The second volume moment of the typical cell and higher moments of edge lengths of the spatial Poisson–Voronoi tessellation

This paper presents analytical results for higher moments of characteristics of a Voronoi tessellation generated by a homogeneous Poisson point process in the three-dimensional Euclidean space. The second moment of the volume of the typical cell as well as higher moments for the edge length distribution and the linear contact distribution are given. These characteristics are calculated analytically and presented in a unified form.     

Nickel N‐heterocyclic carbene complexes in the vinyl polymerization of norbornene

Vinyl polymerized norbornene has some useful properties such as good mechanical strength, optical transparency and heat resistance. Several transition metal complexes have been described in the literature as active catalysts for the vinyl polymerization of norbornene. We now report the use of three types of nickel(II) complexes with N‐heterocyclic carbene (NHC) ligands in the catalytic vinyl polymerization of norbornene under a range of conditions. Specifically, two nickel complexes bearing a chelating bis(NHC) ligand, two nickel complexes bearing two chelating anionic N‐donor functionalized NHC ligands as well as one diiodidonickel(II) complex with two monodentate NHC ligands were tested. The solid‐state structure of bis(1,3‐dimethylimidazol‐2‐ylidene)diiodidonickel(II), as determined by X‐ray crystallography, is presented. The highest polymerization activity of 2.6 × 10⁷ g (mol cat)^?1 h^?1 was observed using the latter nickel complex as catalyst, activated by methylaluminoxane. The norbornene polymers thus obtained are of high molecular weight but with rather low polydispersity. Copyright © 2010 John Wiley & Sons, Ltd.     

NMR at very low fields

Although nuclear magnetic resonance in low fields around or below the Earth's magnetic field is almost as old as nuclear magnetic resonance itself, the recent years have experienced a revival of this technique that is opposed to the common trend towards higher and higher fields. The background of this development is the expectation that the low-field domain may open a new window for the study of molecular structure and dynamics. Here, we will give an overview on the specific features in the low-field domain, both from the technical and from the physical point of view. In addition, we present a short passage on the option of magnetic resonance imaging in fields of the micro-Tesla range.     

Quantum walk with jumps

We analyze a special class of 1-D quantum walks (QWs) realized using optical multi-ports. We assume non-perfect multi-ports showing errors in the connectivity, i.e. with a small probability the multi-ports can connect not to their nearest neighbor but to another multi-port at a fixed distance – we call this a jump. We study two cases of QW with jumps where multiple displacements can emerge at one timestep. The first case assumes time-correlated jumps (static disorder). In the second case, we choose the positions of jumps randomly in time (dynamic disorder). The probability distributions of position of the QW walker in both instances differ significantly: dynamic disorder leads to a Gaussian-like distribution, while for static disorder we find two distinct behaviors depending on the parity of jump size. In the case of even-sized jumps, the distribution exhibits a three-peak profile around the position of the initial excitation, whereas the probability distribution in the odd case follows a Laplace-like discrete distribution modulated by additional (exponential) peaks for long times. Finally, our numerical results indicate that by an appropriate mapping a universal functional behavior of the variance of the long-time probability distribution can be revealed with respect to the scaled average of jump size.