Resonances Introduced by Discretization

This paper examines the effect of spatially discretizing thenon-linear equation chosen to model the integro-differential equations governinginterfacial vortex sheets. Here H is the Hilbert transform and is a spatial average. It is shown numerically and analyticallythat small-amplitude travelling-wave solutions of the discretizedmodel equation are subject to instabilities whose growth rateis proportional to the amplitude and depends in a complicatedway on the number of mesh points per wavelength. The mechanismof the instability is shown to be a resonance not present inthe continuous system and present in the discrete system becausethe frequency of waves with wavelength equal to twice the meshspacing is zero.     

A Conformal Mapping Problem Arising in Elasticity, II

Suppose that B is an infinite right cylinder over a horizontalbase , which is a Jordan domain bounded by a smooth curve .We suppose that a normal pressure p₁(x, y) and a tangentialpressure p₂(x, y) are applied at every point of the boundaryof B, where p₁, p₂ lie in the plane of the cross-section andare independent of the vertical co-ordinate. It was shown by Cassisa (1982) that in this situation, givenan arbitrary normal pressure p₁, the tangential pressure p₂can be so chosen, that a purely plane stress tensor existswith the above hypotheses, provided that a certain 3 ? 3 matrixM, depending only on the curve , is non-singular. In a previous paper (Hayman, 1982) the author showed that thesingular case can occur and further that an arbitrary pointsymmetric curve can be approximated by singular point symmetriccurves. In the present paper it is shown that M can have rank1, 2 or 3. In the case of rank 2 p₁ must satisfy one additionalintegral condition and in the case of rank 1 two such conditions.If these conditions are satisfied p₂ can be chosen to dependon one or two arbitrary parameters respectively. Some geometrical conditions for the various cases are obtained.Thus for curves with line symmetry the rank can be two but notone, whereas curves with point symmetry can yield matrices ofrank 1, 2 or 3.     

Activation analytical determination of129I in bovine thyroid glands

The continued erection of nuclear installations which is expected in the future involves a greater production of long-lived fission products, which result in a concentration increase in the biosphere, the hydrosphere and the atmosphere. In the frame of a broad survey program, a routine method has been developed with the help of the European Communities to investigate the¹²⁹I content of thyroid glands of cows. It is the purpose of this project to determine the present concentration situation of this nuclide, which in the Federal Republic of Germany mainly concerns the North German low plains. Between autumn '76 and summer '77 18 cows have been investigated with respect to¹²⁹I, and thyroid glands have been taken at different times in November '76 and August '77. Without exception, the animals were 13-month old bulls, part of which has pastured, while the other part has been fed. The detection limit of the method is 20fCi of¹²⁹I.     

ESR investigation of Ti3+ compounds supported on inorganic gels

CpTiCl₂-M-surface complexes (M=Al, Si, Mg, Cp=cyclopentadienyl) supported on Al₂O₃, SiO₂, MgO gels are reduced by Et₃Al, C₃H₅MgBr and BuLi to Ti³⁺ surface compounds which exhibit ESR signals. The g and g values and asymmetry of these signals depend on the kind of gel and reducing agent.

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CpTiCl₂-M ( M=Al, Si, Mg Cp=), Al₂O₃, SiO₂ MgO, Et₃Al, C₃H₅MgBr, BuLi (Et=–C₂H₅ Bu=–C₄H₉) Ti⁺³, . g g .

     

Röntgenkleinwinkeluntersuchungen an Lösungen eines Polystyrolpräparates mit enger Molekulargewichtsverteilung

Zusammenfassung Es wurde das Streuverhalten von Polystyrol im thermodynamisch schlechten Lösungsmittel Cyclohexan zwischen Entmischungstemperatur und-Temperatur untersucht. Beim -Punkt und nahe dabei liegt das Verhalten eines statistisch verknäuelten Fadenmoleküls vor. Unterhalb der-Temperatur beginnt eine Aggregation. Knapp oberhalb der Entmischungstemperatur entspricht das Molekulargewicht etwa einer Verhängung zweier Fadenmoleküle. Ein Auftreten von kompakten Polymerknäueln ist bei dieser Temperatur nicht festzustellen. Der Einfluß des Fadenquerschnitts auf die Streukurve ist beträchtlich, da der Querschnitt nicht viel kleiner als die Persistenzlänge ist. Trotzdem läßt sich die Persistenzlänge (a=12,2 Å) aus dem Übergangspunkt zwischen den etwa 1/(2)² und 1/(2) proportionalen Bereichen bestimmen, da der Knick im Übergangsbereich infolge der großen Anzahl von Persistenzlängen pro Molekül sehr ausgeprägt ist.

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X-Ray small-angle investigations on solutions of a polystyrene sample with a narrow molecular weight distribution

Investigations were made of the scattering behaviour of polystyrene in the thermodynamically bad solvent cyclohexane between precipitation-temperature and-temperature. At the-point and close to it the behaviour of a statistically coiled chain molecule is found. Below-temperature an aggregation is beginning. Just above precipitation-temperature the molecular weight corresponds to an entanglement of two chain molecules. Appearance of compact polymer coils could not be noted at this temperature. The influence of the chain crosssection upon the scattering curve is considerable as the crosssection is not much smaller than the persistence length. Nevertheless, the persistence length (a=12.2 Å) may be determined from the transition point between the ranges roughly proportional to 1/(2)² and 1/(2) as the break within the transition range is very distinct on account of the great number of persistence lengths per molecule.

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Mit 3 Abbildungen

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Herrn Prof. Dr.E. Broda zum 60. Geburtstag gewidmet.     

Optical properties of ZnO and ZnO:In nanorods assembled by sol-gel method

Self-assembled zinc oxide (ZnO) and indium-doping zinc oxide (ZnO:In) nanorod thin films were synthesized on quartz substrates without catalyst in aqueous solution by sol-gel method. The samples were characterized by x-ray diffraction (XRD), scanning electron microscope (SEM), Raman-scattering spectroscopy, room-temperature photoluminescence (PL) spectra, and temperature-dependent PL spectra measurements. XRD and Raman spectra illustrated that there were no single In2O3 phase in ZnO lattice after indium doping. The PL spectra of ZnO showed a strong UV emission band located at 394 nm and a very weak visible emission associated with deep-level defects. Indium incorporation induced the shift of optical band gap, quenching of the near-band-edge photoluminescence and enhanced LO mode multiphonon resonant Raman scattering in ZnO crystals at different temperatures. Abnormal temperature dependence of UV emission integrated intensity of ZnO and ZnO:In samples is observed. The local state emission peak of ZnO:In samples at 3.37 eV is observed in low-temperature PL spectra. The near-band-edge emission peak at room temperature was a mixture of excitons and impurity-related transitions for both of two samples.     

Synthesis and Conformational Analysis of the Multidrug Resistance-Reversing Agent Hapalosin and Its Non-N-methyl Analog

Hapalosin was initially synthesized by macrolactonization, and a second synthesis was achieved by cycloamidation. In both syntheses, three of the five stereocenters in hapalosin were established by two Brown allylboration reactions. The synthesis of the non-N-Me analog of hapalosin involved chelation-controlled reduction of a gamma-amino-beta-keto ester and cycloamidation. In CDCl(3) at 25 degrees C, synthetic hapalosin exists as a 2.3:1 mixture of conformers, while its non-N-Me analog exists only as a single conformer. (1)H,(1)H-NOESY and computation reveal that the configuration of the amide bond is responsible for the conformations of the two compounds. The major conformer of hapalosin is found to be an s-cis amide, the minor conformer an s-trans amide, and the non-N-Me analog an s-trans amide. Applying distance constraints to protons that exhibit NOESY correlations, computation shows that the major conformer of hapalosin and the non-N-Me analog have very different conformations. By contrast, the minor conformer of hapalosin and the non-N-Me analog have very similar conformations.     

Adsorption of 1,10-phenanthroline within a dodecanethiol monolayer: an approach to a switchable electrode surface

A simple method was used to prepare a "switchable" electrode surface by using self-assembled monolayers of dodecanethiol on a gold electrode. The dodecane-modified electrode was electrochemically inactive until the monolayer was soaked in solutions of 1,10-phenanthroline or 2,2'-bipyridine. The electroactive form of the electrode could be reverted back to the nonelectroactive form by rinsing the electrode. Surface IR results showed that both dodecanethiol and 1,10-phenanthroline exist in the mixed monolayer.     

Investigation of electronic structure and associated nuclear quadrupole interaction of adsorbed fluorine atoms on silicon surface

The electronic energy levels and wave functions of fluorine and chlorine atoms adsorbed at the <111> surface of silicon are obtained by the Hartree-Fock procedure applied to clusters simulating the surface structure. Minimising the total energy with respect to the positions of the halogen atoms, the Si-Cl distance in the adsorbed system was found to be in good agreement with that from a recent SEXAFS measurement, there being no corresponding data presently available for fluorine on silicon surface. The calculated¹⁹ f ^* nuclear quadrupole coupling constants using the electronic wave functions for SiH₃F and the larger cluster Si₄H₉F, simulating the surface, differed substantially in contrast to the situation for the Si-F distance, indicating that the quadrupole coupling is a more sensitive indicator of the adequacy of the cluster chosen to represent the surface system. Experimental results for the coupling constants are awaited for comparison with theory.     

A search for a thermal spike effect in sputtering

The temperature dependence of the sputtering yield was measured for lOOkeV per atom bombardment of silver with molecular and atomic antimony ions. No exponential increase of the yield was found in the temperature range from 25° to 775 °C, although a pronounced nonlinear effect is observed when the yield of these projectiles is compared,Y(Sb ₂ ⁺ )≈ 1.5×[2Y(Sb⁺)]. We conclude that there is no influence of the lattice temperature on collision spikes.