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A class of numerical methods for constructing bifurcation curves for systems of coupled, non-linear ordinary differential equations is presented. Foundations are discussed, and several variations are outlined along with their respective capabilities. Appropriate background material from dynamical systems theory is presented.
Transmission characteristics of pneumatic pressure to the carotid sinus were evaluated in 19 subjects at rest and during exercise. Either a percutaneous fluid-filled (n = 12) or balloon-tipped catheter (n = 7) was placed at the carotid bifurcation to record internal transmission of external neck pressure/neck suction (NP/NS). Sustained, 5-s pulses, and rapid ramping pulse protocols (+40 to -80 Torr) were recorded. Transmission of pressure stimuli was less with the fluid-filled catheter compared with that of the balloon-tipped catheter (65% vs. 82% negative pressure, 83% vs. 89% positive pressure; P < 0.05). Anatomical location of the carotid sinus averaged 3.2 cm (left) and 3.6 cm (right) from the gonion of the mandible with a range of 0-7.5 cm. Transmission was not altered by exercise or Valsalva maneuver, but did vary depending on the position of the carotid sinus locus beneath the sealed chamber. These data indicate that transmission of external NP/NS was higher than previously recorded in humans, and anatomical variation of carotid sinus location and equipment design can affect transmission results.
Anterograde labeling techniques were used to examine peripheral innervation patterns of vestibular efferent neurons in the crista ampullares of the gerbil. Vestibular efferent neurons were labeled by extracellular injections of biocytin or biotinylated dextran amine into the contralateral or ipsilateral dorsal subgroup of efferent cell bodies (group e) located dorsolateral to the facial nerve genu. Anterogradely labeled efferent terminal field varicosities consist mainly of boutons en passant with fewer of the terminal type. The bouton swellings are located predominately in apposition to the basolateral borders of the afferent calyces and type II hair cells, but several boutons were identified close to the hair cell apical border on both types. Three-dimensional reconstruction and morphological analysis of the terminal fields from these cells located in the sensory neuroepithelium of the anterior, horizontal, and posterior cristae were performed. We show that efferent neurons densely innervate each end organ in widespread terminal fields. Subepithelial bifurcations of parent axons were minimal, with extensive collateralization occurring after the axons penetrated the basement membrane of the neuroepithelium. Axonal branching ranged between the 6th and 27th orders and terminal field collecting area far exceeds that of the peripheral terminals of primary afferent neurons. The terminal fields of the efferent neurons display three morphologically heterogeneous types: central, peripheral, and planum. All cell types possess terminal fields displaying a high degree of anisotropy with orientations typically parallel to or within +/-45 degrees of the longitudinal axis if the crista. Terminal fields of the central and planum zones predominately project medially toward the transverse axis from the more laterally located penetration of the basement membrane by the parent axon. Peripheral zone terminal fields extend predominately toward the planum semilunatum. The innervation areas of efferent terminal fields display a trend from smallest to largest for the central, peripheral, and planum types, respectively. Neurons that innervate the central zone of the crista do not extend into the peripheral or planum regions. Conversely, those neurons with terminal fields in the peripheral or planum regions do not innervate the central zone of the sensory neuroepithelium. The central zone of the crista is innervated preferentially by efferent neurons with cell bodies located in the ipsilateral group e. The peripheral and planum zones of the crista are innervated preferentially by efferent neurons with cell bodies located in the contralateral group e. A model incorporating our anatomic observations is presented describing an ipsilateral closed-loop feedback between ipsilateral efferent neurons and the periphery and an open-loop feed-forward innervation from contralateral efferent neurons. A possible role for the vestibular efferent neurons in the modulation of semicircular canal afferent response dynamics is proposed.
The acoustic characteristics of a model high-speed fan stage were measured in the NASA Glenn 9- by 15-Foot Low Speed Wind Tunnel at takeoff and approach flight conditions. The fan was designed for a corrected rotor tip speed of 442 m/s (1450 ft/s), and had a powered core, or booster stage, giving the model a nominal bypass ratio of 5. A simulated engine pylon and nozzle bifurcation was contained within the bypass duct. The fan stage consisted of all combinations of 3 possible rotors, and 3 stator vane sets. The 3 rotors were (1) wide chord, (2) forward swept, and (3) shrouded. The 3 stator sets were (1) baseline, moderately swept, (2) swept and leaned, and (3) swept integral vane/frame which incorporated some of the swept and leaned features as well as eliminated the downstream support structure. The baseline configuration is considered to be the wide chord rotor with the radial vane stator. A flyover Effective Perceived Noise Level (EPNL) code was used to generate relative EPNL values for the various configurations. The swept and leaned stator showed a 3 EPNdB reduction at lower fan speeds relative to the baseline stator; while the swept integral vane/frame stator showed lowest noise levels at high fan speeds. The baseline, wide chord rotor was typically the quietest of the three rotors. A tone removal study was performed to assess the acoustic benefits of removing the fundamental rotor interaction tone and its harmonics. Reprocessing the acoustic results with the bypass tone removed had the most impact on reducing fan noise at transonic rotor speeds. Removal of the bypass rotor interaction tones (BPF and nBPF) showed up to a 6 EPNdB noise reduction at transonic rotor speeds relative to noise levels for the baseline (wide chord rotor and radial stator; all tones present) configuration.
1. The numbers of type I and type II hair cells were estimated by dissector techniques applied to semithin, stained sections of the horizontal, superior, and posterior cristae in the squirrel monkey and the chinchilla. 2. The crista in each species was divided into concentrically arranged central, intermediate, and peripheral zones of equal areas. The three zones can be distinguished by the sizes of individual hair cells and calyx endings, by the density of hair cells, and by the relative frequency of calyx endings innervating single or multiple type I hair cells. 3. In the monkey crista, type I hair cells outnumber type II hair cells by a ratio of almost 3:1. The ratio decreases from 4-5:1 in the central and intermediate zones to under 2:1 in the peripheral zone. For the chinchilla, the ratio is near 1:1 for the entire crista and decreases only slightly between the central and peripheral zones. 4. Nerve fibers supplying the cristae in the squirrel monkey were labeled by extracellular injections of horseradish peroxidase (HRP) into the vestibular nerve. Peripheral terminations of individual fibers were reconstructed and related to the zones of the cristae they innervated and to the sizes of their parent axons. Results were similar for the horizontal, superior, and posterior cristae. 5. Axons seldom bifurcate below the neuroepithelium. Most fibers begin branching shortly after crossing the basement membrane. Their terminal arbors are compact, usually extending no more than 50-100 microns from the parent exon. A small number of long intraepithelial fibers enter the intermediate and peripheral zones of the cristae near its base, then run unbranched for long distances through the neuroepithelium to reach the central zone. 6. There are three classes of afferent fibers innervating the monkey crista. Calyx fibers terminate exclusively on type I hair cells, and bouton fibers end only on type II hair cells. Dimorphic fibers provide a mixed innervation, including calyx endings to type I hair cells and bouton endings to type II hair cells. Long intraepithelial fibers are calyx and dimorphic units, whose terminal fields are similar to those of other fibers. The central zone is innervated by calyx and dimorphic fibers; the peripheral zone, by bouton and dimorphic fibers; and the intermediate zone, by all three kinds of fibers. Internal (axon) diameters are largest for calyx fibers and smallest for bouton fibers. Of the entire sample of 286 labeled fibers, 52% were dimorphic units, 40% were calyx units, and 8% were bouton units.(ABSTRACT TRUNCATED AT 400 WORDS).
The research facilities on the Svalbard archepelego provide a unique opportunity for observing the temporal and spatial characteristics of the interaction of the solar wind with the magnetosphere-ionosphere system. The first sounding rockets from the SvdRak range at Ny-Alesund have opened a new perspective for separating temporal and spatial effects. Finding a correlation between observations from the rockets and the Wind satellite located nearly 200 R(sub E) upstream in the solar wind that had a lag time less than the advection time forced consideration of tilted phase planes of the interp1anetary electric field. From this it was deduced that the interaction process has to involve high latitude merging, the interplanetary magnetic field (IMF) B(sub Y) bifurcates the cusp relative to the high latitude source regions in the Northern and Southern Hemispheres, IMF B(sub X) controls the interaction time in each hemisphere, and the small convection cell is driven by opposite hemisphere merging. Studies with 4 satellites in the solar wind have shown that the tilt of the phase plane varies on a minute-by-minute basis and change significantly on time scales of tens of minutes. Images of the cusp at 557.7 nm provide a nearly instantaneous picture of the temporal and spatial characteristics of merging at the magnetopause and show that the process can occur at multiple locations. The rate and location vary with time.
Magnetic merging is a primary means for coupling energy from the solar wind into the magnetosphere-ionosphere system. The location and nature of the process remain as open questions. By correlating measurements form diverse locations and using large-scale MHD models to put the measurements in context, it is possible to constrain out interpretations of the global and meso-scale dynamics of magnetic merging. Recent evidence demonstrates that merging often occurs at high latitudes in the vicinity of the cusps. The location is in part controlled by the clock angle in the interplanetary magnetic field (IMF) Y-Z plane. In fact, B(sub Y) bifurcated the cusp relative to source regions. The newly opened field lines may couple to the ionosphere at MLT locations of as much as 3 hr away from local noon. On the other side of noon the cusp may be connected to merging sites in the opposite hemisphere. In face, the small convection cell is generally driven by opposite hemisphere merging. B(sub X) controls the timing of the interaction and merging sites in each hemisphere, which may respond to planar features in the IMF at different times. Correlation times are variable and are controlled by the dynamics of the tilt of the interplanetary electric field phase plane. The orientation of the phase plane may change significantly on time scales of tens of minutes. Merging is temporally variable and may be occurring at multiple sites simultaneously. Accelerated electrons from the merging process excite optical signatures at the foot of the newly opened field lines. All-sky photometer observations of 557.7 nm emissions in the cusp region provide a "television picture" of the merging process and may be used to infer the temporal and spatial variability of merging, tied to variations in the IMF.
One of the propulsion system concepts to be considered for the High-Speed Civil Transport (HSCT) is an underwing, dual-propulsion, pod-per-wing installation. Adverse transient phenomena such as engine compressor stall and inlet unstart could severely degrade the performance of one of these propulsion pods. The subsequent loss of thrust and increased drag could cause aircraft stability and control problems that could lead to a catastrophic accident if countermeasures are not in place to anticipate and control these detrimental transient events. Aircraft system engineers must understand what happens during an engine compressor stall and inlet unstart so that they can design effective control systems to avoid and/or alleviate the effects of a propulsion pod engine compressor stall and inlet unstart. The objective of the Inlet Unstart Propulsion Airframe Integration test program was to assess the underwing flow field of a High-Speed Civil Transport propulsion system during an engine compressor stall and subsequent inlet unstart. Experimental research testing was conducted in the 10- by 10-Foot Supersonic Wind Tunnel at the NASA Glenn Research Center at Lewis Field. The representative propulsion pod consisted of a two-dimensional, bifurcated inlet mated to a live turbojet engine. The propulsion pod was mounted below a large flat plate that acted as a wing simulator. Because of the plate s long length (nominally 10-ft wide by 18-ft long), realistic boundary layers could form at the inlet cowl plane. Transient instrumentation was used to document the aerodynamic flow-field conditions during an unstart sequence. Acquiring these data was a significant technical challenge because a typical unstart sequence disrupts the local flow field for about only 50 msec. Flow surface information was acquired via static pressure taps installed in the wing simulator, and intrusive pressure probes were used to acquire flow-field information. These data were extensively analyzed to determine the impact of the unstart transient on the surrounding flow field. This wind tunnel test program was a success, and for the first time, researchers acquired flow-field aerodynamic data during a supersonic propulsion system engine compressor stall and inlet unstart sequence. In addition to obtaining flow-field pressure data, Glenn researchers determined other properties such as the transient flow angle and Mach number. Data are still being reduced, and a comprehensive final report will be released during calendar year 2000.
One of NASA's objectives is to be able to perform a complete, pre-flight, evaluation of cardiovascular changes in astronauts scheduled for prolonged space missions. Computational fluid dynamics (CFD) has shown promise as a method for estimating cardiovascular function during reduced gravity conditions. For this purpose, MRI can provide geometrical information, to reconstruct vessel geometries, and measure all spatial velocity components, providing location specific boundary conditions. The objective of this study was to investigate the reliability of MRI-based model reconstruction and measured boundary conditions for CFD simulations. An aortic arch model and a carotid bifurcation model were scanned in a 1.5T Siemens MRI scanner. Axial MRI acquisitions provided images for geometry reconstruction (slice thickness 3 and 5 mm; pixel size 1x1 and 0.5x0.5 square millimeters). Velocity acquisitions provided measured inlet boundary conditions and localized three-directional steady-flow velocity data (0.7-3.0 L/min). The vessel walls were isolated using NIH provided software (ImageJ) and lofted to form the geometric surface. Constructed and idealized geometries were imported into a commercial CFD code for meshing and simulation. Contour and vector plots of the velocity showed identical features between the MRI velocity data, the MRI-based CFD data, and the idealized-geometry CFD data, with less than 10% differences in the local velocity values. CFD results on models reconstructed from different MRI resolution settings showed insignificant differences (less than 5%). This study illustrated, quantitatively, that reliable CFD simulations can be performed with MRI reconstructed models and gives evidence that a future, subject-specific, computational evaluation of the cardiovascular system alteration during space travel is feasible.
Results from a numerical and experimental study on the effects of laminate orthotropy and circular cutout size on the response of compression-loaded composite curved panels are presented. Several 60-in-radius composite panels with four different laminate configurations were tested with cutout diameters that range from 10% to 60% of the panel width. Finite-element analyses were performed for each panel in order to identify the effects boundary conditions, measured initial geometric imperfections and thickness variations had on the nonlinear and buckling behavior of the panels. The compression-loaded panels considered herein exhibited two separate types of behavior depending on the laminate stacking sequence and cutout size. More specifically, some of the panels exhibited the classical snap-through type buckling response; however, some of the panels exhibited a monotonically increasing stable response and achieved compressive loads in excess of twice the predicted linear bifurcation buckling load. In general, the finite-element analyses were able to predict accurately the nonlinear response and buckling loads of the panels and the prebuckling and postbuckling out-of-plane deformations and strains.
A novel image segmentation technique for extracting limb and terminator of planetary bodies is proposed. Conventional edge- based histogramming approaches are used to trace object boundaries. The limb and terminator bifurcation is achieved by locating the harmonized segment in the two equations representing the 2-D parameterized boundary curve. Real planetary images from Voyager 1 and 2 served as representative test cases to verify the proposed methodology.
Inversion of previously reportd, delay-doppler images of Castalia yields a 167-parameter, three dimensional shape model that is bifurcated into two distinct, irregular, kilometer-sized lobes.
We study the formation of a very thin current sheet (CS) and associated plasma electrodynamics using three-dimensional (3-D) particle-in-cell simulations with ion to electron mass ratio M/m=1836. The CS is driven by imposed anti-parallel magnetic fields. The noteworthy features of the temporal evolution of the CS are the following: (i) Steepening of the magnetic field profile B,(z) in the central part of the CS, (ii) Generation of three-peak current distribution with the largest peak in the CS center as B,(z) steepens, (iii) Generation of converging electric fields forming a potential well in the CS center in which ions are accelerated. (iv) Electron and ion heating in the central part of the CS by current-driven instabilities (CDI). (v) Re-broadening of the CS due to increased kinetic plasma pressure in the CS center. (vi) Generation of electron temperature anisotropy with temperature perpendicular to the magnetic field being larger than the parallel one. (vii) Current disruption by electron trapping in an explosively growing electrostatic instability (EGEI) and electron tearing instability (ETI). (viii)The onset of EGEI coincides with an increase in the electron temperature above the temperature of the initially hot ions as well as the appearance of new shear in the electron drift velocity. (ix) Bifurcation of the central CS by the current disruption. (x) Magnetic reconnection (MR) beginning near the null in B, and spreading outward. (xi) Generation of highly energized electrons reaching relativistic speeds and having isotropic pitch-angle distribution in the region of reconnected magnetic fields. We compare some of these features of the current sheet with results from laboratory and space experiments.
An analytic approach is developed to predict the shape and displacement with voltage in the quasi-static limit of LaRC Thunder Actuators. The problem is treated with classical lamination theory and Von Karman non-linear analysis. In the case of classical lamination theory exact analytic solutions are found. It is shown that classical lamination theory is insufficient to describe the physical situation for large actuators but is sufficient for very small actuators. Numerical results are presented for the non-linear analysis and compared with experimental measurements. Snap-through behavior, bifurcation, and stability are presented and discussed.
An analytic approach is developed to predict the shape and displacement with voltage in the quasi-static limit of round LaRC Thunder Actuators. The problem is treated with classical lamination theory and Von Karman non-linear analysis. In the case of classical lamination theory exact analytic solutions are found. It is shown that classical lamination theory is insufficient to describe the physical situation for large actuators but is sufficient for very small actuators. Numerical results are presented for the non-linear analysis and compared with experimental measurements. Snap-through behavior, bifurcation, and stability are presented and discussed.
A parabolic iterative solution procedure is investigated that seeks to extend the parabolic approximation used within the internal propagation module of the duct noise propagation and radiation code CDUCT-LaRC. The governing convected Helmholtz equation is split into a set of coupled equations governing propagation in the positive and negative directions. The proposed method utilizes an iterative procedure to solve the coupled equations in an attempt to account for possible reflections from internal bifurcations, impedance discontinuities, and duct terminations. A geometry consistent with the NASA Langley Curved Duct Test Rig is considered and the effects of acoustic treatment and non-anechoic termination are included. Two numerical implementations are studied and preliminary results indicate that improved accuracy in predicted amplitude and phase can be obtained for modes at a cut-off ratio of 1.7. Further predictions for modes at a cut-off ratio of 1.1 show improvement in predicted phase at the expense of increased amplitude error. Possible methods of improvement are suggested based on analytic and numerical analysis. It is hoped that coupling the parabolic iterative approach with less efficient, high fidelity finite element approaches will ultimately provide the capability to perform efficient, higher fidelity acoustic calculations within complex 3-D geometries for impedance eduction and noise propagation and radiation predictions.
Arecibo (2380 MHz, 13 cm) radar observations of 2005 CR37 provide detailed images of a candidate contact binary: a 1.8-km-long, extremely bifurcated object. Although the asteroid's two lobes are round, there are regions of modest topographic relief, such as an elevated, 200-m-wide facet, that suggest that the lobes are geologically more complex than either coherent fragments or homogeneous rubble piles. Since January 1999, about 9% of NEAs larger than approx.200 m imaged by radar can be described as candidate contact binaries.
The two dimensinal bifurcated inlet, down selected for the HSR program, and the engine bay cowling consist of many sealing interfaces. The variable geometry characteristics of this inlet and the size of the propulsion system impose new sealing requirements for commercial transport aircraft. Major inlet systems requiring seal development and testing include the ramp system, the bypass/take-off system, and the inlet/engine interface. Engine bay cowling seal interfaces include the inlet/cowling interface, the keel split line, the hinge beam/engine bay cowling, and the nozzle/cowling interface. These seals have to withstand supersonic flight operating temperatures and pressures with typical commercial aircraft reliability and lives. The operating conditions and expected seal lives will be identified for the various interfaces. Boeing's SST seal development program will also be discussed.