Table of contents

Exact solutions of a generalized nonlinear Schrödinger equation

iu_t + u_xx + q_c|u|²u + q_q|u|⁴u + iq_m|u|_x²u + iq_u|u|²u_x = 0

are obtained by transforming the equation to one whose coefficients satisfy a simple algebraic relationship. The transformed equation also yields conservation laws and sufficient conditions for boundedness and blow-up of solutions for the original equation.

In this comment, the many component magnetic system given by Makhankov et al. [1] is reduced to a quanum nonlinear Schrödinger model without the U(p, q) symmetry. For the ferro- and antiferromagnetic system this model is completely integrable and the bound states of the model are discussed.

By explicitly introducing degrees of freedom for the electromagnetic field into the Hamiltonian for an N-electron system, we propose a variational procedure leading to mean fields different from the Hartree-Fock field. We show that g-Hartree equations result if the electromagnetic field is assumed to be in a coherent state. Since the solutions of these equations, the g-Hartree orbitals, are derived from a variational ansatz more general than the Hartree-Fock functional, we expect them to be particularly suitable to furnish a single-particle basis set for fast converging configuration interaction (CI) calculations. We report configuration interaction studies on the water molecule in a double zeta basis set employing various single-particle basis set transformations for the construction of the configuration state functions and investigate the convergence behaviour of the CI expansion explicitly.

We find that the expansion in terms of g-Hartree orbitals receives substantially larger fractions of the total correlation energy in the case considered, if single excitations with respect to the mean field configuration are retained in the CI procedure.

Group theory is used in four dipolar point groups to determine the infrared selection rules and transition symmetries of a molecule whose dynamics are simultaneously those of the harmonic oscillator and rigid rotor. The motion is governed by the translational quantum number n of the harmonic oscillator and the quantum number J of the rigid rotor. The selection rules for the harmonic oscillator are modified from Δn = ± 1 to Δn = 0, ± 1. Those for the rigid rotor are changed from ΔJ = 0, ± 1 in the absence of translation to (1) ΔJ = 0, ± 1, ± 3; Δn = 0, n odd; (2) ΔJ = 0, ± 1; Δn = 0, n even; (3) ΔJ = 0, ± 2, Δn = ± 1; all n. The relative intensities of the rototranslational far infrared spectral lines are given for point groups C_3v, C_2v, C_1h, and C₁. The theory is in partial agreement with the experimental ΔJ = 1, 2, 3, 4 transitions observed in HD trapped in rare gas crystals at low temperature and with the selection rules for C_∞v symmetry obtained by Friedmann and Kimel.

An extension of the classification of the spectrum of singly ionized praseodymium, based on the analysis of high resolution data in the range 2783-27 920 cm⁻¹, yields new energy levels in the odd configuration 4f²5d6p and in the mixed even configurations 4f²5d² + 4f²5d6s + 4f³6p. A number of experimental characteristics of the levels have been determined or revised; energy, J, and hyperfine structure splitting are given for all known levels (105 odd levels and 187 even levels), and g values are given for 236 levels. Experimental data are presented for 172 classified intense lines in the ultraviolet range, and for 39 unclassified lines. The wavenumber distribution of the different types of observed transitions is studied.

A parametric interpretation of the fine and hyperfine structures is given for all the experimental even levels of singly ionised praseodymium on the basis of the 3 mixed configurations 4f²5d² + 4f²5d6s + 4f³6p. The experimental energies of 187 levels are interpreted with 50 parameters (43 free parameters), with a mean deviation ⟨ΔE⟩ = 80 cm⁻¹; the A-constants for the magnetic hyperfine structure are interpreted with 7 parameters (4 free parameters), with a mean deviation ⟨ΔA⟩ = 4 mK (1 mK = 0.001 cm⁻¹).

A detailed study of the spin forbidden transitions, 1s²¹S → 1snp³P (n = 2,... 7) has been carried out for the first five members of the helium isoelectronic sequence. Non-relativistic time-dependent coupled Hartree-Fock (TDCHF) theory with a spin dependent perturbation has been used to this end. Transition energies for the various excited states generated, have been obtained and suitable analytic representations for these high lying Rydberg states have been given. Also, the magnetic quadrupolar (M2) transition rate has been calculated with the help of the wavefunctions so obtained. These compare favourably with existing data.

We present an alternative approach to the self-energy formalism for the interaction of a projectile with a many-body target. We illustrate the method with examples of charges or atoms interacting with a surface, and with charges or atoms interacting with order atoms. Further applications are briefly discussed.

We give a general discussion of self-organisation in turbulent systems with special reference to Rossby waves in two-dimensional systems. We discuss briefly the rôle of helicity in three-dimensional flow and show how self-organisation can occur in three-dimensional developed turbulence.

We give a brief description of the ball lightning phenomenon and list the properties of the average fireball based on the available data. We then discuss briefly a recent theory to account for the data.

Beat-wave acceleration of particles requires that the particle trajectories closely follow the constant-phase lines of the excited plasma wave. Dephasing phenomena caused by plasma inhomogeneities and by relativistic frequency shifts and the accompanying self-phase modulation of the plasma wave are investigated. Parameter studies of beat-wave experiments indicate the plasma homogeneity will be a critical issue, especially with short wavelength lasers. The plasmon wake suffers most strongly from dephasing effects which fact considerably reduces the efficiency of the wake region in beat-wave acceleration.

We have considered transitions between the Landau levels of an electron moving in a plasma due to its emission of gyro-frequency plasmons in the region of an anomalous and normal Doppler effect. Probabilities for these transitions are obtained. Transitions with spin flipping are also discussed. It is shown that anomalous Doppler emission can contribute to equalizing the populations of (both orbital and spin) energy levels.

Probabilities of longitudinal wave emission by an atom traveling in a plasma in the region of anomalous Doppler effect, are obtained. The role of the recoil effect is evaluated. The question of the influence of the form of a Hamiltonian upon the probabilities indicated is discussed.

A theoretical study has been made of the emission of an atom in inhomogeneous and nonstationary media. The study has revealed emission intensities for a medium with variable dielectric permittivity, indicating the possibility of foremation of spectral line satellites. With applications to atoms in a plasma, we have obtained plasma satellite intensities and we discuss their importance for plasma diagnostics.

The effect of including the electron temperature gradient in the Hasegawa-Mima equation is studied in two different wavelength regions. It is found that one term has been missing in earlier studies of this effect, and that the temperature gradient does not give rise to any new monopole vortex solution. On the other hand, solutions similar to the usual dipole vortices still exist. It is also found that the temperature gradient can prevent the appearance of zonal flows that has been predicted earlier.

Non-oriented electrical steel sheet containing very low amounts of S, N, O, C, and Ti exhibits the loss minimum at far thinner gauge than conventional material. The low carbon material offers the possibility of a non-decarburising final annealing thus avoiding internal oxidation and nitride precipitation. At a thickness of 0.2 mm the loss is improved by about 30%. For medium frequency application the loss decrease enables the employment of electrical steel with reduced alloy content.

The entire concentration range of α-phase Ni_1-xCu_x alloys has been studied by Angular Correlation and Positron Lifetime methods. The results show inapplicability of the Rigid Band Model to description of the electronic structure of this alloy. Linearity of annihilation rate λ(x) as well as of parameters of correlation curves leading to linearity of s-like and d-like electron numbers with x confirms our earlier expectation as to the character of annihilation parameters for split-band alloys with constant Fermi energy. On the ground of the present results and the previous ones for palladium alloys it was postulated that the behaviour of the bulk annihilation rate in binary alloys can predict which type of the electronic structure, split-band or VCA, is the appropriate one in the given case.

Conductance noise measurements done on point contacts of (melt-quenched) glassy metal ribbons are reported. The lower limit of the 1/f noise factor obtained was stronger by 3-5 orders of magnitude than that usual in ordinary metals.

That result supports the "two potential well tunelling" model of 1/f noise in glassy metals.

The conductance fluctuations measured in hydrogenized glassy metals proved to be also 1/f noise. Diffusion noise due to hydrogen has not been found.

The thermal expansion coefficient α of the Cr-Si alloys with 0.5-4.5 at.% Si have been investigated in the temperature range 4.2-360 K. The existence of a negative low-temperature anomaly of α and a magnetic contribution to α in a wide temperature range have been registered for these alloys.

The Total Ownership Cost (TOC) method was used to model and predict usage of various core materials in distribution transformers by weighing both performance and economic factors.

The influence of conventional insulating coatings: MgO ceramic and phthalate enamel on the magnetic properties of Fe₇₈B₁₃Si₉ amorphous ribbons (AFB) is studied. The effect of thermal and thermomagnetic treatment on magnetic parameters of coated and uncoated ribbons is also investigated. The coated ribbons subjected to proper annealing are shown to be characterized by smaller power losses and coercive force then reference uncoated ribbons subjected to the same treatment.

The Viking low frequency wave experiment, with unique two point measurements of plasma density fluctuations and measurements of potential fluctuations, provided detailed diagnostics of small scale, large amplitude solitary structures in the auroral acceleration region. The structures have a spatial scale of the order of 100 m, density depletions up to 50%, negative potentials up to about 5V, and propagate upwards along the magnetic field lines with velocities from about 5 to more than 50 km s⁻¹. Some structures have a net potential drop of up to a few volts, in general directed upwards. The structures are characterized as solitary waves (no net potential drop) and weak double layers (a net potential drop comparable to kT_e/e), or holes in the thermal ion (and electron) phase space distribution. Their occurrence is correlated with that of beams of upward flowing energetic ions, dominated by protons, and electrostatic ion cyclotron waves. The field-aligned currents seem to be relatively weak. A great number of structures with a net potential may account for a large scale potential drop along the geomagnetic field lines and the observed acceleration of auroral particles up to kilovolt energies.

The theories concerning solitary waves and weak double layers in the auroral plasma are discussed. We make comparisons with Viking satellite observations and computer simulation experiment results of similar phenomena. The lack of velocity vs. amplitude relation in the Viking data is not consistent with the predictions of ion acoustic soliton theories and neither are the measured speeds of the structures. Numerical simulations show results, which are somewhat more consistent with Viking measurements but not with the ion acoustic soliton theory predictions. The nonlinear phase space ion hole instability offers another explanation for simulation results and space observations. Even there we still are quite uncertain, since the theory so far is only one-dimensional whereas the observations indicate that the solitary structures have a two- or three-dimensional shape with such scale sizes that the ions cannot be considered as one-dimensional.