Time evolution of the transition radius r_vis/irr (Eq. (5); red lines), snowline r_snow = max(r_snow,vis, r_snow,irr) (Eqs. (6) and (7); blue lines), disk characteristic radius (green lines), and pebble formation front r_pff (Eq. (36); magenta lines) for various disk evolution parameters. The parameters, r_d,0 in units of auand Ṁ_g,0 in units of M_⊙ yr⁻¹ are labeled in the individual panels. The other parameters are the same for the four panels, i.e., Ṁ_pe =10⁻⁹ M_⊙ yr⁻¹ and t_diff = 10⁶ yr.