Conjectural extensions of nonholonomic collective-flow theory

Investigate the extension of the nonholonomic collective-flow framework to active matter on curved substrates and shells, flows interacting with obstacles, and active mechanical metamaterials whose oriented units carry an internal no-slip reaction.

Background

The concluding section identifies three prospective settings for extending the advancing-speed/body-axis/transverse-reaction framework: curved substrates and shells, obstacle interactions beyond the benchmark Mach-cone problem, and active mechanical metamaterials with oriented units. These directions are explicitly presented as conjectures rather than established results. The proposed extensions would test whether the measurable transverse reaction remains a useful organizing principle in intrinsically curved geometries, obstacle-mediated flows, and engineered active materials.

References

Three further directions seem natural: active matter on curved substrates and shells, where the director geometry of Section~\ref{sec:traffic} becomes intrinsic (a setting the author has studied with Turzi); the interaction of these flows with obstacles, of which the Mach cone is the simplest instance; and active mechanical metamaterials whose oriented units carry an internal no-slip reaction. We offer these as conjectures.

— Nonholonomic collective flows: velocity--orientation locking in a continuum with microstructure  (2608.28380 - Napoli, 28 Aug 2026) in Section 10, Concluding remarks