The Three Hundred: $M_{sub}-V_{circ}$ relation
In this study, we investigate a recent finding based on strong lensing observations, which suggests that the sub-halos observed in clusters exhibit greater compactness compared to those predicted by $\Lambda$CDM simulations. To address this discrepancy, we performed a comparative analysis by comparing the cumulative mass function of sub-halos and the $M_{\text{sub}}$-$V_{\text{circ}}$ relation between observed clusters and 324 simulated clusters from The Three Hundred project, focusing on re-simulations using GADGET-X and GIZMO-SIMBA baryonic models. The sub-halos' cumulative mass function of the GIZMO-SIMBA simulated clusters agrees with observations, while the GADGET-X simulations exhibit discrepancies in the lower sub-halo mass range possibly due to its strong SuperNova feedback. Both GADGET-X and GIZMO-SIMBA simulations demonstrate a redshift evolution of the sub-halo mass function and the $V_{max}$ function, with slightly fewer sub-halos observed at lower redshifts. Neither the GADGET-X nor GIZMO-SIMBA(albeit a little closer) simulated clusters' predictions for the $M_{\text{sub}}$-$V_{\text{circ}}$ relation align with the observational result. Further investigations on the correlation between sub-halo/halo properties and the discrepancy in the $M_{\text{sub}}$-$V_{\text{circ}}$ relation reveals that the sub-halo's half mass radius and galaxy stellar age, the baryon fraction and sub-halo distance from the cluster's centre, as well as the halo relaxation state play important roles on this relation. Nevertheless, we think it is still challenging in accurately reproducing the observed $M_{\text{sub}}$-$V_{\text{circ}}$ relation in our current hydrodynamic cluster simulation under the standard $\Lambda$CDM cosmology.