Periodic magnetic geodesics on Heisenberg manifolds

Annals of Global Analysis and Geometry - We study the dynamics of magnetic flows on Heisenberg groups, investigating the extent to which properties of the underlying Riemannian geometry are...     

A Discussion of Probability Functions and Constraints from a Variational Perspective

Set-Valued and Variational Analysis - Probability constraints are a popular modelling mechanism in applications. They help to model feasible decisions when the latter are taken prior to observing...     

Hydrodynamic Limit of the Symmetric Exclusion Process on a Compact Riemannian Manifold

Journal of Statistical Physics - We consider the symmetric exclusion process on suitable random grids that approximate a compact Riemannian manifold. We prove that a class of random walks on these...     

Spectral estimates for saddle point matrices arising in weak constraint four‐dimensional variational data assimilation

We consider the large sparse symmetric linear systems of equations that arise in the solution of weak constraint four‐dimensional variational data assimilation, a method of high interest for numerical weather prediction. These systems can be written as saddle point systems with a 3 × 3 block structure but block eliminations can be performed to reduce them to saddle point systems with a 2 × 2 block structure, or further to symmetric positive definite systems. In this article, we analyse how sensitive the spectra of these matrices are to the number of observations of the underlying dynamical system. We also obtain bounds on the eigenvalues of the matrices. Numerical experiments are used to confirm the theoretical analysis and bounds.     

What is the role of acid–acid interactions in asymmetric phosphoric acid organocatalysis? A detailed mechanistic study using interlocked and non-interlocked catalysts

Organocatalysis has revolutionized asymmetric synthesis. However, the supramolecular interactions of organocatalysts in solution are often neglected, although the formation of catalyst aggregates can have a strong impact on the catalytic reaction. For phosphoric acid based organocatalysts, we have now established that catalyst–catalyst interactions can be suppressed by using macrocyclic catalysts, which react predominantly in a monomeric fashion, while they can be favored by integration into a bifunctional catenane, which reacts mainly as phosphoric acid dimers. For acyclic phosphoric acids, we found a strongly concentration dependent behavior, involving both monomeric and dimeric catalytic pathways. Based on a detailed experimental analysis, DFT-calculations and direct NMR-based observation of the catalyst aggregates, we could demonstrate that intermolecular acid–acid interactions have a drastic influence on the reaction rate and stereoselectivity of asymmetric transfer-hydrogenation catalyzed by chiral phosphoric acids.

Supramolecular acid–acid interactions lead to competing monomeric and dimeric pathways in phosphoric acid catalysis – so that stereoselectivities depend on catalyst concentration.     

Supramolecular Recognition Influences Magnetism in [X@HVIV8VV14O54]6− Self‐Assemblies with Symmetry‐Breaking Guest Anions

Mixed‐valence polyoxovanadates(IV/V) have emerged as one of the most intricate class of supramolecular all‐inorganic host species, able to encapsulate a wide variety of smaller guest templates during their self‐assembly formation process. As showcased herein, the incorporation of guests, though governed solely by ultra‐weak electrostatic and van der Waals interactions, can cause drastic effects on the electronic and magnetic characteristics of the shell complex of the polyoxovanadate. We address the question of methodology for the magnetochemical analysis of virtually isostructural {V^IV/V₂₂O₅₄}‐type polyoxoanions of D_2d symmetry enclosing diamagnetic VO₂F₂^? (C_2v), SCN^? (C_∞v), or ClO₄^? (T_d) template anions. These induce different polarization effects related to differences in their geometric structures, symmetry, ion radii, and valence shells, eventually resulting in a supramolecular modulation of magnetic exchange between the V(3d) electrons that are partly delocalized over the {V₂₂O₅₄} shells. We also include the synthesis and characterization of the novel [V^VO₂F₂@HV^IV₈V^V₁₄O₅₄]^6? system that comprises the rarely encountered discrete difluorovanadate anion as a quasi‐isolated guest species.     

Properties and applications of precision oligomer materials; where organic and polymer chemistry join forces

Precise oligomeric materials constitute a growing area of research with implications for various applications as well as fundamental studies. Notably, this field of science which can be termed macro-organic chemistry, draws inspiration from both traditional polymer chemistry and organic synthesis, combining the molecular precision of organic chemistry with the materials properties of macromolecules. Discrete oligomers enable access to unprecedented materials properties, for example, in self-assembled structures, crystallization, or optical properties. The degree of control over oligomer structures resembles many biological systems and enables the design of materials with tailored properties and the development of fundamental structure–property relationships. This Review highlights recent developments in macro-organic chemistry from synthetic concepts to materials properties, with a focus on self-assembly and molecular recognition. Finally, an outlook for future research directions is provided.