Figure 1

Results for a sample with 4096 vortices and 64 pins. (a) Voronoi plot (see text) for the BrG minimum at 17.8 K, with five-, six-, and seven-coordinated sites indicated by (red) triangles, small (black) dots, and large (green) dots, respectively. Black circles denote pin positions. Dislocations form tightly bound clusters near pin locations. Regions labeled $A$, $B$, and $C$ are discussed in the text and in Fig. 2. (b) Same as (a), but for a BoG minimum at 18.2 K. Here, dislocations are arranged in lines to form grain boundaries. (c) Structure factors at 18.4 K. Results for the BrG, BoG, and IL minima are shown by (yellow) circles, (purple) triangles, and (green) squares, respectively. Vertical lines are guides to the eye.Reuse & Permissions

Figure 2

Main plot: temperature dependence of the free energies of different minima of the sample of Fig. 1. Results for the BrG, BoG, and IL minima are shown by (blue) diamonds, (black) circles, and (red) triangles, respectively. The crossings near 17.9 and 18.3 K correspond to transitions. Upper inset: bond-orientational correlation function $g_6(r)$ (see text), plotted vs $r/a_0$, for BrG [upper (red) curve] and BoG [lower (blue) curve] minima at 17.0 K and $c=1/64$. Lower inset: $T$ dependence of the average local peak density ${\rho }_{\mathrm{a}\mathrm{v}}^p$ for small regions (see text) near the points $A$, $B$, and $C$ in Fig. 1a. Results for $A$, $B$, and $C$ are shown by (red) plus signs, (green) crosses, and (blue) circles, respectively. Solid lines are guides to the eye.Reuse & Permissions