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Theoretical models of g-mode oscillations in white dwarfs are investigated analytically. Numerical results of period-spacing computations for DOV, DAV, and DBV models are presented in tables, and the relationships between period spacings and the composition and structure of the stellar atmospheres are discussed.
Recent work on a unified model of accretion flows and X-ray emission in low mass X-ray binaries is summarized. In this model, a weakly magnetic neutron star accretes gas simultaneously from a Keplerian disk and a corona above the inner part of the disk. Photons are produced and escape through an approximately radial inflow of gas captured from the inner disk corona. Changes in the optical depths of the central corona and the radial flow may explain the Z-shaped hardness-intensity and color-color tracks observed in the most luminous sources. Numerical simulations show that the radial flow oscillates when the luminosity rises to within a few percent of the Eddington critical luminosity L sub E, and that the oscillation frequency is approximately 5 to 10 Hz if the radial flow develops approximately 300 km from the neutron star. The 10 to 20 Hz oscillations observed in Sco X-1 when it is on the flaring branch are discussed.
The processes leading to tidal capture of stars by a massive black hole and the consequences of these processes in a dense stellar cluster are discussed in detail. When the amplitude of a tide and the subsequent oscillations are sufficiently large, the energy deposited in a star after periastron passage and formation of a bound orbit cannot be estimated directly using the linear theory of oscillations of a spherical star, but rather numerical estimates must be used. The evolution of a star after tidal capture is discussed. The maximum ratio R of the cross-section for tidal capture to that for tidal disruption is about 3 for real systems. For the case of a stellar system with an empty capture loss cone, even in the case when the impact parameter for tidal capture only slightly exceeds the impact parameter for direct tidal disruption, tidal capture would be much more important than tidal disruption.
Simulations of simple compressible flows have been performed to enable the direct estimation of the pressure-dilatation correlation. The generally accepted belief that this correlation may be important in high-speed flows has been verified by the simulations. The pressure-dilatation correlation is theoretically investigated by considering the equation for fluctuating pressure in an arbitrary compressible flow. This leads to the isolation of a component of the pressure-dilatation that exhibits temporal oscillations on a fast time scale. Direct numerical simulations of homogeneous shear turbulence and isotropic turbulence show that this fast component has a negligible contribution to the evolution of turbulent kinetic energy. Then, an analysis for the case of homogeneous turbulence is performed to obtain a formal solution for the nonoscillatory pressure-dilatation. Simplifications lead to a model that algebraically relates the pressure-dilatation to quantities traditionally obtained in incompressible turbulence closures. The model is validated by direct comparison with the simulations.
A technique is presented whereby the mutual interaction between a small number of elements in a planar array can be interpolated and extrapolated to accurately predict the combined interactions in a much larger array of many elements. An approximate series expression is developed, based upon knowledge of the analytical characteristic behavior of the mutual admittance between small aperture antenna elements in a conducting ground plane. This expression is utilized to analytically extend known values for a few spacings and orientations to other element configurations, thus eliminating the need to numerically integrate a large number of highly oscillating and slowly converging functions. This paper shows that the technique can predict very accurately the mutual coupling between elements in a very large planar array with a knowledge of the self-admittance of an isolated element and the coupling between only two-elements arranged in eight different pair combinations. These eight pair combinations do not necessarily have to correspond to pairs in the large array, although all of the individual elements must be identical.
A simple nonlinear model is proposed for the El Nino/Southern Oscillation (ENSO) phenomenon. Its key feature is the inclusion of oceanic wave transit effects through a negative, delayed feedback. A linear stability analysis and numerical results are presented, showing that the period of the oscillation is typically several times the delay. It is suggested that such an effect can account for the long time scale of ENSO.
The development of the resistive tearing instability in the case of sheared magnetic fields is considered, taking into account also the occurrence of a radiatively driven thermal instability. It is pointed out that thermal conduction has generally been neglected in theories similar to those discussed. The present investigation is concerned with a consideration of both parallel and perpendicular thermal conduction, in addition to finite resistivity and radiative loss. Attention is given to the equations and the model, the spatial singularity which arises with consideration of only the parallel heat conduction, the removal of this singularity and the formation of temperature oscillations (thermal ripples) by inclusion of the perpendicular heat-flux component, and details regarding the numerical procedure. A brief explanation is provided of the conditions required for the oscillations, and potential implications of the results with respect to the solar flare are discussed.
An analysis of the National Centers for Environmental Prediction (NCEP)/National Center for Atmospheric Research (NCAR) data is presented to provide a more complete description of the stratospheric 5-year semi-decadal (SD) oscillation (Mayr et al., 2007). The zonal-mean temperature and zonal wind data from the Atmospheric Research R-1 analysis are employed, covering the years from 1962 to 2002 in the altitude range from 10 to 30km. For diagnostic purposes, the data are separated into the hemispherically symmetric and anti-symmetric components, and spectral analysis is applied to identify the signatures of the SD oscillations. Through the synthesis or filtering of spectral features, the SD modulations of the annual oscillation (AO) and quasi-biennial oscillation (QBO) are delineated. In agreement with the earlier findings, the magnitude of the SD oscillation is more pronounced when the 30-month QBO dominates during the years from 1975 to 1995. This is consistent with results from a numerical model, which shows that such a QBO generates the SD oscillation through interaction with the 12-month AO. In the zonal winds, the SD oscillation in the NCEP data is confined to equatorial latitudes, where it modulates the symmetric AO and QBO by about 5 m/s below 30 km. In the temperature data, the effect is also seen around the equator, but it is much larger at polar latitudes where the SD oscillation produces variations as large as 2 K. Our data analysis indicates that the SD oscillation is mainly hemispherically symmetric, and it appears to originate at equatorial latitudes where most of the energy resides.
Details are given of a numerical solution of the integral equation which relates oscillatory or steady lift and downwash distributions in subsonic flow. The procedure has been programmed for the IBM 704 electronic data processing machine and yields the pressure distribution and some of its integrated properties for a given Mach number and frequency and for several modes of oscillation in from 3 to 4 minutes, results of several applications are presented.
It is pointed out that a finite difference grid which moves with the solution of the partial differential equation being solved can improve the accuracy and efficiency of a numerical algorithm. This technique is particularly advantageous in the solution of problems involving boundary layers or shocks where a poorly chosen grid may give a numerical solution which is useless because of poor resolution or extreme oscillations. The present investigation is concerned with the development of a scheme which does not excessively distort the grid. The grid generation algorithm is based on the numerical solution of a system of elliptic differential equations. Holst and Brown (1981) have used a preliminary solution to move points on the boundary of the physical region and then resolved the problem on a new grid generated by an elliptic system. In the current investigation, the grid movement and the solution will develop simultaneously. The solution is used to modify the generating equations, thereby controlling the grid point distributions.
Although eastward propagation has long been considered one of the essential features of the Madden-Julian waves, recent observations have revealed a stationary or quasi-stationary component in the oscillations, particularly in measures of the diabatic heating rate. Wave-CISK theories of the low-frequency oscillations have struggled to explain the observed period and vertical structure of the waves. On the other hand, theoretical and numerical studies have shown that low-frequency waves strongly resembling the observed oscillations can be excited by specified low-frequency oscillations of the convective heating. A problem with the latter set of theories is that the cause of the oscillatory heating has not been satisfactorily explained. It is proposed here that the observed low-frequency wave motions are the response to forcing by an essentially stationary, self-excited oscillating heat source that is produced by nonlinear interactions among radiation, cumulus convection, and the surface fluxes of sensible heat and moisture. Feedback of the large-scale motions on the latent heating is not required. Results from two very different one-dimensional models are presented to support this hypothesis. The physical processes included in the models are essentially the same, that is, radiation, cumulus convection, and the surface fluxes of sensible heat and moisture; the first model is highly simplified, however, while the second includes relatively sophisticated parameterizations of all the relevant physical processes. Results from both models show low-frequency oscillations of the latent heating, temperature, and moisture. Experiments show that the oscillations are favored by a warm sea surface and weak surface wind speeds, consistent with the observed conditions over the Indian Ocean and the tropical western Pacific Ocean.
The purpose of the research was to understand large-scale tracer transport processes in the stratosphere. Two approaches were taken. The first is analysis of tracer observations, especially satellite observations of ozone concentration and total column ozone. The second is numerical simulation of tracer transport processes. Topics researched include: quasi-biennial oscillation (QBO) and stratospheric ozone; mixing in the polar vortices; polar stratospheric clouds (PSC) properties from Antarctic lidar data; and statistical methods for numerical experiments.
Difficulties related to the application of the finite element method for numerical solution of the Navier-Stokes equation are discussed. The unsteady flow around a stationary and oscillating NACA 0012 airfoil was analyzed. In an effort to establish the range of applicability of the developed numerical method, the accuracy and stability problems in representing unsteady flow patterns and determining pressure distribution around the airfoil were investigated. Error involved in determining the velocity field and in the numerical integration of the discretized equations were analyzed in terms of geometry of the finite element gridwork, boundary conditions for stationary and oscillating airfoils, angles of attack and flow conditions.
High order accurate centered flux approximations used in the computation of numerical solutions to nonlinear partial differential equations produce large oscillations in regions of sharp transitions. Here, we present a new class of filtering methods denoted by Essentially Nonoscillatory Least Squares (ENOLS), which constructs an upgraded filtered solution that is close to the physically correct weak solution of the original evolution equation. Our method relies on the evaluation of a least squares polynomial approximation to oscillatory data using a set of points which is determined via the ENO network. Numerical results are given in one and two space dimensions for both scalar and systems of hyperbolic conservation laws. Computational running time, efficiency, and robustness of method are illustrated in various examples such as Riemann initial data for both Burgers' and Euler's equations of gas dynamics. In all standard cases, the filtered solution appears to converge numerically to the correct solution of the original problem. Some interesting results based on nonstandard central difference schemes, which exactly preserve entropy, and have been recently shown generally not to be weakly convergent to a solution of the conservation law, are also obtained using our filters.
A large amplitude, high-frequency electromagnetic oscillation is impressed on a nonrelativistic, collisionless plasma from an external source. The frequency is chosen to be far from the plasma frequency (in fact, lower). The resulting electron velocity distribution function strongly modifies the propagation of ion-acoustic waves parallel to the oscillating electric field. The complex frequency is calculated numerically.
The amplification of noise in a laser amplifier is treated theoretically. The model for the active medium and its description using density-matrix techniques, are taken from the theory of laser operation. The spectral behavior of the radiation in the nonlinear regime is studied and the formalism is written from the onset in the frequency domain. The statistics of the light are gradually modified by the nonlinear amplification process, and expressions are derived for the rate of change of fluctuations in intensity as a measure of statistical changes. In addition, the range of validity of Litvak's Gaussian-statistics approximation is discussed. In the homogeneous-broadening case, the evolution of initially broadband Gaussian radiation toward quasimonochromatic oscillations with laserlike statistics is explored in several numerical examples. The connections of this study with the time-domain work on self-pulsing in a ring-laser configuration, are established. Finally, spectral-narrowing and -rebroadening effects in Doppler-broadened media are discussed both analytically and with numerical examples. These examples show the distinct contribution of pulsations in the population ('Raman-type terms'), and saturation phenomena.
Charts showing the variation in dynamic stability with the rudder hinge-moment characteristics are presented. A stabilizing rudder floating tendency combined with a high degree of aerodynamic balance is shown to lead to oscillations of increasing amplitude. This dynamic instability is increased by viscous-friction in the rudder control system. The presence of solid friction in the rudder control system will cause steady oscillations of constant amplitude if the floating angle of the rudder per unit angle of sideslip is stabilizing and greater than a certain critical value that depends on other airplane parameters, such as vertical-tail area and airplane moment of inertia about the vertical axis. The amplitude of the steady oscillation is proportional to the amount of friction and is generally quite small but increases as the condition of dynamic instability is approached. An approximate method of calculating the amplitudes of the steady oscillation is explained and is illustrated by a numerical example. A more accurate step-by-step calculation of the motion is also made and it is shown that the agreement with the approximate method is good.
The first part of our research results are summarized in the recent journal publication: J. Gregory McDaniel and R. Glynn Holt, 'Measurement of aqueous foam rheology by acoustic levitation', Phys. Rev. E 61, 2204 (2000). This aspect of the work was a combination of experiment and analysis. We built a levitation system capable of acoustically levitating small samples of aqueous foam of arbitrary gas and liquid volume fractions. We then modulated the acoustic field to induce normal mode oscillations of the foam samples. The observables from the experiment were frequency and mode number. For dry (roughly > 70% gas by volume) foams and small deformations, we developed an effective medium, normal-modes analysis which took the frequency and mode number from experiment, and gave us the shear elastic modulus of the foam as a function of Poisson's ratio. The second part of our results may be found in a soon-to-be submitted manuscript 'Dynamics of aqueous foam drops', I.Sh. Akhatov, J.G. McDaniel and R.G. Holt, describing our modeling in the wet foam limit by considering the acoustic problem. This aspect of the research is purely theoretical. Beginning from a mass-conserving mixture law, the fully nonlinear equations of motion for a wet (roughly < 10% gas by volume) foam drop of initially spherical shape were derived. The frequencies for normal mode oscillations were derived in the linear inviscid limit. The nonlinear equations were numerically solved to elicit the motion of a foam drop under acoustic excitation. The role of the time-varying void fraction in breathing-mode oscillations is of particular interest. As of the end of the current (NAG#3-2121) grant, this work was not yet concluded. We continue to work on this aspect in order to extend the analysis to cover the transition regime of gas volume fractions, as well as to compare to experiments in the wet regime.