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NASA NTRS1979

Modeling of switching regulator power stages with and without zero-inductor-current dwell time

State-space techniques are employed to derive accurate models for the three basic switching converter power stages: buck, boost, and buck/boost operating with and without zero-inductor-current dwell time. A generalized procedure is developed which treats the continuous-inductor-current mode without dwell time as a special case of the discontinuous-current mode when the dwell time vanishes. Abrupt changes of system behavior, including a reduction of the system order when the dwell time appears, are shown both analytically and experimentally. Merits resulting from the present modeling technique in comparison with existing modeling techniques are illustrated.

Lee, F. C. Y.↗

NASA NTRS1991

A kinematic and proper-motion survey of the Cygnus Loop

H-alpha radial velocities, line widths, and line intensities based on 71 Fabry-Perot interferometer scans of 61 fields in the Cygnus Loop supernova remnant SNR are reported. Also, measurements of proper motions at 39 locations within the Cygnus Loop are summarized. These results show that the remnant is expanding asymmetrically into the ambient interstellar medium, with rest-frame velocities as high as 380 km/s in the near half and 150 km/s in the far half. This can plausibly be interpreted as the result of the progenitor's evolution near a density discontinuity, the consequent formation of a cavity and partial shell, and the SN's interaction with that shell. The remnant's optically observed filamentary structure results from line-of-sight effects as shock waves advance into the irregular inner surface of the shell. In this context, the derived expansion velocities and proper motions give a formal distance to the Cygnus Loop of roughly 600 pc, with 1-sigma limits of 300 and 1200 pc.

Shull, Peter, Jr.↗

NASA NTRS2015

Unsteady Solution of Non-Linear Differential Equations Using Walsh Function Series

Walsh functions form an orthonormal basis set consisting of square waves. The discontinuous nature of square waves make the system well suited for representing functions with discontinuities. The product of any two Walsh functions is another Walsh function - a feature that can radically change an algorithm for solving non-linear partial differential equations (PDEs). The solution algorithm of non-linear differential equations using Walsh function series is unique in that integrals and derivatives may be computed using simple matrix multiplication of series representations of functions. Solutions to PDEs are derived as functions of wave component amplitude. Three sample problems are presented to illustrate the Walsh function series approach to solving unsteady PDEs. These include an advection equation, a Burgers equation, and a Riemann problem. The sample problems demonstrate the use of the Walsh function solution algorithms, exploiting Fast Walsh Transforms in multi-dimensions (O(Nlog(N))). Details of a Fast Walsh Reciprocal, defined here for the first time, enable inversion of aWalsh Symmetric Matrix in O(Nlog(N)) operations. Walsh functions have been derived using a fractal recursion algorithm and these fractal patterns are observed in the progression of pairs of wave number amplitudes in the solutions. These patterns are most easily observed in a remapping defined as a fractal fingerprint (FFP). A prolongation of existing solutions to the next highest order exploits these patterns. The algorithms presented here are considered a work in progress that provide new alternatives and new insights into the solution of non-linear PDEs.

Gnoffo, Peter A.↗

NASA NTRS1996

Dynamical Modeling of Surface Tension

In a recent review it is said that free-surface flows 'represent some of the difficult remaining challenges in computational fluid dynamics'. There has been progress with the development of new approaches to treating interfaces, such as the level-set method and the improvement of older methods such as the VOF method. A common theme of many of the new developments has been the regularization of discontinuities at the interface. One example of this approach is the continuum surface force (CSF) formulation for surface tension, which replaces the surface stress given by Laplace's equation by an equivalent volume force. Here, we describe how CSF formulation might be made more useful. Specifically, we consider a derivation of the CSF equations from a minimization of surface energy as outlined by Jacqmin (1996). This reformulation suggests that if one eliminates the computation of curvature in terms of a unit normal vector, parasitic currents may be eliminated. For this reformulation to work, it is necessary that transition region thickness be controlled. Various means for this, in addition to the one discussed by Jacqmin (1996), are discussed.

Brackbill, Jeremiah U.↗

NASA NTRS2010

Interlaminar Stresses by Refined Beam Theories and the Sinc Method Based on Interpolation of Highest Derivative

Computation of interlaminar stresses from the higher-order shear and normal deformable beam theory and the refined zigzag theory was performed using the Sinc method based on Interpolation of Highest Derivative. The Sinc method based on Interpolation of Highest Derivative was proposed as an efficient method for determining through-the-thickness variations of interlaminar stresses from one- and two-dimensional analysis by integration of the equilibrium equations of three-dimensional elasticity. However, the use of traditional equivalent single layer theories often results in inaccuracies near the boundaries and when the lamina have extremely large differences in material properties. Interlaminar stresses in symmetric cross-ply laminated beams were obtained by solving the higher-order shear and normal deformable beam theory and the refined zigzag theory with the Sinc method based on Interpolation of Highest Derivative. Interlaminar stresses and bending stresses from the present approach were compared with a detailed finite element solution obtained by ABAQUS/Standard. The results illustrate the ease with which the Sinc method based on Interpolation of Highest Derivative can be used to obtain the through-the-thickness distributions of interlaminar stresses from the beam theories. Moreover, the results indicate that the refined zigzag theory is a substantial improvement over the Timoshenko beam theory due to the piecewise continuous displacement field which more accurately represents interlaminar discontinuities in the strain field. The higher-order shear and normal deformable beam theory more accurately captures the interlaminar stresses at the ends of the beam because it allows transverse normal strain. However, the continuous nature of the displacement field requires a large number of monomial terms before the interlaminar stresses are computed as accurately as the refined zigzag theory.

Slemp, Wesley C. H.↗

NASA NTRS1999

Numerical and Analytical Solutions of Hypersonic Interactions Involving Surface Property Discontinuities

The local viscous-inviscid interaction field generated by a wall temperature jump on a flat plate in supersonic flow and on the windside of a Reusable Launch Vehicle in hypersonic flow is studied in detail by both a Navier-Stokes numerical code and an analytical triple-deck model. Treatment of the rapid heat transfer changes both upstream and downstream of the jump is included. Closed form relationships derived from the triple-deck theory are presented. The analytically predicted pressure and heating variations including upstream influence are found to be in generally good agreement with the Computational Fluid Dynamic (CFD) predictions. These analyses not only clarify the interactive physics involved but also are useful in preliminary design of thermal protection systems and as an insertable module to improve CFD code efficiency when applied to such small-scale interaction problems. The analyses only require conditions at the wall and boundary-layer edge which are easily extracted from a baseline, constant wall temperature, CFD solution.

Gnoffo, Peter A.↗

NASA NTRS1973

The velocity structure of the lunar crust.

Seismic refraction data, obtained at the Apollo 14 and 16 sites, when combined with other lunar seismic data, allow a compressional wave velocity profile of the lunar near-surface and crust to be derived. The regolith, although variable in thickness over the lunar surface, possesses surprisingly similar seismic properties. Underlying the regolith at both the Apollo 14 Fra Mauro site and the Apollo 16 Descartes site is low-velocity brecciated material or impact derived debris. Key features of the lunar seismic velocity profile are: (1) velocity increases from 100 to 300 m/sec in the upper 100 m to about 4 km/sec at 5 km depth, (2) a more gradual increase from about 4 km/sec to about 6 km/sec at 25 km depth,(3) a discontinuity at a depth of 25 km, and (4) a constant value of about 7 km/sec at depths from 25 km to about 60 km.

Kovach, R. L.↗

NASA NTRS1999

MOLA-derived Roughness Data Used to Predict Surface Scattering for Mars Subsurface Radar Sounding

The Mars Express orbiter, to be launched by the European Space Agency in 2003, will carry a low-frequency radar sounding instrument, MARSIS (Mars Advanced Radar for Subsurface and Ionospheric Sounding). The primary goal of MARSIS is to map the distribution of water, both solid and (if present) liquid, in the upper several km of the martian crust. Detecting discontinuities in the crust, such as an ice-water transition, presents many challenges for a Mars orbital radar sounder. One challenge that must be overcome is the presence of radar scattering (echoes) from the surface of Mars, expected to be detected by the sounder antennas at the same time as any echoes aris-ing from subsurface interfaces. As the transmitted spherical wavefront spreads within the crust of Mars,. it also interacts with surface topography at off-nadir positions, creating a "clutter" signal that can mask the subsurface echoes. The MARSIS instrument will utilize Doppler filtering to limit the off-nadir clutter in the along-track direction, and a nadir-null secondary antenna to identify strong off-nadir clutter from the cross-track direction. To evaluate the effects of off-nadir surface clutter and the capability of these schemes to reduce the clutter, it is necessary to predict the range of scattering behavior that may be expected from martian surface topography. In this paper, we utilize Mars Orbital Laser Altimeter (MOLA) data from the current Mars Global Surveyor mission to characterize the topographic roughness of a variety of martian terrain types, at scales relevant to the MARSIS clutter problem. Segments of MOLA altimetry profiles are reduced to the topographic parameters rms slope and fractal dimension, which then are used as inputs to a near-nadir radar scattering model to predict the strength of the clutter signal. Additional information is contained in the original extended abstract.

Plaut, J. J.↗

NASA NTRS1972

Investigation of low-Z Coster-Kronig transitions by means of Auger and photoelectron spectroscopy

Experimental intensity ratios of Auger transitions for Co, Ni, Cu, and Zn as well as the relative L sub 2 and L sub 3 level widths of Cu and Zn, derived from their photoelectron spectra, are presented. Evidence is presented that a great deal of vacancy reorganization took place following photoionization and prior to Auger emission. These reorganizations are assumed to be due to Coster-Kronig transitions f sub 23. These results are compared with theoretical calculations and agree with predicted discontinuity at Z = 30 where f sub 23 transitions become energetically impossible.

Yin, L. I.↗

NASA NTRS1974

A general form of the co-moving tensorial derivative

A general expression for the co-moving derivative of a tensor is derived. A variable describing the coordinate velocity field is introduced. Time dependency of the metric elements is expressed in terms of this velocity field. The resulting description of motion is one of which the Eulerian and Lagrangian viewpoints are special cases. This general description is useful in problems involving moving boundaries or discontinuities.

Huckins, E. K., III↗

NASA NTRS1991

The L sub 1 finite element method for pure convection problems

The least squares (L sub 2) finite element method is introduced for 2-D steady state pure convection problems with smooth solutions. It is proven that the L sub 2 method has the same stability estimate as the original equation, i.e., the L sub 2 method has better control of the streamline derivative. Numerical convergence rates are given to show that the L sub 2 method is almost optimal. This L sub 2 method was then used as a framework to develop an iteratively reweighted L sub 2 finite element method to obtain a least absolute residual (L sub 1) solution for problems with discontinuous solutions. This L sub 1 finite element method produces a nonoscillatory, nondiffusive and highly accurate numerical solution that has a sharp discontinuity in one element on both coarse and fine meshes. A robust reweighting strategy was also devised to obtain the L sub 1 solution in a few iterations. A number of examples solved by using triangle and bilinear elements are presented.

Jiang, Bo-Nan↗

NASA NTRS1991

The L sub 1 finite element method for pure convection problems

Jiang, Bo-Nan↗

NASA NTRS2005

Sea Ice Kinematics and Thickness from RGPS: Observations and Theory

The RADARSAT Geophysical Processor System (RGPS) has produced a wealth of data on Arctic sea ice motion, deformation, and thickness with broad geographical coverage and good temporal resolution. These data provide unprecedented spatial detail of the structure and evolution of the sea ice cover. The broad purpose of this study was to take advantage of the strengths of the RGPS data set to investigate sea ice kinematics and thickness, which affect the climate through their influence on ice production, ridging, and transport (i.e. mass balance); heat flux to the atmosphere; and structure of the upper ocean mixed layer. The objectives of this study were to: (1) Explain the relationship between the discontinuous motion of the ice cover and the large-scale, smooth wind field that drives the ice; (2) Characterize the sea ice deformation in the Arctic at different temporal and spatial scales, and compare it with deformation predicted by a state-of-theart ice/ocean model; and (3) Compare RGPS-derived sea ice thickness with other data, and investigate the thinning of the Arctic sea ice cover as seen in ULS data obtained by U.S. Navy submarines. We briefly review the results of our work below, separated into the topics of sea ice deformation and sea ice thickness. This is followed by a list of publications, meetings and presentations, and other activities supported under this grant. We are attaching to this report copies of all the listed publications. Finally, we would like to point out our community service to NASA through our involvement with the ASF User Working Group and the RGPS Science Working Group, as evidenced in the list of meetings and presentations below.

Stern, Harry↗

NASA NTRS1992

On the power spectra of the wind-fed X-ray binary pulsar GX 301 - 2

A phenomenological model of accretion which is applied to the wind-fed X-ray binary pulsar GX 301 - 2 is developed, assuming that the accretion onto the neutron star does not occur from a continuous flux of plasma, but from blobs of matter which are threaded by the magnetic field lines onto the magnetic polar caps of the neutron star. These 'lumps' are produced at the magnetospheric limit by magnetohydrodynamical instability, introducing a 'noise' in the accretion process, due to the discontinuity in the flux of matter onto the neutron star. This model is able to describe the change of slope observed in the continuum component of the power spectra of the X-ray binary pulsar GX 301 - 2, in the frequency range 0.01 - 0.1 Hz. The physical properties of the infalling blobs derived in the model are in agreement with the constraints imposed by observations.

Orlandini, Mauro↗

NASA NTRS1994

Topographic form of the Coast Ranges of the Cascadia Margin in relation ot coastal uplift rates and plate subduction

The Coast Ranges of the Cascadia margin are overriding the subducted Juan de Fuca/Gorda plate. We investigate the extent to which the latitudinal change in attributes related to the subduction process. These attributes include the varibale age of the subducted slab that underlies the Coast Ranges and average vertical crustal velocities of the western margin of the Coast Rnages for two markedly different time periods, the last 45 years and the last 100 kyr. These vertical crustal velocities are computed from the resurveying of highway bech marks and from the present elevation of shore platforms that have been uplifted in the late Quaternary, respectively. Topogarphy of the Coast Ranges is in part a function of the age and bouyancy of the underlying subducted plate. This is evident in the fact that the two highest topographic elements of the Coast Rnages, the Klamath Mountains and the Olympic Mountains, are underlain by youngest subducted oceanic crust. The subducted Blanco Fracture Zone in southernmost Oregon is responsible for an age discontinuity of subducted crust under the Klamath Mountains. The norhtern terminus of hte topographically higher Klamaths is offset to the north relative to the position of the underlying Blanco Fracture Zone, teh offset being in the direction of migration of the farcture zone, as dictated by relative plate motions. Vertical crustal velocities at the coast, derived from becnh mark surveys, are as much as an order of magnitude greater than vertical crustal velocities derived from uplifted shore platforms. This uplift rate discrepancy indicates that strain is accumulating on the plate margin, to be released during the next interplate earthquake. In a latitudinal sense, average Coast Rnage topography is relatively high where bench mark-derived, short-term vertical crustal velocities are highest. Becuase the shore platform vertical crustal velocities reflect longer-term, premanent uplift, we infer that a small percentage of the interseismic strain that accumulates as rapid short-term uplift is not recovered by subduction earthquakes but rather contributes to rock uplift of the Coast Ranges. The conjecture that permanent rock uplift is related to interseismic uplift is consistent with the observation that those segments of the subduction zone subject to greater interseismic uplift rates are at approximately the same latitudes as those segments of the Coast Ranges that have higher magnitudes of rock uplift over the long term.

Kelsey, Harvey M.↗

NASA NTRS2003

The Big Glitcher - the Rotation History of PSR JO537-6910

We report the results of an extensive monitoring campaign of PSR 50537-6910, the 16 ms pulsar in the Large Magellanic Cloud, using data acquired with the Rossi X-ray Timing Explorer. The spin evolution of this pulsar is found to experience extreme episodic discontinuities in its spin-down rate during the 2.6 year campaign. The rate of occurance of these timing glitches is 2.3 per year, comparable to the highest seen for any pulsar. The mean glitch amplitude produced a fraction change in the frequency of Delta(nu)/nu = 0.36 x l0(exp -6) and in the frequency derivative of Delta(dot nu)/dot nu = 3 x 10(exp -4). Despite this prodigous timing activity we are able to derive a phase connected timing solution between glitch events with an average spin-down rate of -1.9743 x 10(exp 10) Hz/s. The integrated effect of the glitches in dot nu was so large that the apparent characteristic age of the pulsar (-nu/2dot nu) decreased significantly during the campaign. We discuss the implications of a large glitch activity and high braking index on the spin evolution of young pulsars.

Marshall, F. E.↗

NASA NTRS2011

Discretely Conservative Finite-Difference Formulations for Nonlinear Conservation Laws in Split Form: Theory and Boundary Conditions

Simulations of nonlinear conservation laws that admit discontinuous solutions are typically restricted to discretizations of equations that are explicitly written in divergence form. This restriction is, however, unnecessary. Herein, linear combinations of divergence and product rule forms that have been discretized using diagonal-norm skew-symmetric summation-by-parts (SBP) operators, are shown to satisfy the sufficient conditions of the Lax-Wendroff theorem and thus are appropriate for simulations of discontinuous physical phenomena. Furthermore, special treatments are not required at the points that are near physical boundaries (i.e., discrete conservation is achieved throughout the entire computational domain, including the boundaries). Examples are presented of a fourth-order, SBP finite-difference operator with second-order boundary closures. Sixth- and eighth-order constructions are derived, and included in E. Narrow-stencil difference operators for linear viscous terms are also derived; these guarantee the conservative form of the combined operator.

Fisher, Travis C.↗

NASA NTRS1987

New main reflector, subreflector and dual chamber concepts for compact range applications

A compact range is a facility used for the measurement of antenna radiation and target scattering problems. Most presently available parabolic reflectors do not produce ideal uniform plane waves in the target zone. Design improvements are suggested to reduce the amplitude taper, ripple and cross polarization errors. The ripple caused by diffractions from the reflector edges can be reduced by adding blended rolled edges and shaping the edge contour. Since the reflected edge continues smoothly from the parabola onto the rolled surface, rather than being abruptly terminated, the discontinuity in the reflected field is reduced which results in weaker diffracted fields. This is done by blending the rolled edges from the parabola into an ellipse. An algorithm which enables one to design optimum blended rolled edges was developed that is based on an analysis of the continuity of the surface radius of curvature and its derivatives across the junction. Futhermore, a concave edge contour results in a divergent diffracted ray pattern and hence less stray energy in the target zone. Design equations for three-dimensional reflectors are given. Various examples were analyzed using a new physical optics method which eliminates the effects of the false scattering centers on the incident shadow boundaries. A Gregorian subreflector system, in which both the subreflector and feed axes are tilted, results in a substantial reduction in the amplitude taper and cross polarization errors. A dual chamber configuration is proposed to eliminate the effects of diffraction from the subreflector and spillover from the feed. A computationally efficient technique, based on ray tracing and aperture integration, was developed to analyze the scattering from a lossy dielectric slab with a wedge termination.

Pistorius, C. W. I.↗