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.
This phenomena is thus by no means restricted to the case of circular conductors
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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.