Liouville Quantum Gravity on the Riemann Sphere

In this paper, we rigorously construct Liouville Quantum Field Theory on the Riemann sphere introduced in the 1981 seminal work by Polyakov. We establish some of its fundamental properties like conformal covariance under PSL\({_2(\mathbb{C})}\)-action, Seiberg bounds, KPZ scaling laws, KPZ formula and the Weyl anomaly formula. We also make precise conjectures about the relationship of the theory to scaling limits of random planar maps conformally embedded onto the sphere.     

The [U2F12]2− Anion of Sr[U2F12]

The D_2h‐symmetric dinuclear complex anion [U₂F₁₂]^2? of pastel green Sr[U₂F₁₂] shows a hitherto unknown structural feature: The coordination polyhedra around the U atoms are edge‐linked monocapped trigonal prisms, the U^V atoms are therefore seven‐coordinated. This leads to a U–U distance of 3.8913(6) Å. A weak U^V–U^V interaction is observed for the dinuclear [U₂F₁₂]^2? complex and described by the antiferromagnetic exchange J_exp of circa ?29.9 cm^?1. The crystalline compound can be easily prepared from SrF₂ and β‐UF₅ in anhydrous hydrogen fluoride (aHF) at room temperature. It was studied by means of single crystal X‐ray diffraction, IR, Raman and UV/VIS spectroscopy, magnetic measurements, and by molecular as well as by solid‐state quantum chemical calculations.     

On fractional Poincaré inequalities

We show that fractional (p, p)-Poincaré inequalities and even fractional Sobolev-Poincaré inequalities hold for bounded John domains, and especially for bounded Lipschitz domains. We also prove sharp fractional (1,p)-Poincaré inequalities for s-John domains.     

Size‐Selective Encapsulation of Hydrophobic Guests by Self‐Assembled M4L6 Cobalt and Nickel Cages

Subtle differences in metal–ligand bond lengths between a series of [M₄L₆]^4? tetrahedral cages, where M=Fe^II, Co^II, or Ni^II, were observed to result in substantial differences in affinity for hydrophobic guests in water. Changing the metal ion from iron(II) to cobalt(II) or nickel(II) increases the size of the interior cavity of the cage and allows encapsulation of larger guest molecules. NMR spectroscopy was used to study the recognition properties of the iron(II) and cobalt(II) cages towards small hydrophobic guests in water, and single‐crystal X‐ray diffraction was used to study the solid‐state complexes of the iron(II) and nickel(II) cages.     

Brake squeal: a literature review

Brake squeal, which usually falls in the frequency range between 1 and 16 kHz, has been one of the most difficult concerns associated with automotive brake systems since their inception. It causes customer dissatisfaction and increases warranty costs. Although substantial research has been conducted into predicting and eliminating brake squeal since the 1930s, it is still rather difficult to predict its occurrence. In this paper, the characteristics and current difficulties encountered in tackling brake squeal are first described. A review of the analytical, experimental and numerical methods used for the investigation of brake squeal is then given. Some of the challenges facing brake squeal research are outlined.     

The effect of the properties of porous media on light scattering

Numerical wave-optical methods for light scattering simulations are used to asses the effect of porosity on the optical properties of paper coating. Both constant porosity profile and media with porosity contrast between layers at different depths are considered. We can predict optimal paper coating structures for both brightness and gloss from the results.     

Solvent exchange in thermally stable resorcinarene nanotubes

The assembly of C-methyl resorcinarene into a tubular supramolecular solid-state structure, its thermal stability, and its hosting properties are reported. Careful control of the crystallisation conditions of C-methyl resorcinarene and 1,4-dimethyl-1,4-diazoniabicyclo[2.2.2]octane (1,4-dimethyl DABCO) dibromide leads to a formation of two crystallographically different, but structurally very similar, solid-state nanotube structures. These structures undergo a remarkable variety of supramolecular interactions, which lead to the formation of 0.5 nm diameter nonpolar tubes through the crystal lattice. The formation of these tubes is templated by suitably sized small alcohols, namely, n-propanol, 2-propanol, or n-butanol. The self-assembly involves close pi...pi interactions between the adjacent resorcinarenes, and C--H...pi and cation...pi interactions between the resorcinarenes and the guest 1,4-dimethyl DABCO dications. The crystals of these supramolecular tube structures are thermally very stable and the included solvent alcohol can be removed from the tubes without breaking the single-crystalline structure of the assembly. After removal of the solvent molecules the tubes can be filled with other small, less polar solvent molecules such as dichloromethane.     

Comparison between the classical theory predictions and molecular simulation results for heterogeneous nucleation of argon

We have performed Monte Carlo simulations of homogeneous and heterogeneous nucleations of Lennard-Jones argon clusters. The simulation results were interpreted using the major concept posing a difference between the homogeneous and heterogeneous classical nucleation theories-the contact parameter. Our results show that the multiplication concept of the classical heterogeneous nucleation theory describes the cluster-substrate interaction surprisingly well even for small molecular clusters. However, in the case of argon nucleating on a rigid monolayer of fcc(111) substrate at T=60 K, the argon-substrate atom interaction being approximately one-third as strong as the argon-argon interaction, the use of the classical theory concept results in an underestimation of the heterogeneous nucleation rate by two to three orders of magnitude even for large clusters. The main contribution to this discrepancy is induced by the failure of the classical theory of homogeneous nucleation to predict the energy involved in bringing one molecule from the vapor to the cluster for clusters containing less than approximately 15 molecules.