---

Mathematical Liquid Crystals

Liquid crystals are states of matter that exhibit characteristics of both fluids and solids. On the one hand, their mechanical properties are fluid-like; they assume the shape of a containing vessel, and start to flow when sheared. However, their optical properties are like those of a crystalline solid. It turns out that the optical properties of liquid crystals can be manipulated rather easily and reversibly by applying electric and magnetic fields; this characteristic underlies their preeminent role in display technologies.

Modeling, simulation, analysis and design of liquid crystalline materials raises many fundamental unanswered questions of physics and mathematics. The study of appropriate phase transitions, defects and singularities in nematic liquid crystals leads to challenging problems in analysis, whose solution can shed light on the essential physics of liquid crystals. We wish to understand the behavior of nematic liquid crystals, including effects of biaxiality, formation, profiles, and evolution of liquid crystal defects. In this project we rely on numerical simulations and analysis of variational problems and partial differential equations arising from the corresponding physical models.

Collaborators: G. DiFratta (Vienna, Austria), I. Fatkullin (U Arizona, USA), R. Ignat (Toulouse, France), G. Kitavtsev (Bristol), L. Nguyen (Oxford, UK), J.M. Robbins (Bristol), A. Zarnescu (BCAM, Spain)

---