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The geometric phases for dynamical processes where the evolution operator becomes the identity (evolution loops) are studied. The case of time-independent Hamiltonians with equally spaced energy levels is considered; special emphasis is made on the potentials having the same spectrum as the harmonic oscillator potential (the generalized oscillator potentials) and their recently found coherent states.
A two-dimensional generalized oscillator with time-dependent parameters is considered to study the two-mode squeezing phenomena. Specific choices of the parameters are used to determine the dispersion matrix and analytic expressions, in terms of standard hermite polynomials, of the wavefunctions and photon distributions.
Generalized oscillator strengths for transitions from an initially excited state of a hydrogenic atom to final states (either discrete or continuum) have complicated structures, including minima and shoulders, as functions of the momentum transfer. Extensive calculations carried out in the present work have revealed certain systematics of these structures. Some implications of the minima to the energy dependence of the inner-shell ionization cross section of heavy atoms by proton impact are discussed.
Born approximation used in calculating wave functions of helium atom for determining generalized oscillator strengths in first ionized continuum of helium
General solution of the initial value problem for longitudinal plasma oscillations
Highlights: • We construct Darboux transformations for Dirac systems with position-dependent mass. • Our systems are either Dirac oscillators or coupled to a magnetic field. • We use our Darboux transformation to construct new solvable Dirac systems. We construct a Darboux transformation for a class of two-dimensional Dirac systems at zero energy. Our starting equation features a position-dependent mass, a matrix potential, and an additional degree of freedom that can be interpreted either as a magnetic field perpendicular to the plane or a generalized Dirac oscillator interaction. We obtain a number of Darboux-transformed Dirac equations for which the zero energy solutions are exactly known.
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The normal mode oscillations of galaxies we reported recently are large enough to produce observational consequences. The two lowest order modes were both very strong and long lived: the fundamental is a "breathing" mode in which the entire galaxy expands and contracts homologously, while the second radial mode is spherically symmetrical and has one radial node. A sheet of neutral hydrogen in an oscillating galaxy partakes of the general oscillations, and the resulting velocity fields would normally be interpreted in terms of warps or oval distortions. More interestingly, the second radial mode might be a dynamical driver for bulges in early-type spiral galaxies. If bulges result from a dynamical process within the galaxy, there might be other observable properties driven by the same dynamical process. The hole often reported in neutral hydrogen in early type spiral galaxies is one such candidate. It has sometimes been reported to be about the same size as the bulge. We will discuss evidence from velocity fields concerning the fundamental mode and from the coincidence of bulge and HI hole sizes as evidence for the second mode.
Forced and naturally occurring, self-sustaining oscillations of transonic flows in two-dimensional diffusers were computed using MacCormack's hybrid method. Depending upon the shock strengths and the area ratios, the flow was fully attached or separated by either the shock or the adverse pressure gradient associated with the enlarging diffuser area. In the case of forced oscillations, a sinusoidal plane pressure wave at frequency 300 Hz was prescribed at the exit. A sufficiently large amount of data were acquired and Fourier analyzed. The distrbutions of time-mean pressures, the power spectral density, and the amplitude with phase angle along the top wall and in the core region were determined. Comparison with experimental results for the forced oscillation generally gave very good agreement; some success was achieved for the case of self-sustaining oscillation despite substantial three-dimensionality in the test. An observation of the sequence of self-sustaining oscillations was given.
A low-speed investigation has been conducted in the Langley stability tunnel to study the effects of frequency and amplitude of sideslipping motion on the lateral stability derivatives of a 60 deg. delta wing, a 45 deg. sweptback wing, and an unswept wing. The investigation was made for values of the reduced-frequency parameter of 0.066 and 0.218 and for a range of amplitudes from +/- 2 to +/- 6 deg. The results of the investigation indicated that increasing the frequency of the oscillation generally produced an appreciable change in magnitude of the lateral oscillatory stability derivatives in the higher angle-of-attack range. This effect was greatest for the 60 deg. delta wing and smallest for the unswept wing and generally resulted in a more linear variation of these derivatives with angle of attack. For the relatively high frequency at which the amplitude was varied, there appeared to be little effect on the measured derivatives as a result of the change in amplitude of the oscillation.
Relativistic electron and proton impact cross sections are obtained and represented by analytic forms which span the energy range from threshold to 1 GeV. For ionization processes, the Massey-Mohr continuum generalized oscillator strength surface is parameterized. Parameters are determined by simultaneous fitting to (1) empirical data, (2) the Bethe sum rule, and (3) doubly differential cross sections for ionization. Branching ratios for dissociation and predissociation from important states of N2 and O2 are determined. The efficiency for the production of atomic nitrogen and oxygen by protons with kinetic energy less than 1 GeV is determined using these branching ratio and cross section assignments.
Analysis of electron energy-loss data at incident electron energies of 40 and 60 eV has led to the determination of normalized absolute differential cross sections for electron-impact excitation of five optically-allowed singlet states, two known triplet states, and two unknown triplet-like states of N2, lying in the energy-loss range 12.5-14.2 eV. The range of scattering angles was 5 to 138 deg. The optically allowed transitions and the known triplet excitations are identified. Cross sections for excitation to two unidentified triplet-like states at 13.155 and 13.395 eV were also obtained. The relationship of the generalized oscillator strength for the dipole-allowed states obtained from the described data to known optical oscillator strengths is discussed.
The indicial method for calculating flutter derivatives for two-dimensional airfoils at transonic speeds is discussed, with particular attention given to the effect of a moving shock on the flow variables in the indicial method. An expression for the pressure coefficient is developed on the basis of an explicit treatment of the shock motion; the pressure distribution may then be calculated for general oscillations through use of the indicial method. Explicit inclusion of the shock motion is not necessary if only the lift and pitching moment coefficients are desired.
Electron impact excitation of the 2p 2P state of Li was studied at 10, 20, 60, 100, 150 and 200 eV. Relative differential cross sections in the angular range 3-120 deg were measured and then normalized to the absolute scale by using the optical f value. Integral and momentum transfer cross sections were obtained by extrapolating the differential cross sections to 0 deg and to 180 deg. The question of normalizing electron-metal-atom collision cross sections in general was examined and the method of normalization to optical f values in particular was investigated in detail. It has been concluded that the extrapolation of the apparent generalized oscillator strength (obtained from the measured differential cross sections) to the zero momentum transfer limit with an expression using even powers of the momentum transfer and normalization of the limit to the optical f value yields reliable absolute cross sections.
The effects of solar activity on stratospheric ozone were studied between 1970 and 1976 by the NIMBUS 4 backscattered ultraviolet experiment. Results show that, after correcting for instrument sensitivity, globally averaged ozone decreased by 3-4 percent above 2 mbar to less than 1 percent at 10 mbar, as solar activity decreased from solar maximum to solar minimum. This systematic ozone decrease (at all pressure levels) and the seemingly periodic oscillation (generally a 2 year period) seem to be associated with conventional indices of solar activity, which suggests a solar UV-ozone relationship. However, since the ozone depletion, especially at 40 km, is characteristic of atmospheric fluorocarbon injection effects, the solar cycle ozone relationship should be qualified: it may exist if the solar UV flux varies by 15-20 percent in the shorter-wavelength region (less than 200 nm).
A preliminary study of the electron-impact excitation of thermally evaporated coronene at 550 C was carried out using electron-energy-loss spectroscopy. Measurements of the energy-loss spectra of coronene at high (100 eV) and low (5-20 eV) impact energies are presented. One of the high-energy spectra was converted to an apparent generalized oscillator strength spectrum and compared to the photoabsorption spectrum of coronene. Observations concerning vibrational excitation of coronene by electron impact are also presented and discussed.
Equatorial oscillations in the zonal-mean temperatures and zonal winds have been well documented in Earth's middle atmosphere. A growing body of evidence from ground-based and Cassini spacecraft observations indicates that such phenomena also occur in the stratospheres of Jupiter and Saturn. Earth-based midinfrared measurements spanning several decades have established that the equatorial stratospheric temperatures on Jupiter vary with a cycle of 4-5 years and on Saturn with a cycle of approximately 15 years. Spectra obtained by the Composite Infrared Spectrometer (CIRS) during the Cassini swingby at the end of 2000, with much better vertical resolution than the ground-based data, indicated a series of vertically stacked warm and cold anomalics at Jupiter's equator; a similar structurc was seen at Saturn's equator in CIRS limb measurements made in 2005, in the early phase of Cassini's orbital tour. The thermal wind equation implied similar patterns of mean zonal winds increasing and decreasing with altitude. On Saturn the peak-to-pcak amplitude of this variation was nearly 200 meters per second. The alternating vertical pattern of wanner and colder cquatorial tcmperatures and easterly and westerly tendencies of the zonal winds is seen in Earth's equatorial oscillations, where the pattern descends with time, The Cassini Jupiter and early Saturn observations were snapshots within a limited time interval, and they did not show the temporal evolution of the spatial patterns. However, more recent Saturn observations by CIRS (2010) and Cassini radio-occultation soundings (2009-2010) have provided an opportunity to follow the change of the temperature-zonal wind pattern, and they suggest there is descent, at a rate of roughly one scale height over four years. On Earth, the observed descent in the zonal-mean structure is associated with the absorption of a combination of vertically propagating waves with easlerly and westerly phase velocities. The peak-to-peak zonal wind amplitude in the oscillation pattern and the rate of descent constrain the absorbed wave flux of zonal momentum. On Saturn this is approximately 0.05 square meters per square seconds, which is comparable to if not greater than that associated with the terrestrial oscillations. We discuss possible candidates for the absorbed waves on Saturn. On Earth the wave forcing of the equatorial oscillation generales secondary circulations that can affcct the temperature and wind structure at latitudes well away from the equator, and we discuss possible evidence of that on Saturn.
The attributes for the simulation of tropical intraseasonal oscillations in the 30 to 60 day range by three GCMs are compared with analyses of the European Center for Medium-Range Weather Forecasts. Models under consideration include the Goddard Laboratory of Atmospheric sciences (GLAS), Goddard Laboratory for Atmospheres (GLA), and UCLA GCMs. They are characterized by the same resolutions of four degrees latitude by five degrees longitude with 9 levels. Observations reveal that the eastward traveling planetary scale structure becomes more stationary over the Indonesian region and accelerates over the Central Pacific. In the tropics a Kelvin wave-type structure is found to be dominant near the center of the oscillation. The simulated winds are realistic although the meridional component is too strong, especially in the GLA GCM. The differences in the structure of the oscillation in the GLAS GCM and GLA GCM are considered to be a consequence of the different numerical schemes used. The GCMs are characterized by preferred zones for diabatic heating, with a turn-on heating occurring when the rising branch of the intraseasonal oscillation passes over these convective regions.