G-band bright points (GBPs) are thought to be the foot-points of magnetic flux tubes. The aim of this paper is to investigate the relation between the diffusion regimes of GBPs and the associated longitudinal magnetic field strengths. Two high resolution observations of different magnetized environments were acquired with the Hinode/Solar Optical Telescope. Each observation was recorded simultaneously with G-band filtergrams and Narrow-band Filter Imager (NFI) Stokes I and V images. GBPs are identified and tracked automatically, and then categorized into several groups by their longitudinal magnetic field strengths, which are extracted from the calibrated NFI magnetograms using a point-by-point method. The Lagrangian approach and the distribution of diffusion indices approach are adopted separately to explore the diffusion regime of GBPs for each group. It is found that the values of diffusion index and diffusion coefficient both decrease exponentially with the increasing longitudinal magnetic field strengths whichever approach is used. The empirical formulas deduced from the fitting equations are proposed to describe these relations. Stronger elements tend to diffuse more slowly than weak elements, independently of the magnetic flux of the surrounding medium. This may be because the magnetic energy of stronger elements is not negligible compared with the kinetic energy of the gas, and therefore the flows cannot perturb them so easily.Yang
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