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On accuracy conditions for the numerical computation of waves

The Helmholtz equation (Delta + K(2)n(2))u = f with a variable index of refraction n, and a suitable radiation condition at infinity serves as a model for a wide variety of wave propagation problems. Such problems can be solved numerically by first truncating the given unbounded domain and imposing a suitable outgoing radiation condition on an artificial boundary and then solving the resulting problem on the bounded domain by direct discretization (for example, using a finite element method). In practical applications, the mesh size h and the wave number K, are not independent but are constrained by the accuracy of the desired computation. It will be shown that the number of points per wavelength, measured by (Kh)(-1), is not sufficient to determine the accuracy of a given discretization. For example, the quantity K(3)h(2) is shown to determine the accuracy in the L(2) norm for a second-order discretization method applied to several propagation models.

Bayliss, A.↗

On accuracy conditions for the numerical computation of waves

The Helmholtz equation (Delta + K(2)n(2))u = f with a variable index of refraction n, and a suitable radiation condition at infinity serves as a model for a wide variety of wave propagation problems. Such problems can be solved numerically by first truncating the given unbounded domain and imposing a suitable outgoing radiation condition on an artificial boundary and then solving the resulting problem on the bounded domain by direct discretization (for example, using a finite element method). In practical applications, the mesh size h and the wave number K, are not independent but are constrained by the accuracy of the desired computation. It will be shown that the number of points per wavelength, measured by (Kh)(-1), is not sufficient to determine the accuracy of a given discretization. For example, the quantity K(3)h(2) is shown to determine the accuracy in the L(2) norm for a second-order discretization method applied to several propagation models.

Bayliss, A.↗

Secondary Fragmentation of Comet Shoemaker-Levy 9 and the Ramifications for the Progenitor's Breakup in July 1992

Comprehensive analysis of discrete events of secondary fragmentation leads to a conceptually new understanding of the process of disintegration of comet Shoemaker-Levy 9. We submit that the jovian tidal forces inflicted extensive cracks throughout the interior of the original nucleus but did not split it apart. The initial disruption was apparently accomplished by stresses exerted on the cracked object by its fast rotation during the early post-perijove period of time. We argue that this disruption was in fact a rapid sequence of episodes during July 1992 that gave birth to the 12 on-train, or primary, fragments: A, C, D, E, G, H, K, L, Q (later Q(sub 1)), R, S, and W. The discrete events of secondary fragmentation, which gave birth to the off-train fragments, are understood in this scenario as stochastic manifestations of the continuing process of progressive disintegration. Of the 13 off-train fragments considered, nine were secondary--B, F, G(sub 2), M, N, P (later P(sub 2) or P(sub 2a)), Q(sub 2), U, and V--and four tertiary (J, P(sub 1), P(sub 2b), and T). The separation parameters of 11 off-train fragments were determined. The vectorial distribution of separation velocities of these fragments shows a strong concentration toward a great circle, unquestionably an effect of the approximately conserved angular momentum of the progenitor comet since the time of its initial disruption. Also apparent is their clumping (except for P(sub 1)) to a segment along the great circle, implying that the fragments were consistently released from one side of their parents, thus explaining for the first time why the off-train fragments preferentially appeared on one side of the nuclear train. In order to obtain a consistent solution, our model requires that the points of separation be on the antisolar side of the parent fragments, where thermal stresses are likely to enhance the effect of rotation. The episodes of secondary fragmentation are found to have nine months after the close encounter with Jupiter in early July 1992, and the separation velocities ranged between 0.36 and 1.7 m/s. The spin-axis position is determined to have been nearly in the jovicentric orbit plane, which rules out the Asphaug-Benz-Solem strengthless aggregate model as a plausible breakup hypothesis. Since the separation velocities are rotational in nature, they cannot substantially exceed the critical limit for centrifugal breakup and offer an estimate for the original nuclear dimensions. The comet's nucleus is found to have been approximately 10 km in diameter and spinning rapidly. With the exception of P(sub 1) and apparently also P(sub 2) and F, no nongravitational deceleration was detected in the motions of the off-train fragments. Serious doubts are cast on continuing appreciable activity of any of these fragments. Indeed, when it was necessary to introduce a deceleration into the equations of motion, the effect appears to have been due to the action of solar radiation pressure on the centroid of centimeter-sized particulates in the disintegrating condensations.

Sekanina, Z.↗

Continuum ionization transition probabilities of atomic oxygen

The technique of photoelectron spectroscopy was used to obtain the relative continuum transition probabilities of atomic oxygen at 584 A for transitions from 3P ground state into the 4S, D2, and P2 states of the ion. Transition probability ratios for the D2 and P2 states relative to the S4 state of the ion are 1.57 + or - 0.14 and 0.82 + or - 0.07, respectively. In addition, transitions from excited O2(a 1 Delta g) state into the O2(+)(2 Phi u and 2 Delta g) were observed. The adiabatic ionization potential of O2(+)(2 Delta g) was measured as 18.803 + or - 0.006 eV.

Samson, J. R.↗

Stellar content of the nuclei of elliptical galaxies determined from 2.3 micron CO band strengths

Observations of the luminosity sensitive CO absorption band at 2.3 micron are presented for the nuclei of 16 epsilon and SO galaxies. Preliminary data on the radial variation of the CO index in 6 galaxies are also given. The data show that the 2-u radiation from the nuclei is dominated by high luminosity stars of integrated spectral type later than K5. There is only a small variation in the CO absorption from galaxy to galaxy, and only a slight variation with measuring aperture size from 17.5 in. to 59 in. The data can be used to synthesize stellar populations for elliptical galaxy nuclei.

Frogel, J. A.↗

The numerical solution of the Helmholtz equation for wave propagation problems in underwater acoustics

The Helmholtz Equation (-delta-K(2)n(2))u=0 with a variable index of refraction, n, and a suitable radiation condition at infinity serves as a model for a wide variety of wave propagation problems. A numerical algorithm was developed and a computer code implemented that can effectively solve this equation in the intermediate frequency range. The equation is discretized using the finite element method, thus allowing for the modeling of complicated geometrices (including interfaces) and complicated boundary conditions. A global radiation boundary condition is imposed at the far field boundary that is exact for an arbitrary number of propagating modes. The resulting large, non-selfadjoint system of linear equations with indefinite symmetric part is solved using the preconditioned conjugate gradient method applied to the normal equations. A new preconditioner is developed based on the multigrid method. This preconditioner is vectorizable and is extremely effective over a wide range of frequencies provided the number of grid levels is reduced for large frequencies. A heuristic argument is given that indicates the superior convergence properties of this preconditioner.

Bayliss, A.↗

Radiometric Calibration Assessment of Commercial High Spatial Resolution Multispectral Image Products

This paper describes the results of commercial high spatial resolution sensors. The topics include: 1) Reflectance-based approach; 2) U of A test sites; 3) Test Site Selection; 4) Resort Living; 5) Aerosol parameters; 6) Surface reflectance retrieval; 7) Accuracy/precision; 8) Data sets; 9) June 23, 2005 for Ikonos; 10) QuickBird Results; 11) Ikonos results; 12) Orbview results; 13) Ikonos redux; and 14) Overall results.

Thome, Kurt↗

Predissociation linewidths in O2 B3Sigma-sub-u(-) (v = 0,2)

Results are presented of measurements of the rotational and fine-structure level-specific linewidths in v = 0 and v = 2 of the O2 B3Sigma-sub-u(-) state, which were carried out using laser-induced fluorescence techniques applied to Schumann-Runge absorption transitions from vibrationally excited O2 X3Sigma-sub-g(-) system. These linewidths represent the first measurements reflecting relative predissociation rates among the B-state levels. The linewidths were found to vary considerably among the various energy levels.

Cosby, P. C.↗

The doubly excited autoionizing states of H2

Neutral doubly excited states of H2 lie in the Franck-Condon region at energies beyound 23 eV above the ground state of H2. These repulsive resonance states may autoionize yielding H2(+) + e(-), H + H(+) + e(-) or dissociate to neutral ground and excited H atoms or H(+) + H(-). These processes are important in determining the thermal balance of interstellar clouds and the chemistry of the Jovian atmosphere. The present investigation is concerned with ab initio calculations of 24 autoionizing states of H2 which have mostly the 2 Sigma u + and first excited 2 Pi u states of H2(+) as the core orbital near R = 1. 4a(0). Of the 24 states reported, 14 have not appeared previously in the literature. For four of the remaining ten states an energy at only a single internuclear distance has been previously reported.

Guberman, S. L.↗

Evidence for Oscillating Two-Stream Instability and Spatial Collapse of Langmuir Waves in a Solar Type II Radio Burst

We present the high time resolution in situ observations of Langmuir waves, likely excited by an electron beam accelerated by a coronal-mass ejection-driven super-critical quasi-perpendicular interplanetary shock into its upstream solar wind, which happens to be the source region of a solar type II radio burst. We show that (1) these waves occur as coherent localized magnetic-field-aligned, one-dimensional wave packets with durations of a few milliseconds and with peak intensities well in excess of the threshold for strong turbulence processes, (2) they provide what is believed to be the first evidence for: (a) the oscillating two-stream instability (OTSI) L(sub 1) + L(sub 2) S/⟶ U + D, where L(sub 1) and L(sub 2), U and D, and S are the pump Langmuir waves, up- and down-shifted side bands, and ion sound waves, respectively, (b) a three-wave interaction U + D ⟶ T(sub 2f(sub pe)), where T(sub 2f(sub pe)) is the second harmonic electromagnetic wave, (3) they satisfy the threshold condition for formation of collapsing solitons, and (4) they are accompanied by their ponderomotive force induced density cavities with δn(sub p)/n(sub e) > δn(sub b)/n(sub e), where δn(sub p)/n(sub e) is the level of ponderomotive force induced density fluctuations and δn(sub b)/n(sub e) is that of the ambient fluctuations. These findings strongly suggest that the observed wave packets provide evidence for the collapsing solitons formed as a result of OTSI. The implication is that the strong turbulence processes probably play very important roles in excitation of type II radio emissions as well as in stabilization of shock-accelerated electron beams.

Sun radio radiation↗

Ocean Turbulence: Mesoscale Modeling in Isopycnal Coordinates the role of the Spectrum of Vertical Shear - Part 4

We study the tracer subgrid term in isopycnal coordinates, S(sub I). We employ two ingredients: the experimental data on vertical spectra of ocean turbulence measured by Gargett et al.(1981) and the stochastic approach recently developed by Dukowicz and Smith (1997). Our result confirms that S(sub I) is made of two parts: an advection and a diffusion term. However, the tracer bolus velocity u** consists of two terms u** = u(sub 1) + u(sub 2) while in the GM model there is only a term related to u(sub 1) which is shown to be: u(sub 1) = k(bar-q)(sup -1)(delta)(sub rho) where bar-q is the thickness weighted average potential vorticity, a result in agreement with the recent suggestions by Treguier et al. (1997), Lee et al. (1997) and Greatbatch (1998). The second component u(sub 2) IS new. We compute it in the geostrophic approximation using the Gargett et al. data (1981) on ocean vertical turbulence. We find that u(sub 2) much greater than u(sub 1) and that u(sub 2) is orthogonal to u(sub 1).

Canuto, V. M.↗

Studies of the chemistry of vibrationally and electronically excited species in planetary upper atmospheres

The vibrational distribution of O2(+) in the atmospheres of Venus and Mars was investigated to compare with analogous values in the Earth's atmosphere. The dipole moment of the Z(2) Pi sub u - X(2) Pi sub g transition of O2(+) is calculated as a function of internuclear distance. The band absorption oscillator strengths and band transition probabilities of the second negative system are derived. The vibrational distribution of O2(+) in the ionosphere of Venus is calculated for a model based on data from the Pioneer Venus neutral mass spectrometer.

Fox, J. L.↗

Analytic theory for the determination of velocity and stability of bubbles in a Hele-Shaw cell. Part 1: Velocity selection

An asymptotic theory is presented for the determination of velocity and linear stability of a steady symmetric bubble in a Hele-Shaw cell for small surface tension. In the first part, the bubble velocity U relative to the fluid velocity at infinity is determined for small surface tension T by determining transcendentally small correction to the asymptotic series solution. It is found that for any relative bubble velocity U in the interval (U(c),2), solutions exist at a countably infinite set of values of T (which has zero as its limit point) corresponding to the different branches of bubble solutions. U(c) decreases monotonically from 2 to 1 as the bubble area increases from 0 to infinity. However, for a bubble of arbitrarily given size, as T approaches 0, solution exists on any given branch with relative bubble velocity U satisfying the relation 2-U = cT to the 2/3 power, where c depends on the branch but is independent of the bubble area. The analytical evidence further suggests that there are no solutions for U greater than 2. These results are in agreement with earlier analytical results for a finger. In Part 2, an analytic theory is presented for the determination of the linear stability of the bubble in the limit of zero surface tension. Only the solution branch corresponding to the largest possible U for given surface tension is found to be stable, while all the others are unstable, in accordance with earlier numerical results.

Tanveer, Saleh↗

Development and analysis of prognostic equations for mesoscale kinetic energy and mesoscale (subgrid scale) fluxes for large-scale atmospheric models

Generated by landscape discontinuities (e.g., sea breezes) mesoscale circulation processes are not represented in large-scale atmospheric models (e.g., general circulation models), which have an inappropiate grid-scale resolution. With the assumption that atmospheric variables can be separated into large scale, mesoscale, and turbulent scale, a set of prognostic equations applicable in large-scale atmospheric models for momentum, temperature, moisture, and any other gaseous or aerosol material, which includes both mesoscale and turbulent fluxes is developed. Prognostic equations are also developed for these mesoscale fluxes, which indicate a closure problem and, therefore, require a parameterization. For this purpose, the mean mesoscale kinetic energy (MKE) per unit of mass is used, defined as E-tilde = 0.5 (the mean value of u'(sub i exp 2), where u'(sub i) represents the three Cartesian components of a mesoscale circulation (the angle bracket symbol is the grid-scale, horizontal averaging operator in the large-scale model, and a tilde indicates a corresponding large-scale mean value). A prognostic equation is developed for E-tilde, and an analysis of the different terms of this equation indicates that the mesoscale vertical heat flux, the mesoscale pressure correlation, and the interaction between turbulence and mesoscale perturbations are the major terms that affect the time tendency of E-tilde. A-state-of-the-art mesoscale atmospheric model is used to investigate the relationship between MKE, landscape discontinuities (as characterized by the spatial distribution of heat fluxes at the earth's surface), and mesoscale sensible and latent heat fluxes in the atmosphere. MKE is compared with turbulence kinetic energy to illustrate the importance of mesoscale processes as compared to turbulent processes. This analysis emphasizes the potential use of MKE to bridge between landscape discontinuities and mesoscale fluxes and, therefore, to parameterize mesoscale fluxes generated by such subgrid-scale landscape discontinuities in large-scale atmospheric models.

Avissar, Roni↗

Branching ratios in photoelectron spectroscopy.

Discussion of the problem of measuring branching ratios or transition probabilities using the technique of photoelectron spectroscopy in terms of the angular distribution of the ejected photoelectrons. Equations are developed that can be used in conjunction with any type of electron-energy analyzer to correct for any discrimination in the analyzer caused by electrons of varying angular distribution. Results are presented for the branching ratios of the A super 2 pi sub u and B super 2 sigma sub u (+) states of CO2(+) produced by 584 A and obtained by a variety of electron-energy analyzers.

Samson, J. A. R.↗

D1((2)B2g) to D0((2)Au) Fluorescence from the Matrix-Isolated Perylene Cation Following Laser Excitation into the D5(2)B3g) and D2 ((2)B3g) Electronic States

Fluorescence spectra of the perylene cation, pumped by direct laser excitation via the D(sub 2)((2)B(sub 3g)) (left arrow) D(sub 0)((2)A(sub u)) and D(sub 5)(2)B(sub 3g)) (left arrow) D(sub 0)((2)A(sub u)) transitions, are presented. Direct excitation into the D5 or D2 states is followed by rapid non-radiative relaxation to D1 that, in turn,relaxes radiatively. Excitation spectroscopy across the D(sub 2)((2)B(sub 3g)) (left arrow) D(sub 0)((2)A(sub u)) transition near 730 nm shows that site splitting plays little or no role in determining the spectral substructure in the ion spectra. Tentative assignments for ground state vibrational frequencies are made by comparison of spectral intervals with calculated normal mode frequencies.

Chillier, Xavier D. F.↗