Fatty Acid Derived Monomers and Related Polymers Via Thiol‐ene (Click) Additions

Thiol‐ene additions of methyl 10‐undecenoate, a castor oil derived renewable platform chemical, were studied with the goal of preparing a set of renewable monomers. Good to excellent yields were obtained for these solvent and initiator free thiol‐ene additions. The resulting monomers were then polymerized using TBD as a catalyst, to linear as well as hyperbranched polyesters that also contain thio‐ether linkages. All thus prepared polymers were fully characterized (NMR, GPC, DSC, and TGA) and the results of these investigations will be discussed within this contribution. The thermal analysis of these polymers revealed melting points in the range from 50 to 71 °C. Moreover, no significant weight loss was observed below 300 °C.

     

Weak Dual Pairs and Jetlet Methods for Ideal Incompressible Fluid Models in $$n \ge 2$$ Dimensions

We review the role of dual pairs in mechanics and use them to derive particle-like solutions to regularized incompressible fluid systems. In our case we have a dual pair resulting from the action of diffeomorphisms on point particles (essentially by moving the points). We then augment our dual pair by considering the action of diffeomorphisms on Taylor series, also known as jets. The augmented weak dual pairs induce a hierarchy of particle-like solutions and conservation laws with particles carrying a copy of a jet group. We call these augmented particles jetlets. The jet groups serve as finite-dimensional models of the diffeomorphism group itself, and so the jetlet particles serve as a finite-dimensional model of the self-similarity exhibited by ideal incompressible fluids. The conservation law associated to jetlet solutions is shown to be a shadow of Kelvin’s circulation theorem. Finally, we study the dynamics of infinite time particle mergers. We prove that two merging particles at the zeroth level in the hierarchy yield dynamics which asymptotically approach that of a single particle in the first level in the hierarchy. This merging behavior is then verified numerically as well as the exchange of angular momentum which must occur during a near collision of two particles. The resulting particle-like solutions suggest a new class of meshless methods which work in dimensions \(n \ge 2\) and which exhibit a shadow of Kelvin’s circulation theorem. More broadly, this provides one of the first finite-dimensional models of self-similarity in ideal fluids.     

N‐(2‐Fluoro­ethyl)‐3β‐(4‐iodo­phenyl)‐8‐methyl‐8‐aza­bi­cyclo­[3.2.1]­octane‐2α‐carbox­amide: a new cocaine derivative with equatorially attached ligands

In the title compound, C₁₇H₂₂FIN₂O, both the amide and the iodo­phenyl substituents of the tropane ring lie in equatorial positions. The crystal packing is determined by N—H⋯O and C—H⋯F intermolecular hydrogen‐bonding interactions.