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The effects of a pulse shape on the transient response of a cylindrical shell are presented. Uniaxial, membrane, and bending theories for isotropic shells were used in this study. In addition to the results of the analytical study, the preliminary results of an experimental study into the generation and measurement of shear waves in a cylindrical shell are included.
A theory of spiky electric fields in 'inverted V' precipitation regions is elaborated and compared with recent spacecraft observations of solitary waves and double layers. A prediction from the theory is that the electric fields propagate along the magnetic field as perturbed ion acoustic solitons that intensify by exchanging momentum with reflected particles. The solitons have minimum scale lengths of approximately 100 m and maximum electric potential and field amplitudes of 1-10 V and 1-10 mV/m. They propagate at the local ion acoustic speed and are Doppler-shifted by the drift speed of upward flowing cold ions. Both rarefactive and compressive solitons with, respectively, negative and positive electric potentials are possible. It is noted that upward propagating compressive modes intensify when the upward flow of ionospheric ions exceeds approximately 10 times the local ion acoustic speed. The kinematic and dynamic properties of rarefactive solitons are found to be consistent with recent observations.
The method of parametric differentiation is shown to be an effective means to transform both the time-linearized and the fully nonlinear transonic small disturbance potential flow equations to a linear system of equations. The globally linearized equations are then solved in phase space by finite difference methods and integral equation methods. The predicted birth, growth, and motion of weak shock waves in two-dimensional transonic flows are compared with existing theory and experiment.
An error in a previous modified adiabatic approximation (Drachman, 1966), due to a lack of generality in the form of the short-range correlation part of the wave function for L greater than zero, is corrected heuristically by allowing the monopole suppression parameter to depend on L. An L-dependent local potential is constructed to fit the well-known positron-hydrogen s, p, and d wave phase shifts below the rearrangement threshold. The same form of potential yields a positron-helium cross-section in agreement with a recent experimental measurement near threshold.
The paper illustrates the use of continuum models in control design for stabilizing flexible structures. A 6-DOF anisotropic Timoshenko beam with discrete nodes where lumped masses or actuators are located provides a sufficiently rich model to be of interest for mathematical theory as well as practical application. We develop concepts and tools to help answer engineering questions without having to resort to ad hoc heuristic ("physical") arguments or faith. In this sense the paper is more mathematically oriented than engineering papers and vice versa at the same time. For instance we make precise time-domain solutions using the theory of semigroups of operators rather than formal "inverse Laplace transforms." We show that the modes arise as eigenvalues of the generator of the semigroup, which are then related to the eigenvalues of the stiffness operator. With the feedback control, the modes are no longer orthogonal and the question naturally arises as to whether there is still a modal expansion. Here we prove that the eigenfunctions yield a biorthogonal Riesz basis and indicate the corresponding expansion. We prove mathematically that the number of eigenvalues is nonfinite, based on the theory of zeros of entire functions. We make precise the notion of asymptotic modes and indicate how to calculate them. Although limited by space, we do consider the root locus problem and show for instance that the damping at first increases as the control gain increases but starts to decrease at a critical value, and goes to zero as the gain increases without bound. The undamped oscillatory modes remain oscillatory and the rigid-body modes go over into deadbeat modes. The Timoshenko model dynamics are translated into a canonical wave equation in a Hilbert space. The solution is shown to require the use of an "energy" norm which is no more than the total energy: potential plus kinetic. We show that, under an appropriate extension of the notion of controllability, rate feedback with a collocated sensor can stabilize the structure in the sense that all modes are damped and the energy decays to zero. An example, non-numeric, is worked out in some detail illustrating the concepts and theory developed.
The Braunbek method is applied to the generalized vector potential associated with the Maggi-rubinowicz representation. Under certain approximations, an asymptotic evaluation of the vector potential is obtained. For observation points away from caustics or shadow boundaries, the field derived from this quantity is the same as that determined from the geometrical theory of diffraction on a singly diffracted edge ray. An evaluation of the field for the simple case of a plane wave normally incident on a circular aperture is presented showing that the field predicted by the Maggi-Rubinowicz theory is continuous across the shadow boundary.
A semiclassical approximation to treat vibrationally inelastic scattering is developed. The vibrational basis set used is adiabatic with respect to a reference potential which is chosen to be as close as possible to the true potential and also gives easily obtainable solutions to the vibrational wave equation. The radial wave functions are obtained using the WKB approximation, and the coupled Schroedinger equations are solved by a first-order perturbation method to yield a phase shift matrix which is exponentiated to give the full scattering matrix. Results were obtained for all the cases computed by Secrest and Johnson and by Clark and Dickinson, and the agreement is better than 10% for half of the cross-sections and rarely off by more than a factor of 2.
A mechanism for the enhanced splitting detected in the millimeter-wave rotational spectra of the first excited S-S stretching state of HSSH (disulfane) has been studied. The mechanism, which involves a potential coupling between the first excited S-S stretching state and excited torsional states, has been investigated in part by the use of ab initio theory. Based on an ab initio potential surface, coupling matrix elements have been calculated, and the amount of splitting has then been estimated by second-order perturbation theory. The result, while not in quantitative agreement with the measured splitting, lends plausibility to the assumed mechanism.
This paper describes a new approach to the study of atom-diatom reactive collisions in three dimensions employing wave packets and the time-dependent Schroedinger equation. The method uses a projection operator approach to couple the inelastic and reactive portions of the total wave function and optical potentials to circumvent the necessity of using product arrangement coordinates. Reactive transition probabilities are calculated from the state resolved flux of the wave packet as it leaves the interaction region in the direction of the reactive arrangement channel. The present approach is used to obtain such vibrationally resolved probabilities for the three-dimensional H + H2 (J = 0) hydrogen exchange reaction, using a body-fixed system of coordinates.
Given here are hard polarization diffraction coefficients for the special case of a wedge that is coated with a lossy dielectric on one face and is perfectly conducting on the other face. Expressions for plane-wave incidence, far-field observation; for cylindrical-wave incidence, far-field observation; and for plane-wave incidence, near-field observation are presented for regular diffractions. In addition, terms for surface-wave and surface-wave transition fields are presented. These expressions are derived from the Uniform Theory of Diffraction (UTD) coefficients for a generalized impedance wedge and are simplified for rapid calculation for the case of one perfectly conducting face. Results from a first-order model for a coated, rectangular plate are examined; and potential problems in extending this modeling approach to more complicated coated structures are identified.
Tsunamis generated by the impacts of asteroids and comets into the Earth oceans are widely recognized as a potential catastrophic hazard to the Earth s population. Our general conclusion is that linear theory is a reasonably accurate guide to behavior of tsunamis generated by impactors of moderate size, where the initial transient impact cavity is of moderate depth compared to the ocean depth. This is particularly the case for long wavelength waves that propagate fastest and would reach coastlines first. Such tsunamis would be generated in the open ocean by impactors of 300 meters in diameter, which might be expected to strike the Earth once every few thousand years, on the average. Larger impactors produce cavities deep enough to reach the ocean floor; even here, linear theory is applicable if the starting point is chosen at a later phase in the calculation when the impact crater has slumped back to produce a cavity of moderate depth and slope.
The ZEUS long-range VLF arrival time difference lightning detection network now covers both Europe and Africa, and there are plans for further expansion into the western hemisphere. In order to fully optimize and assess ZEUS lightning location retrieval errors and to determine the best placement of future receivers expected to be added to the network, a software package is being developed jointly between the NASA Marshall Space Flight Center (MSFC) and the University of Nevada Las Vegas (UNLV). The software package, called the ZEUS Error Analysis for Lightning (ZEAL), will be used to obtain global scale lightning location retrieval error maps using both a Monte Carlo approach and chi-squared curvature matrix theory. At the core of ZEAL will be an implementation of an Iterative Oblate (IO) lightning location retrieval method recently developed at MSFC. The IO method will be appropriately modified to account for variable wave propagation speed, and the new retrieval results will be compared with the current ZEUS retrieval algorithm to assess potential improvements. In this preliminary ZEAL work effort, we defined 5000 source locations evenly distributed across the Earth. We then used the existing (as well as potential future ZEUS sites) to simulate arrival time data between source and ZEUS site. A total of 100 sources were considered at each of the 5000 locations, and timing errors were selected from a normal distribution having a mean of 0 seconds and a standard deviation of 20 microseconds. This simulated "noisy" dataset was analyzed using the IO algorithm to estimate source locations. The exact locations were compared with the retrieved locations, and the results are summarized via several color-coded "error maps."
Both incompressible and compressible linear stability theory are applied to the three-dimensional compressible boundary layer on a particular transonic sweptback wing of infinite span. A spatial stability theory is used which identifies the growth direction with the real part of the complex angle of the group velocity. It is found that in the forward, but not the rear, crossflow instability region, the maximum amplification rates of the steady disturbances may be calculated to within about 10% by the incompressible stability theory. There is little difference between the sixth and eighth-order compressible theories. The maximum amplification rate of the steady disturbances at any chordwise station is closely related to the maximum crossflow at that station independent of the Reynolds number. For other than crossflow instability, there can be large differences between the incompressible and compressible theories, both as to the amplification rate and the angle of the wavenumber vector for maximum instability. Amplitude ratios of individual wave components are obtained by integrating the spatial amplification rate along the growth direction subject to the constraint that the wavenumber vector is irrotational. This procedure yields steady disturbances aligned with the local potential flow direction whose wavelengths are nearly independent of downstream distance.
A three-dimensional numerical cloud model was developed for the general purpose of studying convective phenomena. The model utilizes a time splitting integration procedure in the numerical solution of the compressible nonhydrostatic primitive equations. Turbulence closure is achieved by a conventional first-order diagnostic approximation. Open lateral boundaries are incorporated which minimize wave reflection and which do not induce domain-wide mass trends. Microphysical processes are governed by prognostic equations for potential temperature water vapor, cloud droplets, ice crystals, rain, snow, and hail. Microphysical interactions are computed by numerous Orville-type parameterizations. A diagnostic surface boundary layer is parameterized assuming Monin-Obukhov similarity theory. The governing equation set is approximated on a staggered three-dimensional grid with quadratic-conservative central space differencing. Time differencing is approximated by the second-order Adams-Bashforth method. The vertical grid spacing may be either linear or stretched. The model domain may translate along with a convective cell, even at variable speeds.
The phenomena of dissipative destabilization of external Rossby waves and the acceleration of the zonal mean jet during baroclinic life cycles are described in terms of potential vorticity. The main principle of the potential temperature variations at rigid boundaries have the same effect on the interior flow as do sheets of potential vorticity located just within the boundaries. It is noted that the potential vorticity theory is useful for understanding the dynamical behavior of meterological phenomena.
The effect of topography as a source of mesoscale variability was investigated using aircraft measurements of winds and temperature collected during the Global Atmospheric Sampling Program, with results showing marked increases in the variance of zonal and meridional wind speeds and of potential temperature over rough terrain. In addition, four cases of mesoscale variance enhancements of horizontal velocity and temperature due to frontal activity, nonfrontal convection, and wind shear were studied. The implications of these episodic enhancements of variances for the vertical transports of energy and momentum are considered in the framework of the gravity wave theory.
Experimental and theoretical work on describing the propagation of sferics (electromagnetic waves) in the stratosphere is reviewed. Measurements are made with a double Langmuir probe that measures the potential difference between two identical, separated conductors, thereby permitting calculation of the electric field. The probe is usually mounted on a balloon floated up to the stratosphere. Data are presented that were taken over a thunderstorm and a theory of sferic propagation is developed, including defined relationships among the source, the propagation medium, and the detected signal. It is demonstrated that the signals recorded by the balloon instrumentation can be used to define the upper limit of the current density and total current in the stratosphere when a sferic is propagating.
The motion of a nonuniform flow about a row of moving blades is modeled as that of a three-dimensional rotational disturbance convected by the mean flow. The aerodynamic theories for such flows are reviewed for both linearly propagating disturbances and disturbances distorted by the mean flow. Linear theories results are examined to assess the effects of the gust variables, the Mach number, and the blade spacing, on the unsteady blade response. For loaded blades, the upstream disturbances are distorted by the blade mean flow. For a potential mean flow, the governing equations can be reduced to a single inhomogeneous nonconstant coefficient convective wave equation. A numerical procedure is developed using an elliptic grid system. The accuracy of the solutions strongly depends on the far-field radiation condition and the optimum determination of the grid system. Solutions are presently obtained for thick symmetric airfoils in three-dimensional gusts.