We introduce a framework designed to analyze and classify structural order in particle distributions constrained to the sphere. The classification is based on the concept of hyperuniformity, which was first introduced 15 years ago and since then studied extensively in Euclidean space, yet has only very recently been considered also for spherical surfaces. We employ a generalization of the structure factor on the sphere, which is related to the cap number variance, allowing us to analytically derive different forms of the variance pertaining to different types of distributions. We demonstrate that hyperuniformity on the sphere can be defined either through a vanishing spherical structure factor at low multipole numbers or through a scaling of the cap number variance and demonstrate it on a few examples of spherical distributions.
COBISS.SI-ID: 32163623
We provide a characterization of point defects in droplets of cholesteric liquid crystal, using a combination of experiment, simulation, and theoretical analysis. These droplets display a range of structures including realizations of defects with high topological charge and arrangements of multiple defects in “topological molecules.” We show that there are certain defects that are incompatible with a uniform sense of chiral twisting for topological reasons. Furthermore, those defects that are compatible with twist of a single handedness are shown to have the structure of the gradient field of an isolated critical point and, hence, are described by singularity theory. We show that the mathematical tools of singularity theory reproduce, with excellent agreement, the experimental observations of high charge defects and topological molecules.
COBISS.SI-ID: 3300708
We show that three icosahedral spherical lattices, which are commensurate with each other and possess locally hexagonal order, underlie the proteinaceous shells of the BTV capsid. This interpretation of the multishelled envelope allows us to discuss the so-called ‘‘symmetry mismatch’’ between its layers. We also analyze the structural stability of the considered spherical lattices on the basis of the classical theory of spherical packing and relate the proximity of the outer spherical lattice to destabilization with the fact that during infection of the cell VP2 trimers are detached from the surface of the BTV capsid. An electrostatic mechanism that can assist in this detachment is discussed in detail.
COBISS.SI-ID: 32601895