In sintering of materials, we can have mass flow in the absence of a concentration gradient via surface diffusion. In this process, surface molecules redistribute themselves driven by a gradient in surface curvature. This phenomenon causes metals to bead-up on surfaces when heated and other materials to redistribute themselves over time. It is of fundamental importance to the semiconductor industry. If we express the mass flux as:

\[\overrightarrow{\mathbf{N}}_{a}=-\vec{abla}(\gamma \kappa) \quad \kappa=\frac{ \pm \frac{d^{2} y}{d x^{2}}}{\left[1+\left(\frac{d y}{d x}\right)^{2}\right]^{3 / 2}}\]

where $\gamma$ is a surface energy parameter and $\kappa$ is the curvature, what are the two possible equilibrium surface shapes?