Coupled McKean–Vlasov diffusions: wellposedness,propagation of chaos and invariant measures

In this paper, we study a two-species model in the form of a coupled system of nonlinear stochastic differential equations (SDEs) that arises from a variety of applications such as aggregation of biological cells and pedestrian movements. The evolution of each process is influenced by four different forces, namely an external force, a self-interacting force, a cross-interacting force and a stochastic noise where the two interactions depend on the laws of the two processes. We also consider a many-particle system and a (nonlinear) partial differential equation (PDE) system that associate to the model. We prove the wellposedness of the SDEs, the propagation of chaos of the particle system, and the existence and (non)-uniqueness of invariant measures of the PDE system.     

Ferrocene derivatives of liquid chiral molecules allow assignment of absolute configuration by X-ray crystallography

The present study investigates a synthetically simple ferrocene derivatization of natural products and active pharmaceutical ingredients. Seven new crystal structures are analyzed together with 16 structures of ferrocene derivatives reported previously. In all cases, the unambiguous determination of the absolute structure was established from anomalous dispersion using the methods of Flack and Parsons. A comparison with other derivatization approaches shows the advantage of the described ferrocene derivatization for establishing the absolute configuration of novel compounds.