Hiperuniformity on Curved Surfaces

ARIEL G. MEYRA; ENRIQUE LOMBA GARCIA; GUILLERMO J. ZARRAGOICOECHEA; SALVATORE TORQUATO

Workshop; SatPhys 27 (Buenos Aires); 2019

We study and characterize local density fluctuations of ordered and disordered hyperuniform pointdis tributions on spherical surfaces. In spite of the extensive literature on disordered hyperuniform systems in Euclidean geometries, to date few works have dealt with the problem of hyperuniformity in curved spaces. Indeed, some systems that display disordered hyperuniformity, like the space distribution of photoreceptors in avian retina, actually occur on curved surfaces. Here we will focuson the local particle number variance and its dependence on the size of the sampling window (which we take to be a spherical cap) for regular and uniform point distributions, as well as for equilibrium configurations of fluid particles interacting through Lennard-Jones, dipole-dipole and charge-charge potentials. We show that the scaling of the local number variance as a function of the windowsize enables one to characterize hyperuniform and nonhyperuniform point patterns also on sphericalsurfaces.