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NASA NTRS2010

Optical Tapers as White-Light WGM Resonators

A theoretical analysis has revealed that tapered optical waveguides could be useful as white-light whispering-gallery-mode (WGM) optical resonators. The compactness and the fixed-narrow-frequency-band nature of the resonances of prior microdisk and microsphere WGM resonators are advantageous in low-power, fixed-narrow-frequency-band applications. However for optical-processing applications in which there are requirements for power levels higher and/or spectral responses broader than those of prior microdisk and microsphere WGM resonators, white-light WGM resonators in the form of optical tapers would be preferable. The theoretical analysis was performed for a multimode, axisymmetric, circular-cross-section waveguide having a taper sufficiently smooth and gradual to justify the approximation of adiabaticity. In this approximation, the equation for the dependence of the electromagnetic field upon the axial (longitudinal) waveguide coordinate can be separated from the equation for the dependence upon the radius and the azimuthal angle.

Strekalov, Dmitry V.↗

NASA NTRS2019

NICER X-ray Observations of Seven Nearby Rotation-powered Millisecond Pulsars

The Neutron star Interior Composition Explorer observed several rotation-powered millisecond pulsars (MSPs) to search for or confirm the presence of X-ray pulsations. When broad and sine-like, these pulsations may indicate thermal emission from hot polar caps at the magnetic poles on the neutron star surface. We report confident detections (≥4.7σ after background filtering) of X-ray pulsations for five of the seven pulsars in our target sample: PSR J0614−3329, PSR J0636+5129, PSR J0751+1807, PSR J1012+5307, and PSR J2241−5236, while PSR J1552+5437 and PSR J1744−1134 remain undetected. Of those, only PSR J0751+1807 and PSR J1012+5307 had pulsations previously detected at the 1.7σ and almost 3σ confidence levels, respectively, in XMM-Newton data. All detected sources exhibit broad sine-like pulses, which are indicative of surface thermal radiation. As such, these MSPs are promising targets for future X-ray observations aimed at constraining the neutron star mass–radius relation and the dense matter equation of state using detailed pulse profile modeling. Furthermore, we find that three of the detected MSPs exhibit a significant phase offset between their X-ray and radio pulses.

Sebastien Guillot↗

NASA NTRS1980

The radius-dependence of velocity dispersion in elliptical galaxies

The equations of stellar hydrodynamics are used to derive the radial variation of velocity dispersion in galaxies whose mass-to-light ratios are constant and whose brightness profiles obey the r to the 1/4 law. It is found that the projected central velocity dispersion in such a system should be about 40 percent lower than the peak velocity dispersion. The observability and physical interpretation of this phenomenon is discussed. There is some evidence that a similar effect has been observed in the structure of rich clusters of galaxies.

Binney, J.↗

NASA NTRS1981

Stress-intensity factor equations for cracks in three-dimensional finite bodies

Empirical stress intensity factor equations are presented for embedded elliptical cracks, semi-elliptical surface cracks, quarter-elliptical corner cracks, semi-elliptical surface cracks at a hole, and quarter-elliptical corner cracks at a hole in finite plates. The plates were subjected to remote tensile loading. Equations give stress intensity factors as a function of parametric angle, crack depth, crack length, plate thickness, and where applicable, hole radius. The stress intensity factors used to develop the equations were obtained from three dimensional finite element analyses of these crack configurations.

Newman, J. C., Jr.↗

NASA NTRS1995

On the breakup of viscous liquid threads

A one-dimensional model evolution equation is used to describe the nonlinear dynamics that can lead to the breakup of a cylindrical thread of Newtonian fluid when capillary forces drive the motion. The model is derived from the Stokes equations by use of rational asymptotic expansions and under a slender jet approximation. The equations are solved numerically and the jet radius is found to vanish after a finite time yielding breakup. The slender jet approximation is valid throughout the evolution leading to pinching. The model admits self-similar pinching solutions which yield symmetric shapes at breakup. These solutions are shown to be the ones selected by the initial boundary value problem, for general initial conditions. Further more, the terminal state of the model equation is shown to be identical to that predicted by a theory which looks for singular pinching solutions directly from the Stokes equations without invoking the slender jet approximation throughout the evolution. It is shown quantitatively, therefore, that the one-dimensional model gives a consistent terminal state with the jet shape being locally symmetric at breakup. The asymptotic expansion scheme is also extended to include unsteady and inerticial forces in the momentum equations to derive an evolution system modelling the breakup of Navier-Stokes jets. The model is employed in extensive simulations to compute breakup times for different initial conditions; satellite drop formation is also supported by the model and the dependence of satellite drop volumes on initial conditions is studied.

Papageorgiou, Demetrios T.↗

NASA NTRS1987

Spectral multigrid methods for the solution of homogeneous turbulence problems

New three-dimensional spectral multigrid algorithms are analyzed and implemented to solve the variable coefficient Helmholtz equation. Periodicity is assumed in all three directions which leads to a Fourier collocation representation. Convergence rates are theoretically predicted and confirmed through numerical tests. Residual averaging results in a spectral radius of 0.2 for the variable coefficient Poisson equation. In general, non-stationary Richardson must be used for the Helmholtz equation. The algorithms developed are applied to the large-eddy simulation of incompressible isotropic turbulence.

Erlebacher, G.↗

NASA NTRS1988

Spectral multigrid methods for the solution of homogeneous turbulence problems

Erlebacher, G.↗

NASA NTRS1975

Relaxation methods in fluid mechanics

The present work considers the iterative solution of a coupled set of difference equations and examines methods that carry successive approximates to a state that is invariant with further iteration and independent of the initial guess. Methods are studied with regard to their efficiency and economy of computer resources. The basic principles of classical relaxation are set forth, with attention confined to linear elliptic equations. This discussion involves the evaluation of the spectral radius that is the magnitude of the eigenvalue with largest modulus. The subject of relaxation is then related to the study of ordinary differential equations and hyperbolic partial differential equations. Problems that occur when linearly dependent eigenvectors appear in the relaxation matrix are discussed, leading to multiply connected eigenvalues in the Jordan canonical form. Finally, a brief survey of relaxation methods used in aerodynamics is given.

Lomax, H.↗

NASA NTRS2011

Proposed Framework for Determining Added Mass of Orion Drogue Parachutes

The Crew Exploration Vehicle (CEV) Parachute Assembly System (CPAS) project is executing a program to qualify a parachute system for a next generation human spacecraft. Part of the qualification process involves predicting parachute riser tension during system descent with flight simulations. Human rating the CPAS hardware requires a high degree of confidence in the simulation models used to predict parachute loads. However, uncertainty exists in the heritage added mass models used for loads predictions due to a lack of supporting documentation and data. Even though CPAS anchors flight simulation loads predictions to flight tests, extrapolation of these models outside the test regime carries the risk of producing non-bounding loads. A set of equations based on empirically derived functions of skirt radius is recommended as the simplest and most viable method to test and derive an enhanced added mass model for an inflating parachute. This will increase confidence in the capability to predict parachute loads. The selected equations are based on those published in A Simplified Dynamic Model of Parachute Inflation by Dean Wolf. An Ames 80x120 wind tunnel test campaign is recommended to acquire the reefing line tension and canopy photogrammetric data needed to quantify the terms in the Wolf equations and reduce uncertainties in parachute loads predictions. Once the campaign is completed, the Wolf equations can be used to predict loads in a typical CPAS Drogue Flight test. Comprehensive descriptions of added mass test techniques from the Apollo Era to the current CPAS project are included for reference.

Fraire, Usbaldo, Jr.↗

NASA NTRS1992

Finite grid radius and thickness effects on retarding potential analyzer measured suprathermal electron density and temperature

The effect of finite grid radius and thickness on the electron current measured by planar retarding potential analyzers (RPAs) is analyzed numerically. Depending on the plasma environment, the current is significantly reduced below that which is calculated using a theoretical equation derived for an idealized RPA having grids with infinite radius and vanishingly small thickness. A correction factor to the idealized theoretical equation is derived for the Pioneer Venus (PV) orbiter RPA (ORPA) for electron gasses consisting of one or more components obeying Maxwell statistics. The error in density and temperature of Maxwellian electron distributions previously derived from ORPA data using the theoretical expression for the idealized ORPA is evaluated by comparing the densities and temperatures derived from a sample of PV ORPA data using the theoretical expression with and without the correction factor.

Knudsen, William C.↗

NASA NTRS2011

Gas Flux and Density Surrounding a Cylindrical Aperture in the Free Molecular Flow Regime

The equations for rigorously calculating the particle flux and density surrounding a cylindrical aperture in the free molecular flow regime are developed and presented. The fundamental equations for particle flux and density from a reservoir and a diffusely reflecting surface will initially be developed. Assumptions will include a Maxwell-Boltzmann speed distribution, equal particle and wall temperatures, and a linear flux distribution along the cylindrical aperture walls. With this information, the equations for axial flux and density surrounding a cylindrical aperture will be developed. The cylindrical aperture will be divided into multiple volumes and regions to rigorously determine the surrounding axial flux and density, and appropriate limits of integration will be determined. The results of these equations will then be evaluated. The linear wall flux distribution assumption will be assessed. The axial flux and density surrounding a cylindrical aperture with a thickness-to-radius ratio of 1.25 will be presented. Finally, the equations determined in this study will be verified using multiple methods.

Soulas, George C.↗

NASA NTRS1968

A bound for the spectral radius of a matrix

Bound for spectral radius of matrix derived by constructing integral equation with degenerate kernel

Sloss, J. M.↗

NASA NTRS1979

Estimating tropical cyclone outer surface winds from satellite microwave data

Warm temperature anomalies over tropical cyclones are sensed by the 55.45 GHz channel of the Nimbus 6 Scanning Microwave Spectrometer. Radial brightness temperature gradients are related to radial surface pressure gradients through the hydrostatic and radiative transfer equations. Surface wind speeds outside of the radius of maximum wind are calculated from the pressure gradients and compared with observations.

Kidder, S. Q.↗

NASA NTRS1979

Determination of tropical cyclone surface pressure and winds from satellite microwave data

An approach to the problem of deducing wind speed and pressure around tropical cyclones is presented. The technique, called the Surface Wind Inference from Microwave data (SWIM technique, uses satellites microwave sounder data to measure upper tropospheric temperature anomalies which may then be related to surface pressure anomalies through the hydrostatic and radiative transfer equations. Surface pressure gradients outside of the radius of maximum wind are estimated for the first time. Future instruments may be able to estimate central pressure with + or - 0/1 kPa accuracy.

Kidder, S. Q.↗

NASA NTRS1983

Shocks in spherically accreting black holes - A model for classical quasars

Spherically symmetric accretion onto black holes is thought to be very inefficient if the flow is nondissipative because of the inadequacy of compression heating and the short time available to radiate. It is shown that standing shock solutions exist where the downstream protons are heated to temperatures at which the fluid becomes almost collisionless. The material then moves inwards at the much slower diffusion rate given by the p-e energy exchange time scale. For a given accretion rate, a self-consistent shock radius is found by matching the flow equations above and below that value, showing that such shocks can be self-sustaining. Efficiencies reaching up to 0.1-0.3 can be achieved, with most of the luminosity in the hard X-ray and gamma-ray, as well as optical-IR ranges. This provides a new model for the classical (radio-quiet) quasars and active galactic nuclei and possibly for galactic sources such as Cyg X-1.

Meszaros, P.↗

NASA NTRS1984

The collisionless macroscopic Kelvin-Helmholtz instabiity. I Transverse electrostatic mode

The electrostatic limit of the Kelvin-Helmholtz instability in a collisionless plasma is investigated for a magnetic field perpendicular to the velocity flow. A two-fluid eigenvalue analysis of the transverse electrostatic Kelvin-Helmholtz instability is performed using the Chew-Goldberger-Low hydromagnetic equations with first-order finite Larmer radius corrections, establishing that the transverse electrostatic mode reduces to the incompressible transverse MHD mode in the limit of zero ion gyroradius. The linear growth rates are determined and a strong stabilization of the instability for (k-perpendicular) (rho sub i) of 0.2 or greater is observed. The nonlinear stage of the instability displays large vortices whose size is many times the initial velocity shear length. At saturation the simulation is dominated by the longest-wavelength mode permitted in the system. The simulation results can be understood in terms of a simple model which assumes that saturation occurs when the angular frequency of the vortex motion reaches the linear growth rate of the instability.

Prichett, P. L.↗

NASA NTRS1986

Geometerial description for a proposed aeroassist flight experiment vehicle

One geometry currently under consideration for the Aeroassist Flight Experiment (AFE) vehicle is composed of several segments of simple general conics: an ellipsoidal nose tangent to an elliptical cone and a base skirt with the base plane raked relative to the body axis. An analytic representation for the body coordinates and first and second partial derivatives of this configuration has been developed. Equations are given which define the body radius and partial derivatives for a prescribed axial and circumferential position on the vehicle. The results for a sample case are tabulated and presented graphically.

Cheatwood, F. M.↗

NASA NTRS1989

State-space solutions to standard H2 and H(infinity) control problems

Simple state-space formulas are derived for all controllers solving the standard H(infinity) problem of finding, for a given number gamma greater than 0, all controllers such that the H(infinity) norm of the closed-loop transfer function is (strictly) less than gamma. It is known that a controller exists if and only if the unique stabilizing solutions to two algebraic Riccati equations are positive definite and the spectral radius of their product is less than gamma squared. Under these conditions, a parameterization of all controllers solving the problem is given as a linear fractional transformation (LFT) on a contractive stable free parameter. The state dimension of the coefficient matrix for the LFT, constructed using the two Riccati solutions, equals that of the plant and has a separation structure reminiscent of classical LQG (i.e., H2) theory. A standard H2 solution is developed in parallel.

Doyle, John C.↗