A note on the first passage time problem
Kolmogoroff backward equation for analyzing first passage time problem for linear single degree of freedom vibratory system with linear viscous damping
Shinozuka, M.↗
SEARCH · Search NASA
Results for “first passage times”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
On the probability of cycle-slipping in first-order phase-locked loops.
The first-passage time boundary value problem for first-order phase-locked loops (PLL) is analyzed, and spectral representations are developed for the probability density function (pdf), the distribution function, and the moments of the first time to passage (or cycle-slip). For the sinusoidal PLL, an asymptotic formula, that is surprisingly accurate even at low loop SNR's and large frequency offsets, is obtained for the pdf of the time to cycle-slip, in terms of the mean time to slip.
La Frieda, J. R.↗
Analytic method for calculating properties of random walks on networks
A method for calculating the properties of discrete random walks on networks is presented. The method divides complex networks into simpler units whose contribution to the mean first-passage time is calculated. The simplified network is then further iterated. The method is demonstrated by calculating mean first-passage times on a segment, a segment with a single dangling bond, a segment with many dangling bonds, and a looplike structure. The results are analyzed and related to the applicability of the Einstein relation between conductance and diffusion.
Goldhirsch, I.↗
The isolation limits of stochastic vibration
The vibration isolation problem is formulated as a 1D kinematic problem. The geometry of the stochastic wall trajectories arising from the stroke constraint is defined in terms of their significant extrema. An optimal control solution for the minimum acceleration return path determines a lower bound on platform mean square acceleration. This bound is expressed in terms of the probability density function on the significant maxima and the conditional fourth moment of the first passage time inverse. The first of these is found analytically while the second is found using a Monte Carlo simulation. The rms acceleration lower bound as a function of available space is then determined through numerical quadrature.
Knopse, C. R.↗
Unimolecular diffusion-mediated reactions with a nonrandom time-modulated absorbing barrier
A diffusion-reaction model with time-dependent reactivity is formulated and applied to unimolecular reactions. The model is solved exactly numerically and approximately analytically for the unreacted fraction as a function of time. It is shown that the approximate analytical solution is valid even when the system is far from equilibrium, and when the reactivity probability is more complicated than a square-wave function of time. A discussion is also given of an approach to problems of this type using a stochastically fluctuating reactivity, and the first-passage time for a particular example is derived.
Bashford, D.↗
Limits on the isolation of stochastic vibration for microgravity space experiments
The limitations on the isolation of stochastic vibrations for microgravity space experiments are explored. These limitations result from the restricted interior space available for vibration isolation. A one-degree-of-freedom representation of the experiment-spacecraft system is used, and an ideal vibration actuator is assumed. A kinematic representation results, and the problem becomes one of finding the minimum acceleration trajectory within a pair of stochastic walls. The wall motion is characterized by an ergodic, stationary, zero-mean, Gaussian random process with known power spectral density. The geometry of the wall trajectories is defined in terms of their significant extrema and zero crossings. This geomemtry is used in defining a composite trajectory that has a mean square acceleratiaon lower than that on the optimal path satisfying the stochastic wall inequality constraints. The optimal control problem is solved on a return path yielding the mean square acceleration in terms of the distributions of significant maxima and first-passage time of the wall process. The methodology is applied to a microgravity isolation problem to find the lower bounds on root-mean-square acceleration given the disturbance power spectral density.
Knospe, C. R.↗
Probabilistic evaluation of uncertainties and risks in aerospace components
This paper summarizes a methodology developed at NASA Lewis Research Center which computationally simulates the structural, material, and load uncertainties associated with Space Shuttle Main Engine (SSME) components. The methodology was applied to evaluate the scatter in static, buckling, dynamic, fatigue, and damage behavior of the SSME turbo pump blade. Also calculated are the probability densities of typical critical blade responses, such as effective stress, natural frequency, damage initiation, most probable damage path, etc. Risk assessments were performed for different failure modes, and the effect of material degradation on the fatigue and damage behaviors of a blade were calculated using a multi-factor interaction equation. Failure probabilities for different fatigue cycles were computed and the uncertainties associated with damage initiation and damage propagation due to different load cycle were quantified. Evaluations on the effects of mistuned blades on a rotor were made; uncertainties in the excitation frequency were found to significantly amplify the blade responses of a mistuned rotor. The effects of the number of blades on a rotor were studied. The autocorrelation function of displacements and the probability density function of the first passage time for deterministic and random barriers for structures subjected to random processes also were computed. A brief discussion was included on the future direction of probabilistic structural analysis.
Shah, A. R.↗
The Late-time Afterglow of the Extremely Energetic Short Burst GRB 090510 Revisited
Context. The Swift discovery of the short burst GRB 090510 has raised considerable attention mainly because of two reasons: first, it had a bright optical afterglow, and second it is among the most energetic events detected so far within the entire GRB population (long plus short). The afterglow of GRB 090510 was observed with Swift/UVOT and Swift/XRT and evidence of a jet break around 1.5 ks after the burst has been reported in the literature, implying that after this break the optical and X-ray light curve should fade with the same decay slope. Aims. As noted by several authors, the post-break decay slope seen in the UVOT data is much shallower than the steep decay in the X-ray band, pointing to a (theoretically hard to understand) excess of optical flux at late times. We assess here the validity of this peculiar behavior. Methods. We reduced and analyzed new afterglow light-curve data obtained with the multichannel imager GROND. These additional g'r'i'z' data were then combined with the UVOT and XRT data to study the behavior of the afterglow at late times more stringently. Results. Based on the densely sampled data set obtained with GROND, we find that the optical afterglow of GRB 090510 did indeed enter a steep decay phase starting around 22 ks after the burst. During this time the GROND optical light curve is achromatic, and its slope is identical to the slope of the X-ray data. In combination with the UVOT data this implies that a second break must have occurred in the optical light curve around 22 ks post burst, which, however, has no obvious counterpart in the X-ray band, contradicting the interpretation that this could be another jet break. Conclusions. The GROND data provide the missing piece of evidence that the optical afterglow of GRB 090510 did follow a post-jet break evolution at late times. The break seen in the optical light curve around 22 ks in combination with its missing counterpart in the X-ray band could be due to the passage of the injection frequency across the optical bands, as already theoretically proposed in the literature. This is possibly the first time that this passage has been clearly seen in an optical afterglow. In addition, our results imply that there is no more evidence for an excess of flux in the optical bands at late times.
gamma-ray burst↗
First-passage problems: A probabilistic dynamic analysis for degraded structures
Structures subjected to random excitations with uncertain system parameters degraded by surrounding environments (a random time history) are studied. Methods are developed to determine the statistics of dynamic responses, such as the time-varying mean, the standard deviation, the autocorrelation functions, and the joint probability density function of any response and its derivative. Moreover, the first-passage problems with deterministic and stationary/evolutionary random barriers are evaluated. The time-varying (joint) mean crossing rate and the probability density function of the first-passage time for various random barriers are derived.
Shiao, Michael C.↗
Magnetic Storms
One of the oldest mysteries in geomagnetism is the linkage between solar and geomagnetic activity. The 11-year cycles of both the numbers of sunspots and Earth geomagnetic storms were first noted by Sabine. A few years later, speculation on a causal relationship between flares and storms arose when Carrington reported that a large magnetic storm followed the great September 1859 solar flare. However, it was not until this century that a well-accepted statistical survey on large solar flares and geomagnetic storms was performed, and a significant correlation between flares and geomagnetic storms was noted. Although the two phenomena, one on the Sun and the other on the Earth, were statistically correlated, the exact physical linkage was still an unknown at this time. Various hypotheses were proposed, but it was not until interplanetary spacecraft measurements were available that a high-speed plasma stream rich in helium was associated with an intense solar flare. The velocity of the solar wind increased just prior to and during the helium passage, identifying the solar ejecta for the first time. Space plasma measurements and Skylab's coronagraph images of coronal mass elections (CMES) from the Sun firmly established the plasma link between the Sun and the Earth. One phenomenon associated with magnetic storms is brilliant "blood" red auroras, as shown.
Tsurutani, Bruce T.↗
Gamma time-dependency in Blaxter's compartmental model.
A new two-compartment model for the passage of particles through the gastro-intestinal tract of ruminants is proposed. In this model, a gamma distribution of lifetimes is introduced in the first compartment; thereby, passage from that compartment becomes time-dependent. This modification is strongly suggested by the physical alteration which certain substances, e.g. hay particles, undergo in the digestive process. The proposed model is applied to experimental data.
Matis, J. H.↗
The X-ray Spectral Evolution of eta Carinae as Seen by ASCA
Using data from the ASCA X-ray observatory, we examine the variations in the X-ray spectrum of the supermassive star nu Carinae with an unprecedented combination of spatial and spectral resolution. We include data taken during the recent X-ray eclipse in 1997-1998, after recovery from the eclipse, and during and after an X-ray flare. We show that the eclipse variation in the X-ray spectrum is apparently confined to a decrease in the emission measure of the source. We compare our results with a simple colliding wind binary model and find that the observed spectral variations are only consistent, with the binary model if there is significant high-temperature emission far from the star and/or a substantial change in the temperature distribution of the hot plasma. If contamination in the 2-10 keV band is important, the observed eclipse spectrum requires an absorbing column in excess of 10(exp 24)/sq cm for consistency with the binary model, which may indicate an increase in the first derivative of M from nu Carinae near the time of periastron passage. The flare spectra are consistent with the variability seen in nearly simultaneous RXTE observations and thus confirm that nu Carinae itself is the source of the flare emission. The variation in the spectrum during the flare seems confined to a change in the source emission measure. By comparing 2 observations obtained at the same phase in different X-ray cycles, we find that the current, X-ray brightness of the source is slightly higher than the brightness of the source during the last cycle perhaps indicative of a long-term increase in the first derivative of M, not associated with the X-ray cycle.
Corcoran, M. F.↗
Measurements of SO2 in the Mount St. Helens debris
Routine measurements of ozone and SO2 are made with the Dobson and Brewer spectrophotometers at the Atmospheric Environment Service in Downsview Ontario. On May 20 and 21, 1980, large values of column SO2 were observed with both spectrophotometers at the time of passage of the Mount St. Helens debris. Enhanced SO2 values were first observed at 1800Z on May 20. The maximum column amount of SO2 measured was 0.06 cm at 2200 Z. On May 21, SO2 values slowly decreased from 0.03 cm at 1100 Z cm to 0.01 cm at 2000Z. Typical SO2 amounts due to pollution at the Downsview site are approximately 0.003 to 0.005 cm. At the same time of maximum SO2 enhancement, both Dobson and Brewer spectrophotometers measured a 0.040 cm decrease of total ozone. It is not clear whether the decrease of total ozone was caused by the volcanic cloud or natural ozone variability. Air mass trajectories indicate that the altitude of the debris cloud, which passed over Downsview at the time, was between 10 km and 12 km.
Kerr, J. B.↗
INTEGRAL Observations of the Be/X-ray binary EX0 2030+375 During Outburst
We present a type-I outburst of the high-mass X-ray binary EX0 2030+375, detected during INTEGRAL'S Performance and Verification phase in December 2002 (on-source time about 10(exp 6) seconds). In addition, six more outbursts have been observed during INTEGRAL'S Galactic Plane Scans. X-ray pulsations have been detected with a pulse period of 41.691798 plus or minus 0.000016 s. The X-ray luminosity in the 5-300 keV energy range was 9.7 x 10 (exp 36) erg per second, for a distance of 7.1 kpc. Two unusual features were found in the light curve, with an initial peak before the main outburst and another possible spike after the maximum. RXTE observations confirm only the existence of the initial spike. Although the initial peak appears to be a recurrent feature, the physical mechanisms producing it and the possible second spike are unknown. Moreover, a four-day delay between periastron passage and the peak of the outburst is observed. We present for the first time a 5-300 keV broad-band spectrum of this source. It can be modelled by the sum of a disk black body (kT(sub BB) approximately 8 keV) and either with a power law model with Gamma=2.04 plus or minus 0.11 keV or a Comptonized component (spherical geometry, kT(sub e).=30 keV, tau = 2.64, kT(sub w)=1.5 keV).
Arranz, A. Camero↗
Two Components in Major Solar Particle Events
A study has been made of 29 intense, solar particle events observed in the energy range 25-100 MeV/nuc near Earth in the years 1997 through 2001. It is found that the majority of the events (19/29) had Fe to O ratios which were reasonably constant with time and energy, and with values above coronal. These all originated on the Sun s western hemisphere and most had intensities that rose rapidly at the time of an associated flare, and coronal mass ejection (CME), and then decayed more gradually. Few interplanetary shocks were observed during these increases. The spectra were mainly power laws. The remaining 10 events had different intensity-time profiles and Fe to O ratios that varied with time and energy with values at or below coronal. Most of these originated near central meridian and 6 had strong interplanetary shocks that were observed near Earth. In general the spectra were not power laws but steepened at high energies, particularly for Fe. There were four events with two peaks in the intensity-time profiles, the first near the time of the associated flare and the other at shock passage. The results, considered in the light of other recent work, suggest that the high energy particles that occur shortly after flares are indeed flare particles. At the highest rigidities considered here shock-accelerated particles are uncommon and are observed only in association with unusually fast shocks.
White, Nicholas E.↗
Simplified night sky display system
A portable structure, simply constructed with inexpensive and generally lightweight materials, for displaying a selected portion of the night sky and selected planets, satellites, comets and other astronomically observable objects that are visually perceptible within that portion of the night sky. The structure includes a computer having stored signals representing the observable objects, an image projector that converts and projects the stored signals as visually perceptible images, a first curvilinear light-reflecting surface to receive and reflect the visually perceptible images, and a second curvilinear surface to receive and display the visually perceptible images reflected from the first surface. The images may be motionless or may move with passage of time. In one embodiment, the structure includes an inflatable screen surface that receives gas in an enclosed volume, supports itself without further mechanical support, and optionally self-regulates pressure of the received gas within the enclosed volume.
Castellano, Timothy P.↗
Time-to-Passage Judgments under Violations of Various Constancy Assumptions
Time-to-passage (TTP) derivations typically assume constant translational velocities and consistent object orientation. In our first study, we examined the impact of acceleration, and observer roll and heading (relative to track vector) on TTP judgments. Judgments reflected an insensitivity to acceleration; roll did not affect performance, but the decoupling of observer heading and track vector did. Our second study examined the effect of multi-axis target rotation on TTP and time-to-contact judgments.
Kaiser, Mary K.↗
Diagrammatic theory of transition of pendulum like systems
Orbit-orbit and spin-orbit gravitational resonances are analyzed using the model of a rigid pendulum subject to both a time-dependent periodic torque and a constant applied torque. First, a descriptive model of passage through resonance is developed from an examination of the polynomial equation that determines the extremes of the momentum variable. From this study, a probability estimate for capture into libration is derived. Second, a lowest order solution is constructed and compared with the solution obtained from numerical integration. The steps necessary to systematically improve this solution are also discussed. Finally, the effect of a dissipative term in the pendulum equation is analyzed.
Yoder, C. F.↗