Metric Geometry Governs Optimal Control in Driven Stokes Flows: Magnetic Driving and Beyond
arXiv:2511.14479 · doi:10.1103/b2z3-v4fd
Abstract
In a canonical Stokes flow geometry, the Hele-Shaw cell, we show that tunable circulations induced by Lorentz forces in a conducting fluid enable particle control. We reveal that energy-optimal control paths correspond to geodesics of an emergent Riemannian metric defined over the fluid domain, which are time-optimal under a maximum-power constraint. Subject to random boundary forcing, particle paths exhibit metric-governed anisotropic diffusion. Our geometric concepts governing optimal control, though developed explicitly for circulation-driven flows, generalize to generic driven Stokes flows and so elucidate recent observations in a three-dimensional context.
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