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Liquid-crystal phases are typical examples of soft and complex materials that exhibit an abundance of different phenomena. In this paper we present some of our results contributing to the understanding of the physics of defects in nematic liquid crystals. The examples presented exhibit many features that are also of interest for other branches of physics. We describe nematic point defects, the annihilation dynamics of a defect and anti-defect pair, and the coarsening dynamics of a dense pattern of defects after a sudden symmetry-breaking phase transition.

Even graduate physics students have many misconceptions about basic wave optics phenomena. This suggests that there is much room for improvement of the traditional wave optics curriculum. An effective way for initiating a curriculum change is to reconsider and revise the expected learning outcomes and corresponding assessment instruments. By systematically enriching our wave optics instruction and assessment with conceptual tasks, we may increase the probability of students actively engaging in learning the conceptual aspects of wave optics. In this paper, we present the process of developing an item bank for measuring understanding of wave optics in typical introductory physics courses at universities. Thereby, the Rasch modeling approach has been used. The development of the item bank has been guided by results from multiple expert and student surveys, as well as from group interviews and think aloud interviews. Altogether 65 multiple-choice items with a single correct answer and three distractors have been prepared for field testing. Until now, 35 out of 65 items have been field tested by means of a paper and pencil survey which included 188 participants from five universities in Bosnia and Herzegovina, Croatia, and Slovenia. The field test showed that 32 out of 35 items have good psychometric characteristics and that they may be very useful for uncovering students' misconceptions in wave optics.

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Universal behavior related to continuous symmetry breaking in nematic liquid crystals is studied using Brownian molecular dynamics. A three-dimensional lattice system of rod-like objects interacting via the Lebwohl-Lasher interaction is considered. We test the applicability of predictions originally derived in cosmology and magnetism. In the first part we focus on coarsening dynamics following the temperature driven isotropic-nematic phase transition for different quench rates. The behavior in the early coarsening regime supports predictions made originally by Kibble in cosmology. For fast enough quenches, symmetry breaking and causality give rise to a dense tangle of defects. When the degree of orientational ordering is large enough, well defined protodomains characterized by a single average domain length are formed. With time subcritical domains gradually vanish and supercritical domains grow with time, exhibiting a universal scaling law. In the second part of the paper we study the impact of random-field-type disorder on a range of ordering in the (symmetry broken) nematic phase. We demonstrate that short-range order is observed even for a minute concentration of impurities, giving rise to disorder in line with the Imry-Ma theorem prediction only for the appropriate history of systems.