Kolloide Lösungen von praktisch unlöslichen Goldverbindungen und ihre Umwandlung in Goldsole

Ohne ZusammenfassungUebersetzt und bearbeitet von Wo. Ostwald und R. Köhler (Leipzig).     

Nonlinear Longitudinal Vibrations of Transversally Polarized Piezoceramics: Experiments and Modeling

Nonlinear behavior of piezoceramics at strong electric fields is a well-known phenomenon and is described by various hysteresis curves. On the other hand, nonlinear vibration behavior of piezoceramics at weak electric fields has recently been attracting considerable attention. Ultrasonic motors (USM) utilize the piezoceramics at relatively weak electric fields near the resonance. The consistent efforts to improve the performance of these motors has led to a detailed investigation of their nonlinear behavior. Typical nonlinear dynamic effects can be observed, even if only the stator is experimentally investigated. At weak electric fields, the vibration behavior of piezoceramics is usually described by constitutive relations linearized around an operating point. However, in experiments at weak electric fields with longitudinal vibrations of piezoceramic rods, a typical nonlinear vibration behavior similar to that of the USM-stator is observed at near-resonance frequency excitations. The observed behavior is that of a softening Duffing-oscillator, including jump phenomena and multiple stable amplitude responses at the same excitation frequency and voltage. Other observed phenomena are the decrease of normalized amplitude responses with increasing excitation voltage and the presence of superharmonics in spectra. In this paper, we have attempted to model the nonlinear behavior using higher order (quadratic and cubic) conservative and dissipative terms in the constitutive equations. Hamilton's principle and the Ritz method is used to obtain the equation of motion that is solved using perturbation techniques. Using this solution, nonlinear parameters can be fitted from the experimental data. As an alternative approach, the partial differential equation is directly solved using perturbation techniques. The results of these two different approaches are compared.     

Pyrazole analogues of porphyrins and oxophlorins

A series of porphyrin analogues with pyrazole rings replacing one of the usual pyrrole subunits have been synthesized. This was accomplished by reacting 1-phenyl, 1-methyl and 1-ethyl pyrazole-1,3-dicarbaldehydes with a tripyrrane in the presence of TFA, followed by an oxidation step. The initially formed phlorin product was sufficiently stable for the N-phenyl system to be isolated and characterized, although the related N-alkyl phlorin analogues were less stable. Attempts to dehydrogenate the intermediary phlorins with DDQ resulted in decomposition, but the N-alkylphlorins could be oxidized with 0.2% aqueous ferric chloride solutions. Although the phenyl-substituted phlorin could not be oxidized under these conditions, it did afford the pyrazoloporphyrin upon treatment with silver acetate under acidic conditions. Oxidations with silver acetate also afforded oxophlorin analogues where the oxo-linkage was selectively formed at the 5-position. The pyrazole-containing porphyrin analogues are cross-conjugated and exhibit only a small degree of diatropic character. The internal CH resonances were observed between 5.27 and 5.87 ppm, while the external meso-protons fell into a range of 6.84-7.88 ppm. The borderline overall aromatic character was attributed to dipolar resonance contributors. Protonation considerably increased the diatropicity and the diprotonated dications formed from these porphyrin analogues gave the internal CH resonance at upfield values of 2.65-3.20 ppm. The aromatic character was enhanced by the presence of an electron-donating alkyl substituent on the nitrogen compared to the phenyl-substituted species. The pyrazoloporphyrins reacted with nickel(II) acetate in DMF, or palladium(II) acetate in acetonitrile, to give the corresponding organometallic derivatives. The metal complexes showed increased diatropic character but protonation afforded nonaromatic cations. The oxophlorin analogues were also nonaromatic in the free base and protonated forms. This work extends our understanding of carbaporphyrinoid systems and provides the first detailed studies on pyrazole-containing porphyrin analogues.     

Packing of molecules and hole formation in lyotropic systems

A vector field q (the order parameter of the molecular packing) describing the packing (specifically, the orientation) of membrane-forming amphiphilic molecules is introduced to describe the structures of lyotropic phases constructed from membranes. In the general case q·n≠0 (where n is the unit normal vector) and therefore the singularities of the vector field q are not determined uniquely by the topology of the surface. The condition q·n=0 signifies disruption of the packing of the molecules. This corresponds to holes, which can form in membranes when lyotropic systems are diluted. As an illustration, the simplest type of such singularities, in which the distribution of the field q around a hole is described by a part of an instanton with unit topological charge, is studied. It is shown that such a distribution guarantees the existence of a local minimum under the condition that the tension per unit length λ of the hole boundary is small compared with the deformation energy of the field q: λh/K≪l (K is the modulus of the orientational elasticity of the field q and h is the thickness of the membrane). The radius of the hole which is formed equals L≈2.52(K/λh)^1/3 and the energy E≈59.79K(λh/K)^1/3. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 8, 575–580 (25 October 1996)     

Automatically tunable continuous-wave optical parametric oscillator for high-resolution spectroscopy and sensitive trace-gas detection

We present a high-power (2.75 W), broadly tunable (2.75–3.83 μm) continuous-wave optical parametric oscillator based on MgO-doped periodically poled lithium niobate. Automated tuning of the pump laser, etalon and crystal temperature results in a continuous wavelength coverage up to 450 cm^-1 per poling period at <5×10^-4 cm^-1 resolution. The versatility of the optical parametric oscillator as a coherent light source in trace-gas detection is demonstrated with photoacoustic and cavity ring-down spectroscopy. A 17-cm^-1-wide CO₂ spectrum at 2.8 μm and multi-component gas mixtures of methane, ethane and water in human breath were measured using photoacoustics. Methane (at 3.2 μm) and ethane (at 3.3 μm) were detected using cavity ring-down spectroscopy with detection limits of 0.16 and 0.07 parts per billion by volume, respectively. A recording of ¹²CH₄ and ¹³CH₄ isotopes of methane shows the ability to detect both species simultaneously at similar sensitivities. PACS 42.65.Yj; 42.72.Ai; 42.62.Fi     

Kugo-Ojima confinement and QCD Green''s functions in covariant gauges

In Landau gauge QCD the Kugo-Ojima confinement criterion and its relations to the infrared behaviour of the gluon and ghost propagators are reviewed. It is demonstrated that the realization of this confinement criterion (which is closely related to the Gribov-Zwanziger horizon condition) results from quite general properties of the ghost Dyson-Schwinger equation. The numerical solutions for the gluon and ghost propagators obtained from a truncated set of Dyson-Schwinger equations provide an explicit example for the anticipated infrared behaviour. The results are in good agreement, also quantitatively, with corresponding lattice data obtained recently. The resulting running coupling approaches a fixed point in the infrared, (0) = 8.915/N_c. Solutions for the coupled system of Dyson-Schwinger equations for the quark, gluon and ghost propagators are presented. Dynamical generation of quark masses and thus spontaneous breaking of chiral symmetry takes place. In the quenched approximation the quark propagator functions agree well with those of corresponding lattice calculations. For a small number of light flavours the quark, gluon and ghost propagators deviate only slightly from the ones in quenched approximation. While the positivity violation of the gluon spectral function is manifest in the gluon propagator, there are no clear indications of analogous positivity violations for quarks so far.     

Spektraltheorie verwandter operationen

This is a résumé of A. Pietsch’s concept of related linear operators in the study of spectral properties and homomorphism theorems forp-bounded linear operators on Mackey-complete topological vector spaces. It turns out that many results proved by various authors in the setting of Mackey-complete topological vector spaces follow directly from the corresponding classical results by means of purely algebraic relations.     

Strong Solutions of the Navier–Stokes System in Lipschitz Bounded Domains

Let Ω be a bounded domain in ?³ with a connected Lipschitz boundary ?Ω. Consider the Navier-Stokes system.