A transmission problem on a polygonal partition: regularity and shape differentiability

We consider a transmission problem on a polygonal partition for the two-dimensional conductivity equation. For suitable classes of partitions we establish the exact behaviour of the gradient of solutions in a neighbourhood of the vertexes of the partition. This allows to prove shape differentiability of solutions and to establish an explicit formula for the shape derivative.     

Expanding the Scope of Arylsulfonylacetylenes as Alkynylating Reagents and Mechanistic Insights in the Formation of Csp2?Csp and Csp3?Csp Bonds from Organolithiums

We describe the unexpected behavior of the arylsulfonylacetylenes, which suffer an “anti‐Michael” addition of organolithiums producing their alkynylation under very mild conditions. The broad scope, excellent yields, and simplicity of the experimental procedure are the main features of this methodology. A rational explanation of all these results can be achieved by theoretical calculations, which suggest that the association of the organolithiums to the electrophile is a previous step of their intramolecular attack and is responsible for the unexpected “anti‐Michael” reactions observed for substituted sulfonylacetylenes.     

Self-similar vortex reconnection

As shown by Crow in 1970, the evolution of two almost parallel vortex filaments with opposite circulation exhibits a long-wave instability. Ultimately, the symmetric mode increases its amplitude reconnecting both filaments and ending into the formation of an almost periodic structure of vortex rings. This is a universal process, which appears in a wide range of scales: from the vortex trails behind an airplane to a microscopic scale of superfluids and Bose–Einstein condensates. In this paper, I will focus on the vortex reconnection for the latter case by employing Gross–Pitaevskii theory. Essentially, I focus on the well-known laws of interaction and motion of vortex filaments. By means of numerical simulations, as well as theoretically, I show that a self-similar finite-time dynamics manifests near the reconnection time. A self-similar profile is selected showing excellent agreement with numerical simulations.