid crystals: the Oseen-Frank director theory and the Landau-de Gennes formulation. In particular, I will present the main ideas to derive reliable numerical schemes to approximate these PDE systems. In both cases the key point is to try to preserve the properties of the original model while the numerical schemes are efficient in time.

Finally, I will talk about how these models and the ideas for deriving the associated numerical schemes can be extended to give insights of realistic situations observed in lab experiments.

BIO: Dr. Tierra is an Assistant Professor at University of North Texas with research interests in applied mathematics. In particular, his research focus on modeling, numerical analysis and scientific computing techniques with special emphasis on applications to life and material sciences that are formulated using systems of coupled PDEs.

He obtained his Ph.D. in Mathematics at Universidad de Sevilla (Spain) in 2012 under the supervision of Prof. Francisco Guillen-Gonzalez. Then he held postdoctoral researcher positions in the Department of Applied and Computational Mathematics and Statistics at the University of Notre Dame and in the Mathematical Institute at Charles University in Prague (Czech Republic). After that he was a Research Assistant Professor at Temple University.