SEARCH · Search NASA

Results for “Statistical field theory”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 163 records · Page 9

All sources NASA NTRS DOE OSTI

NASA NTRS1996

Transient Sub-Poissonian Distribution for Single-Mode Lasers

In this paper, the transient photon statistics for single-mode lasers is investigated by making use of the theory of quantum electrodynamics. By taking into account of the transitive time l,we obtain the master equation for Jaynes-Cummings model. The relation between the Mandel factor and the time is obtained by directly solving the master equation. The result shows that a transient phenomenon from the transient super-Poissonian distribution to the transient sub-Poissonian distribution occurs for single-mode lasers. In addition, the influences of the thermal light field and the cavity loss on the transient sub-Poissonian distribution are also studied.

Zang, J. Y.↗

NASA NTRS2015

On Theoretical Broadband Shock-Associated Noise Near-Field Cross-Spectra

The cross-spectral acoustic analogy is used to predict auto-spectra and cross-spectra of broadband shock-associated noise in the near-field and far-field from a range of heated and unheated supersonic off-design jets. A single equivalent source model is proposed for the near-field, mid-field, and far-field terms, that contains flow-field statistics of the shock wave shear layer interactions. Flow-field statistics are modeled based upon experimental observation and computational fluid dynamics solutions. An axisymmetric assumption is used to reduce the model to a closed-form equation involving a double summation over the equivalent source at each shock wave shear layer interaction. Predictions are compared with a wide variety of measurements at numerous jet Mach numbers and temperature ratios from multiple facilities. Auto-spectral predictions of broadband shock-associated noise in the near-field and far-field capture trends observed in measurement and other prediction theories. Predictions of spatial coherence of broadband shock-associated noise accurately capture the peak coherent intensity, frequency, and spectral width.

Miller, Steven A. E.↗

NASA NTRS1982

Statistical mechanics of dilute liquid mixtures of He3 in He4

The Woo-Tan-Massey quantum-mechanical theory of dilute mixtures of He-3 in liquid He-4 is extended to incorporate superfluid flow. Then statistical-mechanical principles are employed to find explicit formulas for thermodyanmic and hydrodynamic properties of mixtures, such as internal energy, free energy, entropy, pressure, chemical potential, and normal-fluid and superfluid densities. This paper is the first in a planned series that applies methods originally developed for pure liquid He-4 to dilute mixtures as a means of establishing a comprehensive theory that includes a theoretical bridge between a microscopic description of the mixtures and a hydrodynamic two-fluid model. Ultimately effects of applied electric and magnetic fields on dilute solutions are also planned to be treated.

Jackson, H. W.↗

NASA NTRS1985

Cometary dynamics

Modern theories of cometary dynamics are described. Attention is given to Oort's hypothesis that the Solar System is surrounded by a spherically symmetrical cloud of about 10 to the 11th to 10 to the 12th comets extending out to interstellar distances. Dynamical modelling and statistical analyses of cometary motion have confirmed the ability of the Oort hypothesis to explain the observed distribution of energies for the long-period cometary orbits. Some of the sources cometary motion perturbations are discussed, including: random passing stars; interstellar clouds; and the galactic gravitational field. Perturbations in cometary motion in the planetary region are attributed to the gravitational fields of the major planets and nongravitational forces resulting from jetting of volatiles on the surfaces of cometary nuclei. Observational evidence for the existence of a massive inner Oort cloud extending from just beyond the orbit of Neptune to 10,000 AU is presented.

Weissman, P. R.↗

NASA NTRS1998

[Cosmic Microwave Background (CMB) Anisotropies]

One of the main areas of research is the theory of cosmic microwave background (CMB) anisotropies and analysis of CMB data. Using the four year COBE data we were able to improve existing constraints on global shear and vorticity. We found that, in the flat case (which allows for greatest anisotropy), (omega/H)0 less than 10(exp -7), where omega is the vorticity and H is the Hubble constant. This is two orders of magnitude lower than the tightest, previous constraint. We have defined a new set of statistics which quantify the amount of non-Gaussianity in small field cosmic microwave background maps. By looking at the distribution of power around rings in Fourier space, and at the correlations between adjacent rings, one can identify non-Gaussian features which are masked by large scale Gaussian fluctuations. This may be particularly useful for identifying unresolved localized sources and line-like discontinuities. Levin and collaborators devised a method to determine the global geometry of the universe through observations of patterns in the hot and cold spots of the CMB. We have derived properties of the peaks (maxima) of the CMB anisotropies expected in flat and open CDM models. We represent results for angular resolutions ranging from 5 arcmin to 20 arcmin (antenna FWHM), scales that are relevant for the MAP and COBRA/SAMBA space missions and the ground-based interferometer. Results related to galaxy formation and evolution are also discussed.

Silk, Joseph↗

NASA NTRS1997

Planar Doppler Velocimetry for Large-Scale Wind Tunnel Testing

Recently, Planar Doppler Velocimetry (PDV) has been shown by several laboratories to offer an attractive means for measuring three-dimensional velocity vectors everywhere in a light sheet placed in a flow. Unlike other optical means of measuring flow velocities, PDV is particularly attractive for use in large wind tunnels where distances to the sample region may be several meters, because it does not require the spatial resolution and tracking of individual scattering particles or the alignment of crossed beams at large distances. To date, demonstrations of PDV have been made either in low speed flows without quantitative comparison to other measurements, or in supersonic flows where the Doppler shift is large and its measurement is relatively insensitive to instrumental errors. Moreover, most reported applications have relied on the use of continuous-wave lasers, which limit the measurement to time-averaged velocity fields. This work summarizes the results of two previous studies of PDV in which the use of pulsed lasers to obtain instantaneous velocity vector fields is evaluated. The objective has been to quantitatively define and demonstrate PDV capabilities for applications in large-scale wind tunnels that are intended primarily for the production testing of subsonic aircraft. For such applications, the adequate resolution of low-speed flow fields requires accurate measurements of small Doppler shifts that are obtained at distances of several meters from the sample region. The use of pulsed lasers provides the unique capability to obtain not only time-averaged fields, but also their statistical fluctuation amplitudes and the spatial excursions of unsteady flow regions such as wakes and separations. To accomplish the objectives indicated, the PDV measurement process is first modeled and its performance evaluated computationally. The noise sources considered include those related to the optical and electronic properties of Charge-Coupled Device (CCD) arrays and to speckle effects associated with coherent illumination from pulsed lasers. The signal noise estimates are incorporated into the PDV signal analysis process and combined with computed scattering signals using a Mie scattering theory for polydisperse smoke particles. The relevant parameters incorporate a range of practical aerodynamic test conditions and facility sizes. The results define the optimum instrument configurations, show that the expected signal levels from a practical PDV system are sufficiently large to allow its useful application in large facilities, and show that the expected velocity measurement uncertainties are small compared to the mean velocities of interest for most subsonic, large-scale wind tunnel testing. Experimental studies using several experimental bench-top setups are then described that validate the physics of the PDV model and to calibrate its computed results. The validated model allows estimates of the uncertainties of PDV measurements and a complete definition of the PDV capabilities to be made with sufficient confidence to decide the viability of PDV for large-scale wind tunnel applications.

McKenzie, Robert L.↗

NASA NTRS1998

The Impact of FU Orionis Outbursts and the Solar Nebula

Protostellar systems are variable on many timescales. One of the most dramatic forms of variability known to occur in low mass stellar systems is the FU Orionis outburst (Herbig 1977). Throughout a typical outburst lasting several decades, system luminosities may be a hundred times what is typical of the quiesent state. FU Orionis outburst events are thought to have significant impact on the thermal structure of the protosolar nebula; their existence has been used to explain features in the meteoritic record from thermally induced homogenization to the formation of chondrules. Until recently, the magnitude of the likely effect from such outbursts has been largely speculative due to the lack of a detailed understanding of the outburst mechanism. Recent numerical models (Bell\& Lin 1994) have demonstrated the viability of the observational hypothesis (Hartmann\& Kenyon 1985) that the radiation observed during outburst is emitted by a luminous circumstellar disk transporting mass at a thousand times the quiesent rate. Light curves and color and line width evolution observed in FU Orionis systems are naturally explained by time dependent outbursting model disks (Bell et al. 1995). The radial temperature structure and shape of the disk during outburst derived from these models may be used to calculate the outburst's expected impact on primitive material at various radii throughout the disk. In this review, we will begin by discussing what is known about the FU Orionis outburst phenomenon from recent observations and theory including statistically deduced outburst timescales and observed peak temperatures. Unless covered by another author, we will discuss the evidence which suggests that outburst radiation is emitted by a circumstellar disk rather than by the star and will briefly review the thermal instability as a mechanism for outburst. We will then report on recent work which investigates the likely heating of solar nebula material due to FU Orionis outbursts including the following effects: (1) heating of the planet forming region by direct radiation from the hot inner nebula; (2) heating by the diffuse radiation field of a coccooning envelope; and (3) time-dependent penetration of the increased luminosity from the above sources into the optically thick nebula. Some of this work is currently in progress. The potential effects on condensation and migration in the nebula and the thermal processing of solids will be evaluated.

Bell, Robbins↗

NASA NTRS2021

A Low-Memory Spectral-Correlation Analyzer for Digital QAM-SRRC Waveforms

Cyclostationary signal processing (CSP) provides the ability to estimate received waveforms' statistical features blindly. Quadrature amplitude modulated (QAM) waveforms, when filtered by the square-root-raised cosine (SRRC) pulse shape function, have cyclic features that CSP can exploit to detect waveform parameters such as symbol rate (SR) and center frequency (CF). The estimation of these SR-CF pairs enables a cognitive radio (CR) to perform spectrum sensing techniques such as spectrum sharing and interference mitigation. Here, we investigate a field-programmable gate array (FPGA) application of a blind symbol rate-center frequency estimator. First, this study provides a background on the theory behind the cyclic spectral density function (CSD), spectral correlation analyzers (SCA), and spectrum sensing. Following this is a discussion on the motivation for CubeSat spectrum sensing. An SCA implementation for low-memory devices, such as FPGA-based CubeSat, is then describes. The paper concludes by reporting the performance characteristics of the newly developed streaming-based SCA.

FPGA↗

NASA NTRS1981

Langmuir probe theory and the problem of anisotropic collection

A more general understanding of Langmuir probe theory by going beyond particular coordinate systems as far as possible was studied. To delineate the role of initial velocities in the problem and to characterize the interaction between the velocity flow field and the electrostatic potential field both of which enter into the determination of particle trajectories are desired. The probe is supposed to be negatively charged throughout and the ensuing region of positive space charge about it differs fundamentally from the plasma region beyond in the sense that the former represents a region in which deterministic trajectories dominate while the lattice is a region dominated by statistical interactions largely controlled by the collisionless stationary Boltzmann equation. A general solution of this Boltzmann equation is given and its relationship to the problem of saturation current density in 3D is elucidated.

Kyrala, A.↗

NASA NTRS2000

Statistics Analysis of the Uncertainties in Cloud Optical Depth Retrievals Caused by Three-Dimensional Radiative Effects

This paper presents a simple approach to estimate the uncertainties that arise in satellite retrievals of cloud optical depth when the retrievals use one-dimensional radiative transfer theory for heterogeneous clouds that have variations in all three dimensions. For the first time, preliminary error bounds are set to estimate the uncertainty of cloud optical depth retrievals. These estimates can help us better understand the nature of uncertainties that three-dimensional effects can introduce into retrievals of this important product of the MODIS instrument. The probability distribution of resulting retrieval errors is examined through theoretical simulations of shortwave cloud reflection for a wide variety of cloud fields. The results are used to illustrate how retrieval uncertainties change with observable and known parameters, such as solar elevation or cloud brightness. Furthermore, the results indicate that a tendency observed in an earlier study, clouds appearing thicker for oblique sun, is indeed caused by three-dimensional radiative effects.

Varnai, Tamas↗

NASA NTRS1992

Ion radial diffusion in an electrostatic impulse model for stormtime ring current formation

Guiding-center simulations of stormtime transport of ring-current and radiation-belt ions having first adiabatic invariants mu is approximately greater than 15 MeV/G (E is approximately greater than 165 keV at L is approximately 3) are surprisingly well described (typically within a factor of approximately less than 4) by the quasilinear theory of radial diffusion. This holds even for the case of an individual model storm characterized by substorm-associated impulses in the convection electric field, provided that the actual spectrum of the electric field is incorporated in the quasilinear theory. Correction of the quasilinear diffusion coefficient D(sub LL)(sup ql) for drift-resonance broadening (so as to define D(sub LL)(sup ql)) reduced the typical discrepancy with the diffusion coefficients D(sub LL)(sup sim) deduced from guiding-center simulations of representative-particle trajectories to a factor of approximately 3. The typical discrepancy was reduced to a factor of approximately 1.4 by averaging D(sub LL)(sup sim), D(sub LL)(sup ql), and D(sub LL)(sup rb) over an ensemble of model storms characterized by different (but statistically equivalent) sets of substorm-onset times.

Chen, Margaret W.↗

NASA NTRS1993

The radiated noise from isotropic turbulence revisited

The noise radiated from isotropic turbulence at low Mach numbers and high Reynolds numbers, as derived by Proudman (1952), was the first application of Lighthill's Theory of Aerodynamic Noise to a complete flow field. The theory presented by Proudman involves the assumption of the neglect of retarded time differences and so replaces the second-order retarded-time and space covariance of Lighthill's stress tensor, Tij, and in particular its second time derivative, by the equivalent simultaneous covariance. This assumption is a valid approximation in the derivation of the second partial derivative of Tij/derivative of t exp 2 covariance at low Mach numbers, but is not justified when that covariance is reduced to the sum of products of the time derivatives of equivalent second-order velocity covariances as required when Gaussian statistics are assumed. The present paper removes these assumptions and finds that although the changes in the analysis are substantial, the change in the numerical result for the total acoustic power is small. The present paper also considers an alternative analysis which does not neglect retarded times. It makes use of the Lighthill relationship, whereby the fourth-order Tij retarded-time covariance is evaluated from the square of similar second order covariance, which is assumed known. In this derivation, no statistical assumptions are involved. This result, using distributions for the second-order space-time velocity squared covariance based on the Direct Numerical Simulation (DNS) results of both Sarkar and Hussaini(1993) and Dubois(1993), is compared with the re-evaluation of Proudman's original model. These results are then compared with the sound power derived from a phenomenological model based on simple approximations to the retarded-time/space covariance of Txx. Finally, the recent numerical solutions of Sarkar and Hussaini(1993) for the acoustic power are compared with the results obtained from the analytic solutions.

Lilley, Geoffrey M.↗

NASA NTRS1962

The Response of Ribbed Panels to Reverberant Acoustic Fields

A statistical method for estimating the response of ribbed panels to acoustic excitation is discussed. It is shown that the acceleration spectrum of the vibrational field is related to the pressure spectrum by a coupling factor which is a simple function of the radiation and mechanical resistance of the structure. The radiation resistance of a ribbed panel is studied as a function of frequency. The analysis predicts that ribbing increases the radiation resistance of the panel and hence its coupling to the acoustic field. The effect of various panel-rib boundary conditions is also considered. The results of experiments which were conducted to test the theory are reported. The agreement between theory and experiments is shown to be satisfactory.

BOUNDARY↗

NASA NTRS1976

Timing of solar cycles by rigid internal rotations

The so-called 11-year cycle of solar activity is really more complex and contains many periods of greatly different lengths. Periods as long as 178 years and as short as 3.1 years are predicted by a theory based on beats between rigidly rotating, inertially oscillating g-modes inside the sun. Most of the beat periods are then confirmed to about 1 percent accuracy in sunspot observations. Since the agreement is of high statistical significance, one can conclude that approximate alignment of major solar oscillation modes contributes to high solar activity. The theory receives further support when tested against an independent class of observations - the large-scale magnetic sector structure. Predicted rotation rates of at least four solar oscillation modes are detected in the sector data with discrepancies all less than 0.3 percent. As a by-product of these successful fits to observation, the mean rotation of the entire solar mass becomes known. Its rotation frequency is 4.49 by 10 to the -7th power Hz, which is a sidereal period of 25.8 days. Magnetic fields have played no role in calculating the length of any of these solar cycles.

Wolff, C. L.↗

NASA NTRS1985

An update on the correlation between the cosmic radiation intensity and the geomagnetic AA index

A statistical study between the cosmic ray intensity, as observed by a neutron monitor, and of the geomagnetic aa index, as representative of perturbations in the plasma and interplanetary magnetic field in the heliosphere, has been updated to specifically exclude time periods around the reversal of the solar magnetic field. The results of this study show a strong negative correlation for the period 1960 through 1968 with a correlation coefficient of approximately -0.86. However, there is essentially no correlation between the cosmic ray intensity and the aa index for the period 1972-1979 (i.e. correlation coefficient less than 0.16). These results would appear to support the theory of preferential particle propagation into the heliosphere vis the ecliptic during the period 1960-1968 and via the solar polar regions during 1972-1979.

Shea, M. A.↗

NASA NTRS1983

Short-term climate variability and atmospheric teleconnections from satellite-observed outgoing longwave radiation. I Simultaneous relationships. II - Lagged correlations

Attention is given to the low-frequency variability of outgoing longwave radiation (OLR) fluctuations, their possible correlations over different parts of the globe, and their relationships with teleconnections obtained from other meteorological parameters, for example, geopotential and temperature fields. Simultaneous relationships with respect to the Southern Oscillation (Namais, 1978; Barnett, 1981) signal and the reference OLR fluctuation over the equatorial central Pacific are investigated. Emphasis is placed on the relative importance of the Southern Oscillation (SO) signal over preferred regions. Using lag cross-correlation statistics, possible lagged relationships between the tropics and midlatitudes and their relationships with the SO are then investigated. Only features that are consistent with present knowledge of the dynamics of the system are emphasized. Certain features which may not meet rigorous statistical significance tests but yet are either expected a priori from independent observations or are predicted from dynamical theories are also explored.

Lau, K.-M.↗

NASA NTRS1986

Discrete Dirac equation on a finite half-integer lattice

The formulation of the Dirac equation on a discrete lattice with half-integer spacing and periodic boundary conditions is investigated analytically. The importance of lattice formulations for problems in field theory and quantum mechanics is explained; the concept of half-integer Fourier representation is introduced; the discrete Dirac equation for the two-dimensional case is derived; dispersion relations for the four-dimensional case are developed; and the spinor formulation for the Dirac fields on the half-integer lattice and the discrete time variable for the four-dimensional time-dependent Dirac equation are obtained. It is argued that the half-integer lattice, because it takes the Dirac Lagrangian into account, is more than a mere relabeling of the integer lattice and may have fundamental physical meaning (e.g., for the statistics of fermions). It is noted that the present formulation does not lead to species doubling, except in the continuum limit.

Smalley, L. L.↗

NASA NTRS1993

Propagation model for the Land Mobile Satellite channel in urban environments

This paper presents the major characteristics of a simulation package capable of performing a complete narrow and wideband analysis of the mobile satellite communication channel in urban environments for any given orbital configuration. The wavelength-to-average urban geometrical dimension ratio has required the use of the Geometrical Theory of Diffraction (GTD). For the RF frequency range, the model has been designed to be (1 up to 60 GHz) extended to include effects of non-perfect conductivity and surface roughness. Taking advantage of the inherent capabilities of such a high frequency method, we are able to provide a complete description of the electromagnetic field at the mobile terminal. Using the information made available at the ray-tracer and GTD solver outputs, the Land Mobile Satellite (LMS) urban model can also give a detailed description of the communication channel in terms of power delay profiles, Doppler spectra, channel scattering functions, and so forth. Statistical data, e.g. cumulative distribution functions, level crossing rates or distributions of fades are also provided. The user can access the simulation tool through a Design-CAD user-friendly interface by means of which she can effectively design her own urban layout and run consequently all the envisaged routines. The software is optimized in its execution time so that numerous runs can be achieved in a considerably short time.

Sforza, M.↗