A direct comparison of high-speed methods for the numerical Abel transform

The Abel transform is a mathematical operation that transforms a cylindrically symmetric three-dimensional (3D) object into its two-dimensional (2D) projection. The inverse Abel transform reconstructs the 3D object from the 2D projection. Abel transforms have wide application across numerous fields of science, especially chemical physics, astronomy, and the study of laser-plasma plumes. Consequently, many numerical methods for the Abel transform have been developed, which makes it challenging to select the ideal method for a specific application. In this work eight transform methods have been incorporated into a single, open-source Python software package (PyAbel) to provide a direct comparison of the capabilities, advantages, and relative computational efficiency of each transform method. Most of the tested methods provide similar, high-quality results. However, the computational efficiency varies across several orders of magnitude. By optimizing the algorithms, we find that some transform methods are sufficiently fast to transform 1-megapixel images at more than 100 frames per second on a desktop personal computer. In addition, we demonstrate the transform of gigapixel images.Comment: 9 pages, 5 figure

Model Compounds of Ruthenium−Alkene Intermediates in Olefin Metathesis Reactions

The development of a model system to study ruthenium−olefin complexes relevant to the mechanism of olefin metathesis is reported. Upon addition of 1,2-divinylbenzene to (H_2IMes)(py_2)(Cl)_2Ru CHPh (H_2IMes = 1,3-dimesityl-4,5-dihydroimidazol-2-ylidene), two ruthenium−olefin adducts are formed. On the basis of ^1H NMR spectroscopy experiments and X-ray crystallographic analysis, these complexes are assigned as side-bound isomers in which the olefin and H_2IMes ligands are coordinated cis to each other. The dynamic interconversion of these two ruthenium complexes was determined to have a barrier of 19.1 ± 0.1 kcal/mol