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At least 181 records · Page 10

Theoretical studies of photoexcitation and ionization in H2O

Theoretical studies using Franck-Condon and static-exchange approximations are reported for the complete dipole excitation and ionization spectrum in H2O, where (1) large Cartesian Gaussian basis sets are used to represent the required discrete and continuum electronic eigenfunctions at the ground state equilibrium geometry, and (2) previously devised moment-theory techniques are employed in constructing the continuum oscillator-strength densities from the calculated spectra. Comparisons are made of the calculated excitation and ionization profiles with recent experimental photoabsorption studies and corresponding spectral assignments, electron impact-excitation cross sections, and dipole and synchrotron-radiation studies of partial-channel photoionization cross sections. The calculated partial-channel cross sections are found to be atomic-like, and dominated by 2p-kd components. It is suggested that the latter transition couples with the underlying 1b(1)-kb(1) channel, accounting for a prominent feature in recent synchrotron-radiation measurements.

Diercksen, G. H. F.↗

Integral dependent spin couplings in CI calculations

Although the number of ways to combine Slater determinants to form spin eigenfunctions increases rapidly with the number of open shells, most of these spin couplings will make only a small contribution to a given state, provided the spin coupling is chosen judiciously. The technique of limiting calculations to the interacting subspace pioneered by Bunge (1970) was employed by Munch and Davidson (1975) to the vanadium atom. The use of an interacting space looses its advantage in more complex cases. However, the problem can always be reduced to only one interacting spin coupling by making the coefficients integral dependent. The present investigation is concerned with the performance of integral dependent interacting couplings, taking into account the results of three test calculations.

Iberle, K.↗

Radiative lifetimes and dipole moments of the A 2Sigma/+/, B 2Sigma /+/, and C 2Sigma/+/ states of OH

After describing independent theoretical studies of the eigenfunctions of the X 2Pi and excited A 2Sigma(+), B 2Sigma(+), and C 2Sigma(+) states of OH, results are presented for the transition dipole moments connecting each excited state to the others and to the ground state. The radiative lifetimes derived from calculation of the bound-bound and bound-free vibrational band transition probabilities are compared with measured values, confirming recent measurements of the A 2Sigma(+) and C 2Sigma(+) states but not the lifetimes measured for the B 2Sigma(+) state.

Langhoff, S. R.↗

Stability of mean flows over an infinite flat plate

The present investigation is mainly concerned with a stability analysis for the linearized Navier-Stokes equations for parallel and nonparallel mean flows over an infinite flat plate. The system of equations for parallel flows is presented. The system is viewed as a generalized Orr-Sommerfeld equation. Attention is given to an explicit criterion characterizing the case when the stability of all physically reasonable solutions is determined by the eigenvalues. The proof given in the investigation is applicable to both the generalized Orr-Somerfeld equations and the modified equations for nonparallel flow. The fact that the criterion is independent of the completeness or incompleteness of eigenfunctions is contrary to some expectations.

Miklavcic, M.↗

Boundary-layer effects in composite laminates. I - Free-edge stress singularities. II - Free-edge stress solutions and basic characteristics

The fundamental nature of the boundary-layer effect in fiber-reinforced composite laminates is formulated in terms of the theory of anisotropic elasticity. The basic structure of the boundary-layer field solution is obtained by using Lekhnitskii's stress potentials (1963). The boundary-layer stress field is found to be singular at composite laminate edges, and the exact order or strength of the boundary layer stress singularity is determined using an eigenfunction expansion method. A complete solution to the boundary-layer problem is then derived, and the convergence and accuracy of the solution are analyzed, comparing results with existing approximate numerical solutions. The solution method is demonstrated for a symmetric graphite-epoxy composite.

Wang, S. S.↗

An approximation theory for nonlinear partial differential equations with applications to identification and control

Approximation results from linear semigroup theory are used to develop a general framework for convergence of approximation schemes in parameter estimation and optimal control problems for nonlinear partial differential equations. These ideas are used to establish theoretical convergence results for parameter identification using modal (eigenfunction) approximation techniques. Results from numerical investigations of these schemes for both hyperbolic and parabolic systems are given.

Banks, H. T.↗

The growth of the tearing mode - Boundary and scaling effects

A numerical model of resistive magnetic tearing is developed in order to verify and relate the results of the principal approximations used in analytic analyses and to investigate the solutions and their growth-rate scalings over a large range of primary parameters which include parametric values applicable to the solar atmosphere. The computations cover the linear behavior for a variety of boundary conditions, emphasizing effects which differentiate magnetic tearing in astrophysical situations from that in laboratory devices. Eigenfunction profiles for long and short wavelengths are computed and the applicability of the 'constant psi' approximation is investigated. The growth rate is computed for values of the magnetic Reynolds number up to a trillion and of the dimensionless wavelength parameter down to 0.001. The analysis predicts significant effects due to differing values of the magnetic Reynolds number.

Steinolfson, R. S.↗

The nonlocal theory of periodic density drift instabilities

The nonlocal theory of electrostatic density drift instabilities is developed for an arbitrary, periodic variation in plasma density. Linear Vlasov theory is applied to Fourier series representations of the plasma density, and the resulting equations are solved numerically. The growth rates of the universal drift instability are compared by using local and nonlocal theories. It is demonstrated that the local theory is inadequate if the nonlocal eigenfunctions of the electrostatic modes have significant amplitude over spatial regions wider than the regions of large plasma density gradients. Nonlocal effects can enhance wave-particle diffusion of a triangular-shaped variation and reduce wave-particle dissipation of a square-shaped irregularity.

Bernhardt, P. A.↗

MHD thermal instabilities in cool inhomogeneous atmospheres

The formation of a coronal state in a stellar atmosphere is investigated. A numerical code is used to study the effects of atmospheric gradients and finite loop dimension on the scale of unstable perturbations, solving for oscillatory perturbations as eigenfunctions of a boundary value problem. The atmosphere is considered as initially isothermal, with density and pressure having scale heights fixed by the hydrostatic equations. Joule mode instability is found to be an efficient mechanism for current filamentation and subsequent heating in initially cool atmospheres. This instability is mainly effective at the top of magnetic loops and is not suppressed by thermal conduction.

Bodo, G.↗

The growth, propagation and decay of global scale Rossby waves during FGGE

A portrait of the evolution of global scale Rossby waves for the FGGE year is presented. Emphasis is placed on the temporal evolution of the amplitude and phase of Hough mode projections, rather than on characteristics of the time spectra of these waves. On the basis of previous work, it was felt that it would be adequate to consider the 500 mb level in isolation from the others, and that the Hough functions (which are vector functions of the horizontal wind components and the height field) were good approximations to the "true' eigenfunctions. Thus, the first steps of the analysis consisted of projecting the 500 mb height and wind data (obtained from the ECMWF analyses) onto Hough functions for each synoptic time. The seasonal cycle and time mean were removed separately for each season, and all remaining eastward propagating components removed on a seasonal basis; all remaining westward propagating components were retained.

Lindzen, R. S.↗

The effects of Ohmic heating and stable radiation on magnetic tearing

A study is made of the effect of a temperature-dependent Coulomb-like resistivity on the planar tearing mode. The local evolution of the temperature is described by an energy equation which includes Joule heating and optically thin radiation. The resulting system of coupled linear magnetohydrodynamic equations is solved numerically, and eigenfunctions and growth rates are obtained. In the absence of radiation, there are two distinct solutions above a critical value of the magnetic Reynolds number S, a tearing-like mode and a Joule-heating mode. Below this point, the growth rates coalesce into a conjugate-complex pair. When stable radiation (dR/dT greater than 0) is added, the heating mode disappears and a modified tearing excitation exists to much lower values of S before its growth is cut off by Ohmic heating. Examples are given for solar coronal parameters, and for those characteristic of fusion-research devices. The introduction of an effective value for the resistivity, in the presence of energy transport, allows a simple qualitative discussion of the different modes.

Tachi, T.↗

Thermospheric gravity waves near the source - Comparison of variations in neutral temperature and vertical velocity at Sondre Stromfjord

Theoretical predictions of thermospheric gravity wave oscillations are compared with observed neutral temperatures and velocities. The data were taken in February 1983 using a Fabry-Perot interferometer located on Greenland, close to impulse heat sources in the auroral oval. The phenomenon was modeled in terms of linearized equations of motion of the atmosphere on a slowly rotating sphere. Legendre polynomials were used as eigenfunctions and the transfer function amplitude surface was characterized by maxima in the wavenumber frequency plane. Good agreement for predicted and observed velocities and temperatures was attained in the 250-300 km altitude. The amplitude of the vertical velocity, however, was not accurately predicted, nor was the temperature variability. The vertical velocity did exhibit maxima and minima in response to corresponding temperature changes.

Herrero, F. A.↗

MMIC devices for active phased array antennas

The study of printed circuit discontinuities is necessary in order to design, for example, transitions between rectangular waveguides and printed circuits. New developments with respect to the analytical approaches to this problem are discussed. A summary of the progress in the experimental approach is presented. The accurate solution for the modes in various millimeter-wave waveguides is essential in the analysis of many integrated circuit components, such as filters and impedance transformers. Problems associated with the numerical computation of these modes in two frequently used waveguide forms, namely, the finline and microstrip, are presented. The spectral domain method of formulation, with a moment method solution, is considered. This approach can be readily extended to analyze an arbitrary configuration of dielectric and metallized regions in a shielded enclosure. Galerkin's method is used, where the testing and basic functions are the same. It is shown that the mode functions, or eigenfunctions, are more sensitive to errors than the phase constants, or eigenvalues. The approximate mode functions do not satisfy the orthogonality relationship well, resulting in difficulties when these modal solutions are used to form an approximate Green's function or are used in a mode matching analysis.

Mittra, R.↗

Planar dynamics of a uniform beam with rigid bodies affixed to the ends

The planar dynamics of a uniform elastic beam subject to a variety of geometric and natural boundary conditions and external excitations were analyzed. The beams are inextensible and capable of small transverse bending deformations only. Classical beam vibration eigenvalue problems for a cantilever with tip mass, a cantilever with tip body and an unconstrained beam with rigid bodies at each are examined. The characteristic equations, eigenfunctions and orthogonality relations for each are derived. The forced vibration of a cantilever with tip body subject to base acceleration is analyzed. The exact solution of the governing nonhomogeneous partial differential equation with time dependent boundary conditions is presented and compared with a Rayleigh-Ritz approximate solution. The arbitrary planar motion of an elastic beam with rigid bodies at the ends is addressed. Equations of motion are derived for two modal expansions of the beam deflection. The motion equations are cast in a first order form suitable for numerical integration. Selected FORTRAN programs are provided.

Storch, J.↗

Transverse vibration and buckling of a cantilevered beam with tip body under constant axial base acceleration

The planar transverse bending behavior of a uniform cantilevered beam with rigid tip body subject to constant axial base acceleration was analyzed. The beam is inextensible and capable of small elastic transverse bending deformations only. Two classes of tip bodies are recognized: (1) mass centers located along the beam tip tangent line; and (2) mass centers with arbitrary offset towards the beam attachment point. The steady state response is studied for the beam end condition cases: free, tip mass, tip body with restricted mass center offset, and tip body with arbitrary mass center offset. The first three cases constitute classical Euler buckling problems, and the characteristic equation for the critical loads/accelerations are determined. For the last case a unique steady state solution exists. The free vibration response is examined for the two classes of tip body. The characteristic equation, eigenfunctions and their orthogonality properties are obtained for the case of restricted mass center offset. The vibration problem is nonhomogeneous for the case of arbitrary mass center offset. The exact solution is obtained as a sum of the steady state solution and a superposition of simple harmonic motions.

Storch, J.↗

A study of internal and distributed damping for vibrating turbomachiner blades

Internal and distributed damping as possible methods for reducing the vibration response of turbomachine blades and theoretical methods for analyzing damped vibration were studied. It is demonstrated how the Ritz-Galerkin methods may be used to straightforwardly to analyze forced vibrations with damping. This is done directly without requiring the free vibration eigenfunctions. The Galerkin method is an effective technique for these types of problems. The Ritz method has the further advantage of not needing to satisfy the force type boundary conditions, which is particularly important for plates and shells. But proper functionals representing the forcing and damping terms must be developed, and this is done. Two types of damping--viscous and material (hysteretic) are considered. Both distributed and concentrated exciting forces are treated. Numerical results are obtained for cantilevered beams and rectangular plates. Studies showing the rates of convergence of the solutions are made. In the case of the cantilever beam, approximate solutions from the present methods are compared with the exact solutions.

Leissa, A. W.↗

The Vertical Structure of Global Rotational Normal Modes

In a recent study, Lindzen et al. (1984) examined the amplitude and phase evolution of Hough mode projections at 500 mb. The Hough modes represent the simplest normal mode approximation available, and correspond to the neutral eigenfunctions of a shallow water fluid with no mean zonal flow. It was found that when the observed amplitude of a rotational Hough mode was large, it tended to propagate at the phase speed of a normal mode in the presence of mean 500 mb winds, giving a strong indication that normal modes are of relevance to the atmosphere. The vertical structure of the approximately defined rotational normal modes were explored by projecting observed data onto Hough functions at levels other than 500 mb. The stationary and eastward propagating components were filtered out at each level. The evolution of the amplitude in time throughout the troposphere is given for several modes during summer and winter.

Straus, D. M.↗

A numerical analysis of transient planetary waves and the vertical structure in a meso-strato-troposphere model, part 1.4A

The structure of unstable planetary waves is computed by a quasi-geostrophic model extending from the surface up to 80 km by means of eigenvalue-eigenfunction techniques in spherical coordinates. Three kinds of unstable modes of distinct phase speeds and vertical structures are identified in the winter climate state: (1) the deep Green mode with its maximum amplitude in the stratosphere; (2) the deep Charney mode with its maximum amplitude in the troposphere: and (3) the shallow Charney mode which is largely confined to the troposphere. Both the Green mode and the deep Charney mode are characterized by very slow phase speeds. They are mainly supported by upward wave energy fluxes, but the local baroclinic energy conversion within the stratosphere also contributes in supporting these deep modes. The mesosphere and the troposphere are dynamically independent in the summer season decoupled by the deep stratospheric easterly. The summer mesosphere supports the easterly unstable waves 1-4. Waves 3 and 4 are identified with the observed mesospheric 2-day wave and 1.7-day wave, respectively.

Zhang, K. S.↗