Editorial. Mathematical models of liquid crystals

Mathematical models and analysis of liquid crystals and gels

In this series of lectures, we address mathematical models of materials systems that, in recent decades, have inspired many developments in partial differential equations. From physical point of view, such problems arise in soft condensed matter and are also linked to relevant applications in optics and mechanics. Liquid crystal phases found in organic and synthetic compounds are intermediate b...

Hard-body models of bulk liquid crystals.

Hard models for particle interactions have played a crucial role in the understanding of the structure of condensed matter. In particular, they help to explain the formation of oriented phases in liquids made of anisotropic molecules or colloidal particles and continue to be of great interest in the formulation of theories for liquids in bulk, near interfaces and in biophysical environments. Ha...

Photoalignment of liquid crystals by liquid crystals

We observed light-induced alignment of the nematic liquid crystal, 4, 4(')-n-pentylcyanobiphenyl (5CB), on a fused quartz. Irradiation of the adsorbed layer with polarized ultraviolet light produced homogeneous alignment in a 5CB-filled liquid crystal cell with the easy orientation axis perpendicular to the polarization direction. The measured anchoring energy increases with illumination up to ...

Models for biaxial nematic liquid crystals

Mathematical models of homochiralisation by grinding of crystals

We review the existing mathematical models which describe physicochemical mechanisms capable of producing a symmetry-breaking transition to a state in which one chirality dominates the other. A new model is proposed, with the aim of elucidating the fundamental processes at work in the crystal grinding systems of Viedma [Phys Rev Lett 94, 065504, (2005)] and Noorduin [J Am Chem Soc 130, 1158, (2...