Font Size: 

A hyperuniform system can be presented as a system of particles that, showing a disordered spatial configuration to short distances, manifest a long range hidden order that allows the material to behave like a crystal or as a liquid. Combined, these characteristics mean that, for example, certain materials of design can be controlled to be sensitive or insensitive to certain wavelengths of light. The hyperuniformity is manifested in the behavior of the structure factor S(k→0)=0, or in the variance of the number of particles σ²(R)~R^(d-1), for a system with dimensionality d. In this work we present a study on the characterization of ordered and disordered hyperuniform point distributions on spherical or curved surfaces. Despite of the amount of work on disordered hyperuniform systems in Euclidean geometries, few works are focused on the problem of hyperuniformity in curved spaces (photoreceptors in avian curved retina, for instance). Here we will study the local particle number variance and its dependence on the size of the sampling window for equilibrium configurations of fluid particles interacting through Lennard-Jones, dipole-dipole, or charge-charge potentials. We will show how the scaling of the local number variance enables the characterization of hyperuniform point patterns on curved surfaces.