Table of contents

An exact solution of a generalized nonlinear Schrödinger equation is presented. The equation is characterized by a new nonlinear dispersion term, and its limiting cases cover a large number of physical problems.

An analysis of the electronic structure of the PO₂ radical is presented on the basis of ab initio calculations performed on the following low-lying electronic states: 1²A₁ (1²Σ_g⁺), 1²B₂, 1²A₂, 1²Π_u (1²B₁, 2²A₁). The results concern the equilibrium geometries, the vibrational frequencies, the term and dissociation energies of the considered states. The topology of the potential hypersurfaces is also analysed and it appears that some of the surfaces exhibit multiple stationary points with some of them implying asymmetrical structures for PO₂. The results concerning the excited states on which very little is known so far can help in the understanding of the complex spectrum of the radical. A comparative analysis of the electronic structure of PO₂ with the isovalent NO₂ species is also presented, showing that an inversion of some of the low-lying configurations leads to the differences observed in their spectra.

The interpretation of the complex UV fluoresence spectrum is revised on the basis of a double band systems 1²B₁-1²A₁ and 2²A₁-1²A₁ in which the possible mixing by vibronic coupling of the vibrational levels of the excited states with highly excited levels of the ground state could explain the quasi-continuous part of the fluorescence.

The methodology used here to include the correlation effects in a partitioned way has been extended to the phosphorus containing systems and test calculations are presented on the X²Π ground state of PO.

An introduction is given to the use of spectral methods in numerical plasma simulation. As examples of the use of spectral methods, solutions to the two-dimensional Euler equations in both a simple, doubly periodic region, and on an annulus will be shown. In the first case, the solution is expanded in a two-dimensional Fourier series, while a Chebyshev-Fourier expansion is employed in the second case. A new, efficient algorithm for the solution of Poisson's equation on an annulus is introduced. Problems connected to aliasing and to short wavelength noise generated by gradient steepening are discussed.

Low level electrostatic ion acoustic turbulence generated by the ion-ion beam instability was investigated numerically. The fluctuations in potential were investigated by a conditional statistical analysis revealing propagating coherent structures having the form of negative potential wells which correspond to ion phase space vortices. The results demonstrate the importance of clump formation in ion phase space for the dynamics of the turbulence. The statistical analysis gives results in terms of averages over a conditionally selected subensemble. Because of the intermittent character of the turbulence it proved possible to devise a method, which permits recognition of essentially all coherent structures. With most of the structures recovered we are able to estimate their distributions of amplitude, width and velocity. A statistical evidence for interaction, i.e., binding, of phase space vortices was obtained.

Electrostatic charging level of a conducting surface in response to injections of electron beams into space plasma is investigated by means of one dimensional Vlasov code. Injection of Maxwellian beams into a vacuum shows that the surface can charge up to an electric potential ϕ_s > W_b/e, where W_b is the average electron beam energy. Since Maxwellian beams have extended tails with electrons having energies > W_b, it is difficult to qunatify the charging level in terms of the energies of the injected electrons. In order to quantitatively understand the charging in excess of W_b, simulations were carried out for water-bag types of beam with velocity distribution functions described by f(V) = A for V_min < V < V_max and f(V) = 0 otherwise, where A is a constant making the normalized beam density unity. It is found tht V_max does not directly determine the charging level. The pressure distribution in the electron sheath determines the electric field distribution near the surface. The electric field in turn determines the electrostatic potential of the vehicle. The pressure distribution is determined by the beam parameters such as the average beam velocity and the velocity spread of the beam.

The effect of the ambient plasma on the charging level is investigated showing that when the ambient plasma density n_a ≪ n_b, the beam density, the surface potential ϕ_s remains greater than W_b/e, but it undergoes oscilations at the plasma frequency corresponding to the ambient plasma density n_a. Under such plasma conditions the majority of the injected electrons return to the surface. Only when the ambient plasma density n_a is sufficiently large so that the time average surface potential ϕ_sa ≲ W_b/e, the injected beam penetrates into the ambient plasma. However, the beam propagation speed depends on ϕ_sa; when ϕ_sa ∼ W_b/e, the propagation velocity is ∼ V_t, the electron thermal speed. Under such a case the propagating beam head is accompanied by a triple-charge-layer potential structure. The net potential drop across such a structure is about ϕ_sa. When ϕ_sa ≪ W_b/e, the beam propagates with the injection velocity V_b.

The purpose of this brief note is to generalize the exact solution of Yu and Chu [1] to be applicable to the nearly-stationary, isothermal motion of a warm fluid.

With the aim to confirm or reject the recent claim of observation of cold d-d fusion, an experimental effort has been made to try to observe MeV protons which should be emitted as a result of d-d fusion. Pd foils, thin enough to allow all protons produced to escape the foil, were electrolytically charged with deuterium. A Si(SB) detector was placed close to the Pd foil during charging in order to detect any protons emitted. The deuterium content was measured to be the expected 0.7 D per Pd. Monte Carlo simulations were made to estimate the detection efficiency of 3.02 MeV protons produced in the Pd foil.

The background in the experiment was so low that fusion rates considerably lower than those reported on by Jones et al. could be detected. A number of experiments have been performed where the charging conditions were varied. In spite of that and the good sensitivity of the experiment no evidence for cold fusion has been found.

This paper deals with the study of physical and technological conditions required for the use of amorphous alloys in the magnetic circuits of a special class of electrical machines supplied at medium frequencies (1-10kHz). Several real scale experimental devices were designed and tested for many annealing treatments and operating conditions in order to define the best process which could lead to high specific powers while minimizing losses.

The effect of ordinary impurities on the Peierls-CDW transition is investigated within a normal state side approach. The 2k_F-phonon frequency is calculated within the Born approximation for the electron self-energy and ladder approximation for the three-legged vertex function. The critical concentration and critical temperature of the soft-mode instability are obtained; they agree with the conditions for the suppression of the Peierls-CDW distortion. A thermal hysteresis effect is suggested for the doped quasi-1D materials.

The valence band photoemission/B.I.S. spectrum of the transition metals is investigated theoretically. The d band is modelled by an N fold degenerate Hubbard Hamiltonian. In the sudden approximation, the photoemission spectrum is given simply by the occupied portion of the density of states and the B.I.S. spectrum is the unoccupied portion of the density of states. We use a tight binding model for the bare non-interacting bands. The effect of the coulomb interactions is introduced via an 1/N expansion. The lowest order term in 1/N produces a mean field theory which does not include the effects of coulomb correlations on the dynamics. The spectrum is calculated to the next order, i.e., 1/N², and this shows satellite features in the B.I.S. of the nearly empty d band and a satellite in the photoemission spectrum of the nearly filled band case. These results are similar to those previously obtained, with other calculational schemes and approximations. The results may be applicable as a description of the 6eV satellite in Ni photoemission, or the satellites suggested as occurring in the B.I.S. spectra of Uranium compounds. The terms of higher order in 1/N are discussed along with the conditions for convergence of the expansion.

Solid state reactions in the Fe₂O₃-Y₂O₃-CaCO₃-ZrO₂ mixtures with different Y-Fe ratios (0 < Fe₂O₃ < 4.75; 3.25 Y₂O₃; 1.0 CaCO₃; 1.0 ZrO₂ molar ratio) sintered at 700-1400°C were investigated by x-ray diffraction and DTG(M) methods. The DTG(M) method proved to be very effective in detecting very small amounts of magnetic constituents in the sample. The most interesting features of the reactions are the following:

– At iron contents higher than 2.75 molar ratio in the temperature region 1200-1400°C Ca and Zr containing garnets are formed.

– In mixtures with a Fe₂O₃ content less than 2.75 molar ratio the formation of orthoferrite is preferred.

– A new Y₂O₃-type phase (Y₂O'₃) is the dominant component in systems with a low iron content.

The polar Slant-E-Condition (SEC) has been investigated using the incoherent scatter radar (ISR) facility installed at Sdr. Strømfjord, Greenland (inv. lat. = 74°) along with co-located and remote ionosondes, riometers, magnetometers and other equipment. SEC events are characterized by the occurrence of diffuse, slanted backscatter traces (slant Es) in ionograms and abnormally high attenuation (lacuna) of the ionosonde return signals at frequencies close to the E-region plasma frequency.

The ISR observations of E-region electron densities, electron and ion temperatures and plasma convection velocities have shown, that SEC occurs during events of substantially elevated electron temperatures related to the occurrence of plasma instabilities driven by strong horizontal electric fields. A self-consistent model for electron heating in an unstable plasma has been applied to the observations and very good agreement was found between observed and calculated electron temperature profile shapes and values of peak temperatures. There was fair agreement between observed and calculated height ranges for the heated electrons. These results and the consequences of the fictitious electron-plasma wave collision term used in the electron heating model are discussed.

There is no quantum chaos, in the sense of exponential sensitivity to initial conditions, but there are several novel quantum phenomena which reflect the presence of classical chaos. The study of these phenomena is quantum chaology.

Dynamic coarsening of crystal surfaces by formation of macrosteps is explained by an improved model for impurity absorption. It is related to interface propagation in random media. Some unusual recursive equations are encountered and are briefly analyzed by functional iteration. The model is studied by various methods and exhibits some universal features. We find coarsening to proceed logarithmically with time in agreement with experiments.

The existence of cantori can lead to specific dynamical phenomena in non-linear systems. They represent partial barriers for the classical probability flow in phase space. We study a physical system, in which a self-similar hierarchy of cantori provides a new mechanism for 1/f-noise. In quantum systems such as the kicked quantum rotator, cantori can represent even stronger barriers and inhibit the diffusive growth of mean-square displacements. In their vicinity, the asymptotic probability distribution decays exponentially. The variation of the penetration depth across a KAM-torus is characterized by a critical exponent.

We discuss several questions related to the predictability of chaotic systems. We first review the information flow through systems with few degrees of freedom and with sensitive dependence on initial conditions, and ways of measuring this flow. We then ask how the knolwedge obtained in this way can be used in improving forecasts, and propose one way of forecasting suggested by dynamical systems concepts. On the more fundamental level, we point out the difference between difficulty and possibility of forecasting, illustrating it with quadratic maps. Next, we ask ourselves how this should be generalized to distributed (i.e., spatially extended) and homogeneous systems. We point out that even the basic concepts of how information is processed by such systems are unknown. Finally, we discuss some intermittency-like effects in coupled maps and cellular automata.

We study the quantum mechanics of a Hamiltonian system which is classically chaotic: the stadium billiard. We have examined many of the eigenstates of the stadium, up to about the 10 000th. Complex periodic orbits play an active role in shaping the eigenstates.

The ability of a finite, autonomous, quantum mechanical system to reflect the ergodic behavior of its classical counterpart is discussed. It is argued that an attempt to identify unambiguously the consequences of rigorous ergodicity in such a quansum system would be futile. Instead, an approximate, temporary, form of ergodicity, called pseudoergodicity, is introduced and compared for the classical and quantum analogs of the Henon-Heiles system. The numerical results illustrate the extent to which quantum systems imitate classical statistical tendencies.

It is shown that the whole spectrum of dimensions and entropies which characterize a strange attractor can be computed by an extension of the Grassberger Procaccia method. A measure of algorithmic complexity is introduced which characterizes pattern formation in space and time.

Adiabatic methods are used to define dynamic potentials that can be viewed as causing quasi-periodic motion. The breakdown of these potentials lead to chaos. Examples include the well known Henon-Heiles and Stadium models.

Some situations of turbulent Rayleigh-Bénard convection are presented with increasing number of spatial degrees of freedom.

Analytical formulas for the critical ionization field of the microwave driven H-atom are derived. Good agreement with measured ionization field is obtained.

We outline several unresolved problems which must be explored in depth before concepts in chaos can provide useful approximate methods in reaction dynamics.

We study transitions leading to rhythms and patterns in non-equilibrium systems. Our approach is inspired in Landau's analysis of phase transitions.

A dissipative quantum system exhibiting chaos in its classical limit is constructed by coupling the quantum kicked rotator to a reservoir with exchange of action. A version of the quantized standard map that incorporates dissipation is derived from this model and iterated numerically to study the long-time behavior in various regions of the damping rate. It is found that even weak damping is capable of disrupting dynamical localization which suppresses chaotic motion in the conservative standard map, and thus restores diffusion in the action variable. On the time scale of classical relaxation, a steady state is reached which is the quantum analogue of a classical strange attractor. For strong dissipation, observable deviations from classical behavior both in the transients and in the steady state are due to quantum noise. They are reproduced by a classical stochastic map which is approached by the dissipative quantum map as its semi-classical limit.

The quantal behavior of some systems, with time dependent Hamiltonians, that are chaotic in the classical limit, is reviewed. Chaos is suppressed by a mechanism that is similar to localization of electrons in disordered solids. Experimental realizations are proposed.

A very brief presentation of how lattice gas hydrodynamics is made. It includes key references.

The photon correlation spectroscopy technique was exploited to study turbulent pipe flow behind a grid. The correlation function of the scattered light intensity, g(t), was found to be a scaling function of qu(L)t(L₀/L)^β when the Reynolds number Re > 460. Here q is the scattering vector, L₀ the outer scale of the turbulent flow, and u(L) is the characteristic turbulent eddy velocity associated with eddies of size L. The exponent β is a function of Re. The measurements of the half-decay time of g(t) as a function of L and Re reveal an abrupt change in the character of the turbulent flow at Re = 460.

Preliminary results from experimental and numerical studies of transport in two-dimensional Rayleigh-Benard convection are presented. Two regimes are identified: a diffusion-limited regime for time-independent flows; and an advection-dominated regime for time-periodic flows, in which impurity trajectories are chaotic, with adjacent tracer particles separating exponentially as a function of time. Experimental measurements of transport rates as a function of the velocity of the flow are made for time-independent flows and are compared with theoretical predictions. Numerical studies of particle trajectories in time-periodic flows show evidence of chaotic behavior.

A numerical comparison is made of algorithms for computing the dimension of attractors using the Grassberger-Procaccia correlation dimension and the Badii-Politi nearest neighbor approach. Using experimentally realizable data sets, the nearest neighbor method appears to have the better power law behavior when the attractor dimension is between 3 and 7.

Quasiperiodically forced nonlinear dynamical systems may exhibit strange nonchaotic attractors. We argue that these attractors occur in a Cantor set of positive Lebesque measure in parameter space. Furthermore, we show that strange nonchaotic attractors have a distinctive frequency spectrum thus making them potentially observable in experiments.

The scaling found in Bernoulli's St. Petersburg Paradox was perhaps not properly understood until Levy's theory of probability limit distributions with infinite integer moments was developed. We use a generalization of these ideas involving a non-local stochastic equation with a coupled space-time memory to formulate a picture of turbulent diffusion.