Spin crossover in iron(II) complexes of 3,5-di(2-pyridyl)-1,2,4-triazoles and 3,5-di(2-pyridyl)-1,2,4-triazolates

The iron coordination chemistry of 3,5-di(2-pyridyl)-1,2,4-triazoles and 3,5-di(2-pyridyl)-1,2,4-triazolates is reviewed. This includes both mononuclear and dinuclear complexes, and both iron(II) and iron(III) oxidation states. The main focus is on the synthesis, structure and magnetic properties of these complexes.     

Duality between phase vortices and Argand-plane caustics

Singularities in the mappings of complex two-dimensional vortical wavefields to Argand space are used here to investigate the duality between vortices in the physical field and caustic-like structures in the Argand plane. Such map singularities are exemplified via a method of optical vortex generation based on low-pass filtering of two-dimensional noise. The presence of Argand-plane fold caustics crossing the Argand-plane origin is tied to changes in vortex numbers in the physical wavefield. Increasing the low-pass filter cutoff leads to higher-order Argand-plane caustic singularities, such as the hyperbolic umbilic catastrophe. This work presents a duality between vortices and caustics, explores the Argand plane as a tool in analysing optical wavefields, and provides a new environment for studying catastrophes.