Volume 49, Issue 3

The relation between small oscillations of one-dimensional mechanical n-particle systems and the theory of orthogonal polynomials is investigated. It is shown how the polynomials provide a natural tool to determine the eigenfrequencies and eigencoordinates completely, where the existence of a specific two-termed recurrence formula is essential. Physical and mathematical statements are formulated in terms of the recurrence coefficients which can directly be obtained from the corresponding secular equation. Several results on Sturm sequences and orthogonal polynomials are presented with respect to the treatment of small oscillations. The relation to the numerical treatment of the generalized eigenvalue problem is discussed and further applications to physical problems from quantum mechanics, statistical mechanics, and spin systems are briefly outlined.

The method of partially invariant solutions of PDE systems was introduced by Ovsiannikov as a generalization of the classical similarity analysis. It offers a possibility to calculate exact solutions possessing a higher degree of freedom than similarity solutions. Ovsiannikov's algorithm, however, is somewhat hard to apply because one has to deal with three equation systems derived from the original PDE system. By means of the two-dimensional Euler equations, we show how the algorithm can be essentially simplified if classical similarity solutions are already known. Further, we prove a necessary criterion for the simplified algorithm to be senseful.

The proton NMR second moment and spin-lattice relaxation time for polycrystalline tetraethyl-and tetrabutylammonium perchlorates have been measured over a wide range of temperatures. Solid-solid phase transitions related to the onset of cation tumbling were found for both compounds and confirmed by DSC. In the low temperature phases methyl-group reorientation was evidenced. For tetrabutylammonium cation a dynamic nonequivalence of one methyl group is found. The geared motion of the alkyl chains related with the onset of successive CH 2 -group reorientations is suggested.

The effects of finite ion Larmor radius (FLR), collisions and Hall currents on thermosolutal instability of a partially ionized plasma in porous medium in the presence of uniform vertical magnetic field are investigated. It is found that the presence of each magnetic field, FLR, Hall currents and collisions, introduces oscillatory modes which were, otherwise, non-existent. In the case of stationary convection, finite Larmor radius, Hall currents, medium permeability and magnetic field may have stabilizing or destabilizing effects, but for a certain wave number range, FLR, magnetic field and Hall currents have a complete stabilizing effect. The stable solute gradient always has stabilizing effect on the system whereas the collisional effects disappear for the case of stationary convection.

An inverse isotope effect on the melting temperature, T m , of lithium nitrate has been observed: T m is by 0.7 °C higher for a sample with 98.6% 6 Li than for one with 92.6% 7 Li. The abnormal sign of the isotope effect on T m has already previously been found in fractionation experiments. Our results are in agreement with Holmberg’s finding for T m of LiNO 3 · 3H 2 0 (30 °C) that the isotope effect is inverse for 6 Li- 7 Li but normal for H-D. Different types of experimental methods have been compared also for lithium sulfate, where a normal isotope effect has been found for both T m (860 °C) and T c (577 °C), the temperature of a monoclinic-cubic phase transition. Otherwise, nonhydrogen isotope effects at solid-solid transitions are usually inverse for displacive transitions, or nearly zero for order-disorder transitions.

Ultrasonic velocity and absorption have been measured in molten (Li,Ag)NO 3 , (Na,Ag)NO 3 , (K ,Ag)NO 3 , (Cs,Ag)NO 3 , (Li,Rb)NO 3 , and (Na ,Rb)NO 3 , and (Na,Rb)NO 3 as functions of composition in the tem­perature range 230 to 300 °C. An improved pulse transmission device was applied. The obtained accuracy was 2‰o for the velocity and 2-4% for the absorption data. The ultrasonic velocity and absorption coefficient (25 MHz) were found to depend linearly on temperature. The dependence of the velocity on the mole fraction could be represented by a cubic polynomial. For the absorption values (referred to the square of frequency) a reasonable general dependence on composition could not be given. The adiabatic compressibility of all mixtures has been calculated from the measured sound velocity. The ratio bulk/shear viscosity and the bulk viscosity itself follow from the measured absorption values together with the velocity values. The conclusion from these data is that ultrasonic absorption in the six investigated systems is governed by the bulk viscosity and that structural rearrangements rather than structural relaxation of the molecules, are the reason for high bulk viscosities in ionic melts.

We present the set-up of a molecular beam Fourier transform microwave spectrometer in the range from 26.6 to 40 GHz. As a test we investigated the deuterium hyperfine structure of deutero-acetonitrile, DCH 2 CN. It is also shown, that the spectrometer can be used to measure highly resolved rotational spectra of van der Waals complexes.

The ground state microwave spectrum of 2-iodopropene has been reinvestigated using Fourier transform microwave spectroscopy. The barrier hindering methyl internal rotation could be ob­ tained from narrow splittings of high-J lines. In addition an improved hyperfme structure and centrifugal distortion analysis resulted in refined constants and an approximate determination of the iodine spin-rotation coupling parameters.

Broadband dielectric relaxation spectra (at 20 to 40 °C) are reported for three liquid alcohol/non­ polar solvent systems: Binary hexanol/mesitylene mixtures and two corresponding ternary mixtures, where 5 percent of hexanol are replaced by a dihydric alcohol, namely resorcinol (1,3-dihydroxyben­ zene) or 2,2´-dihydroxydiphenyl. The concentration of the polar substance(s) ranges from dilute solutions to pure alcohol(s). The lower frequency relaxation contribution, which generally is the more dominating the higher the alcohol concentration, is additionally enhanced by the diol admixture in the case of low and moderate concentrations. This can be understood as a hetero-association effect, the diol molecules playing a bridging role, which also leads to an increase in the mean lifetime of associated states.

An algorithmic analysis of the existence of conjugated patterns for carbocyclic and heterocyclic compounds is presented. This graph theoretical method is applicable to the enumeration of Kekulé patterns for hydrocarbon benzenoids, as a special case.

The photoinduced formation of transients in aqueous 4-chloroanisole (4 ClA), at pH 7 and 9, were studied by conventional flash photolysis. The absorption spectra of various transients in airfree as well as in aqueous solutions saturated with N 2 O , air or pure oxygen, are presented and discussed.

The 35 Cl NQR frequencies and EFG asymmetry parameters at the 35 Cl nuclei have been mea­sured for compounds of the series 4-XC 6 H 4 MCCl 2 C(O)C 6 H 5 (M = S and Se, X = H and CH 3 ) at 77 K. The electron distribution at the Cl atoms in all the compounds studied differs from axial symmetry, and is unequal for the two Cl atoms of the CCl 2 group. The results of the measurements imply p σ -electron density nonequivalence of Cl atoms in the CCl 2 group of these molecules.