Regimes of clump survival versus crushing for clumps with R_cl = 500 AU. The maps show t_cool/t_cc as a function of shock velocity and clump density. The panels correspond to cases with metal-line cooling only (top left), and different dust-to-gas mass ratios: 𝒟 = 10⁻⁴ (top right), 𝒟 = 10⁻³ (bottom left), and 𝒟 = 10⁻² (bottom right). The solid red lines mark t_cool = t_cc. Clumps above the line (lower v_sh or higher n_cl) can cool or grow, while below the line they are crushed. Higher dust-to-gas mass ratios expand the survival region. Dashed blue: Isobaric ℛ = 1. Dotted purple: Isochoric ℛ = 1. Isochoric crossings occur only at v_sh ≲ a few 10² km s⁻¹; realistic clumps fall between these limits. In both cases, regions above the ℛ = 1 lines correspond to grain growth exceeding thermal sputtering. The hatched area indicates the range of observed dusty globules in the Crab Nebula.