We give a causal version of Eisenhart's geodesic characterization of Newtonian dynamics. We emphasize the geometric, coordinate independent properties needed to express Eisenhart's theorem in light of modern studies on the Bargmann structures (lightlike dimensional reduction). The construction of the space metric, Coriolis 1-form and scalar potential through which the theorem is formulated is s...

We show that the Schrödinger equation is a lift of Newton’s third law of motion ∇μ̇ μ̇ = −∇WF (μ) on the space of probability measures, where derivatives are taken w.r.t. the Wasserstein Riemannian metric. Here the potential μ → F (μ) is the sum of the total classical potential energy 〈V, μ〉 of the extended system and its Fisher information ~2 8 ∫ |∇ ln μ|2dμ. The precise relation is established ...

In the framework of covariant classical mechanics (i.e. , generally relativistic classical mechanics on a spacetime with absolute time) developed by Jadczyk and Modugno, we analyse systematically the relations between symmetries of geometric objects. We show that the (holonomic) infinitesimal symmetries of the cosymplectic structure and of its horizontal potentials are also symmetries of spacel...

This paper elucidates the aerodynamic role of the dynamically changing wingspan in bat flight. Based on direct numerical simulations of the flow over a slow-flying bat, it is found that the dynamically changing wingspan can significantly enhance the lift. Further, an analysis of flow structures and lift decomposition reveal that the elevated vortex lift associated with the leading-edge vortices...

NASA’s research into distributed electric propulsion (DEP) includes the design and development of the X-57 Maxwell aircraft. This aircraft has two distinct types of DEP: wingtip propellers and high-lift propellers. This paper focuses on the unique opportunities and challenges that the high-lift propellers—i.e., the small diameter propellers distributed upstream of the wing leading edge to augme...

Nucleotide arrays require controlled surface densities and minimal nucleotide-substrate interactions to enable highly specific and efficient recognition by corresponding targets. We investigated chemical lift-off lithography with hydroxyl- and oligo(ethylene glycol)-terminated alkanethiol self-assembled monolayers as a means to produce substrates optimized for tethered DNA insertion into post-l...

The lift of an association rule is frequently used, both in itself and as a component in formulae, to gauge the interestingness of a rule. The range of values that lift may take is used to standarise lift so that it is more effective as a measure of interestingness. This standardisation is extended to account for minimum support and confidence thresholds. A method of visualising standardised li...

We give a causal version of Eisenhart's geodesic characterization of classical mechanics. We emphasize the geometric, coordinate independent properties needed to express Eisenhart's theorem in light of modern studies on the Bargmann structures (lightlike dimensional reduction). The construction of the space metric, Coriolis 1-form and scalar potential through which the theorem is formulated is ...