Volume 40, Issue 10

The equivalence of magnetic field line equations to a one-dimensional time-dependent Hamiltonian system is used to construct magnetic fields with arbitrary toroidal magnetic surfaces I = const. For this purpose Hamiltonians H which together with their invariants satisfy periodicity constraints have to be known. The choice of H fixes the rotational transform η(I). Arbitrary axisymmetric fields, and nonaxisymmetric fields with constant η(I) are considered in detail. Configurations with coinciding magnetic and current density surfaces are obtained. The approach used is not well suited, however, to satisfying the additional MHD equilibrium condition of constant pressure on magnetic surfaces.

The stability of an infinitely long, inviscid but compressible liquid jet under sinusoidal disturbances of the surface, still assumed to be sharp, is considered. This extends Rayleigh's theory. We show that despite compressibility the unstable region is λ > λ c = 2πa (λ wavelength, a radius) as Rayleigh's criterion for incompressible liquids states. The character of the unstable long wavelength mode changes with compressibility showing a critical onset if the inverse compressibility is only half the surface pressure. The maximum decay rate increases with compressibility and the most unstable wavelength increases too. An infinity of sound-like modes exists; their dispersion relations and flow fields are also given.

In the framework of extended non-equilibrium thermodynamics, the local non-equilibrium state of a liquid is described by the density, temperature, and a structural variable, ζ, and its rate-of-change. ζ is the ensemble average of a function A (Q) of the configuration co-ordinates, and it is assumed to relax to local equilibrium in a time short compared to the time for diffusion of an appreciable number of particles into the system. By a projection operator technique of Grabert, an equation is derived from the Liouville equation for the distribution of fluctuations in TV, the particle number, and in A and Ȧ. An approximate solution is proposed which exhibits nonequilibrium corrections to the Einstein function in the form of a sum of thermodynamic forces. For a particular structural model, the corresponding non-Einstein contributions to correlation functions are estimated to be very small. For variables of the type considered here, the thermodynamic pressure is found to equal the pressure trace.

The specific heat of Ag 2 S has been measured from room temperature up to the melting point (838 °C). The temperature dependence of the specific heat of its ɑ-phase in the temperature range from the β-ɑ. transition point at 179 °C to 586 °C, at which temperature there occurs another crystallographic transition, is well reproduced by supposing a Schottky-type specific heat (excitation of mobile ions) in addition to the normal lattice heat capacity. The latent heat of the latter transition, where the structure of the lattice changes from bcc to fcc, is obtained to be 774 J/mol.

Fourier Transform far infrared spectra of unstable stannyl chloride, bromide and iodide have been measured in the gas phase with a resolution of 0.04 cm -1 . At pressures below 10 mbar, their lifetimes at 0 °C in preconditioned cells were found to be 10-30 min. The v 3 fundamentals and hot bands of the series (n + 1)v 3 - nv 3 have been observed. Rotational J structure has been resolved for monoisotopic samples, and band origins v 3 0 , anharmonicity constants x 33 , ɑ 3 B and D J 0 values have been determined from the rovibrational analyses. The following v 3 0 values were obtained: H 3 116 Sn 35 Cl 375.470 (5), H 3 116 Sn 37 Cl 367.689 (6), H 3 116 Sn 79 Br 263.566 (5) and H 3 116 SnI 209.759 (6) cm -1 .

A new method is proposed, which allows for the determination of the ground state energy and the natural orbitals (NO's) of a two-electron system directly and simultaneously. The basis for this calculation is a system of integrodifferential-equations, which defines those NO's.

The highfield, linear and quadratic Zeeman effect has been observed in Acrylonitrile (Vinyl Cyanide). The Zeeman multiplets are complicated by the presence of the 14 N nuclear quadrupole coupling, however the 14 N nuclear Zeeman effect effectively uncouples 14 N spin from the rotational angular momentum. This uncoupling was used to derive improved molecular electric dipole moments from the Stark-shifts in the 2 11 ← 2 02 and 3 12 ← 3 03 rotational transitions observed under ΔM j =0 selection rule in the presence of a high magnetic field. They are |μ a | = 3.815(12)D and |μ b | = 0.894(68)D, respectively. From the zero field hfs multiplets, observed under high resolution conditions, improved 14 N quadrupole coupling constants were obtained: χ aa N = - 3.7800(21) MHZ, χ bb N - χ cc N = - 0.4200(89) MHz. They are discussed with reference to the structure of the Nitrile group. From the Zeeman splittings of the 1 01 ← 0 00 , 1 10 ← 1 01 , 2 11 ← 2 02 and 3 12 ← 3 03 rotational transitions observed under ΔM j = 0 and ΔM j = ± 1 selection rule, the diagonal elements of the molecular g-tensor and the anisotropics in the diagonal elements of the molecular magnetic susceptibility tensor were obtained as g aa = -0.17901(33), g bb , = - 0.04585(17), g cc = -0.01820(16) and 2 χ aa - χ bb - χ cc = - 7.22(25) 10 -6 erg G -2 mole -1 and 2χ bb - χ cc - χ aa = + 15.90(31) 10 -6 erg G -2 mole -1 . They are discussed with reference to the molecular electric quadrupole moment, the paramagnetic and diamagnetic contributions to the molecular susceptibilities, and the second moments of the electronic charge distribution. The susceptibility data are also used to derive the magnetic susceptibility tensor contribution of the Nitrile group.

A piecewise-linear nerve conduction equation is investigated further. The theory of Poincare halfmaps induced by the flow of a three-dimensional linear saddle-focus is developed. Using a description of the dynamical system in diagonalized coordinates, a canonical formulation of two-dimensional halfmaps is found. This leads for each halfmap to an implicit scalar equation plus a side condition. The effect of the halfmaps on different types of invariant curves occurring is investigated. Thereby the capacity of the halfmaps to separate adjacent points (such that the images acquire a finite distance) is shown. Two of three possible mechanisms for separating points are investigated in detail. The regions in the canonical parameter space where the different separating mechanisms appear are indicated analytically. The possible appearance of chaotic solutions, at least in the neighborhood of homoclinic trajectories in state space, is demonstrated. The underlying separation mechanism is present also in regions of state space far from a homoclinic orbit.

Oxidation of aniline in aqueous solution by ·OH radicals proceeds predominantly via addition to the ring followed by elimination of OH - on the microsecond time scale to form the aniline radical cation. Direct oxidation by electron transfer accounts for less than 4% of the ·OH reactions. The different hydroxycyclohexadienyl isomers produced by ·OH addition decay at different rates with this decay catalyzed both by protons and phosphate. In basic solution the resultant radical cation deprotonates to form the anilino radical. The p K a for the equilibrium between the acidic and basic forms of this radical is 7.05 ± 0.05. Secondary radicals such as Br 2 · - or N 3 · oxidize aniline directly by electron transfer and allow rapid preparation of the radical cation even in basic solution, as is conclusively demonstrated by observation of the Raman spectrum of the radical cation on the nanosecond time scale at pH 10.4. The deprotonation process can be followed directly by time resolved absorption spectrophotometry in the pH range of 9 - 11 and is shown to occur via reaction of the radical cation with OH - at a rate constant of 2.2 x 10 10 M -1 s -1 . Reaction of anilino radical with water is relatively slow (k ~ 2 x 10 3 s -1 ). Time resolved Raman methods show that benzidine radical cation is an important tertiary transient, indicating that second order reaction between radical cations results to an appreciable extent from coupling at ring positions.

Continuous UV-irradiation as well as flash-photolysis of derivatives of 2,6-diphenyl-s-hydrindacene- 1,3,5,7-tetrone (bisindandione - BID), substituted in the p and p' positions of the phenyl rings, was found to result in the formation of stable photoproducts, of which the absorption, emission and excitation maxima coincide with those of the corresponding diarylidene-benzodifurandiones (bis-benzylidenephthalides - BBPh). Studies of light intensity effects gave evidence that this isomerization proceeds via a semi-isomerized intermediate. Additionally, flash-photolysis of BID showed the formation of short lived transients, which, however, are not the precursors of the stable photoproducts. These transients were assigned to 2,6-diphenyl-shydrindacene- 1,3,5,7-tetrone-2-yl free radicals. Their UV-absorption maxima are dependent on the polarity of the solvent and show a bathochromic shift upon substitution.

Phosphorescence in ethanol at 77 K of the cyclophanes 1-14 has been investigated. It is shown that the phosphorescence characteristics are strongly determined by transannular interaction between the benzene rings. This interaction does not occur in cyclophanes 9 and 14. Phosphorescence quenching by silver Perchlorate of paracyclophanes and benzene derivatives 15-20 is due to the formation of arene/Ag + ground state complexes. From the quenching data it is concluded that the complexes of paracyclophanes with Ag + ions are more stable than the corresponding complexes of the benzene derivatives by approximately two orders of magnitude. Various factors are discussed regarding this marked difference in complex stability.

An upper bound on the dimension of eigenspaces of multiparticle Schrödinger operators is given. Its relation to upper and lower bounds on the eigenvalues is discussed.

Approximating the π-electron molecular orbital energy levels by uniformly distributed random variables, a McClelland-type formula for the total π-electron energy is obtained. Conditions are determined under which a given distribution function will result in a formula of McClelland type.

There are no examples of higher spin wave-equations of the Gel'fand-Yaglom form based on the representation (3/2, 5/2) ⊕ (1/2, 5/2) ⊕ (-1/2, 5/2) ⊕ (-3/2, 5/2) having definite charge and propagating causally in an external electromagnetic field.

The thickness dependence of the absolute temperature coefficient of the resistance of ultra-thin metal films is calculated with the help of Monte-Carlo calculations already successfully applied to the simulation of the electrical resistance. An initially strong increase and then a weaker decrease of the ATCR with increasing thickness is found.