Time evolution of the radial positions of clumps forming at different radii at t = 3.5 × 10⁵ yr in a protoplanetary disk with M_MCC = 1 M_⊙, T_MCC = 15 K, and ω = 2.8 × 10⁻¹⁴ s⁻¹. The adopted α_min is 10⁻⁴. Each line represents the time evolution of the radial position of a clump forming at a specific radius, R_init. The solid, dashed, short-dashed, dash-dotted, dotted, and short-dotted lines represent the evolution of the radial positions for clumps forming at R_init = 144 AU, 109 AU, 95 AU, 79 AU, 45 AU, and 27 AU, respectively. The dash-dot-dotted line represents the semi-analytical estimate from Appendix A for the evolution of the radial positions of a clump forming at 50 AU. The short-dash-dotted line represents the evolution of R₀, the radial position where υ_R = 0. The shaded region shows the dead zone. The time t = 0 is set to be the beginning of the collapse of the parent cloud core. The vertical line indicates t_infall, the time when the collapse ends. We chose R_init to be in the fragmentation region where the fragmentation conditions are satisfied.