Figure 2:

Isotropic volume growth guided by a multi-directional field with different growth distributions: an increasing gradient of ϑ^g from the inner core to the outer shell (a, left) and a case in which ϑ^g increases rapidly at the core and slowly at the outer layers (a, right). The local Burgers vector density is computed for each of the two cases and for planes defined by the spherical basis vector corresponding to meridional and circumferential directions ${\overline{\mathbf{\text{n}}}}_{\varphi }$ and ${\overline{\mathbf{\text{n}}}}_{\theta }$. (b, c) The Burgers vector vanishes for planes defined by the radial direction ${\overline{\mathbf{\text{n}}}}_r$ and are thus not shown. Stress components aligned with the direction of the Burgers vectors show similar trends to the degree of incompatibility for the two cases considered (d, e). The growth fields considered, in addition to the two cases illustrated in the top panels, are shown in f, were the blue curve is the case shown in the left column of a, and the red curve is the right column of a. The magnitude of the local Burgers vector density |b| is greater for higher growth gradients, but also greater for smaller growth values (g). The scalar metric Curl F^g : Curl F^g shows the same trends as the magnitude of the local Burgers vector density (h).