Top: Line density ﹩l_{\mathrm{DLA}\,}( X) ﹩ of DLAs with the Si II velocity width higher than ﹩v_{\mathrm{Si}\,\,{}^{{\rm{\small II}}}}﹩ vs. ﹩v_{\mathrm{Si}\,\,{}^{{\rm{\small II}}}}﹩, at ﹩z=3﹩. The lines correspond to models C−1, C0, C1, and C2 (from thinnest to thickest line). The dotted line shows the observed kinematic distribution from data at all redshifts, compiled from Fig. 10 in Wolfe et al. (2005) and normalized to match the cumulative observed value ﹩0.067\pm 0.006﹩ at ﹩z=3﹩ (horizontal line). Bottom: Same as top, except that the three thick lines give ﹩l_{\mathrm{DLA}\,}( X) ﹩ for runs C1 (solid line), B1 (dashed line), and A1 (dotted line).