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Textures (i.e., smooth space non-uniform distributions of the orderparameter) in biaxial nematics turned out to be much more difficult andinteresting than expected. Scanning the literature we find only a very fewpublications on this topic. Thus, the immediate motivation of the present paperis to develop a systematic procedure to study, classify and visualize possibletextures in biaxial nematics. Based on the elastic energy of a biaxial nematic(written in the most simple form that involves the least number ofphenomenological parameters) we derive and solve numerically the Lagrangeequations of the first kind. It allows one to visualize the solutions andoffers a deep insight into their geometrical and topological features.Performing Fourier analysis we find some particular textures possessing two ormore characteristic space periods (we term such solutions quasiperiodic onesbecause the periods are not necessarily commensurate). The problem is not onlyof intellectual interest but also of relevance to optical characteristics ofthe liquid-crystalline textures.

Twisted quasiperiodic textures of biaxial nematics