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Yayoi Terada: „Spatial Dimensionality on Long-Time Self-Diffusion Process of Hard Disks and Hard Spheres”
Institute of Fluid Science, Tohoku University, Japan

The glass transition occurs on both two-dimensional system and three-dimensional system, when the crystallisation can be avoided. Recently spatial dimensionality of the glass transition was argued heatedly. In the present work, the simple model systems, that is, hard disk fluid and hard sphere fluid, are examined to discuss the spatial dimensionality on long-time diffusion process. The volume fraction dependence of the mean-square displacements, the self intermediate scattering function, and non-Gaussian parameter on both systems are fully investigated. It is found that the singular function, which is proposed on three-dimensional systems by Tokuyama theoretically [Physica, vol.364 (2006)23-62], discribes the long-time self-diffusion coefficient of both hard disks and hard spheres. The characteristic times of alpha-relaxation process and beta-relaxation process of hard disks are also similar with those of hard spheres, when the particles have the same long-time self-diffusion coefficient. The spatial dimension d changes the value of glass transition point and peak height of non-Gaussian parameter which are related with the geometric packing characteristics of the hard disks and the hard spheres.