Hypersurfaces of prescribed mean curvature enclosing a given body

Given a smooth domain Ω in ℝ ^m+1 with compact closure and a smooth integrable functionh: ℝ ^m+1→ℝ satisfyingh(x)≥H _∂Ω (x) on ∂Ω whereH _∂ω denotes the mean curvature of ∂Ω calculated w.r.t. the interior unit normal we show that there is a setA⊂ℝ ^m+1 with the properties andH _∂A=h on ∂A.     

β relaxation theory for simple systems: some addenda

The evolution of the tagged particle probability density for a hard sphere system is evaluated within the -relaxation window. Relaxation curves obtained by molecular dynamics studies by Barrat, Hansen and Roux for a binary mixture are analyzed quantitatively with -relaxation scaling formulae. The dynamical light scattering data obtained by Pusey and van Megen for colloidal suspensions are described by the combined - and -relaxation scaling results. The range of validity of asymptotic expressions near a glass transition singularity is discussed for the Debye-Waller factor as a function of packing fraction. The applied theoretical formulae are those of the mode coupling theory for the liquid to glass transition.     

The hydration of the uranyl dication: Incorporation of solvent effects in parallel density functional calculations with the program PARAGAUSS

The parallel density functional program PARA GAUSS has been extended by a tool for computing solvent effects based on the conductor‐like screening model (COSMO). The molecular cavity in the solvent is constructed as a set of overlapping spheres according to the GEPOL algorithm. The cavity tessellation scheme and the resulting set of point charges on the cavity surface comply with the point group symmetry of the solute. Symmetry is exploited to reduce the computational effort of the solvent model. To allow an automatic geometry optimization including solvent effects, care has been taken to avoid discontinuities due to the discretization (weights of tesserae, number of spheres created by GEPOL). In this context, an alternative definition for the grid points representing the tesserae is introduced. In addition to the COSMO model, short‐range solvent effects are taken into account via a force field. We apply the solvent module to all‐electron scalar‐relativistic density functional calculations on uranyl, UO₂²⁺, and its aquo complexes in aqueous solution. Solvent effects on the geometry are very small. Based on the model [UO₂(H₂O)₅]²⁺, the solvation energy of uranyl is estimated to be about ?400 kcal/mol, in agreement with the range of experimental data. The major part of the solvation energy, about ?250 kcal/mol, is due to a donor–acceptor interaction associated with a coordination shell of five water ligands. One can interpret this large solvation energy also as a compounded effect of an effective reduction of the uranyl moiety plus a solvent polarization. The energetic effect of the structure relaxation in the solution is only about 8 kcal/mol. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Novel Aspects in the Synthesis of Carbenoids Containing P/C-pπ-Bonds

Abstract

The synthesis and x-ray structure analysis of a novel type of carbenoids, aryl-P(=E)=C(Cl)Li(thf)₃ (E=N-aryl, C(SiMe₃)₂), as well as the first example of a 1,3-diphosphetane-2,4-diyl, (aryl-PCCl)₂, is reported and on the basis of quantum chemical calculations its bonding situation is discussed. Furthermore, selected examples for the varying reaction behavior of both types of compounds are presented.     

Horizontal bridges in polar dielectric liquids

When a high-voltage direct-current is applied to two beakers filled with polar liquid dielectrica like water or methanol, a horizontal bridge forms between the two beakers. By repeating a version of Pellat’s experiment, it is shown that a horizontal bridge is stable by the action of electrohydrodynamic pressure. Thus, the static and dynamic properties of the phenomenon called a ‘floating water bridge’ can be explained by the gradient of Maxwell pressure, replenishing the liquid within the bridge against any drainage mechanism. It is also shown that a number of liquids can form stable and long horizontal bridges. The stability of such a connection, and the asymmetry in mass flow through such bridges caused by the formation of ion clouds in the vicinity of the electrodes, is also discussed by two further experiments.