Applications of time-dependent perturbation theory.
Atomic and molecular time-dependent quantum- mechanical perturbation theory with differential equation formulation within Hartree-Fock approximation
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Results for “perturbation analysis”
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Reanalysis information for eigenvalues derived from a differential equation analysis formulation
The investigation reported demonstrates that in the case considered perturbation methods can be used in a straightforward manner to obtain reanalysis information. A perturbation formula for the buckling loads of a general shell of revolution is derived. The accuracy of the obtained relations and their range of application is studied with the aid of a specific example involving a particular stiffened shell of revolution.
Thornton, W. A.↗
The radiation pressure-driven Rayleigh-Taylor instability - Analysis and application to QSO emission line clouds
The growth of perturbations in a photoionized gas slab accelerated by radiation pressure under conditions like those in QSO emission-line regions is analyzed. A linear dispersion relation is derived, and numerical radiation-transfer calculations are performed to evaluate the coefficients and roots of that dispersion relation for L-alpha optical depths between 0.1 and 10,000. The nonlinear growth of the waves is estimated, and it is concluded that complete dispersal of the clouds is likely. On the basis of qualitative arguments it is suggested that clouds of greater optical depth are linearly stable.
Krolik, J. H.↗
Absolute barotropic instability and monsoon depressions
Monsoon depressions over the Bay of Bengal develop almost entirely in July and August. After studies conducted by Lindzen et al. (1980) and Stevens and Lindzen (1978), only barotropic instability remains as a mechanism for the development of the wave disturbances associated with monsoon depressions. The present investigation has the objective to show that barotropic instability is able to explain the wave aspects of monsoon depressions, but that normal mode analysis is inadequate. It is found that the local barotropically unstable response to regional perturbations in the Bay of Bengal during July and August will be dominated by the lower troposphere. The analysis clearly identifies the features of the mean flow which lead to monsoon depressions in July. The features include the development of an easterly jet as opposed to semijet structure in the mean flow, and the development of a modest easterly flow at the jet center as opposed to westerly flow.
Lindzen, R. S.↗
Sensitivity of a Cloud-Resolving Model to the Bulk and Explicit Bin Microphysical Schemes
A cloud-resolving model is used to study sensitivities of two different microphysical schemes, one is the bulk type, and the other is an explicit bin scheme, in simulating a mid-latitude squall line case. Simulations using different microphysical schemes are compared with each other and also with the observations. Both the bulk and bin models reproduce the general features during the developing and mature stage of the system. The leading convective zone, the trailing stratiform region, the horizontal wind flow patterns, pressure perturbation associated with the storm dynamics, and the cool pool in front of the system all agree well with the observations. Both the observations and the bulk scheme simulation serve as validations for the newly incorporated bin scheme. However, it is also shown that the bulk and bin simulations have distinct differences, most notably in the stratiform region. Weak convective cells exist in the stratiform region in the bulk simulation, but not in the bin simulation. These weak convective cells in the stratiform region are remnants of the previous stronger convections at the leading edge of the system. The bin simulation, on the other hand, has a horizontally homogeneous stratiform rain structure, which agrees better with the observations. Further analysis of the downdraft core strength, the potential temperature perturbation, and the evaporative cooling rate shows that the differences between the bulk and bin models are due mainly to the stronger low-level evaporative cooling simulated in the bulk model. Further quantitative analysis and sensitivity tests for this case using both the bulk and bin models will be presented in the talk.
Tao, Wei-Kuo↗
Probabilistic design analysis using Composite Loads Spectra (CLS) coupled with Probabilistic Structural Analysis Methodologies (PSAM)
Composite loads spectra (CLS) were applied to generate probabilistic loads for use in the PSAM nonlinear evaluation of stochastic structures under stress (NESSUS) finite element code. The CLS approach allows for quantifying loads as mean values and distributions around a central value rather than maximum or enveloped values typically used in deterministic analysis. NESSUS uses these loads to determine mean and perturbation responses. These results are probabilistically evaluated with the distributional information from CLS using a fast probabilistic integration (FPI) technique to define response distributions. The main example discussed describes a method of obtaining load descriptions and stress response of the second-stage turbine blade of the Space Shuttle Main Engine (SSME) high-pressure fuel turbopump (HPFTP). Additional information is presented on the on-going analysis of the high pressure oxidizer turbopump discharge duct (HPOTP) where probabilistic dynamic loads have been generated and are in the process of being used for dynamic analysis. Example comparisons of load analysis and engine data are furnished for partial verification and/or justification for the methodology.
Newell, J. F.↗
Amplitude and polarization asymmetries in a ring laser
Asymmetric amplitude effects between the oppositely directed traveling waves in a He-Ne ring laser are analyzed both theoretically and experimentally. These effects make it possible to detect angular orientations of an inner-cavity bar with respect to the plane of the ring cavity. The amplitude asymmetries occur when a birefringent bar is placed in the three-mirror ring cavity, and an axial magnetic field is applied to the active medium. A simplified theoretical analysis is performed by using a first order perturbation theory to derive an expression for the polarization of the active medium, and a set of self-consistent equations are derived to predict threshold conditions. Polarization asymmetries between the oppositely directed waves are also predicted. Amplitude asymmetries similar in nature to those predicted at threshold occur when the laser is operating in 12-15 free-running modes, and polarization asymmetry occurs simultaneously.
Campbell, L. L.↗
Attitude control of a spinning Skylab.
Active attitude control of a spinning Skylab is analyzed to determine a simple control law that will provide a satisfactory response, considering the dynamics of attached flexible appendages. A simplified model of the complex Skylab vehicle is selected to make it analytically tractable. The vehicle is modeled as a single rigid-core body with two attached flexible massless booms having masses on their tips. The equations of motion describing the attitude dynamics of the model are presented as a linear matrix-differential equation. The states of the vehicle are small perturbations about its steady-state spin. An analysis is performed to determine the domain of stability. Next, attitude dynamics are analyzed; both frequency domain (parameter plane) and time domain (an optimal linear quadratic loss program) techniques are compared. An analysis of the nonlinear effect of control torque saturation of Skylab's control moment gyroscopes is discussed. The results of the analysis compare favorably with a large-scale digital simulation of the Skylab.
Seltzer, S. M.↗
Attitude control of a spinning flexible spacecraft
The dynamics of rotational motion of a spinning orbiting spacecraft consisting of two rigid bodies connected by a flexible joint and arbitrary number of flexible appendages (two of which are flexible massless booms having masses on their tips) is analyzed. Active attitude control is provided by momentum exchange devices (e.g. control moment gyroscopes) or a mass expulsion system. The linearized equations of motion describing the vehicle are presented, and a large scale digital simulation that has been developed at the Marshall Space Flight Center is presented. A simplified model of the geometrically complex vehicle is selected to make it analytically tractable. The simplified model consists of a single rigid core body with two attached flexible massless booms having tip masses. The states of the vehicle are defined as small perturbations about its steady-state spin. An analysis is performed to determine the domain of stability.
Seltzer, S. M.↗
Nonlinear Equations of Motion for Cantilever Rotor Blades in Hover with Pitch Link Flexibility, Twist, Precone, Droop, Sweep, Torque Offset, and Blade Root Offset
Nonlinear equations of motion for a cantilever rotor blade are derived for the hovering flight condition. The blade is assumed to have twist, precone, droop, sweep, torque offset and blade root offset, and the elastic axis and the axes of center of mass, tension, and aerodynamic center coincident at the quarter chord. The blade is cantilevered in bending, but has a torsional root spring to simulate pitch link flexibility. Aerodynamic forces acting on the blade are derived from strip theory based on quasi-steady two-dimensional airfoil theory. The equations are hybrid, consisting of one integro-differential equation for root torsion and three integro-partial differential equations for flatwise and chordwise bending and elastic torsion. The equations are specialized for a uniform blade and reduced to nonlinear ordinary differential equations by Galerkin's method. They are linearized for small perturbation motions about the equilibrium operating condition. Modal analysis leads to formulation of a standard eigenvalue problem where the elements of the stability matrix depend on the solution of the equilibrium equations. Two different forms of the root torsion equation are derived that yield virtually identical numerical results. This provides a reasonable check for the accuracy of the equations.
Hodges, D. H.↗
Laser-enhanced dynamics in molecular rate processes
The present discussion deals with some theoretical aspects associated with the description of molecular rate processes in the presence of intense laser radiation, where the radiation actually interacts with the molecular dynamics. Whereas for weak and even moderately intense radiation, the absorption and stimulated emission of photons by a molecular system can be described by perturbative methods, for intense radiation, perturbation theory is usually not adequate. Limiting the analysis to the gas phase, an attempt is made to describe nonperturbative approaches applicable to the description of such processes (in the presence of intense laser radiation) as electronic energy transfer in molecular (in particular atom-atom) collisions; collision-induced ionization and emission; and unimolecular dissociation.
George, T. F.↗
Inlet flow distortion in turbomachinery - Comparison of theory and experiment in a transonic fan stage
Consideration is given to both velocity and temperature circumferential inlet distortions at upstream infinity (Seidel et al., 1980). The blade rows here are modeled as semiactuator disks, and losses and quasi-steady deviation angle correlations are included in the analysis. The governing equations are linearized, and the perturbations in stagnation pressure and stagnation temperature at upstream infinity are represented as Fourier series. The flow in the rotor is modeled as inviscid, one-dimensional, unsteady, and compressible. the flow is steady elsewhere. The deviation angles for the rotor and stator are taken to be functions of the relative inlet angle and Mach number, and use is made of the correlations contained in Johnson and Bullock (1965). It is assumed that the losses in relative stagnation pressure in the rotor and stator occur across the trailing edge. Boundary conditions applied at the various stations furnish the equations that make it possible to solve for the several quantities introduced in the linearization of the governing equations.
Seidel, B. S.↗
Transonic calculations for a flexible supercritical wing and comparison with experiment
Pressure data measured on the flexible DAST ARW-2 wing are compared with results calculated using the transonic small perturbation code XTRAN3S. A brief description of the analysis is given and a recently-developed grid coordinate transformation is described. Calculations are presented for the rigid and flexible wing for Mach numbers from 0.60 to 0.90 and dynamic pressures from 0 to 1000 psf. Calculated and measured static pressures and wing deflections are compared, and calculated static aeroelastic trends are given. Attempts to calculate the transonic instability boundary of the wing are described.
Bennett, R. M.↗
Calculation of transonic steady and oscillatory pressures on a low aspect ratio model and comparison with experiment
Pressure data measured by the British Royal Aircraft Establishment for the AGARD SMP tailplane are compared with results calculated using the transonic small perturbation code XTRAN3S. A brief description of the analysis is given and a recently developed finite difference grid is described. Results are presented for five steady and nine harmonically oscillating cases near zero angle of attack and for a range of subsonic and transonic Mach numbers.
Bennett, R. M.↗
Transonic calculations for a flexible supercritical wing and comparison with experiment
Pressure data measured on the flexible DAST ARW-2 wing are compared with results calculated using the transonic small perturbation code XTRAN3S. A brief description of the analysis is given and a recently developed grid coordinate transformation is described. Calculations are presented for the rigid and flexible wing for Mach numbers from 0.60 to 0.90 and dynamic pressures from 0 to 1000 psf. Calculated and measured static pressures and wing deflections are compared, and calculated static aeroelastic trends are given. Attempts to calculate the transonic instability boundary of the wing are described.
Bennett, R. M.↗
Calculation of transonic steady and oscillatory pressures on a low aspect ratio model and comparison with experiment
Pressure data measured by the British Royal Aircraft Establishment for the AGARD SMP tailplane are compared with results calculated using the transonic small perturbation code XTRAN3S. A brief description of the analysis is given and a recently developed finite difference grid is described. Results are presented for five steady and nine harmonically oscillating cases near zero angle of attack and for a range of subsonic and transonic Mach numbers.
Bennett, R. M.↗
Nonlinear mechanisms in physiology and pathophysiology Toward a dynamical theory of health and disease
The application of nonlinear analysis both to normal physiological dynamics and pathophysiological perturbations in a variety of different systems leads to observations not predicted by traditional models. Such analyses may have important implications for diagnostic and prognostic assessment as well as for therapeutics.
Goldberger, A. L.↗
The relationship of satellite-inferred stratospheric aerosol extinction to the position of the 50-mb north polar jet stream
The relationship between stratospheric aerosols and the location of the north polar night stratospheric jet stream was investigated for selected periods of four successive winters (1979-1982), using measurements from SAM II (Stratospheric Aerosol Measurement II) and SAGE I (Stratospheric Aerosol and Gas Experiment I) satellite-borne sun photometers and corresponding meteorological observations. Each period investigated included a polar stratospheric warming during which major dynamic meteorological changes are known to have perturbed the structure of the polar vortex. The analysis of variations in aerosol extinction mixing ratio patterns among winters and during major stratospheric warming events within separate winters showed a well-defined positive gradient in extinction mixing ratio and temperature across the jet stream from the cyclonic side to the anticyclonic side at altitudes between 20 and 30 km during each winter period. Estimates of extinction mixing ratio profiles measured near the center of the polar vortex suggest that a gradual subsidence took place within the polar vortex during at least three of the four winter periods.
Livingston, John M.↗