Energy-optimal particle control paths in driven Stokes flows are geodesics of an emergent Riemannian metric on the fluid domain and govern anisotropic diffusion under random forcing.
In canonical geometries, the solution can be written exactly in terms of the Schottky-Klein prime function crowdy2020solving
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Metric Geometry Governs Optimal Control in Driven Stokes Flows: Magnetic Driving and Beyond
Energy-optimal particle control paths in driven Stokes flows are geodesics of an emergent Riemannian metric on the fluid domain and govern anisotropic diffusion under random forcing.