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DOE OSTI2020

Normal modes in thermal AdS via the Selberg zeta function

The heat kernel and quasinormal mode methods of computing 1-loop partition functions of spin s s fields on hyperbolic quotient spacetimes \mathbb{H}^{3}/\mathbb{Z} ℍ 3 / ℤ are related via the Selberg zeta function. We extend that analysis to thermal \text{AdS}_{2n+1} AdS 2 n + 1 backgrounds, with quotient structure \mathbb{H}^{2n+1}/\mathbb{Z} ℍ 2 n + 1 / ℤ . Specifically, we demonstrate the zeros of the Selberg function encode the normal mode frequencies of spin fields upon removal of non-square-integrable modes. With this information we construct the 1-loop partition functions for symmetric transverse traceless tensors in terms of the Selberg zeta function and find exact agreement with the heat kernel method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1982

Normal modes of a compound drop

The modes are characterized by their frequency, the attendant displacement of fluid boundaries, and the flow pressure fields within the fluids. The drops consist of three fluids; a core fluid, a fluid shell surrounding the core, and a host fluid surrounding the shell. These fluids are assumed to be inviscid and incompressible, and the core and the shell to be concentric. The theory is obtained by linearization of the equations of fluid motion to the lowest order of nonlinearity that yields the normal modes. Numerical values of mode frequencies and the associated relative displacements of the fluid boundaries are presented for several specific systems, and the results compared with observations.

Saffren, M.↗
NASA NTRS1976

Accretion onto magnetized neutron stars - Normal mode analysis of the interchange instability at the magnetopause

Results are reported for a linearized hydromagnetic stability analysis of the magnetopause of an accreting neutron star. The magnetosphere is assumed to be slowly rotating, and the plasma just outside the magnetopause is assumed to be weakly magnetized. The plasma layer is assumed to be bounded above by a shock wave and to be thin compared with the radius of the magnetosphere. Under these circumstances, the growing modes are shown to be localized in the direction parallel to the zero-order magnetic field, but the structure of the modes is still similar to the flute mode. An expression for the growth rate at each magnetic latitude is obtained in terms of the magnitude of the gravitational acceleration normal to the surface, the azimuthal mode number, the radius of the magnetosphere, the height of the shock above the magnetopause, and the effective Atwood number which embodies the stabilizing effects of favorable curvature and magnetic tension. The effective Atwood number is calculated, and the stabilizing effects of viscosity and aligned flow parallel to the magnetopause are discussed.

Arons, J.↗
NASA NTRS1994

Substorm recurrence during steady and variable solar wind driving: Evidence for a normal mode in the unloading dynamics of the magnetosphere

Farrugia et al (1993) have recently studied substorm activity driven by the passage of an interplanetary magnetic cloud during which the interplanetary magnetic field turned southward for approximately 18 hours. It was shown that both the epsilon and the VB(sub s) parameters varied slowly on the timescale of a substorm but changed considerably over the interval as a whole. The substorm occurrence rate did not reflect the variation in magnetospheric energy loading rate as measured by these parameters but, rather, remained roughly constant with a 50-min average period. Klimas et al. (1992) showed that the Faraday loop analog model of geomagnetic activity predicts this single unloading rate under various constant loading rates. However, various model parameters were adjusted to yield a 1-hour unloading period in agreement with the Bargatze et al. (1985) linear prediction filters and in approximate agreement with the Farrugia et al. (1993) results. It has since been found necessary to add a slow relaxation mechanism to the Faraday loop model to allow for its approach to a ground state during long periods of inactivity. It is proposed that the relaxation mechanism is provided by slow convection of magnetic flux out of the magnetotail to the dayside magnetosphere. In addition, a rudimentary representation of magnetotail-ionosphere coupling has been added to enable comparison of model output to measured AL. The present study is of the modified Faraday loop model response to solar wind input from the Bargatze et al. data set with comparison of its output to concurrent AL. This study has removed the degree of freedom in parameter choice that had earlier allowed adjustments toward the 1-hour unloading period and has, instead, yielded the 1-hour unloading period under various constant loading rates. It is demonstrated that the second peak of the bimodal Bargatze et al. linear prediction filters at approximately equal 1-hour lag and the approximately constant substorm recurrence rate observed by Farrugia et al. can be interpreted as both being due to the existence of a normal unloading recurrence period in the dynamics of the magnetosphere.

Klimas, A. J.↗
NASA NTRS1971

Skin-stringer panel normal mode response experimental data and finite element computer program documentation

Detailed information is presented for the analytical and the experimental programs described in the report on Effects of Design Details on Structural Response to Acoustic Excitation, NASA CR-1959. This is a supplement to the basic report and detailed experimental data from all the specimens described in that report are discussed and presented in tabular form.

Rudder, F. F., Jr.↗
NASA NTRS1975

Effect of damping on excitability of high-order normal modes

The effect of localized structural damping on the excitability of higher-order large space telescope spacecraft modes is investigated. A preprocessor computer program is developed to incorporate Voigt structural joint damping models in a finite-element dynamic model. A postprocessor computer program is developed to select critical modes for low-frequency attitude control problems and for higher-frequency fine-stabilization problems. The selection is accomplished by ranking the flexible modes based on coefficients for rate gyro, position gyro, and optical sensor, and on image-plane motions due to sinusoidal or random PSD force and torque inputs.

Merchant, D. H.↗
NASA NTRS1977

Drive Train Normal Modes Analysis for the ERDA/NASA 100-Kilowatt Wind Turbine Generator

Natural frequencies, as a function of power were determined using a finite element model. Operating conditions investigated were operation with a resistive electrical load and operation synchronized to an electrical utility grid. The influence of certain drive train components on frequencies and mode shapes is shown. An approximate method for obtaining drive train natural frequencies is presented.

Sullivan, T. L.↗
NASA NTRS1984

Empirical orthogonal functions and normal modes

An attempt to provide physical insight into the empirical orthogonal function (EOF) representation of data fields by the study of fields generated by linear stochastic models is presented in this paper. In a large class of these models, the EOFs at individual Fourier frequencies coincide with the orthogonal mechanical modes of the system - provided they exist. The precise mathematical criteria for this coincidence are derived and a physical interpretation is provided. A scheme possibly useful in forecasting is formally constructed for representing any stochastic field by a linear Hermitian model forced by noise.

North, G. R.↗
NASA NTRS1984

A simple derivation of the formula to calculate synthetic long-period seismograms in a heterogeneous earth by normal mode summation

A simple modification of Gilbert's formula to account for slight lateral heterogeneity of the earth leads to a convenient formula to calculate synthetic long period seismograms. Partial derivatives are easily calculated, thus the formula is suitable for direct inversion of seismograms for lateral heterogeneity of the earth. Previously announced in STAR as N83-29893

Tanimoto, T.↗
NASA NTRS1985

Numerical solution of the vertical structure equation in the normal mode method

In the present model of multilayered stability stratification, aimed at obtaining the analytic eigensolutions of the vertical structure equation, each layer is characterized by its own static stability value. By requiring continuity of pressure and vertical velocity across each interface level, and by imposing suitable upper and lower boundary conditions, matching eigensolutions are obtained in terms of the Bessel functions. Attention is given to an explicit example of a double-layered stratified atmosphere which demonstrates the mathematical manipulations involved; the resultant vertical structure functions are used to check the accuracy of the numerical solutions by the finite difference and finite element methods.

Sasaki, Y. K.↗