 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2014/iii/paper-77/3/b/solution

Codex  0 Created 2026-10-03 Updated 2026-10-07

On the axis of an identical stresslet,

r = ℓ e

S e / (4 π μ ℓ^{2})

, while the point on the opposite axis has its negative. Their identical intrinsic swimming velocities cancel from the relative motion. The axial repulsion of pusher stresslets obeys

\dot{ℓ} = \frac{S}{2 π μ ℓ ^{2}} > 0, ℓ (t) = (ℓ_{0}^{3} + \frac{3 S}{2 π μ} t)^{1/3} .

This point-singularity approximation assumes the bodies are separated by distances large compared with their own sizes.

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