Search NASA⌕ Search

SEARCH · Search NASA

Results for “probability amplitudes”

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.

At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Reactant conversion in homogeneous turbulence: Mathematical modeling, computational validations and practical applications

Closed form analytical expressions are obtained for predicting the limited rate of reactant conversion in a binary reaction of the type F + rO yields (1 + r) Product in unpremixed homogeneous turbulence. These relations are obtained by means of a single point Probability Density Function (PDF) method based on the Amplitude Mapping Closure. It is demonstrated that with this model, the maximum rate of the reactants' decay can be conveniently expressed in terms of definite integrals of the Parabolic Cylinder Functions. For the cases with complete initial segregation, it is shown that the results agree very closely with those predicted by employing a Beta density of the first kind for an appropriately defined Shvab-Zeldovich scalar variable. With this assumption, the final results can also be expressed in terms of closed form analytical expressions which are based on the Incomplete Beta Functions. With both models, the dependence of the results on the stoichiometric coefficient and the equivalence ratio can be expressed in an explicit manner. For a stoichiometric mixture, the analytical results simplify significantly. In the mapping closure, these results are expressed in terms of simple trigonometric functions. For the Beta density model, they are in the form of Gamma Functions. In all the cases considered, the results are shown to agree well with data generated by Direct Numerical Simulations (DNS). Due to the simplicity of these expressions and because of nice mathematical features of the Parabolic Cylinder and the Incomplete Beta Functions, these models are recommended for estimating the limiting rate of reactant conversion in homogeneous reacting flows. These results also provide useful insights in assessing the extent of validity of turbulence closures in the modeling of unpremixed reacting flows. Some discussions are provided on the extension of the model for treating more complicated reacting systems including realistic kinetics schemes and multi-scalar mixing with finite rate chemical reactions in more complex configurations.

Madnia, C. K.↗
DOE OSTI2020

A quantum algorithm to efficiently sample from interfering binary trees

Quantum computers provide an opportunity to efficiently sample from probability distributions that include non-trivial interference effects between amplitudes. Using a simple process wherein all possible state histories can be specified by a binary tree, we construct an explicit quantum algorithm that runs in polynomial time to sample from the process once. The corresponding naive Markov Chain algorithm does not produce the correct probability distribution and an explicit classical calculation of the full distribution requires exponentially many operations. Finally, the problem can be reduced to a system of two qubits with repeated measurements, shedding light on a quantum-inspired efficient classical algorithm.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1995

Equalization and detection for digital communication over nonlinear bandlimited satellite communication channels

This dissertation evaluates receiver-based methods for mitigating the effects due to nonlinear bandlimited signal distortion present in high data rate satellite channels. The effects of the nonlinear bandlimited distortion is illustrated for digitally modulated signals. A lucid development of the low-pass Volterra discrete time model for a nonlinear communication channel is presented. In addition, finite-state machine models are explicitly developed for a nonlinear bandlimited satellite channel. A nonlinear fixed equalizer based on Volterra series has previously been studied for compensation of noiseless signal distortion due to a nonlinear satellite channel. This dissertation studies adaptive Volterra equalizers on a downlink-limited nonlinear bandlimited satellite channel. We employ as figure of merits performance in the mean-square error and probability of error senses. In addition, a receiver consisting of a fractionally-spaced equalizer (FSE) followed by a Volterra equalizer (FSE-Volterra) is found to give improvement beyond that gained by the Volterra equalizer. Significant probability of error performance improvement is found for multilevel modulation schemes. Also, it is found that probability of error improvement is more significant for modulation schemes, constant amplitude and multilevel, which require higher signal to noise ratios (i.e., higher modulation orders) for reliable operation. The maximum likelihood sequence detection (MLSD) receiver for a nonlinear satellite channel, a bank of matched filters followed by a Viterbi detector, serves as a probability of error lower bound for the Volterra and FSE-Volterra equalizers. However, this receiver has not been evaluated for a specific satellite channel. In this work, an MLSD receiver is evaluated for a specific downlink-limited satellite channel. Because of the bank of matched filters, the MLSD receiver may be high in complexity. Consequently, the probability of error performance of a more practical suboptimal MLSD receiver, requiring only a single receive filter, is evaluated.

Gutierrez, Alberto, Jr.↗
NASA NTRS1997

Torque Reversal and Spin-Down of the Accretion-Powered Pulsar 4U 1626-67

Over 5 yr of hard X-ray (20-60 keV) monitoring of the 7.66 s accretion-powered pulsar 4U 1626-67 with the Compton Gamma Ray Observatory/BATSE large-area detectors has revealed that the neutron star is now steadily spinning down, in marked contrast to the steady spin-up and spin-down torques differ by only 15% with the neutron star spin changing on a timescale |v/v| approximately equals 5000 yr in both states. The current spin-down rate is itself decreasing on a timescale |v/v| approximately equals 26 yr. The long-term timing history shows small-amplitude variations on a 4000 day timescale, which are probably due to variations in the mass transfer rate. The pulsed 20-60 keV emission from 4U 1626-67 is well-fitted by a power-law spectrum with photon index gamma = 4.9 and a typical pulsed intensity of 1.5 x 10(exp -10) ergs cm (exp -2)s(exp -1). The low count rates with BATSE prohibited us from constraining the reported 42 minute binary orbit, but we can rule out long-period orbits in the range 2 days < or = P(orb) < or = 900 days. We compare the long-term torque behavior of 4U 1626-67 to other disk-fed accreting pulsars and discuss the implications of our results for the various theories of magnetic accretion torques. The abrupt change in the sign of the torque is difficult to reconcile with the extremely smooth spin-down now observed. The strength of the torque noise in 4U 1626-67, approximately 10(exp -22) Hz(exp 2)s(exp -2) Hz(exp -1), is the smallest ever measured for an accreting X-ray pulsar, and it is comparable to the timing noise seen in young radio pulsars. We close by pointing out that the core temperature and external torque (the two parameters potentially relevant to internal sources of timing noise) of an accreting neutron star are also comparable to those of young radio pulsars.

Chakrabarty, Deepto L.↗
DOE OSTI2020

BeyondPlanck I. Global Bayesian analysis of the Planck Low Frequency Instrument data

We describe the BeyondPlanck project in terms of motivation, methodology and main products, and provide a guide to a set of companion papers that describe each result in fuller detail. Building directly on experience from ESA's Planck mission, we implement a complete end-to-end Bayesian analysis framework for the Planck Low Frequency Instrument (LFI) observations. The primary product is a joint posterior distribution P(omega|d), where omega represents the set of all free instrumental (gain, correlated noise, bandpass etc.), astrophysical (synchrotron, free-free, thermal dust emission etc.), and cosmological (CMB map, power spectrum etc.) parameters. Some notable advantages of this approach are seamless end-to-end propagation of uncertainties; accurate modeling of both astrophysical and instrumental effects in the most natural basis for each uncertain quantity; optimized computational costs with little or no need for intermediate human interaction between various analysis steps; and a complete overview of the entire analysis process within one single framework. As a practical demonstration of this framework, we focus in particular on low-l CMB polarization reconstruction, paying special attention to the LFI 44 GHz channel. We find evidence of significant residual systematic effects that are still not accounted for in the current processing, but must be addressed in future work. These include a break-down of the 1/f correlated noise model at 30 and 44 GHz, and scan-aligned stripes in the Southern Galactic hemisphere at 44 GHz. On the Northern hemisphere, however, we find that all results are consistent with the LCDM model, and we constrain the reionization optical depth to tau = 0.067 +/- 0.016, with a low-resolution chi-squared probability-to-exceed of 16%. The marginal CMB dipole amplitude is 3359.5 +/- 1.9 uK. (Abridged.)

Andersen, KJ↗
NASA NTRS1986

Observations and a model of gravity-wave variability in the middle atmosphere

A major goal was to determine what portion of the gravity-wave frequency spectrum accounted for the majority of the momentum flux and divergence, as this has important implications for the middle atmosphere response. It was found that approx. 70% of the total flux and divergence was due to wave motions with observed periods less than 1 hour, consistent with expectations based on the shape of the observed gravity-wave spectrum (FrItts, 1984). This dominance of the momentum flux and divergence by high-frequency motions implies a potential for the modulation of those quantities by large-amplitude motions at lower frequencies. A second, striking aspect of the velocity and momentum flux data is its dramatic diurnal variability, particularly at certain levels. This variability is illustrated with the momentum flux, computed in 8-hr blocks. The dominant contributions here are due to waves with periods less than 1 hr. The variability with height and size of the mean square velocity in the west beam and the momentum flux, energed over the 3-day period. A detailed analysis of the various tidal motions present during this data interval was performed, and it was determined that variations in the zontal wind profile imposed by the diurnal tidal motion are probably responsible for the modulation of the gravity-wave amplitudes and momentum fluxes.

Fritts, D. C.↗
NASA NTRS1994

The peculiar type II supernova 1993J in M81: Transition to the nebular phase

We present optical spectra of the bright, peculiar Type II supernova 1993J in M81 spanning the first 14 months of its existence, revealing its transition to the nebular phase. Unlike the case in normal Type II supernovae, during the first 2-10 months the H-alpha emission line gradually becomes less prominent relative to other features such as (O I) lambda lambda 6300, 6364 and (Ca II) lambda lambda 7291, 7324, as we had predicted based on early-time (tau less than or approximately equal to 2 months) spectra. The nebular spectrum resembles those of the Type Ib/Ic supernovae 1985F and 1987M, although weak H-alpha emission is easily visible even at late times in SN 1993J. At tau = 8 months a close similarity is found with the spectrum of SN 1987K, the only other Type II supernova known to have undergone such a metamorphosis. The emission lines are considerably broader than those of normal Type II supernovae at comparable phases, consistent with the progenitor having lost a majority of its hydrogen envelope prior to exploding. Consequently, there is now little doubt that Type Ib, and probably Type Ic, supernovae result from core collapse in stripped, massive stars; models of the chemical evolution of galaxies in which these subtypes are ascribed to exploding white dwarfs must be appropriately modified. Although all of the emission lines in spectra of SN 1993J fade roughly exponentially for a considerable time, the fading of H-alpha begins to slow down at tau approximately = 8 months, and in the interval tau = 10-14 months its flux is constant, or even slightly rising in the wings of the line. This behavior, together with the box-like shape and great breadth (full width at half maximum (FWHM) approximately = 17 000 km/s) of the line profile, suggests that the H-alpha emission is being produced by the high-velocity outer layer of hydrogen ejecta interacting with circumstellar gas released by the progenitor prior to its explosion. A similar phenomenon has previously been seen at later phases in several Type II supernovae, most notably SN 1980K. Bumps (FWHM approximately = 1000 km/s, amplitude approximately = 20%) in the H-alpha profile are probably indicative of Rayleigh-Taylor instabilities in the cool gas behind the reverse shock. A very narrow component (unresolved, FWHM less than or approximately equal to 200 km/s) of H-alpha at the symmetric velocity of SN 1993J may instead be produced by a superposed H II region, or perhaps by recombination in a large circumstellar shell or ring that was ionized during the first few hours after outburst. In the near future the spectrum of SN 1993J should become increasingly dominated by broad H-alpha emission.

Filippenko, Alexei V.↗
NASA NTRS1967

FM carrier deviation measured by differential probability method

Differential probability FM system measures deviation of a carrier modulated by a complex signal. The peak-to-peak amplitude is measured and related to the frequency shift of the carrier signal. The deviation is described in terms of a probability as well as a peak value.

Daquin, A. F., Jr.↗
DOE OSTI2020

Comparison between mirror Langmuir probe and gas-puff imaging measurements of intermittent fluctuations in the Alcator C-Mod scrape-off layer

Statistical properties of the scrape-off layer plasma fluctuations are studied in ohmically heated plasmas in the Alcator C-Mod tokamak. For the first time, plasma fluctuations as well as parameters that describe the fluctuations are compared across measurements from a mirror Langmuir probe (MLP) and from gas-puff imaging (GPI) that sample the same plasma discharge. This comparison is complemented by an analysis of line emission time-series data, synthesized from the MLP electron density and temperature measurements. The fluctuations observed by the MLP and GPI typically display relative fluctuation amplitudes of order unity together with positively skewed and flattened probability density functions. Such data time series are well described by an established stochastic framework that models the data as a superposition of uncorrelated, two-sided exponential pulses. The most important parameter of the process is the intermittency parameter, $γ=τ_d/τ_w$, where τd denotes the duration time of a single pulse and $τ_w$ gives the average waiting time between consecutive pulses. In this study we show, using a new deconvolution method, that these parameters can be consistently estimated from different statistics of the data. We also show that the statistical properties of the data sampled by the MLP and GPI diagnostic are very similar. Finally, a synthetic GPI signal using only plasma parameters sampled by the MLP shows qualitatively different fluctuation statistics from the measured GPI signal.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Distinct critical behaviors from the same state in quantum spin and population dynamics perspectives

There is a deep connection between the ground states of transverse-field spin systems and the late-time distributions of evolving viral populations—within simple models, both are obtained from the principal eigenvector of the same matrix. However, that vector is the wave-function amplitude in the quantum spin model, whereas it is the probability itself in the population model. We show that this seemingly minor difference has significant consequences: Phase transitions that are discontinuous in the spin system become continuous when viewed through the population perspective, and transitions that are continuous become governed by new critical exponents. We introduce a more general class of models that encompasses both cases and that can be solved exactly in a mean-field limit. Numerical results are also presented for a number of one-dimensional chains with power-law interactions. We see that well-worn spin models of quantum statistical mechanics can contain unexpected new physics and insights when treated as population-dynamical models and beyond, motivating further studies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1973

Recursive ideal observer detection of known M-ary signals in multiplicative and additive Gaussian noise.

This paper presents the derivation of the recursive algorithms necessary for real-time digital detection of M-ary known signals that are subject to independent multiplicative and additive Gaussian noises. The motivating application is minimum probability of error detection of digital data-link messages aboard civil aircraft in the earth reflection multipath environment. For each known signal, the detector contains one Kalman filter and one probability computer. The filters estimate the multipath disturbance. The estimates and the received signal drive the probability computers. Outputs of all the computers are compared in amplitude to give the signal decision. The practicality and usefulness of the detector are extensively discussed.

Painter, J. H.↗
NASA NTRS1982

Solution to the backward-Kolmogorov equation for a nonstationary oscillation problem

The transition probability density function of a Markovian approximation of the response amplitude of an oscillator under nonstationary excitation is determined in an analytical form. A solution is presented for the associated backward-Kolmogorov equation by transforming the equation into a form amenable to solution by the method of the separation of variables. This procedure results in a boundary value problem which is then solved by using an infinite series of Laguerre polynomials. It is found that the infinite series solution is equivalent to a closed-form solution involving a Bessel function.

Solomos, G. P.↗
NASA NTRS1983

Reliability considerations in the placement of control system components

This paper presents a methodology, along with applications to a grid type structure, for incorporating reliability considerations in the decision for actuator placement on large space structures. The method involves the minimization of a criterion that considers mission life and the reliability of the system components. It is assumed that the actuator gains are to be readjusted following failures, but their locations cannot be changed. The goal of the design is to suppress vibrations of the grid and the integral square of the grid modal amplitudes is used as a measure of performance of the control system. When reliability of the actuators is considered, a more pertinent measure is the expected value of the integral; that is, the sum of the squares of the modal amplitudes for each possible failure state considered, multiplied by the probability that the failure state will occur. For a given set of actuator locations, the optimal criterion may be graphed as a function of the ratio of the mean time to failure of the components and the design mission life or reservicing interval. The best location of the actuators is typically different for a short mission life than for a long one.

Montgomery, R. C.↗
NASA NTRS1985

Results of November 1981 and May 1982 ATMAP Campaigns at Adelaide (35 Deg S, 138 Deg E)

The mean zonal circulation for both the November and May campaigns are representative of early summer and winter conditions. The mean meridional flow in November was stable and typical of summer conditions at Adelaide. The conditions in May were, however, more variable and appeared to be changing significantly during the campaign. It is possible that there was a strong influence from a large scale wave which could account for the large meridional wind values observed. Overall, the mean tidal structures observed during the core periods were not significantly different from those observed in two-week intervals centered on the cores. In May both components show evidence for propagating components with 30 to 40 km vertical wavelengths. For the semidiurnal components, the phase structures show evidence for vertical propagation with apparent vertical wavelengths of the order of 50 km. The mean amplitudes for the semidiurnal components in May are close to the noise level. Typical errors from the harmonic analysis are + or - 1 to 2 ms(-1) in amplitude and + or - 0.5 hr in phase, but these are probably underestimates.

Vincent, R. A.↗
NASA NTRS1993

Large-amplitude auroral electric fields measured with DE 1

A large fraction of the available electric field data from the plasma wave instrument (PWI) on the Dynamics Explorer (DE) 1 satellite has recently been searched for events with large-amplitude electric fields. The magnitude and distribution of these peak events as functions of altitude have been determined. The largest amplitudes were found between 1.4 and 2.5 RE and the probability of finding large electric fields was greatest in the range of 1.5 to 1.7 RE. However, when the measured electric field values are 'mapped' to the Earth's surface in order to account for the geometry of the geomagnetic field lines, then the mapped values always increase with increasing altitude. This radial dependence is considered to be evidence for magnetic field-aligned electric fields. The largest electric field that was detected with the DE 1 instrument had a magnitude exceeding 840 mV/m and was found at 1.45 R(E). This field appears to be associated with a low-frequency wave. At subauroral latitudes the average mapped electric field is nearly constant with altitude, as it should be where there are no magnetic field-aligned potential drops. Within auroral latitudes the average value of the mapped electric field increases as altitude increases. The largest gradients are found between 1.3 and 2 R(E).

Weimer, D. R.↗
NASA NTRS2002

A Bayesian Approach to Estimating Coupling Between Neural Components: Evaluation of the Multiple Component, Event-Related Potential (mcERP) Algorithm

Accurate measurement of single-trial responses is key to a definitive use of complex electromagnetic and hemodynamic measurements in the investigation of brain dynamics. We developed the multiple component, Event-Related Potential (mcERP) approach to single-trial response estimation. To improve our resolution of dynamic interactions between neuronal ensembles located in different layers within a cortical region and/or in different cortical regions. The mcERP model assets that multiple components defined as stereotypic waveforms comprise the stimulus-evoked response and that these components may vary in amplitude and latency from trial to trial. Maximum a posteriori (MAP) solutions for the model are obtained by iterating a set of equations derived from the posterior probability. Our first goal was to use the ANTWERP algorithm to analyze interactions (specifically latency and amplitude correlation) between responses in different layers within a cortical region. Thus, we evaluated the model by applying the algorithm to synthetic data containing two correlated local components and one independent far-field component. Three cases were considered: the local components were correlated by an interaction in their single-trial amplitudes, by an interaction in their single-trial latencies, or by an interaction in both amplitude and latency. We then analyzed the accuracy with which the algorithm estimated the component waveshapes and the single-trial parameters as a function of the linearity of each of these relationships. Extensions of these analyses to real data are discussed as well as ongoing work to incorporate more detailed prior information.

Shah, Ankoor S.↗
NASA NTRS2007

On the Evolution of Localized Disturbances and their Spanwise Interactions Leading to Breakdown

Localized disturbances in a laminar boundary layer represent a more realistic model of transition than the extensively studies, two or quasi three-dimensional perturbations regardless of the fact if they evolve in a linear manner or not. Localized disturbances can originate by surface imperfections, insects or dust. The disturbances can be harmonic (i.e. containing a single frequency and a complete set of spanwise wave numbers) or Pulsed (i.e. containing a band of streamwise and spanwise wave numbers). At sufficiently low amplitudes localized disturbances behave according to a linear stability model. It is highly probably that in a natural transition process such localized disturbances will overslap and interact. These interactions could either delay transition because of a partial wave cancellation resulting in an attenuation of the disturbance, or adversely enhance it by promoting nonlinear interactions. The nonlinearity could be simply amplitude dependent or cause a triad resonance. Nonlinear processes in a wave packet lead to breakdown and to the formation of turbulent spots. When the amplitude of the harmonic disturbance saturates, nonlinear processes widen the band of the lower amplified frequencies adjacent to the frequency of excitation. Experimental results describing the spanwise interactions of harmonic and pulsed localized disturbances leading to breakdown will be presented and discussed. A comparison to the evolution and breakdown of a single localized disturbance will be provided.

Seifert, Avi↗
NASA NTRS1982

Focusing of waves in turbulent inhomogeneous media

A stochastic method using geometrical acoustics is employed to investigate the growth of a large fluctuation in the amplitude of high-frequency waves or shocks propagating through turbulent, inhomogeneous media. Nonlinear terms are retained in the analysis to correctly model focusing and growth of singular fluctuations in the amplitude. A two-dimensional analysis reveals that fluctuations in the ray-tube area grow exponentially and every ray displays caustics. Probability densities for the appearance of caustics are provided, and moments of the ray-tube area distribution and amplitude-related statistics are formulated for distances far into the region of caustic formation. Finally, a relationship is defined between theoretical predictions and measurements on an image plane.

Kulkarny, V. A.↗