This article analyzes modulated phases in liquid crystals, from the long-established
cholesteric and blue phases to the recently discovered twist-bend, splay-bend, and splay …

Many solid materials and liquid crystals exhibit geometric frustration, meaning that they have
an ideal local structure that cannot fill up space. For that reason, the global phase must be a …

Geometric frustration arises whenever the constituents of a physical assembly locally favor
an arrangement that cannot be realized globally. Recently, such frustrated assemblies were …

By analyzing elastic theory for nematic liquid crystals, we distinguish three regimes of elastic
constants. In one regime, the Ericksen inequalities are satisfied, and the ground state of the …

We give a description of the intrinsic geometry of elastic distortions in three-dimensional
nematic liquid crystals and establish necessary and sufficient conditions for a set of functions …

Cholesteric liquid crystals exhibit great morphological richness of static metastable states.
Understanding the transitions between such states is key for the development of switchable …

Frustration in nematic-ordered media (endowed with a director field) is treated in a purely
geometric fashion in a flat, two-dimensional space. We recall the definition of quasi-uniform …

Integer winding disclinations are unstable in a nematic and are removed by anescape into
the third dimension', resulting in a non-singular texture. This process is frustrated in a …

Morphodynamic descriptions of fluid deformable surfaces are relevant for a range of
biological and soft matter phenomena, spanning materials that can be passive or active, as …

The topological understanding of nematic liquid crystals is traditionally centered on
singularities, or defects, and their classification via homotopy theory. However, this approach …