Topological and Steric Constraints to Stabilize Heteroleptic Copper(I) Complexes Combining Phenanthroline Ligands and Phosphines

Heteroleptic copper(I) complexes combining phenanthroline derivatives (NN) and chelating bisphosphine ligands (PP) are an important class of luminescent materials for various applications. Although thermodynamically stable, [Cu(NN)(PP)]⁺ derivatives are also kinetically unstable. As a result, a dynamic ligand-exchange reaction is often observed in solution, leading to a dynamic mixture of heteroleptic and homoleptic complexes. To prevent the formation of the homoleptic species, macrocyclic phenanthroline ligands have been used for the preparation of [Cu(NN)(PP)]⁺ pseudorotaxanes. The topological constraint resulting from the macrocyclic structure of the NN ligand drives the thermodynamic equilibrium towards the exclusive formation of the heteroleptic complex as long as the macrocycle is large and flexible enough to allow for the threading of the PP ligand. Conversely, when the threading is prevented by steric constraints, unprecedented copper(I) complexes with a trigonal coordination geometry are obtained. These results are summarized in the present concept article.     

In memoriam: Boris Dubrovin

Letters in Mathematical Physics -     

Hydrodynamic modes in a gas of magnons

Density waves analogous to second sound are studied in a gas of magnons. Quasiparticle interaction is considered for both equilibrium and non equilibrium thermodynamics. The non equilibrium theory is based on a Boltzmann equation for magnon-magnon scattering. Contrary to the total energy and magnetization, (quasi)-momentum is not strictly conserved. In the hydrodynamic regime, the transport equation is reduced to a set of two coupled equations for the magnetization and the local temperature. For low temperatures these have diffusive and propagating solutions while for high temperatures, where momentum is dissipated by Umklapp processes, the solutions are only diffusive. The magnetization response function and the corresponding spectral function are discussed for various wavenumbers and temperatures.     

Simulation of certain multivariate generalized Pareto distributions

The investigation of multivariate generalized Pareto distributions (GPDs) has begun only recently. For further progress with these distributions simulation methods are an important part. We describe several methods of simulating GPDs, beginning with an efficient method for the logistic GPD. The algorithm is based on the Shi transformation, which was already used for the simulation of multivariate extreme value distributions (EVDs) of logistic type. In the sequel another algorithm is presented simulating a broader class of GPDs. Due to its numerical complexity it is only practicably applicable in low dimensions. A method is given to generate unconditional GPD random vectors from conditionally GPD distributed random vectors. A short application of the simulation methods in the analysis of a real hydrological data set concludes the article. The simulation algorithms are available on the author’s home page .      

Path Relinking, Cycle-Based Neighbourhoods and Capacitated Multicommodity Network Design

In this paper, we propose a path relinking procedure for the fixed-charge capacitated multicommodity network design problem. Cycle-based neighbourhoods are used both to move along paths between elite solutions and to generate the elite candidate set by a tabu-like local search procedure. Several variants of the method are implemented and compared. Extensive computational experiments indicate that the path relinking procedure offers excellent results. It systematically outperforms the cycle-based tabu search method in both solution quality and computational effort and offers the best current meta-heuristic for this difficult class of problems.     

Notes sur la fonction ζ de Riemann, 4

Opération fondamentale de l'arithmétique, familière depuis des millénaires, la division euclidienne n'a pas livré tous ses secrets. Ainsi, notons pour k et a entiers positifs, le reste de la division euclidienne de k par a, et imaginons un instant que, par un choix convenable d'un entier n et de réels c₂,…,c_n, nous sachions rendre arbitrairement petite la quantité

     

Silver ionic conductivity enhancement by network former mixed in oxide-based glasses

Glasses in the binary system xAg₂P₂O₆ − (1 − x)Ag₂Te₂O₅ have been prepared for 0 x 1. For each composition only one glass transition temperature is observed in the temperature range of 180–220 °C. All glasses appear homogeneous considering their optical and electrical properties. Nevertheless, in SEM observations, some glass compositions appear to be heterogeneous after decoration following short nitric acid etching. For each composition, conductivity data obtained in the temperature range of 25–200 °C using impedance techniques obey an Arrhenius relationship with a composition independent pre-exponential term. Variation of the conductivity activation energy with x induces correlative variations of isothermal conductivity curves leading to an increase of the ionic conductivity of about one order of magnitude compared with linearity at 25 °C. This behaviour is discussed with respect to the thermodynamic properties of the glassy solutions.     

Long-Time Bath Correlations in the Pollak–Grabert–Hänggi Theory

We analyze some cases for which the Pollak–Grabert–Hänggi theory on the activated rate processes for generalized Langevin dynamics exhibits unexplained disagreements with numerical results. First we analyze carefully the PGH theory and we show that a kind of Markovian hypothesis implicitly made in the reasoning is sometimes violated. Then we propose modifications of the original theory in order to take into account the possible effects caused by this violation, and we compare the corrected results with simulations.     

Weak invariance of the multidimensional rank statistic for nonstationary absolutely regular processes

In this paper, we study the weak invariance of the multidimensional rank statistic when the underlying random variables are nonstationary absolutely regular.