Volume 47, Issue 4

A finitistic quantum field theory, as a model for a unified theory of elementary particles is proposed, making the assumption that all spatial and temporal distances can only assume integer values of a fundamental length and time, for which we have chosen the Planck length and Planck time. To satisfy the condition of causality in its quantized version, the theory must be exactly nonrelativistic, because only then can the concept that points in space are separated by multiples of a fundamental length be formulated in an invariant way. The theory is formulated as a partial finite difference equation, invariant under translations and rotations in space, and translations in time, and can be expressed as a partial differential equation of infinite order. The theory is free of all divergencies, has a positive definite metric in Hilbert space and therefore no ghost states. Possessing a fundamental length, chosen to be equal the Planck length, the theory has an inbuilt cut-off at the Planck energy. For energies sufficiently below the Planck energy, the theory can be approximated by the previously described Planck aether model, which can be viewed as a superfluid consisting of Planck masses, leading to special relativity as a dynamic symmetry in the asymptotic limit of low energies.

The effect of surface deformation on the onset of thermosolutal convection in a horizontal thin layer heated from below and salted from above is examined, using linear stability theory. It is found that two critical Crispation numbers Cr 1 and Cr 2 exist. For Cr ≦ Cr 1 the instability mechanism remains unefTected by the deformation of the free surface, whereas for Cr 1 < Cr < Cr 2 the critical Marangoni number (M c ) decreases, showing instability due to deformation. If Cr = Cr 2 , Mc is obtained for two values of the wave number. When Cr > Cr 2 , Mc decreases as the wave number tends to zero. Further, the effect of the Marangoni number, Biot number, Bond number etc. on the stability characteristics of the problem is discussed.

The onset of thermosolutal convection driven by a temperature and concentration dependent surface tension is investigated for a thin layer of fluid having a deformable free surface. It is shown that there exist two Crispation numbers (Cr) for oscillatory modes of instability. It is further shown that Cr and the frequency of the oscillatory mode are strongly coupled for large values of Cr. It is found that Cr destabilizes the system for both cases, salted from below and salted from above

The static properties of nematic liquid crystals are summarized. The mean field potential emerging from the static distribution function has been used to the hydrodynamic theory. Rotational viscosity coefficients have been investigated. The Parodi relation has been shown to be completely satisfied. Static and hydrodynamic properties have been predicted on the basis of one intermolecular potential

The 14 N hyperfine multiplets of low-7 rotational transitions of the E and Z isomers of HN = CH - C ≡ N, produced by flash pyrolysis from (CH 3 ) 2 N -C ≡ N as precursor, were observed and analysed. The quadrupole coupling constants determined are (c -axis perpendicular to the molecular plane): The observed hfs multiplets were predicted with reasonable accuracy from RHF/6-311G** field gradients, once the latter had been scaled appropriately to compensate partly for the typical errors in the RHF-wave functions. The hitherto unmeasured 14 N hyperfine multiplets of the related pyruvonitriles, H - N = C(CH 3 ) - C ≡ N, are predicted.

Deuteron spin-lattice relaxation time (TJ measurements of binary mixtures 2,6-lutidine/D20 have been done near the lower critical solution point (T C , L ), ε = (T - T C , L )/T C , L ≧ 10 -5 . Singularities are observed at T C , L . The changes in the slope of T 1 ( 2 H) = ƒ ( T ) can be interpreted as due to the effect of concentration changes on Ty and simultaneously strong overlaping of 2 H NMR signals from coexisting phases. In the two-phase region, ca. 2°C above T C , L two D 2 O signals with very strong temperature evolution have been detected. Similar doubling of 2,6-lutidine 1 H NMR signals has been observed already at T - T C , L ≦ 1 °C. It is shown that the two signals arise from the nuclei in two coexisting phases; they are not due to pecularities of hydrogen bond. The difference between chemical shifts of both D 2 O signals δ’ - δ” possess the property of an order parameter, i.e. δ’ - δ” ~ ε β with β = 0.336±0.030

The microwave spectrum of γ-thiobutyrolactone has been reinvestigated using microwave Fourier transform spectroscopy. The μ c rotation inversion transitions have been found to be splitted for the first excited state of the vibration at ~ 250 cm -1 . An inversion splitting of 0.014 MHz has been measured directly from these transitions. These splittings indicate that the vibration is related to a double minimum potential function describing two ring-twisted conformations connected by inversion. A one-dimensional reduced potential function has been derived for this vibration and gives a barrier to ring inversion of 1380± 350 cm -1 .

The dinstinct vibronic structure of the δ → δ* transition of Cs 3 [Tc 2 Br 8 ] with its mixed valence is well resolved at 6 K. The electronic origin at about 5970 cm -1 is split into four components, each giving rise to progressions entirely assignable in terms of nν 1 and nν 1 + ν 2 up to n = 9, utilizing the totally symmetric stretching modes ν 1 (TcTc) and ν 2 (TcBr) exclusively.

Pure carbon clusters, formed by Nd/YAG laser ablation of graphite, have been trapped in an argon matrix at 12 K. The temperature dependence of the prominent infrared absorption bands attributable to C 3 , C 5 , C 6 , and C 9 clusters has been investigated between 12 K and 38 K. The former two are observed to decay and the latter two to grow with increased matrix annealing. A new kinetic model based on solid state diffusion theory and involving thermally activated diffusion and aggregation is introduced. All possible pairwise interactions of the linear carbon clusters from C 1 to C 10 are included in the model. The coupled differential equations are solved numerically and provide a reasonable fit to the experimental temperature profiles of the known clusters. Predictions emerge from the fit for the unknown matrix infrared frequencies for the C 7 cluster. On the basis of the predicted concentration invariance with temperature for C 7 , the infrared bands at 2128 cm -1 and 1894 cm -1 are ascribed to this linear cluster. This attribution supports the recent assignment of the gaseous 2138 cm -1 band to linear C 7 .

It is shown that TI 3+ as a bromide removing perturbant of the BZ oscillators is superior to Ag + in several aspects. A most important advantage is that the upper limit of the actual Br - concentration can be calculated from the potential of a bromide selective electrode in the presence of the corrosive TI 3+ ions. Experimental Potentiometrie traces of a bromide selective electrode in a TI 3+ perturbed BZ system show that the Br - concentration stays much below its critical concentration during the oscillations. These observations suggest that free Br - is not the critical intermediate formed during reduction of Ce 4+ and responsible for the negative feedback associated with the oscillations.

By ab initio quantum mechanical calculations on P2S 2- 6 its equilibrium energy, geometry and vibrational frequencies along with their PED values have been obtained. The basis sets STO-5G, 6-31G, STO-5G* and 6-31G* were employed, and force field calculations were carried out at the STO-5G and the STO-5G* levels. The calculations show that the assignment for some bands between 180 and 260 cm -1 should be corrected. Two scaling factors were needed to fit the calculated frequencies with the observed frequencies within a deviation of less then 20 cm -1 for all vibrations, with the exception of v 6 (B 1g ). The calculated frequency of this vibration is very dependent on the polarization functions, and use of STO-2G for the 3d-orbitals corrects most of the deviation. STO-5G* and 6-31G* both give a good description of the geometry of the title ion, although STO-5G* yields a 0.04 Å too short terminal P - S distance.

After a discussion of the one-component Schrödinger (1926) and the four-component Dirac(1928) representation of hydrogen it is shown that the six-component electrodyamic picture turns out to be considerably simpler and clearer. The computational effort is reduced to a fraction.

The calculation of the viscosity of liquid crystals based on the rotational diffusion approximation recently reported by Osipov and Terentjev [1 a] is critically examined. It is shown that the main result of their treatment - the evaluation of the activational exponent - arises from the neglect of the second derivative of the distribution function with respect to the azimuthal angle in the Fokker-Planck equation. The correct asymptotic formula for the rotational viscosity coefficient is derived.