Metric Geometry Governs Optimal Control in Driven Stokes Flows: Magnetic Driving and Beyond
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866913111921917952 |
|---|---|
| author | McKee, Kyle |
| author_facet | McKee, Kyle |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_14479 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Metric Geometry Governs Optimal Control in Driven Stokes Flows: Magnetic Driving and Beyond McKee, Kyle Fluid Dynamics Complex Variables 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. |
| title | Metric Geometry Governs Optimal Control in Driven Stokes Flows: Magnetic Driving and Beyond |
| topic | Fluid Dynamics Complex Variables |
| url | https://arxiv.org/abs/2511.14479 |