 Solution

ID: past-exam-of-the-mphil-in-micro-and-nanotechnology-enterprise-course-of-the-university-of-cambridge/2020/paper-2/section-b/22/iii/b/solution

z = 0

permits uniform

n = \hat{x}

, as in the sketch. A rubbed surface can select one in-plane axis; degenerate planar anchoring selects only the tangent plane.

For the degenerate case,

f_{s} = (W /2) (n \cdot ν)^{2}

has minima at

n \cdot ν = 0

. A remote incompatible boundary produces elastic distortion. Tangency alone does not specify an azimuthal direction within the surface.

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